arX

iv1

101

2221

v2 [

astr

o-ph

EP]

13

Jul 2

011

Solar dynamo as host power pacemaker of the Earth global climate

VD Rusov1 lowast EP Linnik1 VN Vaschenko2 S Cht Mavrodiev3 ME Beglaryan1

TN Zelentsova1 VA Tarasov1 DA Litvinov1 VP Smolyar1 and B Vachev3

1Department of Theoretical and Experimental Nuclear PhysicsOdessa National Polytechnic University Odessa Ukraine

2State Ecological Academy for Postgraduate Education and Management Kiev Ukraine3Institute for Nuclear Research and Nuclear Energy BAS Sofia Bulgaria

(Dated 30 June 2011)

It is known that the so-called problem of solar power pacemaker related to possible existenceof some hidden but key mechanism of energy influence of the Sun on fundamental geophysicalprocesses is one of the principal and puzzling problems of modern climatology The rdquotracksrdquo ofthis mechanism have been shown up in different problems of solar-terrestrial physics for a long timeand in particular in climatology where the solar-climate variability is stably observed Howeverthe mechanisms by which small changes in the Sunrsquos energy (solar irradiance or insolation) outputduring the solar cycle can cause change in the weather and climate are still unknown

We analyze possible causes of the solar-climate variability concentrating onersquos attention on thephysical substantiation of strong correlation between the temporal variations of magnetic flux ofthe solar tachocline zone and the Earth magnetic field (Y-component) We propose an effectivemechanism of solar dynamo-geodynamo connection which plays the role of the solar power pacemakerof the Earth global climate

Keywords Solar dynamo-geodynamo connection Earthrsquos global climate Solar-climate variability Solar

axions

I INTRODUCTION

It is known that in spite of a long history the nature ofthe energy source maintaining a convection in the liquidcore of the Earth or more exactly the mechanism of themagnetohydrodynamic dynamo (MHD) generating themagnetic field of the Earth still has no clear and unam-biguous physical interpretation (see [1] and refs therein)The problem is aggravated because of the fact that noneof candidates for an energy source of the Earth magnetic-field [1] (secular cooling due to the heat transfer from thecore to the mantle internal heating by radiogenic iso-topes eg 40K latent heat due to the inner core solid-ification compositional buoyancy due to the ejection oflight element at the inner core surface) canrsquot in principleexplain one of the most remarkable and mystic phenom-ena in solar-terrestrial physics which consists in strong(negative) correlation [2] [3] between temporal variationsof the magnetic flux in the tachocline zone (the bottomof the Sun convective zone) [4] and the Earth magneticfield [5] (Figure 1)At the same time supposing that the transversal (ra-

dial) surface area of tachocline zone through which amagnetic flux passes is constant in the first approxima-tion we can consider that the magnetic flux variationsdescribe also the magnetic field temporal variations in thetachocline zone of the Sun In this sense it is obviousthat a future candidate for an energy source of the Earthmagnetic field must play not only the role of a naturaltrigger of solar-terrestrial connection but also directly

lowast Corresponding author E-mail siiistenetua

generate the solar-terrestrial magnetic correlation by itsown participation

The fact that the solar-terrestrial magnetic correlationhas undoubtedly fundamental importance for evolutionof all the Earthrsquos geospheres is confirmed by existenceof a stable and strong correlation between the temporalvariations of the Earth magnetic field the Earth angularvelocity the average global ocean level and the number oflarge earthquakes (with the magnitude Mge7) whose gen-eration is apparently predetermined by a common phys-ical cause of unknown nature (see Figure 1)

On the other hand it is clear that understanding ofthe mechanism of solar-terrestrial magnetic correlationcan become the clue of so-called problem of solar powerpacemaker related to possible existence of some hiddenbut key mechanism of energy influence of the Sun on thefundamental geophysical processes It is interesting thatthe rdquotracksrdquo of this mechanism have been observed for along time and manifest themselves in different problemsof solar-terrestrial physics and in particular in clima-tology where the mechanisms by which small changes inthe Sunrsquos energy output during the solar cycle can causechange in the weather and climate have been a puzzleand the subject of intense research in recent decadesThus it becomes obvious that purposeful or unpurposedneglect of the mechanism of solar power pacemaker inany point or multi-zonal models of the Earth global cli-mate can result in serious errors in interpretation of theexperimental temperature and other geophysical trendsespecially in the compilation of short-term and all themore long-term forecasts

In this paper we consider hypothetical particles (57Fesolar axions) as the main carriers of the solar-terrestrialconnection which can transform into photons in exter-

2

nal fluctuating electric or magnetic fields by virtue ofthe inverse coherent Primakoff effect [6] At the sametime we ground and develop the axion mechanism of so-lar dynamo ndash geodynamo connection where the energyof axions is modulated at first by the magnetic field ofthe solar tachocline zone (due to the inverse coherent Pri-makoff effect) and after that is resonantly absorbed inthe iron core of the Earth thereby playing the role of anenergy source and modulator of the Earth magnetic fieldJustification of the axion mechanism of solar dynamo ndashgeodynamo connection and its account within the frame-work of the bifurcation model of the Earth global climateon different time scales is the goal of this article

II PECULIARITIES OF THE BIFURCATION

MODEL OF THE EARTH GLOBAL CLIMATE ON

DIFFERENT TIME SCALES

As is shown in our papers [10 11] the basic equation ofenergy-balance model of the Earth global climate is thebifurcation equation (with respect to the Earth surfacetemperature (see Figure 2)) of assembly-type catastrophewith two governing parameters which describe insolationvariations and the Earth magnetic field variations (or thevariations of cosmic ray intensity in the atmosphere) Ageneral bifurcation problem of this energy-balance model(see equations (20)-(23) and (26)-(28) in [10 11]) which

consists in determination of the global temperature T (t)and its increment ∆T (t) is reduced to finding the stablesolution set of equations

part

partTUlowast(T t) = T 3

t + a(t) middot Tt + b(t) = 0 (1)

where

a(t) = minus1

4δσamicroHoplus(t) (2)

b(t) = minus1

4δσ

[

ηαS0

4+

1

2β +

1

2bmicroHoplus(t)

]

(3)

and

part

partT∆Ulowast(∆T t) sim= ∆T 3

t + a(t) middot∆Tt + b(t) = 0 (4)

where

a(t) = minus376

σT 3t

amicroHoplus(t) = minusa0Hoplus(t) (5)

b(t) = minus376

σT 3t

[

ηαS0 +∆W (t)σs

4minus 4δσT 3

t +1

2β +

1

2(2amicroTt + bmicro)Hoplus(t)

]

=

minusb0

[

ηαWreduced(t)minus 4δσT 3t +

1

2β +

1

2(2amicroTt + bmicro)Hoplus(t)

]

(6)

Ulowast(T t) describes with an accuracy up to constant theso-called rdquoinertialrdquo power of heat variations in the Earthclimate system ∆Ulowast(T t) is the variation of Ulowast(T t)Hoplus is the relative intensity of terrestrial magnetism Tt

is the average global temperature of the Earth surfaceat the time t K ∆Tt is the variation of Tt S0 =13662 Wmminus2 is rdquosolar constantrdquo δ = 095 is coeffi-cient of gray chromaticity of the Earth surface radia-tion σ = 5 67 middot 10minus8 is the Stephen-Boltzmann con-stant Wmminus2Kminus4 ηα = 0 0295Kminus1 β is the accu-mulation rate of carbon dioxide in the atmosphere nor-malized by unit of temperature kgKminus1 amicro and bmicroare constants whose dimensions are Wmminus2Kminus2 andWmminus2Kminus1 respetively ∆W (t) is the insolation reducednormalized variation σs is the root-mean-square devia-tion Wreduced = S0 + ∆W (t)σs is the reduced annualinsolation

Within the framework of proposed bifurcation model(i) comparison of the solution of energy-balance modelof the Earth global climate and the EPICA Dome C

and Vostok experimental data of the Earth surfacepalaeotemperature evolution over past 420 and 740 kyris given (ii) possible sharp warmings of the Dansgaard-Oeschger type during the last glacial period due tostochastic resonance is theoretically argued (iii) the con-cept of climatic sensitivity of water in the atmospherewhose temperature instability has the form of so-calledhysteresis loop is proposed and based on this conceptthe time series of total fresh water mass (or vice versathe global ice volume) over the past 1000 kyr whichis in good agreement with the time series of δ18O con-centration in sea sediments (Figure 3) is obtained (iiii)groundlessness of the so-called rdquoCO2 doublingrdquo problemis discussed

One of the main features of bifurcation model of theEarth global climate lies in the wonderful fact that prioriknowledge of only two governing parameters which areset by the known time series of insolation variations andvariations of the Earth magnetic field (or the variationsof cosmic ray intensity in the atmosphere) is required to

3

-700

-600

-500

-400

-300

-200

-100

0

100

200

300

Time years

Prediction

(a)

(b)

(c)

(d)

(e)

Oce

an

lev

el v

ari

ati

on

s c

my

ear

-3

-2

-1

0

1

2

Sim

ula

ted

so

lar

ma

gn

etic

flu

x

x1

023 M

x

120

100

80

60

40

20

0

Ea

rth

ro

tati

on

vel

oci

ty a

no

ma

ly

x1

0-1

0

Ea

rth

qu

ak

es

yea

r-1

10

15

20

Geo

ma

gn

etic

fie

ld v

ari

ati

on

(n

Ty

ear)

20

40

60

80

100

120

1880 1900 1920 1940 1960 1980 2000 2020 2040

1880 1900 1920 1940 1960 1980 2000 2020 2040

FIG 1 Time evolution (a) the variations of magnetic flux in the bottom (tachocline zone) of the Sun convective zone (see Figure7f [4]) (b) of the geomagnetic field secular variations (Y-component nTyear) whose values are obtained at the Eskdalemuirobservatory (England) [5] where the variations (δYδt) are directly proportional to the westward drift of magnetic features (c)the variation of the Earthrsquos rotation velocity [7] (d) the variations of the average global ocean level (PDO+AMO cmyear) [8]and (e) the number of large earthquakes (with the magnitude M ge 7) [9] All curves are smoothed by sliding intervals in 5 and11 years The pink area is the prediction region Note formation of the second peaks on curves (c)-(e) is mainly predeterminedby nuclear tests in 1945-1990

atmosphere

Earth

PSunαPSun

IEarth

Gfriction

(Gw+ G

v+ G

CO2) 1

2

FIG 2 The energy fluxes balance on the Earth surface HereGw Gv GCO are the heat energy power re-emitted 2 byliquid water water vapour and carbon dioxide respectivelyGfriction is the heat or dissipation energy generated by theEarth surface-to-atmosphere bottom layer friction

solve the basic equations (1)-(6) of energy-balance model(or to determine theoretical temperature trends) Othernot less interesting feature of this model is the so-calledprinciple of structural invariance which means that theshape of global climatic potential (assembly-type catas-trophe)

U(T t) =1

4T 4 +

1

2a(t)T 2 + b(t) (7)

is structurally invariant on different time scales Inother words the principle of structural invariance of thebalance equations of climate models evolving on the dif-ferent time scales is not only a direct indicator of thecorrectly guessed physics of non-uniformly scaled pro-cesses but it simultaneously specifies unambiguous rulesfor transition from one time scale to the other within theframework of one global model as well as for transitionfrom the (one-zonal) model of the Earth global climateon any time scale to the multizonal model of global cli-mate or weather on a short time scale It means that thesystem of equations of the multizonal model of global cli-mate or weather convoluted into the balance equation ofone-zonal model must fully keep the structure and prop-erties (governing parameters) of the bifurcation model ofglobal climate on different time scales Since the bifurca-tion model describes the climatic trends of paleotemper-ature and global ice volume well without considerationof the mechanism of solar power pacemaker the natural

4

δ18O

-mari

ne

(permil)

2

1

0

-1

-2

0 100 200 300 400 500 600 700 800 900 1000

(a)

Cli

mati

c se

nsi

tivit

y λ

wv

-150

-100

-50

0

50

100

150

(b)

OD

P 6

59

δ1

8O

Age (kyr BP)

3

4

5

0 100 200 300 400 500 600 700 800 900 1000

(c)

FIG 3 Comparison of the theoretical time series of climaticsensitivity λw+v calculated by equations (3) and (19) from [11](b) with the time series of δ18O isotopic concentration (theconditional analogue of ice volume) measured in the deep-water experiments (a) Bassinot et al [12] (solid blue line)and Imbrie et al [13] (dashed red line) (c) Tidemann et al[14]

question arises here rdquoIs it possible that this fact contra-dicts the assigned taskrdquo Below we will show that thereis no contradiction here because actually the mechanismof solar power pacemaker is implicitly taken into accountin the climatic potential (7) and it is non-trivial confir-mation of significance of the principle of structural in-variance

