Period and damping factor of Pi2 pulsations during

oscillatory flow braking in the magnetotailE.V. Panov,

1W. Baumjohann,

1R. Nakamura,

1M.V. Kubyshkina,

2K.-H.

Glassmeier,3V. Angelopoulos,

4A.A. Petrukovich,

5V.A. Sergeev

2

E. V. Panov, Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 6, 8042

Graz, Austria (evgeny panov@mail.ru)

1Space Research Institute, Austrian

Academy of Sciences, Graz, Austria.

2St. Peterburg State University, St.

Peterburg, Russia.

3Institut fur Geophysik und

extraterrestrische Physik, Technische

Universitat Braunschweig, Germany.

4Institute of Geophysics and Planetary

Physics, University of California, Los

Angeles, CA, USA.

This article has been accepted for publication and undergone full peer review but has not been throughthe copyediting, typesetting, pagination and proofreading process, which may lead to differencesbetween this version and the Version of Record. Please cite this article as doi: 10.1002/2013JA019633

c⃝2014 American Geophysical Union. All Rights Reserved.

Abstract. Using 25 observations of damped oscillatory flow behavior in

the near-Earth plasma sheet by the THEMIS probes during the 2008-2009

magnetotail seasons, we compare the oscillation period and the damping fac-

tor of the plasma sheet flows with those of the Pi2 magnetic pulsations on

the ground at auroral and mid-latitudes near the local time of the conjugate

ionospheric THEMIS footprints. Whereas the damping of the plasma sheet

flows and of the pulsations on the ground occurs on the same time scales,

the frequency of the pulsations is on average twice the frequency of the plasma

sheet flows. We conclude that larger-amplitude ground pulsations at auro-

ral latitudes were caused by the oscillatory flow braking in the plasma sheet,

presumably through alternating field-aligned currents as suggested by Panov

et al. [2013c].

5Space Research Institute, Russian

Academy of Sciences, Moscow, Russian

Federation.

c⃝2014 American Geophysical Union. All Rights Reserved.

1. Introduction

Nightside magnetic pulsations in the Pi2 frequency range have been attributed to plasma

sheet bursty bulk flows (BBFs) [McPherron et al., 1973; Kepko and Kivelson, 1999; Kepko

et al., 2001; Keiling and Takahashi , 2011; Keiling et al., 2012; Hsu et al., 2012; Nishimura

et al., 2012]. BBFs [Hayakawa et al., 1982; Baumjohann et al., 1990; Angelopoulos et al.,

1994], which are often associated with substorms [Baumjohann et al., 1991, 1999], are be-

lieved to provide magnetic flux transport to overcome the ”pressure balance inconsistency”

[Erickson and Wolf , 1980; Pontius and Wolf , 1990; Baumjohann, 2002]. Multispacecraft

observations have revealed that BBFs occur in very localized channels only 2-3 RE wide

[Angelopoulos et al., 1996; Sergeev et al., 1996; Nakamura et al., 2004]. Between -20 RE

and -10 RE, they are suddenly decelerated by the dominant dipolar magnetic field, and

pressure gradients pile up at the near-Earth edge of the plasma sheet. This may lead to

a substorm current wedge [Shiokawa et al., 1997; Baumjohann, 2002; Birn et al., 1999;

Ohtani et al., 2009] and substorm onset. As BBFs decelerate, they may oscillate [Semenov

and Lebedeva, 1991; Chen and Wolf , 1999; Panov et al., 2010; Birn et al., 2011]. Their

oscillation periods can be derived by analytical MHD approximation using oscillating flux

tube and background plasma sheet parameters [Wolf et al., 2012a, b]. More recently it

was shown that oscillating BBFs may cause a modulation of the current wedge’s magnetic

disturbance on the ground through alternating parallel currents, which indeed may lead

to magnetic pulsations [Panov et al., 2013c].

Here we employ observations from 25 cases of BBF oscillatory flows in the near-Earth

plasma sheet from the THEMIS probes [Angelopoulos , 2008] during the 2008-2009 magne-

c⃝2014 American Geophysical Union. All Rights Reserved.

totail seasons. In our previous work [Panov et al., 2013b] we derived the oscillation period

and the damping factor for the 25 events of damped oscillating flows. Now we expand on

that work first by using the AM-03 version of the field line mapping model by Kubyshkina

et al. [2011] during the events to find THEMIS footprints. We next statistically compare

the period and damping factor of the plasma sheet oscillating flows with those of the

magnetic pulsations at the conjugate ionospheric locations.

