INSTITUTE OF PLASMA PHYSICS

NAGOYA UNIVERSITY

THE DYNAMICS OF MICROPROCESSES

AND CURRENT TURBULENT HEATING OF IONS

IN "URAGAN-2" STELLARATOR

*N.F. Perepelkin, V.A. Suprunenko, A.S. Slavny,

M.P. Vasil'ev, A.G. Dikii, V.D. Kotsubanov,

B.V. Kravchin, A.E. Kulaga(Received - Jan. 19, 1981)

IPPO- 548 Oct. 1981

56,11,11

R E S E A R C T T R E P O R T

NAGOYA, JAPAN

THE DYNAMICS OF MICROPROCESSES

AND CURRENT TURBULENT HEATING OF IONS

IN "URAGAN-2" STELLARATCR

*N.F. Perepelkin, V.A. Suprunenko, A.S. Slavny,

M.P. Vasil'ev, A.G. Dikii • V.D. Kotsubanov,

B.V. Kravchin, A.E. Kulaga(Received - Jan. 19, 1981)

IPPO- 548 Oct. 1981

This is a record of the talk given by N.F. Perepelkin

at the Institute of Plasma Physics, Nagoya University, under

the same title.

Further communication about this report is to be

sent to the Research Information Center, Institute of Plasma

Physics, Nagoya University, Nagoya 464 Japan.

* Kharkov Institute of Physics & Technology, Ukrainian

Academy of Sciences, Kharkov, USSR.

ABSTRACT

Some investigations of noise spectra and UHF-railiations

within a wide range of electron-cyclotron, electron plasma

and ion plasma frequencies have been performed in "Uragan-2"

stellarator. Threshold dependences on electrical and magnetic

fields of kinetic instability excitations have been studied

as well as of ion heating and disruption of quasi-stationary

run-away of electrons in a plasma heated by a powerful currentucepulse in high magnetic fields - ^ > 1.

uce U p eIt was shown that near — — * i the threshold character

Vof growth of hot ion number and energy, as well as of the

excitation of epithermal nonstationary electromagnetic

radiations on Langmuir frequency and ion plasma frequency

harmonics were connected with the ion-acoustic turbulence

and the processes of nonlinear sound transformation.

These effects are increased with the rise of magnetic field

strength and are followed by the drop of a resistance absolute

value.

At the rise of electrical field strength no restrictions

in injection of high ohmic power into a plasma and ion temper-

ature rise were observed. Energy lifetime of hot ions was

40 ysec, that being one order of magnitude lower than a

design neoclassical time. The results of ion heating in

tokamaks were compared.

- 2 -

INTRODUCTION

Two-temperature energetic distributions of ions in a

magnetized plasma of an ohmic discharge in tokamaks and

stellarators arise, as a rule, at high value of a drift para-

meter z 0.5 on the background of intensive ion plasmavTe

oscillations [1-5]. The excitation mechanism of these

oscillations and the conditions of pumping turbulent energy

to particles are not clearly understood. For such compara-

tively low-density discharges with run-away electrons, at;

for example, in the tokamak Alkator [6] the term of "slide-

away" regime has consolidated where preference is given to

instability on Doppler anomalous effect and heating is

associated with oblique Langmuir modes (1)=^ to . However,i\ pe

the registered oscillation spectrum does not conform to

quasi-linear theory predictions [7]. In these regimes

nonlinear processes in ion-acoustic spectrum are expressed

more preferably as intensive noises are registered close to

even ion plasma harmonics 2to . and 4co . [8] . According to

[3 6] in tokamak with run-away electrons the induced scatter-

ing of intense Langmuir waves by ions can transfer the energy

of waves into ion frequency range to heat resonance ions.

On the other hand, in linear and toroidal turbulent

discharges at E>>E the ion heating to temperatures comparable

with electron temperature is a well-known experimental fact

[9-16]. A number of hypotheses based on an ion-acoustic

- 3 -

turbulence model were expressed about an ion-heating

mechanism [17,18]. For example, the ion resonance heating

due to quasi-linear effects [19] and the heating of the bulk

ions due to nonlinear effects induced scattering of ion-acoustic

oscillations on ions [20,21]. Besides, the ion heating can

occur very fast due to particle trapping by an ion-acoustic

wave [22].

In spite of great difference in values of electric fields

E, there exist a lot of common regularities at the ion heating

in quasi-stationary and turbulent pulsed discharges. In

particular, this deals with two-temperature kind of energetic

spectrum of observed neutral charge-exchange atoms and with

temperature dependence of hot ion "tail" on discharge para-

meters. Besides, for a substantial ion heating in quasi-

stationary discharges a high specific ohmic power is required.