III AXION MECHANISM OF SOLAR

DYNAMO - GEODYNAMO CONNECTION

We have shown that strong correlation between thetemporal variations of magnetic field of the Earth (Y-component) and the magnetic field toroidal componentof tachocline zone of the Sun really takes place There-upon we have asked ourselves rdquoMay hypothetical solaraxions[15] which can transform into photons in externalelectric or magnetic field (the so-called inverse Primakoffeffect) be the instrument by which the magnetic field ofthe solar tachocline zone modulates the magnetic field ofthe Earth In other words may solar axions be an effec-tive energy source and modulator of the Earth magneticfieldrdquoIt turns out that it is really possible [6] Following [6]

let us consider without loss of generality the simplifiedaxion mechanism of solar dynamo-geodynamo connec-tion As is known the reaction of the solar cycle that

produces solar energy is one of axion sources Since ax-ions are pseudoscalar particles they can be emitted innuclear magnetic transitions On the other hand sincethe temperature in the center of the Sun is 13 keV somenuclei having low-lying nuclear level can be excited ther-mally At the same time monochromatic axions can beemitted in the nuclear magnetic transitions from the firstthermally excited level to the ground state Below weconsider only 144 keV solar axions emitted by the M1transition in 57Fe nuclei because just these axions canbe resonantly absorbed in the iron core of the Earth gen-erating 144 keV γ-quanta by the discharge of the excitednuclear level (Figure 4)It is interesting that exactly these γ-quanta with the

energy 144 keV are the supplementary energy source inthe Earth core which can pretend to the role of energysource of generation and modulator of the Earth mag-netic field At the same time there is a natural questionis this energy sufficient for generation of the magneticfield of the Earth and how this source can execute therole of the modulator of the Earth magnetic field Toanswer these questions let us briefly consider the axionrdquocourse of liferdquo inside the Sun before it leaves the SunIt appears [6] that passing through the solar tachoclinezone (the bottom of the Sun convective zone) where theSun magnetic field is generated axions can be convertedinto γ-quanta and thereby to decrease the solar axionsflux to the Earth As is shown in [6] in this case theprobability that an axion converts back to a rdquoobservablerdquophoton inside the magnetic field can be represented bythe following simple form

Paγsim=

(gaγBL

2

)2

(8)

where gaγ sim 164 middot 109 GeV minus1 is the strength of an axioncoupling to a photon L sim 35 middot10minus7 m is the thickness ofsolar tachocline zone B sim 35 T is the conservative valuefor the magnetic field of the active Sun From this itfollows that the solar axion flux outgoing beyond the Sunis modulated by the value of the Sun magnetic field (see(7)) At the same time it is obvious that the axion fluxto the Earth is low during the active Sun and converselyit is practically maximal during the quiet SunNow let us show that the total energy of axions during

the quiet Sun is sufficient to generate the Earth magneticfield It is not difficult to show [6] that the axion resonantabsorption rate in the Earth core which contains the N57

Fe

nuclei of 57Fe isotope is about

Ra asymp 52 middot 10minus3(

geffaN

)4

N57Fe [1minus Pararrγ ] (9)

where

Pararrγ sim

1 at BST asymp 35T

0 at BST le 50T (10)

5

a

FIG 4 Schematic picture of the solar tachocline zone Earthrsquos liquid outer (red region) and inner (brown region) core Solaraxions are resonance absorbed in iron of the Earth core conversing into γ-quanta which are the supplementary energy sourcein the Earth core Blue lines on the Sun designate the magnetic field Note In the conventional concept the molten iron ofliquid phase of Earthrsquos core circulates along a spiraling in columns aligned in the north-south direction generating electricalcurrents that set up the dipolar magnetic field The concentration of field lines into anticyclonic vortices (rotating in the sameas air around a region of high pressure) has been thought to explain the intense magnetic lobes found in Earthrsquos field at thetop of the core

It is known that the number of 57Fe nuclei in theEarth core is N57

Fe sim 3 middot 1047 [6] and the average energyof 57Fe solar axions is 〈Ea〉= 144 keV If in (9) for an

axion-nucleon coupling geffaN sim 10minus5 [6] to take into ac-count the factor 2 related to uncertainty of iron concen-tration profile at the Sun then with an allowance of (9)the maximum energy release rate Wγ in the Earth coreis equal to

Wγ = Ra middot 〈Ea〉 sim 1 TW (11)

Analysis of modern model parameters of thermal stateof the Earthrsquos core [1] shows that in spite of known dif-ficulties in interpretation of the results of evolutionarygeodynamo simulation such a thermal power (1 TW) issufficient for generation and maintenance of the Earthmagnetic field [1] It is easy to show that it is exactlyso by the known dependence of magnetic field BE on thetotal ohmic dissipation D in the Earth core

D simη middot V

micro middot d2BB2

E (12)

where η is the magnetic diffusivity V = (43)πr3coreis thecore volume micro is the permeability dB is the character-istic length scale on which the field vector changes Ifconsider that η sim 1 m2s rcore sim dB and micro sim 1 in thecase D sim Wγ sim 1 TW we obtain the value of toroidalmagnetic field BE sim 03 T which is in good agreementwith theoretical estimations [6]At the same time in spite of the fact that the axion

mechanism of solar dynamo-geodynamo connection ex-plains well the strong negative correlation between the

magnetic field of the solar tachocline zone and the Earthmagnetic field from the physical standpoint it can notexplain other correlations in Figure 1 (between the mag-netic field of the solar tachocline zone and variations ofthe Earth angular velocity average global ocean leveland the number of large earthquakes with the magni-tude Mge7) from the energy standpoin However undercertain conditions ie within the framework of the hy-pothesis of natural nuclear georeactor existence on theboundary of the liquid and solid phases of the Earthcore [16 17] the axion mechanism can effectively pro-vide these correlations

IV SOLITON-LIKE NUCLEAR GEOREACTOR

AND AXION MECHANISM OF THE EARTH

CORE rdquoHEATINGrdquo

Now it is obvious that the magnificent experiments ofthe KamLAND-collobaration over the last 8 years [18]have been extremely important not only for observationof reactor antineutrino oscillations They make it pos-sible for the first time to verify one of most vivid andmysterious ideas in nuclear geophysics the hypothesis ofnatural nuclear georeactor existence (see [16] and refstherein) In spite of its singularity and long history thishypothesis becomes especially attractive today becauseit enables to explain clearly from the physical stand-point different unrelated at the first glance geophysi-cal anomalous phenomena whose fundamental nature isbeyond doubt [19]We have to note that in spite of the fact that the

experimental KamLAND-data are well described within

6

FIG 5 Prompt event energy spectrum of νe candidate events(the years 2002-2009) [17] The shaded background andgeoneutrino histograms are cumulative Statistical uncertain-ties are shown for the data the violet band on the blue his-togram indicates the event rate systematic uncertainty withinthe framework of the georeactor hypothesis The total geore-actor power is 297 TW Georeactors are at a distance of 6400and 6830 km from the KamLAND-detector

the framework of georeactor model [16 17] (see Figure 5)and the location of soliton-like nuclear georeactors (Fig-ure 6 [17]) is determined by triangulation of the Kam-LAND [18] and Borexino data [19] some geophysicistshave doubts not only about existence of the georeactorbut in the first place about its power In this connectionwe would like to pay attention to the strange restriction(W le 62 TW) on the value of nuclear georeactor thermalpower W which unfortunately has been frequently metin the scientific literature recently [19ndash22] This restric-tion terrifically masks and distorts clear understandingof the problem of georeactor existence which is intricateenough by itselfIndeed one of the conclusions of the KamLANDcollob-

oration is the upper bound of nuclear georeactor thermalpower (W le 62 TW at 90 CL) which is a direct con-sequence of uncertainty of KamLAND experimental data[20] However it is necessary to keep firmly in mind thatthis restriction is true only for the concrete parameters ofmixing (∆m2

21 = 758middot10minus5 eV 2 tan θ12 = 056) obtainedwithin the framework of the concrete χ2-hypothesis ofKamLAND-experiment which takes into account the ex-istence of georeactor within the framework of nonzerohypothesis [21] but absolutely ignores such a nontriv-ial property of the nuclear georeactor as an uncertaintyof georeactor antineutrino spectrum which in the caseof soliton-like nuclear georeactor reaches sim100 [17] Asshown in Ref [17] the account of this uncertainty withinthe framework of maximum likelihood function leads (inthe minimization of the χ2-function) to considerable ex-pansion of restriction on the nuclear georeactor heatpower (sim30 TW) and accordingly to the new oscillationparameters (∆m2

21 = 25 middot 10minus5 eV 2 tan θ12 = 0437) forreactor antineutrinoHowever in spite of obvious attractiveness of the hy-

pothesis of natural nuclear georeactor existence there aresome difficulties for its perception predetermined by non-trivial properties which georeactor must possess At firstnatural ie unenriched uranium or thorium must beused as a nuclear fuel Secondly traditional control rodsare completely absent in the reactivity regulation systemof reactor Thirdly in spite of the absence of controlrods a reactor must possess the property of so-called in-ner safety It means that the critical state of the reac-tor core must be permanently maintained in any situa-tion ie normal operation of the reactor is automaticallymaintained not as a result of operatorrsquos activity but byvirtue of physical reasons-laws preventing the explosivedevelopment of chain reaction by natural way [24] Fig-uratively speaking the reactor with inner safety is therdquonuclear installation which never explodesrdquo [25]

It seems to be strange but reactors satisfying such un-usual requirements are possible in reality For the firsttime the idea of such a self-regulating fast reactor (so-called mode of breed-and-burn) was expressed in a gen-eral form by Russian physicists Feynberg and Kunegin[26] and relatively recently rdquoreanimatedrdquo as an idea ofthe self-regulating fast reactor in traveling-wave mode ofnuclear burning by L Feoktistov [27] and independentlyby Teller Ishikawa and Wood [28]

The discussed nuclear georeactor located on theboundary of the liquid and solid phases of the Earth corehas an unique and important for our aims feature whichconsists in the fact that the fission cross-section of 239Pu(generated due to the georeactor operating) is the sharplynonlinear function of temperature in the range 3000-5000K (Figure 7a) It means that the variations of the Earthcore temperature generated by the mechanism of solardynamo-geodynamo connection will induce correspond-ing variations of the nuclear georeactor thermal powerItrsquos strange but it is true and it is confirmed by inversecorrelation between the solar magnetic field (Figure 1)and the nuclear georeactor thermal power over the pe-riod 2002-2009 (Figure 7b) Thus on the one hand sucha coordinated behavior of the solar magnetic field andthe nuclear georeactor thermal power is an indirect con-firmation of reality of the rdquoaxion mechanism-nuclear geo-reactorrdquo energy chain and on the other hand accordingto the estimated power of various geophysical processes[29] such a generalized mechanism can provide the solar-terrestrial correlations shown in Figure 1 effectively

If the georeactor hypothesis is true the fluctuations ofgeoreactor thermal power can influence the Earthrsquos globalclimate in the form of anomalous temperature jumps inthe following way Strong fluctuations of the georeactorthermal power can lead to partial blocking of convectionin the liquid core [11] and change of angular velocity ofliquid geosphere rotation thereby by virtue of the con-servation law of Earthrsquos angular moment to change ofangular velocity of the mantle and the Earthrsquos surfacerespectively It means that the heat or more preciselydissipation energy caused by friction of earthly surfaceand bottom layer can make a considerable contribution

7

FIG 6 Distribution of geothermal power density on the Earth [23] superposed with the conjugate rdquopseudogeoreactorrdquo ellipsoidalclosed curves which were built on basis of KamLAND (red lines) and Borexino (blue lines) experimental data [17] (⋆) operatingnuclear georeactors (copy) and () nuclear georeactors whose power (if they are operating) is an order of magnitude or moreless than the thermal power of reactors designated by (⋆)

U2

35 f

issi

on

cross

-secti

on

b

arn

0

50

100

150

200

250

300

350

400

Pu

23

9 f

issi

on

cross

-secti

on

b

arn

600

700

800

900

1 000

1 100

1 200

1 300

1 400

T K

0 1 000 2 000 3 000 4 000 5 000 6 000

0 1 000 2 000 3 000 4 000 5 000 6 000

U235

Pu239

(a)

W T

W

0

10

20

30

40

50

Year

2 000 2 005 2 010

KamLAND

Borexino

(b)

FIG 7 (a) Dependence of the 239Pu fission cross-section averaged over the neutron spectrum on fuel medium temperature forlimiting energy (3kT) of the Fermi and Maxwell spectra The similar dependence for the 235U fission cross-section is shown forcomparison (b) Time evolution of the nuclear georeactor thermal power W

to the total energy balance of the atmosphere and therebysignificantly influence on the Earth global climate evolu-tion [10 11]

V BIFURCATION MODEL OF THE EARTH

GLOBAL CLIMATE ON THE ANNUAL TIME

SCALE

Newtonrsquos second law for friction rough surfaces (theEarth surface and the atmosphere surface layer) with an

allowance for nonlinear friction by Gilmore [30] and theclimatic potential (7) has the form of the van der Pole-Duffing type equation (see Figure 2)

mx = minusmicro(

x2 minus λ)

xminus partxU (13)

where x is the average shift length of the atmosphere sur-face layer relative to the Earth surface m is the effectivemass of boundary layer micro and λ are parameters U is theclimatic potential of (7) type

8

Using the substitutions x = ∆ω middot R middot ∆t ξ = ωRν = ∆ωω we can write down (13) in the following form

ξmν = minusmicro[

ξ2 (∆t)2ν2 minus λ

]

ξν minus1

ξ∆t

partU

partν (14)

where ω is the angular velocity of the Earth rotation and∆ω is its change over ∆t= 1 year R is the average Earthradius ν is the dimensionless quantity which describesby definition the Earth rotational velocity [7] (Figure 1)Since temporal variations of the global ocean level and

temporal variations of the Earth average temperaturestrongly correlate without time lag whereas the tem-poral variations of the global ocean level and temporalvariations of the Earth rotational velocity strongly cor-relate with the lag tlag sim5 years (see Figure 1) (14) withconsideration of the approximate equality ν sim kTtminustlag

can be rewritten in the following form

ξkmT = minusmicroξk[

ξ2k2 (∆t)2T 2 minus λ

]