Magnetotail observations were provided by the probes’ fluxgate magnetometers (FGM)

[Auster et al., 2008] and electrostatic analyzers’ (ESA) [McFadden et al., 2008] particle

detectors. The magnetic field on the ground was measured by the THEMIS magnetometer

array [Mende et al., 2008].

2. THEMIS observations

Table 1 shows the time intervals and parameters for the 25 THEMIS events of oscillatory

flow braking: event number, date, start time, end time, observed oscillation period τ ,

oscillation period τW predicted by Equation (33) in Wolf et al. [2012a], [see Panov et al.

[2013b] for details], damping factor α as a fraction of the oscillation angular frequency

ω = 2π/τ , and THEMIS footprints’ geographic latitude and longitude ranges predicted

by the the AM-03 model.

2.1. Pi2 pulsations’ periods and damping factors

Using the THEMIS magnetometer array [Mende et al., 2008], we identified onsets of

Pi2 magnetic pulsations near the footprints (at auroral latitudes) and at mid-latitudes for

all of the 25 events.

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Figure 1 shows an example of an oscillating BBF event observed by THEMIS on 19

March 2009 between 8:20 and 9:10 UT. The top panel in Figure 1 depicts the radial

plasma velocity VR for five THEMIS probes. The other panels in the figure show the H-

component of the magnetic field from the ground-based THEMIS magnetometer at Snap

Lake, Canada (next two panels), and at Ukiah, Oregon, USA (lowermost panels). Both

the original H-component of the magnetic field and the one that is band-pass filtered in the

Pi2 range to highlight the power in that mode are shown in Figure 1. One can see that the

oscillations in the plasma sheet flows and the ground magnetic pulsations at both auroral

latitudes, i.e. near the longitude of THEMIS footprints, and at mid-latitudes, decayed

with a similar (rather small) damping factor. The oscillation period of the magnetic

pulsations appears to be substantially smaller than that of the plasma sheet flows. Note

that while the Pi2 oscillation period does not reveal any strong deviation (exceeding 20%)

at different location the amplitude of Pi2 pulsations decreases both towards mid-latitudes

and away from the local time of the BBF sector (not shown here).

Figure 2 shows THEMIS data on 15 March 2009 between 8:40 and 9:20 UT in the same

layout as in Figure 1, when the plasma sheet flows and the ground magnetic pulsations

were damped substantially stronger than during the event shown in Figure 1. Whereas

the damping of the oscillations is substantially larger than in Figure 1, the oscillations

in the plasma sheet and on the ground, again, decay at a similar rate. Similarly, the

oscillation period of the ground magnetic pulsations is substantially smaller.

Figures 3A and 3B show the radial plasma velocity VR at THEMIS P2 on 15 March

2009 between 8:40 and 9:10 UT, and its wavelet spectrum (P2). An integration of this

spectrum over frequency domain (Figure 3C) shows the damping rate of VR. The best fit

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of the curve in Figure 3C between 8:49 and 9:10 UT is overplotted in red. The calculated

damping rate α appeared to be about 0.135 rad/min. Similarly (cf. Figures 3D, 3E, and

3F) one can find the damping rate αPi2 of the ground Pi2 pulsations shown in Figure 2,

with the help of the ground-based THEMIS magnetometer at Hot Springs, MT, USA.

The calculated damping rate αPi2 appeared to be about 0.174 rad/min (cf. Figure 3F).

Furthermore, Figures 3G and H show vertical cuts of the corresponding VR and BH

wavelet spectra at 8:49 UT (denoted by the two vertical white lines in Figures 3B and

3E). The maximum locations in these cuts provide us with oscillation frequency in VR

and BH (vertical black lines in Figures 3B and 3E). We chose the frequency interval over

which the spectral power decreases by 10% from its peak value (horizontal red lines in

Figures 3B and 3E) as a measure of the uncertainty of the oscillation frequency.