The theoretical analysis performed in paper [23] showed

that in closed magnetic traps, where the ohmic heating was

limited by losses, the current turbulent heating in a high

magnetic field when u >u could be caused by a simultaneous=* ce p e •*

action of the ion sound and instability on electron-cyclotron

frequency harmonics \<Lnv,,=M-SLu> , where £=0,+l, • • • . In these

conditions the quasi-stationary electron acceleration can

vanish. On the ion distribution function a peculiar fracture

in energy range e.^y^C—)2 occurs and is associated with

resonance absorption of ion-acoustic oscillations by hot ions.

Besides, because of wave-vector cone tapering of excited ion-

- 4 -

acoustic oscillations in a high magnetic field, the effect of

these oscillations on anomalous resistance has to be weakened

markedly.

The experiments showed that in "Uragan-2" stellarator [4]

at the excitation of intensive ion-plasma noises u ., in the

electric field E>E_, r the process of quasi-stationary run-away

of electrons was really stopped. The energy of accelerated

electrons remains finite, 10-20 keV, and depends slightly on

electric field strength. The increase of magnetic field

strength results in exponential growth of energy content of

hot ion. Visible contradiction arose from the fact that the

increase of plasma turbulent level led to decrease of plasma

resistance. As a result, in a magnetic field higher thanwcecritical value = 1 the plasma anomalous resistance dropped"pe „

with the increase of magnetic field strength as R ~ 1 - 5 —nmax

and the enerqy of turbulent noises was effectively pumped

over to ions.

In this work the regimes of ion current heating have been

studied and the dynamics of ohmic discharge transfer into a

turbulent regime with low resistance has been investigated in

order to identify an instability in the high magnetic fieldu >u in "Uragan-2" stellarator. The spectra of noises andce pe ^

UHF-radiations in a wide frequency range have been investigated,

and the comparison of results of ion heating in "Uragan-2"

stellarator with data obtained on tokamaks has been performed.

- 5 -

1. The regimes of plasma ohmic heating in the stellarator

The distinguishing feature of experiments on turbulent

heating of a plasma in "Uragan-2" stellarator involved the

fact that comparatively short powerful discharges were

developed. The duration of a turbulent discharge active phase

was determined, on the one hand, from inductance of a plasma

column and an iron core, on the ether hand, it was restricted

by the rate of impurity influx into a plasma and non-controlled

density growth associated with impurities. Therefore, the main

results were obtained during the first 500psec in a discharge

pure phase when the impurities of heavy ions and a cold gas

absorbed on chamber walls haven't yet entered a plasma. A

chamber surface was cleaned beforehand for a long time by

ohmic discharges with high repetition rate. Investigations

were performed with and without a stainless steel diaphragm

in the chamber. In so doing the negative role of a diaphragm

as a source of impurities was mentioned. Preliminarily the

low-density plasma 'vS-lO^cm was generated by means of r.f.

ionization of a working gas. R.f. generator power is 100 kW,

frequency -100 kHz, duration -1.5 msec.

The system of plasma ohmic heating with a powerful

current pulse have a capacitor bank of C=800yF charged to

U=5 kV and the iron transformer with coil ratio 20:1 or 10:1

which ensures the magnetic flux of 0.26 V-s. The searching

of optimal regimes for ion turbulent heating in a high magnetic

- 6 -

fieldr w >UJ , was performed in discharges of two types :ce pe

without an additional ohmic ionization of the gas and with an

ohmic pre-ionization. In the first case the rise of ionization

degree of the gas was achieved by a powerful current pulse of

turbulent heating and duration of this phase changed within

150-500ysec depending on electrical field strength on the

bypass of the discharge chamber. In the second case full gas

ionization in the chamber without any appreciable signs of

impurities was achieved by a short current pulse during 500

ysec at a low electric field strength in a plasma, and after

this a powerful pulse of turbulent heating was switched on.

The parameters of the ohmic pre-ionization system are the

following : C=800 yF, U=l kV, coil relation 5:1, plasma power

150-300 kW, discharge duration 700ysec, n=0.2-1.1013cm~ T =

15 eV.

Fig. 1 shows oscillograms which exhibit various character

of powerful discharges in the stellarator with pre-ionization

by ohmic current and without pre-ionization. It is seen from

the analysis of oscillograms that in the absence of pre-ioniza-

tion a substantial part of power injected into a discharge is

used for ionization. This essentially increases the flux of

charge-exchange neutrals with the range of low energies,

320-640 eV. In the case of ohmic pre-ionization the part of

low-energy atoms dropped and the flux of charge-exchange atoms

of high energies increased. Besides, the flux of hard X-ray

in the energy range e 'vlO-lOO keV grew within three orders ofe

- 7 -

magnitude in a rather short time, 3 0]jsec. As in both cases

the maximum energy of X-ray quanta did not change and slightly

depended on electrical field strength, it indicated an effective

heating of electrons.

It should be emphasized that turbulent heating by a high

current pulse under controllable conditions could be obtained

only with the operation of "Uragan-2" machine in stellarator

regime. Fig. 2 shows that when stellarator helical conductors

are switched off, the impurities and plasma density grow

without any control. It results in a sharp drop of heating

efficiency of electrons and ions.