T minus1

ξk∆t

partU

partT (15)

that explicitly takes into account the mechanism of solarpower pacemakerNontrivial properties of the basic equation of bifurca-

tion model of the Earth global climate on the annualtime scale are exhibited in Figure 8 by the variety ofphase portraits depending on the governing parameters(a b) Moreover the change of shape of the assembly-type catastrophe potentials (7) on the plane (a b) directlyspecifies the conditions of rdquowarm-coldrdquo phase transitionsin the climatic self-oscillatory system of the van der Pole-Duffing type (13)Here it is interesting to note the following remarkable

fact It was found that the low order dynamic modelsof the time evolution of the toroidal magnetic field ofthe Sun derived from mean field dynamo theory are alsodescribed by the nonlinear oscillator equations of the vander Pole-Duffing type [31 32] In this sense the identicaltype of equations describing the time evolution both ofthe Sun magnetic field and the Earth global climate isone more confirmation and at the same time naturalconsequence of physical ie really existing mechanismof solar dynamo-geodynamo connectionNow we return to the problem of taking into account

of the mechanism of solar power pacemaker within theframework of the bifurcation model of the Earth globalclimate on different time scales It is known that on thelarge time scales (from several to ten thousands years) onwhich our bifurcation model was considered above theequilibrium state of the global climate is reached at every

time point It is obvious that in this case the left-handside of (15) can be set equal to zero and (7) itself can bewritten down in the following form

partTUprime = T 3 + aprimeT + bprime = 0 (16)

-4 -2 0 2 4

1

0

-1

-2

-3

-4

-5

2 a

b

FIG 8 A plane of the parameters (a b) the typical shapesof the assembly-type catastrophe potential (red lines) and thephase portraits (black lines on the pink squares) of the self-oscillating system of the van der Pole-Duffing type (13) atmλ = 1 Blue circles are points to whose coordinates thephase portraits and the assembly-type catastrophe potentialcorrespond

It means that the bifurcation model of the Earth globalclimate on the ten thousandth time scale really takesinto account not only the laws of atmospheric physicsin particular the laws of geometrical optics of climaticbilliards which generalize the cosmic rays-clouds effectby Sven-smark the first (the Twomey effect) and secondindirect aerosol effects [10] but also the mechanism of so-lar power pacemaker which was masked before [10 11]by renormalization procedure of the governing parame-ters to take into account the initial conditions In otherwords theoretical solutions of the bifurcation model ofthe Earth global climate on the ten thousandth time scalewith respect to the temperature and the global ice vol-ume not only take into account the mechanism of so-lar dynamo-geodynamo connection but in combinationwith high quality of description of the known experimen-tal trends of the temperature and the global ice volume[10 11] are reliable confirmation of correct and holis-tic understanding of the basic foundations of nonlinearphysics of the Earth global climate formation

[1] B A Buffet Science 299 1675 (2003)[2] Note that the strong (negative) correlation between the

temporal variations of magnetic flux in the tachocline

zone and the Earth magnetic field (Y-component) willbe observed only for experimental data obtained at thatobservatories where the temporal variations of declina-

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718

3

-700

-600

-500

-400

-300

-200

-100

0

100

200

300

Time years

Prediction

(a)

(b)

(c)

(d)

(e)

Oce

an

lev

el v

ari

ati

on

s c

my

ear

-3

-2

-1

0

1

2

Sim

ula

ted

so

lar

ma

gn

etic

flu

x

x1

023 M

x

120

100

80

60

40

20

0

Ea

rth

ro

tati

on

vel

oci

ty a

no

ma

ly

x1

0-1

0

Ea

rth

qu

ak

es

yea

r-1

10

15

20

Geo

ma

gn

etic

fie

ld v

ari

ati

on

(n

Ty

ear)

20

40

60

80

100

120

1880 1900 1920 1940 1960 1980 2000 2020 2040

1880 1900 1920 1940 1960 1980 2000 2020 2040

FIG 1 Time evolution (a) the variations of magnetic flux in the bottom (tachocline zone) of the Sun convective zone (see Figure7f [4]) (b) of the geomagnetic field secular variations (Y-component nTyear) whose values are obtained at the Eskdalemuirobservatory (England) [5] where the variations (δYδt) are directly proportional to the westward drift of magnetic features (c)the variation of the Earthrsquos rotation velocity [7] (d) the variations of the average global ocean level (PDO+AMO cmyear) [8]and (e) the number of large earthquakes (with the magnitude M ge 7) [9] All curves are smoothed by sliding intervals in 5 and11 years The pink area is the prediction region Note formation of the second peaks on curves (c)-(e) is mainly predeterminedby nuclear tests in 1945-1990

atmosphere

Earth

PSunαPSun

IEarth

Gfriction

(Gw+ G

v+ G

CO2) 1

2

FIG 2 The energy fluxes balance on the Earth surface HereGw Gv GCO are the heat energy power re-emitted 2 byliquid water water vapour and carbon dioxide respectivelyGfriction is the heat or dissipation energy generated by theEarth surface-to-atmosphere bottom layer friction

solve the basic equations (1)-(6) of energy-balance model(or to determine theoretical temperature trends) Othernot less interesting feature of this model is the so-calledprinciple of structural invariance which means that theshape of global climatic potential (assembly-type catas-trophe)

U(T t) =1

4T 4 +

1

2a(t)T 2 + b(t) (7)

is structurally invariant on different time scales Inother words the principle of structural invariance of thebalance equations of climate models evolving on the dif-ferent time scales is not only a direct indicator of thecorrectly guessed physics of non-uniformly scaled pro-cesses but it simultaneously specifies unambiguous rulesfor transition from one time scale to the other within theframework of one global model as well as for transitionfrom the (one-zonal) model of the Earth global climateon any time scale to the multizonal model of global cli-mate or weather on a short time scale It means that thesystem of equations of the multizonal model of global cli-mate or weather convoluted into the balance equation ofone-zonal model must fully keep the structure and prop-erties (governing parameters) of the bifurcation model ofglobal climate on different time scales Since the bifurca-tion model describes the climatic trends of paleotemper-ature and global ice volume well without considerationof the mechanism of solar power pacemaker the natural

4

δ18O

-mari

ne

(permil)

2

1

0

-1

-2

0 100 200 300 400 500 600 700 800 900 1000

(a)

Cli

mati

c se

nsi

tivit

y λ

wv

-150

-100

-50

0

50

100

150

(b)

OD

P 6

59

δ1

8O

Age (kyr BP)

3

4

5

0 100 200 300 400 500 600 700 800 900 1000

(c)

FIG 3 Comparison of the theoretical time series of climaticsensitivity λw+v calculated by equations (3) and (19) from [11](b) with the time series of δ18O isotopic concentration (theconditional analogue of ice volume) measured in the deep-water experiments (a) Bassinot et al [12] (solid blue line)and Imbrie et al [13] (dashed red line) (c) Tidemann et al[14]

question arises here rdquoIs it possible that this fact contra-dicts the assigned taskrdquo Below we will show that thereis no contradiction here because actually the mechanismof solar power pacemaker is implicitly taken into accountin the climatic potential (7) and it is non-trivial confir-mation of significance of the principle of structural in-variance

III AXION MECHANISM OF SOLAR

DYNAMO - GEODYNAMO CONNECTION

We have shown that strong correlation between thetemporal variations of magnetic field of the Earth (Y-component) and the magnetic field toroidal componentof tachocline zone of the Sun really takes place There-upon we have asked ourselves rdquoMay hypothetical solaraxions[15] which can transform into photons in externalelectric or magnetic field (the so-called inverse Primakoffeffect) be the instrument by which the magnetic field ofthe solar tachocline zone modulates the magnetic field ofthe Earth In other words may solar axions be an effec-tive energy source and modulator of the Earth magneticfieldrdquoIt turns out that it is really possible [6] Following [6]

let us consider without loss of generality the simplifiedaxion mechanism of solar dynamo-geodynamo connec-tion As is known the reaction of the solar cycle that

produces solar energy is one of axion sources Since ax-ions are pseudoscalar particles they can be emitted innuclear magnetic transitions On the other hand sincethe temperature in the center of the Sun is 13 keV somenuclei having low-lying nuclear level can be excited ther-mally At the same time monochromatic axions can beemitted in the nuclear magnetic transitions from the firstthermally excited level to the ground state Below weconsider only 144 keV solar axions emitted by the M1transition in 57Fe nuclei because just these axions canbe resonantly absorbed in the iron core of the Earth gen-erating 144 keV γ-quanta by the discharge of the excitednuclear level (Figure 4)It is interesting that exactly these γ-quanta with the

energy 144 keV are the supplementary energy source inthe Earth core which can pretend to the role of energysource of generation and modulator of the Earth mag-netic field At the same time there is a natural questionis this energy sufficient for generation of the magneticfield of the Earth and how this source can execute therole of the modulator of the Earth magnetic field Toanswer these questions let us briefly consider the axionrdquocourse of liferdquo inside the Sun before it leaves the SunIt appears [6] that passing through the solar tachoclinezone (the bottom of the Sun convective zone) where theSun magnetic field is generated axions can be convertedinto γ-quanta and thereby to decrease the solar axionsflux to the Earth As is shown in [6] in this case theprobability that an axion converts back to a rdquoobservablerdquophoton inside the magnetic field can be represented bythe following simple form

Paγsim=

(gaγBL

2

)2

(8)

where gaγ sim 164 middot 109 GeV minus1 is the strength of an axioncoupling to a photon L sim 35 middot10minus7 m is the thickness ofsolar tachocline zone B sim 35 T is the conservative valuefor the magnetic field of the active Sun From this itfollows that the solar axion flux outgoing beyond the Sunis modulated by the value of the Sun magnetic field (see(7)) At the same time it is obvious that the axion fluxto the Earth is low during the active Sun and converselyit is practically maximal during the quiet SunNow let us show that the total energy of axions during

the quiet Sun is sufficient to generate the Earth magneticfield It is not difficult to show [6] that the axion resonantabsorption rate in the Earth core which contains the N57

Fe

nuclei of 57Fe isotope is about

Ra asymp 52 middot 10minus3(

geffaN

)4

N57Fe [1minus Pararrγ ] (9)

where

Pararrγ sim

1 at BST asymp 35T

0 at BST le 50T (10)

5

a

FIG 4 Schematic picture of the solar tachocline zone Earthrsquos liquid outer (red region) and inner (brown region) core Solaraxions are resonance absorbed in iron of the Earth core conversing into γ-quanta which are the supplementary energy sourcein the Earth core Blue lines on the Sun designate the magnetic field Note In the conventional concept the molten iron ofliquid phase of Earthrsquos core circulates along a spiraling in columns aligned in the north-south direction generating electricalcurrents that set up the dipolar magnetic field The concentration of field lines into anticyclonic vortices (rotating in the sameas air around a region of high pressure) has been thought to explain the intense magnetic lobes found in Earthrsquos field at thetop of the core

It is known that the number of 57Fe nuclei in theEarth core is N57

Fe sim 3 middot 1047 [6] and the average energyof 57Fe solar axions is 〈Ea〉= 144 keV If in (9) for an

axion-nucleon coupling geffaN sim 10minus5 [6] to take into ac-count the factor 2 related to uncertainty of iron concen-tration profile at the Sun then with an allowance of (9)the maximum energy release rate Wγ in the Earth coreis equal to

Wγ = Ra middot 〈Ea〉 sim 1 TW (11)

Analysis of modern model parameters of thermal stateof the Earthrsquos core [1] shows that in spite of known dif-ficulties in interpretation of the results of evolutionarygeodynamo simulation such a thermal power (1 TW) issufficient for generation and maintenance of the Earthmagnetic field [1] It is easy to show that it is exactlyso by the known dependence of magnetic field BE on thetotal ohmic dissipation D in the Earth core

D simη middot V

micro middot d2BB2

E (12)

where η is the magnetic diffusivity V = (43)πr3coreis thecore volume micro is the permeability dB is the character-istic length scale on which the field vector changes Ifconsider that η sim 1 m2s rcore sim dB and micro sim 1 in thecase D sim Wγ sim 1 TW we obtain the value of toroidalmagnetic field BE sim 03 T which is in good agreementwith theoretical estimations [6]At the same time in spite of the fact that the axion

mechanism of solar dynamo-geodynamo connection ex-plains well the strong negative correlation between the

magnetic field of the solar tachocline zone and the Earthmagnetic field from the physical standpoint it can notexplain other correlations in Figure 1 (between the mag-netic field of the solar tachocline zone and variations ofthe Earth angular velocity average global ocean leveland the number of large earthquakes with the magni-tude Mge7) from the energy standpoin However undercertain conditions ie within the framework of the hy-pothesis of natural nuclear georeactor existence on theboundary of the liquid and solid phases of the Earthcore [16 17] the axion mechanism can effectively pro-vide these correlations

IV SOLITON-LIKE NUCLEAR GEOREACTOR

AND AXION MECHANISM OF THE EARTH

CORE rdquoHEATINGrdquo

Now it is obvious that the magnificent experiments ofthe KamLAND-collobaration over the last 8 years [18]have been extremely important not only for observationof reactor antineutrino oscillations They make it pos-sible for the first time to verify one of most vivid andmysterious ideas in nuclear geophysics the hypothesis ofnatural nuclear georeactor existence (see [16] and refstherein) In spite of its singularity and long history thishypothesis becomes especially attractive today becauseit enables to explain clearly from the physical stand-point different unrelated at the first glance geophysi-cal anomalous phenomena whose fundamental nature isbeyond doubt [19]We have to note that in spite of the fact that the

experimental KamLAND-data are well described within

6

FIG 5 Prompt event energy spectrum of νe candidate events(the years 2002-2009) [17] The shaded background andgeoneutrino histograms are cumulative Statistical uncertain-ties are shown for the data the violet band on the blue his-togram indicates the event rate systematic uncertainty withinthe framework of the georeactor hypothesis The total geore-actor power is 297 TW Georeactors are at a distance of 6400and 6830 km from the KamLAND-detector

the framework of georeactor model [16 17] (see Figure 5)and the location of soliton-like nuclear georeactors (Fig-ure 6 [17]) is determined by triangulation of the Kam-LAND [18] and Borexino data [19] some geophysicistshave doubts not only about existence of the georeactorbut in the first place about its power In this connectionwe would like to pay attention to the strange restriction(W le 62 TW) on the value of nuclear georeactor thermalpower W which unfortunately has been frequently metin the scientific literature recently [19ndash22] This restric-tion terrifically masks and distorts clear understandingof the problem of georeactor existence which is intricateenough by itselfIndeed one of the conclusions of the KamLANDcollob-

oration is the upper bound of nuclear georeactor thermalpower (W le 62 TW at 90 CL) which is a direct con-sequence of uncertainty of KamLAND experimental data[20] However it is necessary to keep firmly in mind thatthis restriction is true only for the concrete parameters ofmixing (∆m2