2.2. Correlation with oscillatory flow braking

This way we analyzed the oscillation parameters of the magnetic pulsations for all

25 events from Table 1 both in the vicinity of THEMIS footprints (at the auroral lati-

tudes) and equatorward from them (down to mid-latitudes), see columns ’GeoLats’ and

’GeoLons’ of Table 1). Columns 10 and 11 of Table 1 show the observed period of the

magnetic pulsations around the THEMIS footprints, τPi2, and pulsations’ damping factor,

αPi2, as a fraction of the oscillation angular frequency, ωPi2 = 2π/τPi2.

Figure 4 shows a scatter plot of τPi2 against τ , the flow oscillation period in the equato-

rial magnetosphere, with confidence bounds from Table 1 and a linear best fit (red line);

we assumed a linear dependence starting from (0,0). One can see that the ratios of the

two periods all lie between 1 and 1/3 (with an average 0.58 and a deviation of about 0.23),

and that the Pi2 pulsations all have shorter periods than the corresponding flow period.

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Figure 5 shows scatter plot of αPi2 against α with 95% confidence bounds from Table

1 and its linear best fit (red line). One can see that the best fit is close to αPi2 = α (blue

line). Hence, whereas the frequency of the pulsations is on average twice the frequency of

the plasma sheet flows, the damping of the plasma sheet flows and of the pulsations on

the ground occurs on the same time scales.

Good correlation of periods and damping factors of Pi2 pulsations on the ground with

those of oscillatory flows in the near-Earth plasma sheet suggests that the oscillatory

flows drive the ground Pi2 pulsations. Specifically, larger-amplitude ground pulsations at

auroral latitudes were probably caused by the oscillatory flow braking in the plasma sheet

through alternating field-aligned currents as suggested by Panov et al. [2013c].

2.3. Comparison with Alfven travel time from the near-Earth PS

Smaller-amplitude Pi2 pulsations at mid-latitudes may also be driven by field-line res-

onances: Figure 6 shows the Alfven travel time between the equatorial plasma sheet and

the ionosphere estimated from the AM-03 model assuming constant plasma density of

1 cc−1 for two events shown in Figures 1-2 and also for oscillatory braking event on 17

March 2008 [Panov et al., 2010]. Note that using a constant density for field lines in the

range L = 8-12 is a rather poor assumption and may be misleading. Also, no plasmapause

is included in the modeling. Hence, we refer to Figure 6 in a more qualitative context.

Though, as shown in Figures 1 and 2, period of Pi2 pulsations appeared to be nearly

the same from auroral to mid-latitudes, in the region of oscillatory braking (between -8

and -14 RE downtail) the Alfven travel time changes more than five times. The range of

Alfven travel times is from below 20 to over 100 s. Hence, there are nearly always field

lines whose fundamental period for a poloidal, odd, symmetric field line resonance (4τA)

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matches the period of the flux tube oscillating in the near-Earth plasma sheet. Therefore,

such field lines may drive Pi2 pulsations through field line resonances. Indeed, we find

that the values of τPi2 are on the order of 4τA (cf. last column in Table 1).

3. Discussion

Our analysis reveals that the period and the damping factor of Pi2 pulsations during

oscillatory flow braking does not change drastically with location which is in agreement

with previous study ofOlson and Rostoker [1977] who showed that there was no correlation

between the spectral content of Pi2 and the latitude of the station. We also find that Pi2

pulsations decrease in amplitude both towards mid-latitudes and away from the local

time of the BBF sector, being in agreement with Rostoker and Samson [1981], Pashin

et al. [1982], and Samson [1982] who showed that the maximum Pi2 amplitudes are

observed in the auroral region near the equatorward border of the electrojet and the

Harang discontinuity, which maps to the near-Earth edge of the plasma sheet. This fact

also confirms the analysis of Panov et al. [2013c] who used conjugate THEMIS probes

and ground-based magnetometer network observations to show that the wedge current

oscillates with the period of the oscillatory braking in the plasma sheet (Figure 2 in

[Panov et al., 2013c]). The ground signature of such oscillations is an ionospheric double-

vortex current system [see, e.g. Pashin et al., 1982; Baumjohann and Glassmeier , 1984;

Behrens and Glassmeier , 1986; Glassmeier et al., 1988], where the vorticity changes sign

at the period of the Pi2s.