A set of standard diagnostics has been used in experiments.

The electrical field strength and plasma current were measured

by a loop embracing the discharge chamber and by the Rogowski

belt. Interferometers with the wave lengths 2 mm and 8 mm

were also used, as well as the analysis of charge-exchange

neutrals, spectral measurements in a visible region, registra-

tion of a hard component of X-ray radiation of 10-500 keV

emerging from discharge-chamber walls and from a target in a

plasma. Magnetic measurements of the noise spectrum in the

vicinity of ion plasma frequencies and the analysis of UHF-

radiation spectrum from a plasma in a wide range of electron

plasma and cyclotron frequencies were performed.

The main plasma parameters in "Uragan-2" stellarator are

the followings:

T i

a

r p

e

t r

= 0 .

= 10

= 6 .

= 0 .

= t

2-0

cm

5-4

14

+

.75

.5

l_

t

keV

cm

= 0 .

= i

56

.2

H = 5-zO kG

E = 6.10"3-0.2 V/cm

I = 1.5-20 kA

n = 6 B 1 0 cin

Te= 0.3-1 keV

Fig. 3 gives dependences of various plasma parameters on

electrical field strength on the bypass of the discharge

chamber for the cases of low and high magnetic fields in two

gases, H and D . The data were obtained in discharges with-

out the ohmic pre-ionization at a constant plasma density of

n=6*10'zcm"'3. Electron temperature T was measured by laser

scattering, brightness temperature of UHF-radiation in a

plasma frequency range T, was defined by a UHF-radiometer.

It is seen that in weak OJ <to and in strong to >to magnetic

ce pe ce pe =

fields near a threshold value of electrical field E~E the

excitation of intensive noises to • takes place and the intensity

of hard X-ray radiation y from a discharge chamber wall and a

target in a plasma sharply drops. It is also seen that in a

high magnetic field the stripping of quasi-stationary electron

acceleration does not lead to a full stripping or epithermalUHF-radiation to and its intesity rises with ion plasma noises

pe

w .. As shown later, in electrical fields E>E the maximum

energy of hard quanta does not depend on an electrical field,

and this energy is much lower than the energy connected with

the effect of electron classical run-away.

- 9 -

In low magnetic fields, u "<co , for a central reqion ofce pe

plasma column in the regime of run-away electron braking,

when E>E , the UHF-radiation near plasma frequency w has a

thermal character, and its brightness temperature growswceproportionally with electrical field strength T^ "v E.

It has been discovered that in high magnetic fields the

regimes of acceleration and braking of electrons, as well as

the excitation of intensive turbulent noises comply with

various levels of current drift velocity stabilization. Fig. 4

gives the dependence of drift parameter - — and the intensityVTe

of hard X-ray radiation from the target y o n ~ — value. AnEDr

effective quasi-stationary electron acceleration is seen to

be. observed in very low electrical fields - — =0.1+0.2 V/cm.EDr

In this case the energy of hard quanta reaches the value of

e *450 keV.e

The region of run-away electron braking at - — <1 conformsEDr

to regime I, where current velocity is stabilized at a level

- — =0.25. Near the threshold § — =1 the drift parametervTe EDrjump, the excitation of intensive ion noises u •, and the

stripping of electron quasi-stationary acceleration are

observed. In a region where — — >1, conforming to the regimeD r u

II the current velocity is stabilized at a level - — =0.5.Te

In this regime the plasma transits into a state of highturbulization and an effective ion heating is obser/ed.

Fig. 5 gives the dynamics of discharge transition into

a high-turbulence regime with magnetic field growth. It is

- 10 -

seen that the excitation of epithermal sporadic UHF-radiation

a) and ion noises u . as well as the change of anomalous

resistance nature associated with its dependence on magnetic

field Ra,l-- and the drift parameter ^ — jump take place inmax VTe

the high electrical field = — >1 [4].EDr

An essential experimental fact obtained on "Uragan-2"

stellarator lies in exponential growth of total energy of

plasma hot ion component <n. T. > with the growth of super-

critical magnetic field under an inherent two-temperature

distribution of ions by energies. The growth of ion "tail"

full energy is connected both with an increase of particle

number and their energy.

The foregoing experimental results allow to classify ohmic

heating regimes of the plasma confined in the stellarator by

high magnetic fields u >u • In particular, there exist three

regimes of ohmic heating in a plasma according to electrical

field strength of a discharge. These regimes can be relatively

defined as : the high-temperature - E/E <<1, the acceierative

E Eone - - — <1 (regime I), and the turbulent one - - — >1 (regime

EDr EDr

II, fig. 4). These regimes are distinguished by plasma

resistance, by stabilization level of drift velocity, and

by the spectrum of excited oscillations in a plasma as well.

An important feature of turbulent regime lies in the excitation

of rather intensive ion plasma noises and in effective ion

heating.