21 = 758middot10minus5 eV 2 tan θ12 = 056) obtainedwithin the framework of the concrete χ2-hypothesis ofKamLAND-experiment which takes into account the ex-istence of georeactor within the framework of nonzerohypothesis [21] but absolutely ignores such a nontriv-ial property of the nuclear georeactor as an uncertaintyof georeactor antineutrino spectrum which in the caseof soliton-like nuclear georeactor reaches sim100 [17] Asshown in Ref [17] the account of this uncertainty withinthe framework of maximum likelihood function leads (inthe minimization of the χ2-function) to considerable ex-pansion of restriction on the nuclear georeactor heatpower (sim30 TW) and accordingly to the new oscillationparameters (∆m2

21 = 25 middot 10minus5 eV 2 tan θ12 = 0437) forreactor antineutrinoHowever in spite of obvious attractiveness of the hy-

pothesis of natural nuclear georeactor existence there aresome difficulties for its perception predetermined by non-trivial properties which georeactor must possess At firstnatural ie unenriched uranium or thorium must beused as a nuclear fuel Secondly traditional control rodsare completely absent in the reactivity regulation systemof reactor Thirdly in spite of the absence of controlrods a reactor must possess the property of so-called in-ner safety It means that the critical state of the reac-tor core must be permanently maintained in any situa-tion ie normal operation of the reactor is automaticallymaintained not as a result of operatorrsquos activity but byvirtue of physical reasons-laws preventing the explosivedevelopment of chain reaction by natural way [24] Fig-uratively speaking the reactor with inner safety is therdquonuclear installation which never explodesrdquo [25]

It seems to be strange but reactors satisfying such un-usual requirements are possible in reality For the firsttime the idea of such a self-regulating fast reactor (so-called mode of breed-and-burn) was expressed in a gen-eral form by Russian physicists Feynberg and Kunegin[26] and relatively recently rdquoreanimatedrdquo as an idea ofthe self-regulating fast reactor in traveling-wave mode ofnuclear burning by L Feoktistov [27] and independentlyby Teller Ishikawa and Wood [28]

The discussed nuclear georeactor located on theboundary of the liquid and solid phases of the Earth corehas an unique and important for our aims feature whichconsists in the fact that the fission cross-section of 239Pu(generated due to the georeactor operating) is the sharplynonlinear function of temperature in the range 3000-5000K (Figure 7a) It means that the variations of the Earthcore temperature generated by the mechanism of solardynamo-geodynamo connection will induce correspond-ing variations of the nuclear georeactor thermal powerItrsquos strange but it is true and it is confirmed by inversecorrelation between the solar magnetic field (Figure 1)and the nuclear georeactor thermal power over the pe-riod 2002-2009 (Figure 7b) Thus on the one hand sucha coordinated behavior of the solar magnetic field andthe nuclear georeactor thermal power is an indirect con-firmation of reality of the rdquoaxion mechanism-nuclear geo-reactorrdquo energy chain and on the other hand accordingto the estimated power of various geophysical processes[29] such a generalized mechanism can provide the solar-terrestrial correlations shown in Figure 1 effectively

If the georeactor hypothesis is true the fluctuations ofgeoreactor thermal power can influence the Earthrsquos globalclimate in the form of anomalous temperature jumps inthe following way Strong fluctuations of the georeactorthermal power can lead to partial blocking of convectionin the liquid core [11] and change of angular velocity ofliquid geosphere rotation thereby by virtue of the con-servation law of Earthrsquos angular moment to change ofangular velocity of the mantle and the Earthrsquos surfacerespectively It means that the heat or more preciselydissipation energy caused by friction of earthly surfaceand bottom layer can make a considerable contribution

7

FIG 6 Distribution of geothermal power density on the Earth [23] superposed with the conjugate rdquopseudogeoreactorrdquo ellipsoidalclosed curves which were built on basis of KamLAND (red lines) and Borexino (blue lines) experimental data [17] (⋆) operatingnuclear georeactors (copy) and () nuclear georeactors whose power (if they are operating) is an order of magnitude or moreless than the thermal power of reactors designated by (⋆)

U2

35 f

issi

on

cross

-secti

on

b

arn

0

50

100

150

200

250

300

350

400

Pu

23

9 f

issi

on

cross

-secti

on

b

arn

600

700

800

900

1 000

1 100

1 200

1 300

1 400

T K

0 1 000 2 000 3 000 4 000 5 000 6 000

0 1 000 2 000 3 000 4 000 5 000 6 000

U235

Pu239

(a)

W T

W

0

10

20

30

40

50

Year

2 000 2 005 2 010

KamLAND

Borexino

(b)

FIG 7 (a) Dependence of the 239Pu fission cross-section averaged over the neutron spectrum on fuel medium temperature forlimiting energy (3kT) of the Fermi and Maxwell spectra The similar dependence for the 235U fission cross-section is shown forcomparison (b) Time evolution of the nuclear georeactor thermal power W

to the total energy balance of the atmosphere and therebysignificantly influence on the Earth global climate evolu-tion [10 11]

V BIFURCATION MODEL OF THE EARTH

GLOBAL CLIMATE ON THE ANNUAL TIME

SCALE

Newtonrsquos second law for friction rough surfaces (theEarth surface and the atmosphere surface layer) with an

allowance for nonlinear friction by Gilmore [30] and theclimatic potential (7) has the form of the van der Pole-Duffing type equation (see Figure 2)

mx = minusmicro(

x2 minus λ)

xminus partxU (13)

where x is the average shift length of the atmosphere sur-face layer relative to the Earth surface m is the effectivemass of boundary layer micro and λ are parameters U is theclimatic potential of (7) type

8

Using the substitutions x = ∆ω middot R middot ∆t ξ = ωRν = ∆ωω we can write down (13) in the following form

ξmν = minusmicro[

ξ2 (∆t)2ν2 minus λ

]

ξν minus1

ξ∆t

partU

partν (14)

where ω is the angular velocity of the Earth rotation and∆ω is its change over ∆t= 1 year R is the average Earthradius ν is the dimensionless quantity which describesby definition the Earth rotational velocity [7] (Figure 1)Since temporal variations of the global ocean level and

temporal variations of the Earth average temperaturestrongly correlate without time lag whereas the tem-poral variations of the global ocean level and temporalvariations of the Earth rotational velocity strongly cor-relate with the lag tlag sim5 years (see Figure 1) (14) withconsideration of the approximate equality ν sim kTtminustlag

can be rewritten in the following form

ξkmT = minusmicroξk[

ξ2k2 (∆t)2T 2 minus λ

]

T minus1

ξk∆t

partU

partT (15)

that explicitly takes into account the mechanism of solarpower pacemakerNontrivial properties of the basic equation of bifurca-

tion model of the Earth global climate on the annualtime scale are exhibited in Figure 8 by the variety ofphase portraits depending on the governing parameters(a b) Moreover the change of shape of the assembly-type catastrophe potentials (7) on the plane (a b) directlyspecifies the conditions of rdquowarm-coldrdquo phase transitionsin the climatic self-oscillatory system of the van der Pole-Duffing type (13)Here it is interesting to note the following remarkable

fact It was found that the low order dynamic modelsof the time evolution of the toroidal magnetic field ofthe Sun derived from mean field dynamo theory are alsodescribed by the nonlinear oscillator equations of the vander Pole-Duffing type [31 32] In this sense the identicaltype of equations describing the time evolution both ofthe Sun magnetic field and the Earth global climate isone more confirmation and at the same time naturalconsequence of physical ie really existing mechanismof solar dynamo-geodynamo connectionNow we return to the problem of taking into account

of the mechanism of solar power pacemaker within theframework of the bifurcation model of the Earth globalclimate on different time scales It is known that on thelarge time scales (from several to ten thousands years) onwhich our bifurcation model was considered above theequilibrium state of the global climate is reached at every

time point It is obvious that in this case the left-handside of (15) can be set equal to zero and (7) itself can bewritten down in the following form

partTUprime = T 3 + aprimeT + bprime = 0 (16)

-4 -2 0 2 4

1

0

-1

-2

-3

-4

-5

2 a

b

FIG 8 A plane of the parameters (a b) the typical shapesof the assembly-type catastrophe potential (red lines) and thephase portraits (black lines on the pink squares) of the self-oscillating system of the van der Pole-Duffing type (13) atmλ = 1 Blue circles are points to whose coordinates thephase portraits and the assembly-type catastrophe potentialcorrespond

It means that the bifurcation model of the Earth globalclimate on the ten thousandth time scale really takesinto account not only the laws of atmospheric physicsin particular the laws of geometrical optics of climaticbilliards which generalize the cosmic rays-clouds effectby Sven-smark the first (the Twomey effect) and secondindirect aerosol effects [10] but also the mechanism of so-lar power pacemaker which was masked before [10 11]by renormalization procedure of the governing parame-ters to take into account the initial conditions In otherwords theoretical solutions of the bifurcation model ofthe Earth global climate on the ten thousandth time scalewith respect to the temperature and the global ice vol-ume not only take into account the mechanism of so-lar dynamo-geodynamo connection but in combinationwith high quality of description of the known experimen-tal trends of the temperature and the global ice volume[10 11] are reliable confirmation of correct and holis-tic understanding of the basic foundations of nonlinearphysics of the Earth global climate formation

[1] B A Buffet Science 299 1675 (2003)[2] Note that the strong (negative) correlation between the

temporal variations of magnetic flux in the tachocline

zone and the Earth magnetic field (Y-component) willbe observed only for experimental data obtained at thatobservatories where the temporal variations of declina-

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718

4

δ18O

-mari

ne

(permil)

2

1

0

-1

-2

0 100 200 300 400 500 600 700 800 900 1000

(a)

Cli

mati

c se

nsi

tivit

y λ

wv

-150

-100

-50

0

50

100

150

(b)

OD

P 6

59

δ1

8O

Age (kyr BP)

3

4

5

0 100 200 300 400 500 600 700 800 900 1000

(c)

FIG 3 Comparison of the theoretical time series of climaticsensitivity λw+v calculated by equations (3) and (19) from [11](b) with the time series of δ18O isotopic concentration (theconditional analogue of ice volume) measured in the deep-water experiments (a) Bassinot et al [12] (solid blue line)and Imbrie et al [13] (dashed red line) (c) Tidemann et al[14]

question arises here rdquoIs it possible that this fact contra-dicts the assigned taskrdquo Below we will show that thereis no contradiction here because actually the mechanismof solar power pacemaker is implicitly taken into accountin the climatic potential (7) and it is non-trivial confir-mation of significance of the principle of structural in-variance

III AXION MECHANISM OF SOLAR

DYNAMO - GEODYNAMO CONNECTION

We have shown that strong correlation between thetemporal variations of magnetic field of the Earth (Y-component) and the magnetic field toroidal componentof tachocline zone of the Sun really takes place There-upon we have asked ourselves rdquoMay hypothetical solaraxions[15] which can transform into photons in externalelectric or magnetic field (the so-called inverse Primakoffeffect) be the instrument by which the magnetic field ofthe solar tachocline zone modulates the magnetic field ofthe Earth In other words may solar axions be an effec-tive energy source and modulator of the Earth magneticfieldrdquoIt turns out that it is really possible [6] Following [6]

let us consider without loss of generality the simplifiedaxion mechanism of solar dynamo-geodynamo connec-tion As is known the reaction of the solar cycle that

produces solar energy is one of axion sources Since ax-ions are pseudoscalar particles they can be emitted innuclear magnetic transitions On the other hand sincethe temperature in the center of the Sun is 13 keV somenuclei having low-lying nuclear level can be excited ther-mally At the same time monochromatic axions can beemitted in the nuclear magnetic transitions from the firstthermally excited level to the ground state Below weconsider only 144 keV solar axions emitted by the M1transition in 57Fe nuclei because just these axions canbe resonantly absorbed in the iron core of the Earth gen-erating 144 keV γ-quanta by the discharge of the excitednuclear level (Figure 4)It is interesting that exactly these γ-quanta with the

energy 144 keV are the supplementary energy source inthe Earth core which can pretend to the role of energysource of generation and modulator of the Earth mag-netic field At the same time there is a natural questionis this energy sufficient for generation of the magneticfield of the Earth and how this source can execute therole of the modulator of the Earth magnetic field Toanswer these questions let us briefly consider the axionrdquocourse of liferdquo inside the Sun before it leaves the SunIt appears [6] that passing through the solar tachoclinezone (the bottom of the Sun convective zone) where theSun magnetic field is generated axions can be convertedinto γ-quanta and thereby to decrease the solar axionsflux to the Earth As is shown in [6] in this case theprobability that an axion converts back to a rdquoobservablerdquophoton inside the magnetic field can be represented bythe following simple form

Paγsim=

(gaγBL

2

)2

(8)

where gaγ sim 164 middot 109 GeV minus1 is the strength of an axioncoupling to a photon L sim 35 middot10minus7 m is the thickness ofsolar tachocline zone B sim 35 T is the conservative valuefor the magnetic field of the active Sun From this itfollows that the solar axion flux outgoing beyond the Sunis modulated by the value of the Sun magnetic field (see(7)) At the same time it is obvious that the axion fluxto the Earth is low during the active Sun and converselyit is practically maximal during the quiet SunNow let us show that the total energy of axions during

the quiet Sun is sufficient to generate the Earth magneticfield It is not difficult to show [6] that the axion resonantabsorption rate in the Earth core which contains the N57