The good statistical correlation of the damped oscillation parameters (period and damp-

ing factor) of the radial flow oscillations observed by THEMIS in the near-Earth plasma

sheet with those of the Pi2 pulsations on the ground at auroral (near THEMIS footprints)

c⃝2014 American Geophysical Union. All Rights Reserved.

and mid-latitudes indicates that the Pi2 pulsations are indeed forced by oscillatory flow

braking in the plasma sheet, presumably through alternating field-aligned currents as

shown in Panov et al. [2013c]. Such interpretation is in agreement with the analysis

of polarization of Pi2 pulsations which appears to be organized by the location of the

substorm current wedge [Lester et al., 1983, 1984; Hughes and Singer , 1985; Nishimura

et al., 2012] when the major axis of the polarization ellipses points toward the head of the

westward traveling surge [Gelpi et al., 1987]. Hence, the Pi2 pulsations probably indicate

that a depleted flux tube arrived at its equilibrium position and oscillates around it.

It appears, however, that the frequency of magnetic pulsations during 25 oscillatory

braking events is on average twice the frequency of the plasma sheet flow oscillations.

Note that auroral forms and dipolarization fronts appeared to be observed during both

earthward flow and its tailward rebound, i.e., also twice a flow period [Panov et al.,

2013c, a]. There are several factors which could affect the frequency of Pi2 pulsations.

For instance, current wedge is made up of several segments, which may move as a whole,

e.g., oscillating back and forth. Also, magnetotail dipolarization may force the whole

equatorial part of the current wedge stretch tailward. Furthermore, Alfven waves traveling

in the current wedge may reflect from the ionosphere.

Early work on Alfven wave reflection from the ionosphere led to the transient mechanism

of Pi2 pulsation [Maltsev et al., 1974, 1977; Nishida, 1979; Kan et al., 1982; Lysak and

Dum, 1983; Baumjohann and Glassmeier , 1984; Glassmeier et al., 1984]. The period of

ground magnetic pulsations generated by this mechanism is crucially dependent on the

Alfven travel time: the waves are expected to bounce between the northern and southern

footprints of the magnetic flux tube. It is interesting to note that the period of the Pi2

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oscillations observed by THEMIS was found on the order of 4τA (fundamental period for

a poloidal, odd, symmetric field line resonance), as given in the last column in Table 1

(though the errors are large due to ambiguity in the location of the equilibrium position

up to few RE, and the fast growth of τA between 8 and 14 RE downtail, see Figure 6).

Though this period is not different drastically at different latitudes, as would be expected

from the fast changes in the Alfven travel time given in Figure 6, there are always field

lines whose resonant period matches the period of the flux tube oscillating in the near-

Earth plasma sheet (compare Alfven travel time between 8 and 14 RE downtail in Figure 6

with the periods during oscillatory BBF braking). Hence, mid-latitude Pi2s could also be

driven by field-line resonances [e.g., Takahashi et al., 1996; Glassmeier et al., 1999] from

compressional waves that move radially inward [Russell and McPherron, 1973; Chang and

Lanzerotti , 1975], with following injection in the inner magnetosphere. The onset of the

compressional waves could be quasi-periodic plasma variations near the leading edge of the

plasma sheet or in the injected plasma [Smits et al., 1986; Saka et al., 1996;Maynard et al.,

1996]. This may be the reason that mid-latitude Pi2s are observed more globally (though

with smaller amplitudes) than the plasma sheet oscillating flows (which are localized

within BBF channels 2-3 RE wide). Indeed, conjugate GOES spacecraft observations

at synchronous orbit (not shown here) reveal, that the magnetic field oscillations in the

inner magnetosphere have similar frequency as Pi2 pulsations on the ground, and observed

through wider range of magnetic local times than the BBF channel width.

Note that the strong gradient in the Alfven travel time occurred not only because of the

flux tube length, but also due to change in the Alfven speed. The former factor makes the

near-Earth plasma sheet (between about 8 and 14 RE) potentially important for phase

c⃝2014 American Geophysical Union. All Rights Reserved.

mixing and magnetosphere-ionosphere coupling through kinetic Alfven waves [Scholer ,

1970; Hasegawa, 1976; Goertz and Boswell , 1979; Chaston et al., 2002; Lysak and Song ,

2011].