- 11 -

2. Noises and epithermal UHF-radiation

The information on the turbulence nature and localization

degree of turbulent energy near ion plasma frequencies has

been obtained from the spectra of cyclotron and plasma UHF-

radiation, as well as from the spectra of radio-noises recorded

by a magnetic antenna outside a plasma. The essence of applied

methods lies in the analysis of fine structure of UHF-spectra

and in the measurement of a relative level of plasma harmonicspzwDe

1-2- [24] . In the experiments on "Uragan-2" machine suchPwpe

measurements turned out to be possible, as the width of UHF-

radiation lines associated with inhomogeneity of plasma

density and magnetic field was less than an inherent ion plasma

frequency.

Fig. 6 shows the evolution of the spectrum of cyclotron

harmonic 2w versus an electrical field strength in hydrogen

and deuterium discharges for the three above-mentioned regimes

of ohmic heating. In all the regimes plasma density was

constant. On the spectra the cross-hatched regions show

magnetic broadening in the racetrack area of the stellarator

where radiation acception was achieved and where magneticA H

field inhomogeneity accounted for — = 1.5%. In all three

regimes cyclotron apectra are seen to be broadened anomalously

and +-o be changed substantially from one regime to another.

In low electrical field (high-temperature regime, spectrum

3, fig. 6) the intensity of synchrotron radiation of hot

- 12 -

electrons small fraction ^0.1% near the line centre of

resonance absorption is determined by the temperature of basic

electron mass [25]. Therefore the anomalously broadened

cyclotron spectrum has got a dip in a cyclotron-resonance zone.

The transition into accelerative regime is characterized by a

relativistic red shift of the spectrum and by synchrotron

radiation bursts within the frequency range io<2u) (spectrum 2) .

However, in the cyclotron-resonance zone the radiation level

is at a thermal level and slightly depends on energy of run-away

electrons. The braking of run-away electrons with the electri-

cal field growth and the transition into turbulent! regime in

the fields E>E is followed by the stripping of nonstationary

synchrotron radiation with a characteristic red shift of

frequency. Near the cyclotron harmonic 2u there appears anCc

anomalously broadened stationary Raman spectrum. As seen

form Fig. 6 (spectrum 1), its fine structure depends on a gas

mass, as frequency intervals between satellites are equal to

Aa)=(i) . ; 4u . and Au=/—^ . These data point to the excitation

of a rather intensive stationary turbulence near harmonics of

ion plasma frequencies. In this case the plasma brightness

temperature in the cyclotron resonance zone is higher by a

factor of 2-2.5 than the electron temperature measured by a

laser.

Simultanelusly intensive splashes of noises near the

harmonics of ion plasma frequency to .;2u . were registered

out of a plasma as electromagnetic fields "penetrating" into

- 1 3 - •

vacuum near the plasma column surface. These signals were

received by a loop (d=110 cm which was used as an external

magnetic antenna. The noise spectrum was analyzed by means

of a four-channel system of superheterodynes with special

calibration

Fig. 7 shows frequency spectra of epithermal turbulence

w .. In high electrical fields it has been detected the

excitation of two types of noise spectra : the stationary

spectrum (V) approximating in its character the stationary

ion-acoustic Kadomtsev spectrum [26] and the explosive sporadic

spectrum (o) near the harmonics of ion plasma harmonics was

followed by bursts of X-ray-radiation from the target in a

plasma over the energy range of 10-20 keV [27] as well as by

generation of epithermal UHF-radiation near Langrauir frequency

u) , the modulation spectrum of UHF-radiation being given in

Fig. 7 (lower spectrum). The generation of epithermal UHF-

radiation u) is seen to be directly connected with the excita-

tion of nonstationary spectrum near the harmonics of ion plasma

frequency 2to . and 4u . .

The spectrum of epithermal UHF-radiation u is typical

as well. It is seen from Fig. 8, where the evolution in time

is presented for UHF-spectra for a wide frequency range in

turbulent discharge, that strong localization of radiation

power near Langmuir frequency takes place. In this case the

radiation intensity is 2-3 orders of magnitude higher than

thermal noise level.

- 14 -

As mentioned above, an intensive epithermal UHF-radiation

near Langmuir frequency u arises only in a high magnetic

field when w c e> t o

p e- T n e excitation process has a threshold

character for a wide range of electrical fields (see Fig. 5).

However, in a low electrical field E<E the radiation intensity

is much higher than a thermal noise level within 4-5 orders of

magnitude (see Fig. 3). In accelerative regime the generation

mechanism is connected with two-dimensional Langmuir solitons

which are excited by run-away electrons [28].