Fe

nuclei of 57Fe isotope is about

Ra asymp 52 middot 10minus3(

geffaN

)4

N57Fe [1minus Pararrγ ] (9)

where

Pararrγ sim

1 at BST asymp 35T

0 at BST le 50T (10)

5

a

FIG 4 Schematic picture of the solar tachocline zone Earthrsquos liquid outer (red region) and inner (brown region) core Solaraxions are resonance absorbed in iron of the Earth core conversing into γ-quanta which are the supplementary energy sourcein the Earth core Blue lines on the Sun designate the magnetic field Note In the conventional concept the molten iron ofliquid phase of Earthrsquos core circulates along a spiraling in columns aligned in the north-south direction generating electricalcurrents that set up the dipolar magnetic field The concentration of field lines into anticyclonic vortices (rotating in the sameas air around a region of high pressure) has been thought to explain the intense magnetic lobes found in Earthrsquos field at thetop of the core

It is known that the number of 57Fe nuclei in theEarth core is N57

Fe sim 3 middot 1047 [6] and the average energyof 57Fe solar axions is 〈Ea〉= 144 keV If in (9) for an

axion-nucleon coupling geffaN sim 10minus5 [6] to take into ac-count the factor 2 related to uncertainty of iron concen-tration profile at the Sun then with an allowance of (9)the maximum energy release rate Wγ in the Earth coreis equal to

Wγ = Ra middot 〈Ea〉 sim 1 TW (11)

Analysis of modern model parameters of thermal stateof the Earthrsquos core [1] shows that in spite of known dif-ficulties in interpretation of the results of evolutionarygeodynamo simulation such a thermal power (1 TW) issufficient for generation and maintenance of the Earthmagnetic field [1] It is easy to show that it is exactlyso by the known dependence of magnetic field BE on thetotal ohmic dissipation D in the Earth core

D simη middot V

micro middot d2BB2

E (12)

where η is the magnetic diffusivity V = (43)πr3coreis thecore volume micro is the permeability dB is the character-istic length scale on which the field vector changes Ifconsider that η sim 1 m2s rcore sim dB and micro sim 1 in thecase D sim Wγ sim 1 TW we obtain the value of toroidalmagnetic field BE sim 03 T which is in good agreementwith theoretical estimations [6]At the same time in spite of the fact that the axion

mechanism of solar dynamo-geodynamo connection ex-plains well the strong negative correlation between the

magnetic field of the solar tachocline zone and the Earthmagnetic field from the physical standpoint it can notexplain other correlations in Figure 1 (between the mag-netic field of the solar tachocline zone and variations ofthe Earth angular velocity average global ocean leveland the number of large earthquakes with the magni-tude Mge7) from the energy standpoin However undercertain conditions ie within the framework of the hy-pothesis of natural nuclear georeactor existence on theboundary of the liquid and solid phases of the Earthcore [16 17] the axion mechanism can effectively pro-vide these correlations

IV SOLITON-LIKE NUCLEAR GEOREACTOR

AND AXION MECHANISM OF THE EARTH

CORE rdquoHEATINGrdquo

Now it is obvious that the magnificent experiments ofthe KamLAND-collobaration over the last 8 years [18]have been extremely important not only for observationof reactor antineutrino oscillations They make it pos-sible for the first time to verify one of most vivid andmysterious ideas in nuclear geophysics the hypothesis ofnatural nuclear georeactor existence (see [16] and refstherein) In spite of its singularity and long history thishypothesis becomes especially attractive today becauseit enables to explain clearly from the physical stand-point different unrelated at the first glance geophysi-cal anomalous phenomena whose fundamental nature isbeyond doubt [19]We have to note that in spite of the fact that the

experimental KamLAND-data are well described within

6

FIG 5 Prompt event energy spectrum of νe candidate events(the years 2002-2009) [17] The shaded background andgeoneutrino histograms are cumulative Statistical uncertain-ties are shown for the data the violet band on the blue his-togram indicates the event rate systematic uncertainty withinthe framework of the georeactor hypothesis The total geore-actor power is 297 TW Georeactors are at a distance of 6400and 6830 km from the KamLAND-detector

the framework of georeactor model [16 17] (see Figure 5)and the location of soliton-like nuclear georeactors (Fig-ure 6 [17]) is determined by triangulation of the Kam-LAND [18] and Borexino data [19] some geophysicistshave doubts not only about existence of the georeactorbut in the first place about its power In this connectionwe would like to pay attention to the strange restriction(W le 62 TW) on the value of nuclear georeactor thermalpower W which unfortunately has been frequently metin the scientific literature recently [19ndash22] This restric-tion terrifically masks and distorts clear understandingof the problem of georeactor existence which is intricateenough by itselfIndeed one of the conclusions of the KamLANDcollob-

oration is the upper bound of nuclear georeactor thermalpower (W le 62 TW at 90 CL) which is a direct con-sequence of uncertainty of KamLAND experimental data[20] However it is necessary to keep firmly in mind thatthis restriction is true only for the concrete parameters ofmixing (∆m2

21 = 758middot10minus5 eV 2 tan θ12 = 056) obtainedwithin the framework of the concrete χ2-hypothesis ofKamLAND-experiment which takes into account the ex-istence of georeactor within the framework of nonzerohypothesis [21] but absolutely ignores such a nontriv-ial property of the nuclear georeactor as an uncertaintyof georeactor antineutrino spectrum which in the caseof soliton-like nuclear georeactor reaches sim100 [17] Asshown in Ref [17] the account of this uncertainty withinthe framework of maximum likelihood function leads (inthe minimization of the χ2-function) to considerable ex-pansion of restriction on the nuclear georeactor heatpower (sim30 TW) and accordingly to the new oscillationparameters (∆m2

21 = 25 middot 10minus5 eV 2 tan θ12 = 0437) forreactor antineutrinoHowever in spite of obvious attractiveness of the hy-

pothesis of natural nuclear georeactor existence there aresome difficulties for its perception predetermined by non-trivial properties which georeactor must possess At firstnatural ie unenriched uranium or thorium must beused as a nuclear fuel Secondly traditional control rodsare completely absent in the reactivity regulation systemof reactor Thirdly in spite of the absence of controlrods a reactor must possess the property of so-called in-ner safety It means that the critical state of the reac-tor core must be permanently maintained in any situa-tion ie normal operation of the reactor is automaticallymaintained not as a result of operatorrsquos activity but byvirtue of physical reasons-laws preventing the explosivedevelopment of chain reaction by natural way [24] Fig-uratively speaking the reactor with inner safety is therdquonuclear installation which never explodesrdquo [25]

It seems to be strange but reactors satisfying such un-usual requirements are possible in reality For the firsttime the idea of such a self-regulating fast reactor (so-called mode of breed-and-burn) was expressed in a gen-eral form by Russian physicists Feynberg and Kunegin[26] and relatively recently rdquoreanimatedrdquo as an idea ofthe self-regulating fast reactor in traveling-wave mode ofnuclear burning by L Feoktistov [27] and independentlyby Teller Ishikawa and Wood [28]

The discussed nuclear georeactor located on theboundary of the liquid and solid phases of the Earth corehas an unique and important for our aims feature whichconsists in the fact that the fission cross-section of 239Pu(generated due to the georeactor operating) is the sharplynonlinear function of temperature in the range 3000-5000K (Figure 7a) It means that the variations of the Earthcore temperature generated by the mechanism of solardynamo-geodynamo connection will induce correspond-ing variations of the nuclear georeactor thermal powerItrsquos strange but it is true and it is confirmed by inversecorrelation between the solar magnetic field (Figure 1)and the nuclear georeactor thermal power over the pe-riod 2002-2009 (Figure 7b) Thus on the one hand sucha coordinated behavior of the solar magnetic field andthe nuclear georeactor thermal power is an indirect con-firmation of reality of the rdquoaxion mechanism-nuclear geo-reactorrdquo energy chain and on the other hand accordingto the estimated power of various geophysical processes[29] such a generalized mechanism can provide the solar-terrestrial correlations shown in Figure 1 effectively

If the georeactor hypothesis is true the fluctuations ofgeoreactor thermal power can influence the Earthrsquos globalclimate in the form of anomalous temperature jumps inthe following way Strong fluctuations of the georeactorthermal power can lead to partial blocking of convectionin the liquid core [11] and change of angular velocity ofliquid geosphere rotation thereby by virtue of the con-servation law of Earthrsquos angular moment to change ofangular velocity of the mantle and the Earthrsquos surfacerespectively It means that the heat or more preciselydissipation energy caused by friction of earthly surfaceand bottom layer can make a considerable contribution

7

FIG 6 Distribution of geothermal power density on the Earth [23] superposed with the conjugate rdquopseudogeoreactorrdquo ellipsoidalclosed curves which were built on basis of KamLAND (red lines) and Borexino (blue lines) experimental data [17] (⋆) operatingnuclear georeactors (copy) and () nuclear georeactors whose power (if they are operating) is an order of magnitude or moreless than the thermal power of reactors designated by (⋆)

U2

35 f

issi

on

cross

-secti

on

b

arn

0

50

100

150

200

250

300

350

400

Pu

23

9 f

issi

on

cross

-secti

on

b

arn

600

700

800

900

1 000

1 100

1 200

1 300

1 400

T K

0 1 000 2 000 3 000 4 000 5 000 6 000

0 1 000 2 000 3 000 4 000 5 000 6 000

U235

Pu239

(a)

W T

W

0

10

20

30

40

50

Year

2 000 2 005 2 010

KamLAND

Borexino

(b)

FIG 7 (a) Dependence of the 239Pu fission cross-section averaged over the neutron spectrum on fuel medium temperature forlimiting energy (3kT) of the Fermi and Maxwell spectra The similar dependence for the 235U fission cross-section is shown forcomparison (b) Time evolution of the nuclear georeactor thermal power W

to the total energy balance of the atmosphere and therebysignificantly influence on the Earth global climate evolu-tion [10 11]

V BIFURCATION MODEL OF THE EARTH

GLOBAL CLIMATE ON THE ANNUAL TIME

SCALE

Newtonrsquos second law for friction rough surfaces (theEarth surface and the atmosphere surface layer) with an

allowance for nonlinear friction by Gilmore [30] and theclimatic potential (7) has the form of the van der Pole-Duffing type equation (see Figure 2)

mx = minusmicro(

x2 minus λ)

xminus partxU (13)

where x is the average shift length of the atmosphere sur-face layer relative to the Earth surface m is the effectivemass of boundary layer micro and λ are parameters U is theclimatic potential of (7) type

8

Using the substitutions x = ∆ω middot R middot ∆t ξ = ωRν = ∆ωω we can write down (13) in the following form

ξmν = minusmicro[

ξ2 (∆t)2ν2 minus λ

]

ξν minus1

ξ∆t

partU

partν (14)

where ω is the angular velocity of the Earth rotation and∆ω is its change over ∆t= 1 year R is the average Earthradius ν is the dimensionless quantity which describesby definition the Earth rotational velocity [7] (Figure 1)Since temporal variations of the global ocean level and

temporal variations of the Earth average temperaturestrongly correlate without time lag whereas the tem-poral variations of the global ocean level and temporalvariations of the Earth rotational velocity strongly cor-relate with the lag tlag sim5 years (see Figure 1) (14) withconsideration of the approximate equality ν sim kTtminustlag

can be rewritten in the following form

ξkmT = minusmicroξk[

ξ2k2 (∆t)2T 2 minus λ

]

T minus1

ξk∆t

partU

partT (15)

that explicitly takes into account the mechanism of solarpower pacemakerNontrivial properties of the basic equation of bifurca-

tion model of the Earth global climate on the annualtime scale are exhibited in Figure 8 by the variety ofphase portraits depending on the governing parameters(a b) Moreover the change of shape of the assembly-type catastrophe potentials (7) on the plane (a b) directlyspecifies the conditions of rdquowarm-coldrdquo phase transitionsin the climatic self-oscillatory system of the van der Pole-Duffing type (13)Here it is interesting to note the following remarkable

fact It was found that the low order dynamic modelsof the time evolution of the toroidal magnetic field ofthe Sun derived from mean field dynamo theory are alsodescribed by the nonlinear oscillator equations of the vander Pole-Duffing type [31 32] In this sense the identicaltype of equations describing the time evolution both ofthe Sun magnetic field and the Earth global climate isone more confirmation and at the same time naturalconsequence of physical ie really existing mechanismof solar dynamo-geodynamo connectionNow we return to the problem of taking into account

of the mechanism of solar power pacemaker within theframework of the bifurcation model of the Earth globalclimate on different time scales It is known that on thelarge time scales (from several to ten thousands years) onwhich our bifurcation model was considered above theequilibrium state of the global climate is reached at every

time point It is obvious that in this case the left-handside of (15) can be set equal to zero and (7) itself can bewritten down in the following form

partTUprime = T 3 + aprimeT + bprime = 0 (16)

-4 -2 0 2 4

1

0

-1

-2

-3

-4

-5

2 a

b

FIG 8 A plane of the parameters (a b) the typical shapesof the assembly-type catastrophe potential (red lines) and thephase portraits (black lines on the pink squares) of the self-oscillating system of the van der Pole-Duffing type (13) atmλ = 1 Blue circles are points to whose coordinates thephase portraits and the assembly-type catastrophe potentialcorrespond