An interesting result of the above analysis is that the reconnection-inner magnetosphere-

ionosphere system appears to be strongly coupled. The details of this coupling, such as

partially reflecting ionosphere or the coupling of Alfven and compressional waves in a

curved geometry, are tempting for future work, where advanced coupled modeling [e.g.,

de Zeeuw et al., 2004; Pembroke et al., 2012] may be useful.

4. Conclusions

By comparing 25 damped oscillatory flow events observed in the near-Earth plasma

sheet by the five THEMIS probes with the ground-based magnetometer observations of

Pi2 pulsations around THEMIS footprints during 2008-2009 magnetotail seasons we found

that whereas the damping of the plasma sheet flows and of the magnetic pulsations on

the ground occurs on the same time scales, the frequency of the pulsations is on average

twice the frequency of the plasma sheet flows. We conclude that oscillatory flow braking

in the plasma sheet is indeed the source of the magnetic pulsations with periods between

about 60 and 210 s in the ionosphere and inner magnetosphere.

Acknowledgments. We acknowledge NASA contract NAS5-02099 for use of data from

the THEMIS Mission. Specifically: U. Auster for the use of FGM data provided under

the lead of the Technical University of Braunschweig and with financial support through

the German Ministry for Economy and Technology and the German Center for Aviation

and Space (DLR) under contract 50 OC 0302, C. W. Carlson and J. P. McFadden for use

c⃝2014 American Geophysical Union. All Rights Reserved.

of ESA data. The authors gratefully acknowledge CANMOS, CARISMA, DTU, GIMA,

MACCS, STEP, THEMIS, and USGS for the use of groundbased magnetic field data over

Greenland and North America. The work was partly supported by the Austrian Science

Fund (FWF) I429-N16, by the Seventh Framework European Commission Programme

(FP7, project 269198 - ’Geoplasmas’). The authors thank Profs R.A. Wolf and V.S.

Semenov for insightful discussions that stimulated to prepare this manuscript.

c⃝2014 American Geophysical Union. All Rights Reserved.

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c⃝2014 American Geophysical Union. All Rights Reserved.

−400

0

400

−200

200

VR

[km

/s]

19 March 2009 − Weak damping

7 600

7 700

7 800

BH

[n

T]

−20

−10

0

10

δBH

[n

T]

08:20 08:30 08:40 08:50 09:00 09:10−1

−0,5

0

0,5

δBH

[n

T]

UT [hh:mm]

18 420

18 425

18 430

BH

[n

T]

P5 @ (−11.5,0.0,−2.1) RE

P1 @ (−12.2,0.7,−0.0) RE

P2 @ (−13.2,0.4,−0.7) RE

P3 @ (−11.3,−0.7,−0.7) RE

P4 @ (−11.5,0.1,−1.2) RE

Lat=63.6, Long=249.1,Snap Lake, Canada

Lat=45.1, Long=241.1,Ukiah, Oregon, USA

~20° equatorward from THEMIS footprints

Near THEMIS footprints

Figure 1. THEMIS data on 19 March 2009 between 8:20 and 9:10 UT. (a) Radial plasma

velocity VR for five THEMIS probes with an envelope function (red). (b) H-component of the

magnetic field from ground-based THEMIS magnetometer at Ukiah, Oregon, USA and (c) its

filtered Pi2 pulsations. (d) H-component of the magnetic field from ground-based THEMIS

magnetometer at Snap Lake, Canada and (e) its filtered Pi2 pulsations.

c⃝2014 American Geophysical Union. All Rights Reserved.

−200

0

200

400

−400

VR [k

m/s

]15 March 2009 − Strong damping

7400

7500

7600

7700

7800

BH [n

T]

−20

−10

0

10

20

δBH [n

T]

18930

18935

18940

18945

BH [n

T]

08:40:00 08:48:00 08:56:00 09:04:00 09:12:00 09:20:00−2

−1

0

1

2

δBH [n

T]

UT [hh:mm]

P5 @ (−8.5; 4.5; −1.9) RE

P1 @ (−12.7; 3.3; −0.2) RE

P2 @ (−11.1; 2.7; −1.2) RE

P3 @ (−9.6;2.1;−1.3) RE

P4 @ (−10.2; 3.3; −1.9) RE

Lat=63.6, Long=249.1,Snap Lake, Canada

Lat=47.6, Long=245.3Hot Springs, MT, USA

~20° southward from THEMIS footprints

Near THEMIS footprints

Figure 2. Same as in Figure 1 for THEMIS data on 15 March 2009 between 8:40 and 9:20 UT.

c⃝2014 American Geophysical Union. All Rights Reserved.