In the turbulent regime the epithermal sporadic UHF-radia-

tion a) has a combinative spectrum as well as a spectrum near

the cyclotron harmonic (Fig. 6-1). The frequency disadjustment

between satellites also depends on the mass and is equal to

ion plasma frequency. The most typical is the doublet of lines,

the interval between which equals 2Ato=2w ., where up to 80% of

UHF-burst energy is concentrated. Q-factor of radiation lines

is of 103 order. The fine structure of UHF-radiation spectra

to for various gases is given in Fig. 9. The spectrum sweep

was obtained in 5psec by means of a fast UHF-analyzer [27,29].

Duration of analyzed bursts was as long as 15-20)jsec and greatly

decreased with the rise of electrical field. It is also seen

from Fig. 9 that the combinative spectrum of UHF-radiation near

the Langmuir frequency u> is fully determined by plasma density

and mass, as the intervals between satellites are equal to

. /4TT neMIThe relation between plasma harmonics in the UHF-radiation

- 15 -

spectrum allows to estimate redistribution of energy of

turbulent noises in a plasma within a wide frequency range.

According to [24] this relation can be written in a simple

form :P R ,W_, MP =3(rr-) rr- i where K is a typical scale of turbulence,

o>pe u iW and W. are the energy density of Langmuir and ion-acoustic

oscillations, respectively. As the turbulence scale K satisfieswpethe condition K<K < K = —*-— and can only drop with the increase

of oscillation energy due to energy repumping into a region ofKn - -i

long waves, so even at slight changes in K <•=— for K-3.10 2 cmP2

iand the value of the relation _ MP e a.3.10 ** derived in thewpe

turbulent regime (see Figs. 8-II and III), the energy density

of the ion plasma oscillations greatly exceeds the energyW

density of Langmuir oscillations — >10.I

The dynamics of pumping over the energy of R.F.-oscillations

in a plasma from the Langmuir region of the spectrum into the

low-hybrid region was investigated in "Uragan-2" stellarator

in the high magnetic field — — *2.2 under the turbulent heating

of a plasma with preliminary gas ionization. Investigations

showed [4] that the value of r^- really depended on electricali

field and, accordingly, on the number of accelerated electrons

which arise in foreplasma produced by ohmic pre-ionization,

and then their hampering takes place in a turbulent discharge

with E>E_ . Fig. 10 gives the dependences of P ., y and -

on electrical field in a hampering (t =200ysec) and a turbulent1

discharge phases (t =400ysec). The exponential drop of hard

- 16 -

X-ray-radiation intensity y(e <10Q keV) in the braking phase

t (when the noise level P . is low) is seen to correlatei "P1 W

with energy drop of Langmuir oscillations*within r -=i

In the turbulent phase t when the flux of hard quanta practi-2

cally vanishes, the exponential growth of ion noises PW "

stabilizes the relation at the level ^-

The estimation of Langmuir turbulence degree from the

data of radiation intensity on the second harmonic of

frequency P_ gives the value which is much lower than

excitation threshold of modulative instability in the Langmuirspectrum [30]:

W „-~<<(=—)2^ 10 3. At the same time, the high radiationn i • i\o

level on plasma frequency P y2 •10~6W/cm3could be quitely connect-

ed with the state of high turbulence in a low-hybrid spectrum

region with electron trapping by a low-hybrid wave field, as

well as with the development of modulative instability, as

1The high noise level in a plasma near ion plasma frequency

harmonics and the combinative radiation spectra on electron

cyclotron harmonics and Langmuir frequency, whera the width of

radiation lines is much smaller than the ion plasma frequency,

attest the hypothesis connected with caviton formation. In

these conditions high perturbations of density -~ -\.1C~1 and

magnetic field in a plasma == %10~- were observed and they were

correlated in time with discharges of epithermal electrons with

the energy e <v5-6 keV [27,31].

- 17 -

the cyclotron harmonic 2u and of sporadic combinativece

Thus, modulative processes in a plasma caused by the

stationary pumping with the epithermal turbulence current near

the harmonics of ion plasma frequencies 2^ . and 4w ., thatill 1

is, in the low-hybrid spectrum region w=to . (1+ ^ p e ) ~ 2 are thew ce

main reasons of stationary combinative spectrum radiation near

the cyclotron harmonic 2u and ofce

spectrum near Langmuir frequency w

The concentration of turbulent energy in a low-hybrid

spectrum region creates, in our opinion, real premises for

effective heating of plasma ions. However, obtained experimen-

tal data do not allow to point out the particular excitation

mechanism of epithermal spectra near ion plasma harmonics.

The most probable two mechanisms could be supposed which are

associated either with a nonlinear stage of ion-acoustic

turbulence in a high magnetic field (ion-acoustic plasmon

coupling), or with a nonlinear stage of low-hybrid turbulence

excited by epithermal electrons on the anomalous Doppler

effect [32]. In processes under consideration the role of

the "tail" of quasi-stationary run-away electrons is vanishing-

ly small.