It means that the bifurcation model of the Earth globalclimate on the ten thousandth time scale really takesinto account not only the laws of atmospheric physicsin particular the laws of geometrical optics of climaticbilliards which generalize the cosmic rays-clouds effectby Sven-smark the first (the Twomey effect) and secondindirect aerosol effects [10] but also the mechanism of so-lar power pacemaker which was masked before [10 11]by renormalization procedure of the governing parame-ters to take into account the initial conditions In otherwords theoretical solutions of the bifurcation model ofthe Earth global climate on the ten thousandth time scalewith respect to the temperature and the global ice vol-ume not only take into account the mechanism of so-lar dynamo-geodynamo connection but in combinationwith high quality of description of the known experimen-tal trends of the temperature and the global ice volume[10 11] are reliable confirmation of correct and holis-tic understanding of the basic foundations of nonlinearphysics of the Earth global climate formation

[1] B A Buffet Science 299 1675 (2003)[2] Note that the strong (negative) correlation between the

temporal variations of magnetic flux in the tachocline

zone and the Earth magnetic field (Y-component) willbe observed only for experimental data obtained at thatobservatories where the temporal variations of declina-

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718

5

a

FIG 4 Schematic picture of the solar tachocline zone Earthrsquos liquid outer (red region) and inner (brown region) core Solaraxions are resonance absorbed in iron of the Earth core conversing into γ-quanta which are the supplementary energy sourcein the Earth core Blue lines on the Sun designate the magnetic field Note In the conventional concept the molten iron ofliquid phase of Earthrsquos core circulates along a spiraling in columns aligned in the north-south direction generating electricalcurrents that set up the dipolar magnetic field The concentration of field lines into anticyclonic vortices (rotating in the sameas air around a region of high pressure) has been thought to explain the intense magnetic lobes found in Earthrsquos field at thetop of the core

It is known that the number of 57Fe nuclei in theEarth core is N57

Fe sim 3 middot 1047 [6] and the average energyof 57Fe solar axions is 〈Ea〉= 144 keV If in (9) for an

axion-nucleon coupling geffaN sim 10minus5 [6] to take into ac-count the factor 2 related to uncertainty of iron concen-tration profile at the Sun then with an allowance of (9)the maximum energy release rate Wγ in the Earth coreis equal to

Wγ = Ra middot 〈Ea〉 sim 1 TW (11)

Analysis of modern model parameters of thermal stateof the Earthrsquos core [1] shows that in spite of known dif-ficulties in interpretation of the results of evolutionarygeodynamo simulation such a thermal power (1 TW) issufficient for generation and maintenance of the Earthmagnetic field [1] It is easy to show that it is exactlyso by the known dependence of magnetic field BE on thetotal ohmic dissipation D in the Earth core

D simη middot V

micro middot d2BB2

E (12)

where η is the magnetic diffusivity V = (43)πr3coreis thecore volume micro is the permeability dB is the character-istic length scale on which the field vector changes Ifconsider that η sim 1 m2s rcore sim dB and micro sim 1 in thecase D sim Wγ sim 1 TW we obtain the value of toroidalmagnetic field BE sim 03 T which is in good agreementwith theoretical estimations [6]At the same time in spite of the fact that the axion

mechanism of solar dynamo-geodynamo connection ex-plains well the strong negative correlation between the

magnetic field of the solar tachocline zone and the Earthmagnetic field from the physical standpoint it can notexplain other correlations in Figure 1 (between the mag-netic field of the solar tachocline zone and variations ofthe Earth angular velocity average global ocean leveland the number of large earthquakes with the magni-tude Mge7) from the energy standpoin However undercertain conditions ie within the framework of the hy-pothesis of natural nuclear georeactor existence on theboundary of the liquid and solid phases of the Earthcore [16 17] the axion mechanism can effectively pro-vide these correlations

IV SOLITON-LIKE NUCLEAR GEOREACTOR

AND AXION MECHANISM OF THE EARTH

CORE rdquoHEATINGrdquo

Now it is obvious that the magnificent experiments ofthe KamLAND-collobaration over the last 8 years [18]have been extremely important not only for observationof reactor antineutrino oscillations They make it pos-sible for the first time to verify one of most vivid andmysterious ideas in nuclear geophysics the hypothesis ofnatural nuclear georeactor existence (see [16] and refstherein) In spite of its singularity and long history thishypothesis becomes especially attractive today becauseit enables to explain clearly from the physical stand-point different unrelated at the first glance geophysi-cal anomalous phenomena whose fundamental nature isbeyond doubt [19]We have to note that in spite of the fact that the

experimental KamLAND-data are well described within

6

FIG 5 Prompt event energy spectrum of νe candidate events(the years 2002-2009) [17] The shaded background andgeoneutrino histograms are cumulative Statistical uncertain-ties are shown for the data the violet band on the blue his-togram indicates the event rate systematic uncertainty withinthe framework of the georeactor hypothesis The total geore-actor power is 297 TW Georeactors are at a distance of 6400and 6830 km from the KamLAND-detector

the framework of georeactor model [16 17] (see Figure 5)and the location of soliton-like nuclear georeactors (Fig-ure 6 [17]) is determined by triangulation of the Kam-LAND [18] and Borexino data [19] some geophysicistshave doubts not only about existence of the georeactorbut in the first place about its power In this connectionwe would like to pay attention to the strange restriction(W le 62 TW) on the value of nuclear georeactor thermalpower W which unfortunately has been frequently metin the scientific literature recently [19ndash22] This restric-tion terrifically masks and distorts clear understandingof the problem of georeactor existence which is intricateenough by itselfIndeed one of the conclusions of the KamLANDcollob-

oration is the upper bound of nuclear georeactor thermalpower (W le 62 TW at 90 CL) which is a direct con-sequence of uncertainty of KamLAND experimental data[20] However it is necessary to keep firmly in mind thatthis restriction is true only for the concrete parameters ofmixing (∆m2

21 = 758middot10minus5 eV 2 tan θ12 = 056) obtainedwithin the framework of the concrete χ2-hypothesis ofKamLAND-experiment which takes into account the ex-istence of georeactor within the framework of nonzerohypothesis [21] but absolutely ignores such a nontriv-ial property of the nuclear georeactor as an uncertaintyof georeactor antineutrino spectrum which in the caseof soliton-like nuclear georeactor reaches sim100 [17] Asshown in Ref [17] the account of this uncertainty withinthe framework of maximum likelihood function leads (inthe minimization of the χ2-function) to considerable ex-pansion of restriction on the nuclear georeactor heatpower (sim30 TW) and accordingly to the new oscillationparameters (∆m2

21 = 25 middot 10minus5 eV 2 tan θ12 = 0437) forreactor antineutrinoHowever in spite of obvious attractiveness of the hy-

pothesis of natural nuclear georeactor existence there aresome difficulties for its perception predetermined by non-trivial properties which georeactor must possess At firstnatural ie unenriched uranium or thorium must beused as a nuclear fuel Secondly traditional control rodsare completely absent in the reactivity regulation systemof reactor Thirdly in spite of the absence of controlrods a reactor must possess the property of so-called in-ner safety It means that the critical state of the reac-tor core must be permanently maintained in any situa-tion ie normal operation of the reactor is automaticallymaintained not as a result of operatorrsquos activity but byvirtue of physical reasons-laws preventing the explosivedevelopment of chain reaction by natural way [24] Fig-uratively speaking the reactor with inner safety is therdquonuclear installation which never explodesrdquo [25]

It seems to be strange but reactors satisfying such un-usual requirements are possible in reality For the firsttime the idea of such a self-regulating fast reactor (so-called mode of breed-and-burn) was expressed in a gen-eral form by Russian physicists Feynberg and Kunegin[26] and relatively recently rdquoreanimatedrdquo as an idea ofthe self-regulating fast reactor in traveling-wave mode ofnuclear burning by L Feoktistov [27] and independentlyby Teller Ishikawa and Wood [28]

The discussed nuclear georeactor located on theboundary of the liquid and solid phases of the Earth corehas an unique and important for our aims feature whichconsists in the fact that the fission cross-section of 239Pu(generated due to the georeactor operating) is the sharplynonlinear function of temperature in the range 3000-5000K (Figure 7a) It means that the variations of the Earthcore temperature generated by the mechanism of solardynamo-geodynamo connection will induce correspond-ing variations of the nuclear georeactor thermal powerItrsquos strange but it is true and it is confirmed by inversecorrelation between the solar magnetic field (Figure 1)and the nuclear georeactor thermal power over the pe-riod 2002-2009 (Figure 7b) Thus on the one hand sucha coordinated behavior of the solar magnetic field andthe nuclear georeactor thermal power is an indirect con-firmation of reality of the rdquoaxion mechanism-nuclear geo-reactorrdquo energy chain and on the other hand accordingto the estimated power of various geophysical processes[29] such a generalized mechanism can provide the solar-terrestrial correlations shown in Figure 1 effectively

If the georeactor hypothesis is true the fluctuations ofgeoreactor thermal power can influence the Earthrsquos globalclimate in the form of anomalous temperature jumps inthe following way Strong fluctuations of the georeactorthermal power can lead to partial blocking of convectionin the liquid core [11] and change of angular velocity ofliquid geosphere rotation thereby by virtue of the con-servation law of Earthrsquos angular moment to change ofangular velocity of the mantle and the Earthrsquos surfacerespectively It means that the heat or more preciselydissipation energy caused by friction of earthly surfaceand bottom layer can make a considerable contribution

7

FIG 6 Distribution of geothermal power density on the Earth [23] superposed with the conjugate rdquopseudogeoreactorrdquo ellipsoidalclosed curves which were built on basis of KamLAND (red lines) and Borexino (blue lines) experimental data [17] (⋆) operatingnuclear georeactors (copy) and () nuclear georeactors whose power (if they are operating) is an order of magnitude or moreless than the thermal power of reactors designated by (⋆)

U2

35 f

issi

on

cross

-secti

on

b

arn

0

50

100

150

200

250

300

350

400

Pu

23

9 f

issi

on

cross

-secti

on

b

arn

600

700

800

900

1 000

1 100

1 200

1 300

1 400

T K

0 1 000 2 000 3 000 4 000 5 000 6 000

0 1 000 2 000 3 000 4 000 5 000 6 000

U235

Pu239

(a)

W T

W

0

10

20

30

40

50

Year

2 000 2 005 2 010

KamLAND

Borexino

(b)

FIG 7 (a) Dependence of the 239Pu fission cross-section averaged over the neutron spectrum on fuel medium temperature forlimiting energy (3kT) of the Fermi and Maxwell spectra The similar dependence for the 235U fission cross-section is shown forcomparison (b) Time evolution of the nuclear georeactor thermal power W

to the total energy balance of the atmosphere and therebysignificantly influence on the Earth global climate evolu-tion [10 11]

V BIFURCATION MODEL OF THE EARTH

GLOBAL CLIMATE ON THE ANNUAL TIME

SCALE

Newtonrsquos second law for friction rough surfaces (theEarth surface and the atmosphere surface layer) with an

allowance for nonlinear friction by Gilmore [30] and theclimatic potential (7) has the form of the van der Pole-Duffing type equation (see Figure 2)

mx = minusmicro(

x2 minus λ)

xminus partxU (13)

where x is the average shift length of the atmosphere sur-face layer relative to the Earth surface m is the effectivemass of boundary layer micro and λ are parameters U is theclimatic potential of (7) type

8

Using the substitutions x = ∆ω middot R middot ∆t ξ = ωRν = ∆ωω we can write down (13) in the following form

ξmν = minusmicro[

ξ2 (∆t)2ν2 minus λ

]

ξν minus1

ξ∆t

partU

partν (14)

where ω is the angular velocity of the Earth rotation and∆ω is its change over ∆t= 1 year R is the average Earthradius ν is the dimensionless quantity which describesby definition the Earth rotational velocity [7] (Figure 1)Since temporal variations of the global ocean level and

temporal variations of the Earth average temperaturestrongly correlate without time lag whereas the tem-poral variations of the global ocean level and temporalvariations of the Earth rotational velocity strongly cor-relate with the lag tlag sim5 years (see Figure 1) (14) withconsideration of the approximate equality ν sim kTtminustlag

can be rewritten in the following form

ξkmT = minusmicroξk[

ξ2k2 (∆t)2T 2 minus λ

]

T minus1

ξk∆t

partU

partT (15)

that explicitly takes into account the mechanism of solarpower pacemakerNontrivial properties of the basic equation of bifurca-

tion model of the Earth global climate on the annualtime scale are exhibited in Figure 8 by the variety ofphase portraits depending on the governing parameters(a b) Moreover the change of shape of the assembly-type catastrophe potentials (7) on the plane (a b) directlyspecifies the conditions of rdquowarm-coldrdquo phase transitionsin the climatic self-oscillatory system of the van der Pole-Duffing type (13)Here it is interesting to note the following remarkable

fact It was found that the low order dynamic modelsof the time evolution of the toroidal magnetic field ofthe Sun derived from mean field dynamo theory are alsodescribed by the nonlinear oscillator equations of the vander Pole-Duffing type [31 32] In this sense the identicaltype of equations describing the time evolution both ofthe Sun magnetic field and the Earth global climate isone more confirmation and at the same time naturalconsequence of physical ie really existing mechanismof solar dynamo-geodynamo connectionNow we return to the problem of taking into account

of the mechanism of solar power pacemaker within theframework of the bifurcation model of the Earth globalclimate on different time scales It is known that on thelarge time scales (from several to ten thousands years) onwhich our bifurcation model was considered above theequilibrium state of the global climate is reached at every

time point It is obvious that in this case the left-handside of (15) can be set equal to zero and (7) itself can bewritten down in the following form

partTUprime = T 3 + aprimeT + bprime = 0 (16)

-4 -2 0 2 4

1

0

-1

-2

-3

-4

-5

2 a

b

FIG 8 A plane of the parameters (a b) the typical shapesof the assembly-type catastrophe potential (red lines) and thephase portraits (black lines on the pink squares) of the self-oscillating system of the van der Pole-Duffing type (13) atmλ = 1 Blue circles are points to whose coordinates thephase portraits and the assembly-type catastrophe potentialcorrespond

It means that the bifurcation model of the Earth globalclimate on the ten thousandth time scale really takesinto account not only the laws of atmospheric physicsin particular the laws of geometrical optics of climaticbilliards which generalize the cosmic rays-clouds effectby Sven-smark the first (the Twomey effect) and secondindirect aerosol effects [10] but also the mechanism of so-lar power pacemaker which was masked before [10 11]by renormalization procedure of the governing parame-ters to take into account the initial conditions In otherwords theoretical solutions of the bifurcation model ofthe Earth global climate on the ten thousandth time scalewith respect to the temperature and the global ice vol-ume not only take into account the mechanism of so-lar dynamo-geodynamo connection but in combinationwith high quality of description of the known experimen-tal trends of the temperature and the global ice volume[10 11] are reliable confirmation of correct and holis-tic understanding of the basic foundations of nonlinearphysics of the Earth global climate formation

[1] B A Buffet Science 299 1675 (2003)[2] Note that the strong (negative) correlation between the

temporal variations of magnetic flux in the tachocline

zone and the Earth magnetic field (Y-component) willbe observed only for experimental data obtained at thatobservatories where the temporal variations of declina-

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718

6

FIG 5 Prompt event energy spectrum of νe candidate events(the years 2002-2009) [17] The shaded background andgeoneutrino histograms are cumulative Statistical uncertain-ties are shown for the data the violet band on the blue his-togram indicates the event rate systematic uncertainty withinthe framework of the georeactor hypothesis The total geore-actor power is 297 TW Georeactors are at a distance of 6400and 6830 km from the KamLAND-detector

the framework of georeactor model [16 17] (see Figure 5)and the location of soliton-like nuclear georeactors (Fig-ure 6 [17]) is determined by triangulation of the Kam-LAND [18] and Borexino data [19] some geophysicistshave doubts not only about existence of the georeactorbut in the first place about its power In this connectionwe would like to pay attention to the strange restriction(W le 62 TW) on the value of nuclear georeactor thermalpower W which unfortunately has been frequently metin the scientific literature recently [19ndash22] This restric-tion terrifically masks and distorts clear understandingof the problem of georeactor existence which is intricateenough by itselfIndeed one of the conclusions of the KamLANDcollob-

oration is the upper bound of nuclear georeactor thermalpower (W le 62 TW at 90 CL) which is a direct con-sequence of uncertainty of KamLAND experimental data[20] However it is necessary to keep firmly in mind thatthis restriction is true only for the concrete parameters ofmixing (∆m2

21 = 758middot10minus5 eV 2 tan θ12 = 056) obtainedwithin the framework of the concrete χ2-hypothesis ofKamLAND-experiment which takes into account the ex-istence of georeactor within the framework of nonzerohypothesis [21] but absolutely ignores such a nontriv-ial property of the nuclear georeactor as an uncertaintyof georeactor antineutrino spectrum which in the caseof soliton-like nuclear georeactor reaches sim100 [17] Asshown in Ref [17] the account of this uncertainty withinthe framework of maximum likelihood function leads (inthe minimization of the χ2-function) to considerable ex-pansion of restriction on the nuclear georeactor heatpower (sim30 TW) and accordingly to the new oscillationparameters (∆m2

21 = 25 middot 10minus5 eV 2 tan θ12 = 0437) forreactor antineutrinoHowever in spite of obvious attractiveness of the hy-

pothesis of natural nuclear georeactor existence there aresome difficulties for its perception predetermined by non-trivial properties which georeactor must possess At firstnatural ie unenriched uranium or thorium must beused as a nuclear fuel Secondly traditional control rodsare completely absent in the reactivity regulation systemof reactor Thirdly in spite of the absence of controlrods a reactor must possess the property of so-called in-ner safety It means that the critical state of the reac-tor core must be permanently maintained in any situa-tion ie normal operation of the reactor is automaticallymaintained not as a result of operatorrsquos activity but byvirtue of physical reasons-laws preventing the explosivedevelopment of chain reaction by natural way [24] Fig-uratively speaking the reactor with inner safety is therdquonuclear installation which never explodesrdquo [25]

It seems to be strange but reactors satisfying such un-usual requirements are possible in reality For the firsttime the idea of such a self-regulating fast reactor (so-called mode of breed-and-burn) was expressed in a gen-eral form by Russian physicists Feynberg and Kunegin[26] and relatively recently rdquoreanimatedrdquo as an idea ofthe self-regulating fast reactor in traveling-wave mode ofnuclear burning by L Feoktistov [27] and independentlyby Teller Ishikawa and Wood [28]

The discussed nuclear georeactor located on theboundary of the liquid and solid phases of the Earth corehas an unique and important for our aims feature whichconsists in the fact that the fission cross-section of 239Pu(generated due to the georeactor operating) is the sharplynonlinear function of temperature in the range 3000-5000K (Figure 7a) It means that the variations of the Earthcore temperature generated by the mechanism of solardynamo-geodynamo connection will induce correspond-ing variations of the nuclear georeactor thermal powerItrsquos strange but it is true and it is confirmed by inversecorrelation between the solar magnetic field (Figure 1)and the nuclear georeactor thermal power over the pe-riod 2002-2009 (Figure 7b) Thus on the one hand sucha coordinated behavior of the solar magnetic field andthe nuclear georeactor thermal power is an indirect con-firmation of reality of the rdquoaxion mechanism-nuclear geo-reactorrdquo energy chain and on the other hand accordingto the estimated power of various geophysical processes[29] such a generalized mechanism can provide the solar-terrestrial correlations shown in Figure 1 effectively

If the georeactor hypothesis is true the fluctuations ofgeoreactor thermal power can influence the Earthrsquos globalclimate in the form of anomalous temperature jumps inthe following way Strong fluctuations of the georeactorthermal power can lead to partial blocking of convectionin the liquid core [11] and change of angular velocity ofliquid geosphere rotation thereby by virtue of the con-servation law of Earthrsquos angular moment to change ofangular velocity of the mantle and the Earthrsquos surfacerespectively It means that the heat or more preciselydissipation energy caused by friction of earthly surfaceand bottom layer can make a considerable contribution

7

FIG 6 Distribution of geothermal power density on the Earth [23] superposed with the conjugate rdquopseudogeoreactorrdquo ellipsoidalclosed curves which were built on basis of KamLAND (red lines) and Borexino (blue lines) experimental data [17] (⋆) operatingnuclear georeactors (copy) and () nuclear georeactors whose power (if they are operating) is an order of magnitude or moreless than the thermal power of reactors designated by (⋆)

U2

35 f

issi

on

cross

-secti

on

b

arn

0

50

100

150

200

250

300

350

400

Pu

23

9 f

issi

on

cross

-secti

on

b

arn

600

700

800

900

1 000

1 100

1 200

1 300

1 400

T K

0 1 000 2 000 3 000 4 000 5 000 6 000

0 1 000 2 000 3 000 4 000 5 000 6 000

U235

Pu239

(a)

W T

W

0

10

20

30

40

50

Year

2 000 2 005 2 010

KamLAND

Borexino

(b)

FIG 7 (a) Dependence of the 239Pu fission cross-section averaged over the neutron spectrum on fuel medium temperature forlimiting energy (3kT) of the Fermi and Maxwell spectra The similar dependence for the 235U fission cross-section is shown forcomparison (b) Time evolution of the nuclear georeactor thermal power W

to the total energy balance of the atmosphere and therebysignificantly influence on the Earth global climate evolu-tion [10 11]

V BIFURCATION MODEL OF THE EARTH

GLOBAL CLIMATE ON THE ANNUAL TIME

SCALE

Newtonrsquos second law for friction rough surfaces (theEarth surface and the atmosphere surface layer) with an

allowance for nonlinear friction by Gilmore [30] and theclimatic potential (7) has the form of the van der Pole-Duffing type equation (see Figure 2)

mx = minusmicro(

x2 minus λ)

xminus partxU (13)

where x is the average shift length of the atmosphere sur-face layer relative to the Earth surface m is the effectivemass of boundary layer micro and λ are parameters U is theclimatic potential of (7) type

8

Using the substitutions x = ∆ω middot R middot ∆t ξ = ωRν = ∆ωω we can write down (13) in the following form

ξmν = minusmicro[

ξ2 (∆t)2ν2 minus λ

]

ξν minus1

ξ∆t

partU

partν (14)

where ω is the angular velocity of the Earth rotation and∆ω is its change over ∆t= 1 year R is the average Earthradius ν is the dimensionless quantity which describesby definition the Earth rotational velocity [7] (Figure 1)Since temporal variations of the global ocean level and

temporal variations of the Earth average temperaturestrongly correlate without time lag whereas the tem-poral variations of the global ocean level and temporalvariations of the Earth rotational velocity strongly cor-relate with the lag tlag sim5 years (see Figure 1) (14) withconsideration of the approximate equality ν sim kTtminustlag

can be rewritten in the following form

ξkmT = minusmicroξk[

ξ2k2 (∆t)2T 2 minus λ

]

T minus1

ξk∆t

partU

partT (15)

that explicitly takes into account the mechanism of solarpower pacemakerNontrivial properties of the basic equation of bifurca-

tion model of the Earth global climate on the annualtime scale are exhibited in Figure 8 by the variety ofphase portraits depending on the governing parameters(a b) Moreover the change of shape of the assembly-type catastrophe potentials (7) on the plane (a b) directlyspecifies the conditions of rdquowarm-coldrdquo phase transitionsin the climatic self-oscillatory system of the van der Pole-Duffing type (13)Here it is interesting to note the following remarkable

fact It was found that the low order dynamic modelsof the time evolution of the toroidal magnetic field ofthe Sun derived from mean field dynamo theory are alsodescribed by the nonlinear oscillator equations of the vander Pole-Duffing type [31 32] In this sense the identicaltype of equations describing the time evolution both ofthe Sun magnetic field and the Earth global climate isone more confirmation and at the same time naturalconsequence of physical ie really existing mechanismof solar dynamo-geodynamo connectionNow we return to the problem of taking into account

of the mechanism of solar power pacemaker within theframework of the bifurcation model of the Earth globalclimate on different time scales It is known that on thelarge time scales (from several to ten thousands years) onwhich our bifurcation model was considered above theequilibrium state of the global climate is reached at every

time point It is obvious that in this case the left-handside of (15) can be set equal to zero and (7) itself can bewritten down in the following form

partTUprime = T 3 + aprimeT + bprime = 0 (16)

-4 -2 0 2 4

1

0

-1

-2

-3

-4

-5

2 a

b

FIG 8 A plane of the parameters (a b) the typical shapesof the assembly-type catastrophe potential (red lines) and thephase portraits (black lines on the pink squares) of the self-oscillating system of the van der Pole-Duffing type (13) atmλ = 1 Blue circles are points to whose coordinates thephase portraits and the assembly-type catastrophe potentialcorrespond

It means that the bifurcation model of the Earth globalclimate on the ten thousandth time scale really takesinto account not only the laws of atmospheric physicsin particular the laws of geometrical optics of climaticbilliards which generalize the cosmic rays-clouds effectby Sven-smark the first (the Twomey effect) and secondindirect aerosol effects [10] but also the mechanism of so-lar power pacemaker which was masked before [10 11]by renormalization procedure of the governing parame-ters to take into account the initial conditions In otherwords theoretical solutions of the bifurcation model ofthe Earth global climate on the ten thousandth time scalewith respect to the temperature and the global ice vol-ume not only take into account the mechanism of so-lar dynamo-geodynamo connection but in combinationwith high quality of description of the known experimen-tal trends of the temperature and the global ice volume[10 11] are reliable confirmation of correct and holis-tic understanding of the basic foundations of nonlinearphysics of the Earth global climate formation

[1] B A Buffet Science 299 1675 (2003)[2] Note that the strong (negative) correlation between the

temporal variations of magnetic flux in the tachocline

zone and the Earth magnetic field (Y-component) willbe observed only for experimental data obtained at thatobservatories where the temporal variations of declina-

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718

7

FIG 6 Distribution of geothermal power density on the Earth [23] superposed with the conjugate rdquopseudogeoreactorrdquo ellipsoidalclosed curves which were built on basis of KamLAND (red lines) and Borexino (blue lines) experimental data [17] (⋆) operatingnuclear georeactors (copy) and () nuclear georeactors whose power (if they are operating) is an order of magnitude or moreless than the thermal power of reactors designated by (⋆)

U2

35 f

issi

on

cross

-secti

on

b

arn

0

50

100

150

200

250

300

350

400

Pu

23

9 f

issi

on

cross

-secti

on

b

arn

600

700

800

900

1 000

1 100

1 200

1 300

1 400

T K

0 1 000 2 000 3 000 4 000 5 000 6 000

0 1 000 2 000 3 000 4 000 5 000 6 000

U235

Pu239

(a)

W T

W

0

10

20

30

40

50

Year

2 000 2 005 2 010

KamLAND

Borexino

(b)

FIG 7 (a) Dependence of the 239Pu fission cross-section averaged over the neutron spectrum on fuel medium temperature forlimiting energy (3kT) of the Fermi and Maxwell spectra The similar dependence for the 235U fission cross-section is shown forcomparison (b) Time evolution of the nuclear georeactor thermal power W

to the total energy balance of the atmosphere and therebysignificantly influence on the Earth global climate evolu-tion [10 11]

V BIFURCATION MODEL OF THE EARTH

GLOBAL CLIMATE ON THE ANNUAL TIME

SCALE

Newtonrsquos second law for friction rough surfaces (theEarth surface and the atmosphere surface layer) with an

allowance for nonlinear friction by Gilmore [30] and theclimatic potential (7) has the form of the van der Pole-Duffing type equation (see Figure 2)

mx = minusmicro(

x2 minus λ)

xminus partxU (13)

where x is the average shift length of the atmosphere sur-face layer relative to the Earth surface m is the effectivemass of boundary layer micro and λ are parameters U is theclimatic potential of (7) type