3. Turbulent heating and confinement of hot ions in the

stellarator

A rather substantial rise of energy and hot ions volume

in stellarator was discovered only when injecting high ohmic

- 18 -

power into the stellarator. As already mentioned, this was

achieved by decreasing inductance of a discharge circuit, by

means of previous generation of a fully ionized dense plasma

in the stellarator under conditions of ultimate attainable

value of magnetic field strength and energy store of turbulent

heating capacitor bank. The energy content of a hot ion

component was revealed to grow in a threshold manner both with

the electrical and magnetic field rise. The threshold field

values lie near characteristic values :

EDr wpe

Fig. 11 shows energy spectra of ions from the data of

charge-exchange neutrals for various values of electrical and

magnetic field strengths in "Uragan-2" stellarator. The

spectra were obtained by means of a single-channel analyzer

at a constant density of ,6*1012cm~3. The recording system

for neutral atoms escaping across a plasma column in a race-

track region had magnetic separation by masses.

In a first approximation the energy spectra of ions can

be presented by two-temperature distributions. The energy

content of the hot ion "tail" in the E>E region is seen to

grow substantially with the magnetic field rise (see also

Fig. 5). At the same time and a constant magnetic field ofw

15.8 kG corresponding to = 2.03 an essential growth of theupe

"tail" energy content is observed.

The threshold nature of the dependence of hot ion component

- 19 -

temperature T. on electrical field strength is presented in

Fig. 12. A set of dependences which characterize the rise of

ohmic power injected into a plasma, the ion temperature growth,

and energy stabilization of hard X-ray quanta radiation from

a target in a plasma at the increase of electrical field streng-

th in the E>ED region (E =0.05 V/cm), show the influence of

ohmic ?re-ionization and magnetic field on ion heating effect.

Here an essential fact lies in ion heating not being connected

with run-away of electrons. The maximum energy of accelerated

elections in a wide range of electrical fields is seemed not

to depend on the value of electrical field strength. At the

same time, the "tail" temperature of ions grows linearly with

the increase of electrical field and current in a plasma : T.

' E'vl. It is also seen that in the case of the ohmic pre-ion-

ization the maximum value of power injected into a plasma

reached the value of P_ =3.8 MW, ion temperature of -the "tail"

' —3

was T. =0.75 keV at T.=250 eV and plasma density n=6*1012cm

in the magnetic field of 19.4 kG. In this case only 10% of

ions acquire high temperature.

The effect of the factor of plasma magnetization in

turbulent regime at E>E on the ion heating can be derived

from comparison of observation results in various machines.

Fig. 13 ? presents the dependences of ion "tail" temperature

on the value of — — for tokamaks and stellarators. It should

Vbe borne in mind that a monotone growth of ion temperature

from magnetic fields in stellarators "Uragan-2" and "Sirius"- 20 -

[3] and the tokamak TM-3 [1] at a plasma density decrease in

a constant magnetic field was observed beforehand in turbulent

regimes when E>E . The ion temperature jumps in the tokamak

"Alcator" [33] under plasma density decrease within the valuesw

of =4.5 and in the tokamak TRIAM-1 [34] with magnetic fieldwpe

rise at a constant plasma density are likely to take place near

a threshold value of electrical field when E-E , that is, when

passing into a high-turbulence regime (see Fig. 4, regime II).

This is confirmed by a low temperature level at plasma densitywcerise in the tokamak "Alcator", when changes within 4+2.5wpe

and by the Coulomb heating of the ion bulk in very low electri-wcecal fields E<<E_ in the classical tokamak regime at =1.5+2.

Thus, in the stellarator "Uragan-2" with field strength

of 20 kG the current turbulent heating of ions has been perform-

ed under the injection of high ohmic peer P z 4 MW into aOn

plasma. The lack of appreciable limitations in the growth of

ohmic current and ion temperature points to the promising

character of ion turbulent heating method in high magnetic

fields in a big stellarator at high degree of plasma magneti-

zation.

Discussion of results

1. A search for optimal regimes of ion turbulent heating with

plasma current has been accomplished in the "Uragan-2" stella-

rator. It is shown that in the high magnetic field u c e> w

D e

the plasma ohmic heating in a stellarator can be conditionally

- 21 -

divided into three regimes : the high temperature regime with

preferential electron heating (E<<E ), the accelerative one

(E"?EDr) , and the turbulent one (E>E ) - The heating regimes

are distinguished by the character of plasma resistance, by

the level of current drift velocity stabilization, and by the

spectrum of oscillations excited in a plasma. A transition

from the accelerative regime to the turbulent one near Dreicer

critical field is the most typical which is followed by an

effective braking of run-away electrons, jumping character of

the increase of drift parameter and by ion heating.Te

2. In experiments under discussion the classification of the

ohmic heating regimes is based on synchronous spectra of plasma

radiation. It was shown that these spectra allowed to make a

number of assumptions about the kind of electron distribution

function. In particular, a high-temperature regime in a very

low electrical field E<<E is characterized by two-temperature

distribution of electrons by energies where a small fractioni t

of particles n =10~'tn has the following temperature : T =:102T .

In the accelerative regime E<E about 1% of electrons from

the distribution function tail are in the state of quasi-

stationary acceleration. The energy of these electrons can

reach the value of e 0.5 mev and they transport an appreciable

part of current in a plasma. An increase of electrical field

strength above the critical value E>E results in the stripp-

ing of quasi-stationary electron acceleration and is followed

by a stationary pumping with current of turbulent noises on

- 22 -

ion plasma frequency harmonics w ., the energy density ofp l W.

which is much higher than Langmuir oscillation energy ^

The most typical feature of the turbulent regime lies in

the fact that beginning with a threshold value of the magneticwce

field ;1, the plasma anomalous resistance drops with theWpe H

magnetic field rise in direct proportion to R' l- — , as the, max

temperature of a hot ion component grows : T.O.I-H.

3. The distribution of turbulent energy in a plasma within a

wide frequency range has been investigated. At the transition

from the accelerative to the turbulent regime the oscillation

energy is shown to be pumped over from the Langmuir spectrum

region to an ion plasma frequency region. Accumulation of

noises near ion plasma frequency harmonics results in develop-

ment of modulation processes in a plasma which are followed

by strong perturbations of density and magnetic field, radia-

tion of combinative spectra near Langmuir frequency UJ and

on the harmonics of electron cyclotron frequencies.

4. The concentration of turbulent energy near ion plasma

frequencies is shown to provide an effective heating of plasma

ions in a high magnetic field. Energy spectra of ions have

two-temperature distributions, and ion heating is not connected

with quasi-stationary run-away of electrons. It has been

noticed the threshold character of ion noise excitation and

of the increase of energy content of a plasma hot ion component

with the growth of both magnetic field strength near the value

"ce Eof ~1 and electrical field strength at — — = 1.

uPe

EDr

- 23 -

The excitation mechanism of intensive oscillations on

ion plasma frequency harmonics is most likely associated with

nonlinear processes of plasmon coupling of an anisotropic ion

sound 2a) . =u' +o)" excited by current electrons in a highp i s s

magnetic field. It is on a basis of an ion-sound model of

plasma turbulent heating by current that two-temperature

energy distributions of ions obtained in experiments on "Uragan-

2" n.-vO.l-n., T.=0.25 keV and T.=0.75 keV could be explained.

Appropriate mechanisms of resonance n• and nonresonance n• i° n

heating which were connected with quasi-linear effects and

with effects of nonlinear induced scattering of acoustic

oscillations on ions were treated earlier in some theoretical

papers [20-23]. However, complete clearness in the question

of the excitation of ion plasma harmonic spectrum has not yet

been obtained and the data gained from the experiment do nto

allow to draw unambiguous conclusions.

5. Comparison of the results of ion current heating in "Uragan-2"

stellarator with the data obtained in the machines "Alcator"

[2,33], "Sirius" [3], TM-3 [1] and TRIAM-1 [5,34] showed that

monotone temperature rise of hot ions with a magnetic field

which complies with the dependence T.^I-H was observed only

in high electrical fields E>E .

6. In optimal conditions of plasma turbulent heating in "Uragan-

2" it was not observed the limitation on injecting high ohmic

power into a plasma and on the rise of ion temperature T. while

increasing electrical field strength. Heating conditions are

completely determined by the quality of stellarator magnetic

- 24 -

surfaces in spite of a big summation angle of rotational

transform ty=1.2-1.7. Functional relationships of energy

lifetime of hot ions on discharge parameters follow Galeev-

Sagdeev neoclassical dependence for plateau [35] :H2ty

T . '• . . However, the energy time observed in theE,i (T!)

3/2

experiment and calculated from energy balance for an ion

component camprises T E • ~ —-t. ~ 40^sec, that being one

order of magnitude lower than a computed value.

- 25 -

FIGURE CAPTIONS

Fig. 1 Oscillograms illustrating various character of power-

ful turbulent discharges without and with gas pre-

ionization by ohmic current: V - the voltage on the

bypass of stellarator discharge chamber; I - plasma

current; n -average density; H. and C III - intensityP

o oof spectral lines 4861 A and 4647 A;n and y - intensity

o

of neutral discharge atoms with energies 3 20-64 0 eV

and intensity of hard X-ray-radiation from the target

in a plasma within energy range of 10-100 keV.

Fig. 2 Oscillograms showing the uncontrollable plasma density

growth in a turbulent discharge with switched off

stellarator helical conductors (solid line). The

broken line - a discharge in stellarator field.

All notations are taken from Fig. 1.

Fig. 3 Ohmic plasma parameters versus electrical field streng-

th in "Uragan-2" for two values of magnetic field

strength: u <u and u >w under the discharge in

H and D with constant density of 6»1012cm~3. I -2 2

i

plasma current; T - electron temperature from laser

measurements; T fF - plasma brightness temperature on

the Langmuir frequency u ; Pu _ - noise intensity

from magnetic measurement data;y - intensity of hard-

X-ray-radiation from a discharge chamber wall. The

horizontal dashed line is the recorder threshold

- 26 -

response at a level of 30 keV.