8

Using the substitutions x = ∆ω middot R middot ∆t ξ = ωRν = ∆ωω we can write down (13) in the following form

ξmν = minusmicro[

ξ2 (∆t)2ν2 minus λ

]

ξν minus1

ξ∆t

partU

partν (14)

where ω is the angular velocity of the Earth rotation and∆ω is its change over ∆t= 1 year R is the average Earthradius ν is the dimensionless quantity which describesby definition the Earth rotational velocity [7] (Figure 1)Since temporal variations of the global ocean level and

temporal variations of the Earth average temperaturestrongly correlate without time lag whereas the tem-poral variations of the global ocean level and temporalvariations of the Earth rotational velocity strongly cor-relate with the lag tlag sim5 years (see Figure 1) (14) withconsideration of the approximate equality ν sim kTtminustlag

can be rewritten in the following form

ξkmT = minusmicroξk[

ξ2k2 (∆t)2T 2 minus λ

]

T minus1

ξk∆t

partU

partT (15)

that explicitly takes into account the mechanism of solarpower pacemakerNontrivial properties of the basic equation of bifurca-

tion model of the Earth global climate on the annualtime scale are exhibited in Figure 8 by the variety ofphase portraits depending on the governing parameters(a b) Moreover the change of shape of the assembly-type catastrophe potentials (7) on the plane (a b) directlyspecifies the conditions of rdquowarm-coldrdquo phase transitionsin the climatic self-oscillatory system of the van der Pole-Duffing type (13)Here it is interesting to note the following remarkable

fact It was found that the low order dynamic modelsof the time evolution of the toroidal magnetic field ofthe Sun derived from mean field dynamo theory are alsodescribed by the nonlinear oscillator equations of the vander Pole-Duffing type [31 32] In this sense the identicaltype of equations describing the time evolution both ofthe Sun magnetic field and the Earth global climate isone more confirmation and at the same time naturalconsequence of physical ie really existing mechanismof solar dynamo-geodynamo connectionNow we return to the problem of taking into account

of the mechanism of solar power pacemaker within theframework of the bifurcation model of the Earth globalclimate on different time scales It is known that on thelarge time scales (from several to ten thousands years) onwhich our bifurcation model was considered above theequilibrium state of the global climate is reached at every

time point It is obvious that in this case the left-handside of (15) can be set equal to zero and (7) itself can bewritten down in the following form

partTUprime = T 3 + aprimeT + bprime = 0 (16)

-4 -2 0 2 4

1

0

-1

-2

-3

-4

-5

2 a

b

FIG 8 A plane of the parameters (a b) the typical shapesof the assembly-type catastrophe potential (red lines) and thephase portraits (black lines on the pink squares) of the self-oscillating system of the van der Pole-Duffing type (13) atmλ = 1 Blue circles are points to whose coordinates thephase portraits and the assembly-type catastrophe potentialcorrespond

It means that the bifurcation model of the Earth globalclimate on the ten thousandth time scale really takesinto account not only the laws of atmospheric physicsin particular the laws of geometrical optics of climaticbilliards which generalize the cosmic rays-clouds effectby Sven-smark the first (the Twomey effect) and secondindirect aerosol effects [10] but also the mechanism of so-lar power pacemaker which was masked before [10 11]by renormalization procedure of the governing parame-ters to take into account the initial conditions In otherwords theoretical solutions of the bifurcation model ofthe Earth global climate on the ten thousandth time scalewith respect to the temperature and the global ice vol-ume not only take into account the mechanism of so-lar dynamo-geodynamo connection but in combinationwith high quality of description of the known experimen-tal trends of the temperature and the global ice volume[10 11] are reliable confirmation of correct and holis-tic understanding of the basic foundations of nonlinearphysics of the Earth global climate formation

[1] B A Buffet Science 299 1675 (2003)[2] Note that the strong (negative) correlation between the

temporal variations of magnetic flux in the tachocline

zone and the Earth magnetic field (Y-component) willbe observed only for experimental data obtained at thatobservatories where the temporal variations of declina-

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718

8

Using the substitutions x = ∆ω middot R middot ∆t ξ = ωRν = ∆ωω we can write down (13) in the following form

ξmν = minusmicro[

ξ2 (∆t)2ν2 minus λ

]

ξν minus1

ξ∆t

partU

partν (14)

where ω is the angular velocity of the Earth rotation and∆ω is its change over ∆t= 1 year R is the average Earthradius ν is the dimensionless quantity which describesby definition the Earth rotational velocity [7] (Figure 1)Since temporal variations of the global ocean level and

temporal variations of the Earth average temperaturestrongly correlate without time lag whereas the tem-poral variations of the global ocean level and temporalvariations of the Earth rotational velocity strongly cor-relate with the lag tlag sim5 years (see Figure 1) (14) withconsideration of the approximate equality ν sim kTtminustlag

can be rewritten in the following form

ξkmT = minusmicroξk[

ξ2k2 (∆t)2T 2 minus λ

]

T minus1

ξk∆t

partU

partT (15)

that explicitly takes into account the mechanism of solarpower pacemakerNontrivial properties of the basic equation of bifurca-

tion model of the Earth global climate on the annualtime scale are exhibited in Figure 8 by the variety ofphase portraits depending on the governing parameters(a b) Moreover the change of shape of the assembly-type catastrophe potentials (7) on the plane (a b) directlyspecifies the conditions of rdquowarm-coldrdquo phase transitionsin the climatic self-oscillatory system of the van der Pole-Duffing type (13)Here it is interesting to note the following remarkable

fact It was found that the low order dynamic modelsof the time evolution of the toroidal magnetic field ofthe Sun derived from mean field dynamo theory are alsodescribed by the nonlinear oscillator equations of the vander Pole-Duffing type [31 32] In this sense the identicaltype of equations describing the time evolution both ofthe Sun magnetic field and the Earth global climate isone more confirmation and at the same time naturalconsequence of physical ie really existing mechanismof solar dynamo-geodynamo connectionNow we return to the problem of taking into account

of the mechanism of solar power pacemaker within theframework of the bifurcation model of the Earth globalclimate on different time scales It is known that on thelarge time scales (from several to ten thousands years) onwhich our bifurcation model was considered above theequilibrium state of the global climate is reached at every

time point It is obvious that in this case the left-handside of (15) can be set equal to zero and (7) itself can bewritten down in the following form

partTUprime = T 3 + aprimeT + bprime = 0 (16)

-4 -2 0 2 4

1

0

-1

-2

-3

-4

-5

2 a

b

FIG 8 A plane of the parameters (a b) the typical shapesof the assembly-type catastrophe potential (red lines) and thephase portraits (black lines on the pink squares) of the self-oscillating system of the van der Pole-Duffing type (13) atmλ = 1 Blue circles are points to whose coordinates thephase portraits and the assembly-type catastrophe potentialcorrespond

It means that the bifurcation model of the Earth globalclimate on the ten thousandth time scale really takesinto account not only the laws of atmospheric physicsin particular the laws of geometrical optics of climaticbilliards which generalize the cosmic rays-clouds effectby Sven-smark the first (the Twomey effect) and secondindirect aerosol effects [10] but also the mechanism of so-lar power pacemaker which was masked before [10 11]by renormalization procedure of the governing parame-ters to take into account the initial conditions In otherwords theoretical solutions of the bifurcation model ofthe Earth global climate on the ten thousandth time scalewith respect to the temperature and the global ice vol-ume not only take into account the mechanism of so-lar dynamo-geodynamo connection but in combinationwith high quality of description of the known experimen-tal trends of the temperature and the global ice volume[10 11] are reliable confirmation of correct and holis-tic understanding of the basic foundations of nonlinearphysics of the Earth global climate formation

[1] B A Buffet Science 299 1675 (2003)[2] Note that the strong (negative) correlation between the

temporal variations of magnetic flux in the tachocline

zone and the Earth magnetic field (Y-component) willbe observed only for experimental data obtained at thatobservatories where the temporal variations of declina-

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718

9

tion (δDδt) or the closely associated east component(δYδt) are directly proportional to the westward driftof magnetic features [3] This condition is very impor-tant for understanding of physical nature of indicatedabove correlation so far as it is known that just mo-tions of the top layers of the Earthrsquos core are responsiblefor most magnetic variations and in particular for thewestward drift of magnetic features seen on the Earthrsquossurface on the decade time scale Europe and Australiaare geographical places where this condition is fulfilled(see Figure 2 in [3])

[3] J-L L Mouel T R Madden J Ducruix and V Cour-tillot Nature 290 763 (1981)

[4] M Dikpati G de Toma and P A Gilman The Astro-physics Journal 675 920 (2008)

[5] Data of the observatory Eskdalemuir (Eng-land) Tech Rep (World Data Centre forGeomagnetic (Edinburg) 2007) worldwidehttpwwwgeomagbgsakukgifsannual_meansshtml

[6] V D Rusov E P Linnik K Kudela S C MavrodievI V Sharph T N Zelentsova M E Beglaryan V PSmolyar and K K Merkotan ldquoAxion mechanism of thesun luminosity and solar dynamo - geodynamo connec-tionrdquo () arXiv10093340

[7] N S Sidorenkov The Interaction Between Earths Rota-tion and Geophysical Processes (Wiley-VCH 2009)

[8] ldquoPacific decade-oscillation (pdo)+atlantic multi-decaded oscillation (oma)rdquo Internet AvailablehttpwwwappinsyscomGlobalWarmingPDO_AMOhtm

[9] E R Engdahi and A Villsenor ldquoGlobal seismicity 1990-1999rdquo (Academic Press 2002) Chap Part A (Interna-tional Geophysics)

[10] V D Rusov A V Glushkov V N Vaschenko O TMyhalus Y A Bondartchuk V P Smolyar E P Lin-nik S C Mavrodiev and B I Vachev J AtmosSol-Terr Phys 72 398 (2010) arXiv physicsao-ph08032765

[11] V D Rusov V N Vaschenko E P Linnik T My-halus Y A Bondartchuk V P Smolyar S KosenkoS C Mavrodiev and B I Vachev J Atmos Sol-TerrPhys 72 389 (2010) arXiv physicsao-ph 08032766

[12] F C Bassinot L D Labeyrie E Vincent X QuidelleurN J Shackleton and Y Lancelot Earth Planet SciLett 126 91 (1994)

[13] J Imbrie A Berger E A Boyle S C ClemensA Duffy W R Howard G Kukla J Kutzbach D GMartinson A McIntyre A C Mix B Molfino J JMorley L C Peterson N G P adn W L Prell M ERaymo N J Shackleton and J R Toggweiler Paleo-ceanography 8 699 (1993) doi10102993PA02751

[14] R Tidemann M Sarnthein and N Shackleton Paleo-ceanography 9 619 (1994) doi10102994PA00208

[15] Axion models are motivated by the strong CP problem -the apparent vanishing of the CP- and T-violating elec-trical dipole moment (EDM) of the neutron The ax-ion model offers a dynamical solution to the strong CPproblem by introducing a new scalar field which rollswithin its potential into a state of minimum action a

CP-conserving QCD vacuum state Any imbalance be-tween the contributions to the EDM from TeV and GeVscales is absorbed into the scalar field value The quan-tized excitations of the scalar field about the potentialminimum are called axions (see [33] and refs therein)

[16] V D Rusov V N Pavlovich V N Vaschenko V ATarasov T N Zelentsova V N Bolshakov D A Litvi-nov S I Kosenko and O A Byegunova J GeophysRes 112 B09203 (2007) doi1010292005JB004212

[17] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 1 compari-son of theory with experimentrdquo () arXiv10113568

[18] A Gando and others (KamLAND Collaboration) PhysRev D 83 (2011) arXiv10094771

[19] G Bellini and others (Borexino Collaboration) PhysLett B687 299 (2010)

[20] T Araki and others (KamLAND Collaboration) Nature436 499 (2005)

[21] S Abe and others (KamLAND Collaboration) PhysRev Lett 100 2218031 (2008)

[22] S T Dye Phys Lett B679 15 (2009)[23] V M Hamza R R Cardoso and C F P Neto Inter-

national Journal of Earth Sciences 97 205 (2008)[24] V D Rusov V A Tarasov and D A Litvinov Reactor

Antineutrinos Physics (URSS Moscow 2008)[25] L P Feoktistov From the Past towards the Future from

the Hopes of Bomb to the Safe Reactor (Publ of RFNC-ANRISPh Snezhinsk Russia 1998)

[26] S M Feinberg in Record of Proceedings Session B-10 International Conference on the Peaceful Uses forAtomic Energy (United Nations Geneva Switzerland1958) pp 447ndash44

[27] L P Feoktistov Reports of Academy of Sciences of USSR309 864 (1989)

[28] E Teller M Ishikawa and L Wood in Proceed-ings Frontiers in Physical Symposium Joint AmericanPhysical Society and American Association of PhysicsTeachers Texas Meeting (Lubbock Texas 1995) preprintUCRL-JC-122708

[29] V D Rusov D A Litvinov S C Mavrodiev E P Lin-nik V N Vaschenko T N Zelentsova M E BeglaryanV A Tarasov S A Chernezhenko V P Smolyar P OMolchinikolov and K K Merkotan ldquoThe kamland-experiment and soliton-like georeactor part 2 fundemen-tal geophysical consequencesrdquo () in preparation

[30] R Gilmore Catastrophe Theory for Scientists and Engi-neers (New York - Chichester - Brisbane - Toronto Wiley-Interscience Publication John WileySons 1985)

[31] D Passos and I Lopes J Atmos Sol-Terr Phys 73191 (2011)

[32] P D Mininni D O Gomez and G B Mindlin SolPhys 201 203 (2001)

[33] S C Aaron ldquoExperimental probes of axionsrdquoArXiv10094718