Fig. 4 The dependence of drift parameter and intensityvTe

of hard X-ray-radiation from the target in a plasmai7

Y on = — value. The horizontal dashed line is theEDr

recorder threshold response of 10 keV.

Fig. 5 The dependences characterizing discharge threshold

transition into a high-turbulence regime with low

resistance under magnetic field rise at constant

density of 6«1012cm~3 and electrical field strength

E=0.1 V/cm in two gases: - drift parameter; R -Te

plasma resistance; T - electron temperature fromwpelaser measurements; T, - plasma brightness temperature

* i i

on Langmuir frequency;<n.T.> is an average energy

density of plasma hot ion component from the data of

measuring neutrals charge-exchange.

Fig. 6 Evolution of radiation spectra near the second cyclotronharmonic 2u versus the electrical field (n=6<1012cm~3,

ce

= 1.7,(- - -} hydrogen, ( ) deuterium):1 - E=v0.1, 2 - E=1.5 lO"2, 3 - E=5-8-10~3 V/cm. The cross-

hatched band is the broadening due to magnetic field

inhomogeneity in stellarator racetrack area.

Fig. 7 Turbulent noise spectra. The upper spectrum is the

power spectrum from magnetic measurement data (V -

stationary spectrum, O - epithermal sporadic spectrum).

The bottom spectrum is the modulation spectrum of

epithermal sporadic UHF-radiation near frequency OJ ;

- 27 -

( m= _ = o.D.Ato Wpe

Fig. 8 Time dynamics of UHF-spectra of hydrogen turbulentwceplasma in the high magnetic field =2.2, 11=16.8 kG.V

The oscillograms : 1 - electrical field strength E=

0.05 V cm~a/div, discharge current 3.8 kA/div, impurity

line C III 4647 A (---); 2 - average density 2.1012

cm~3 between lines; 3,4 - UHF-radiation on frequencies

23, 17, 28 and 22 GHz respectively, the vertical scale

is the logarithmic one of the 3-4th order of magnitude,

the time scale is lOOpsec/div. The spectra have been

obtained for the following time instants : I - 180

( ), 200psec ( ); II - 320ysec ( ), 350ysec( );

III - 370ysec ( ) , 390psec ( ) ; IV - 450;isec ( ) ,

550psec ( ); the cross-hatched region is the threshold

response of receiving system.

Fig. 9 Fine structure of the spectrum of sporadic UHF-bursts

on plasma frequency co for various gases and various

plasma densities.

Fig. 10 Dependences characterizing the ratio of energy density

of Langmuir and ion plasma oscillations on electrical

field in the stellarator in accelerative (t =200ysec)I

and turbulent (t =300-400ysec) discharge phases:y/ Pu .

- intensity of hard X-ray-radiation and ion plasma

noises; r^ - the ratio of energy densities of Langmuir

and ion plasma oscillations. H=16,8kG, n=6»1012cm"3,(D

—=^ =2.2, ( ) - the dashed line denotes the threshold

- 28 -

of ion turbulence excitation.

Fig. 11 Energy spectra of ions from the data of neutral charge-

exchange measurements in hydrogen plasma at various

values of magnetic and electrical field strengths.

Fig. 12 Dependences on electrical field of ohmic power injected

into the discharge, on ion temperature of the hot ion

component, and on maximum energy of hard X-ray-radiation

in discharges with gas pre-ionization (solid line) and

without pre-ionization (dashed line).

Fig. 13 Ion temperature of the hot ion component versus plasma

magnetization degree for different machines :

TRIM-1 [5,34] : n=4-1013cm~3, H=27 kG, H=31 kG;

URAGAN-2 [4] : n=6-101 2cnT3 , H=7.8;12.1;15.8;19.4 kG

n=5'1012cm-3, H=19.4 kG

SIRIUS [3] : n=2.7«1012cm"3, H=8 kG, n=2.8-1012cnT3

H=12 kG, n=3.3-1012crrr3, H=16 kG

TM-3 [1] : H=10 kG, n=5«10 *2cm~3, 2.65-1012cm~3,

1.3-10I2cnr3, 1.1012cm-3

ALCATOR [33] : H=45 kG, n=9-1013-7-1012cm~3.

JlPP-lb [37] : n=3-5«1011cm"3, H=2.6; 4,0; 5,1 kG

- 29 -

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- 35 -

withoul with OH pjeioniz.

200

0

-1

-

i i i i i

^ " Z ^

1

1

—r

1 I i .

yi i i i

' i i

—

Flfi.3

20.

-10, , / HT5

Dpi 2(Jpi

Fig.

A C 3 ••" , 2 2 . 4 5% IGHzl

Fia-8

ift. 10

Fig. 12 13