−300−200−100

0100200300400

VR [

km

/s]

0.06250.03125

0.0156250.0078125

0.003906250.00195313

f [H

z]

(δV)2f

[km2/s]

3.7E−2

1.5E+4

2.3E+5

1.1E+6

0

200

400

600[k

m2/s

2]

1.8932

1.8934

1.8936

1.8938

x 104

BX [n

T]

0.250.125

0.06250.03125

0.0156250.0078125

0.00390625

f [H

z]

(δB)2f

[nT2/Hz]

1.8E−7

6.7E+0

1.0E+2

5.2E+2

08:40:00 08:46:00 08:52:00 08:58:00 09:04:00 09:10:000

20

40

[nT

2]

UT [hh:mm:ss]

2E−42E−52E−62E−72E−82E−92E−105

1015202530

(δV

)2 f

[km

2/s

]

f [Hz]

2E−22E−32E−42E−52E−62E−72E−8012345

f [Hz]

(δB

)2 f

[nT

2/H

z]

f−integrated powerStart of fittingEnd of fitting

Best fit ~e−0.14t

f−integrated powerStart of fittingEnd of fitting

Best fit ~e−0.17t

P2

Power spectrum cut@8:49UT Maximum Distance to 0.9*maximum

F

A

B

C

D

E

G H

Figure 3. THEMIS data on 15 March 2009 between 8:40 and 9:10 UT. (A) Radial plasma

velocity VR for THEMIS P2, (B) it’s wavelet spectrum, and (C) frequency-integrated profile

of the spectrum. (D) H-component of the magnetic field (BH) from ground-based THEMIS

magnetometer at Hot Springs, MT, USA, (E) it’s wavelet spectrum, and (F) frequency-integrated

profile of the spectrum. VR (G) and BH (H) wavelet spectra cut at 8:49:00 UT with corresponding

maxima locations (vertical black lines) and distances to 0.9 of the maximum height (horizontal

red lines).

c⃝2014 American Geophysical Union. All Rights Reserved.

0 1 2 3 4 5 6 7 8 9 100

1

2

3

4

5

τ [min]

τ Pi2

[min

]

dataτ

Pi2=0.5τ

Best fitτ

Pi2=0.498τ

<τPi2

/τ>=0.58±0.23

Figure 4. Scatter plot of τPi2 against τ with confidence bounds from Table 1. Linear best fit

is shown in red, assuming linear dependencies starting from (0,0).

c⃝2014 American Geophysical Union. All Rights Reserved.

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.40.40

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.40.4

α [rad/min]

α Pi2

[rad

/min

]

dataα

Pi2=α

Best fitα

Pi2=0.82α

<αPi2

/α>=0.93±0.33

Figure 5. Scatter plot of αPi2 against α with 95% confidence bounds from Table 1 and its

linear best fit; we assumed a linear dependence starting from (0,0).

c⃝2014 American Geophysical Union. All Rights Reserved.

-4 -8 -12 -16Radial distance [Re]

0

40

80

120

160

Alfventraveltimeb/w

PSandionosphere

[s]

20080317 1020-1040 UT

20090315 840-920 UT

20090319 820-910 UT

Figure 6. Alfven travel time between the equatorial plasma sheet and the ionosphere estimated

from the AM-03 model assuming constant plasma density of 1 cc−1 for three events shown in

Figures 1-2 and also for oscillatory braking event on 17 March 2008 [Panov et al., 2010]. Note

that plasmapause is not included in the modeling (see legend for details).

c⃝2014 American Geophysical Union. All Rights Reserved.

Table

1.

Twenty-five

oscillatoryflow

brakingevents

observed

byTHEMIS:eventnumber,date,

starttime,

endtime,

observed

oscillation

period

τ,oscillation

period

τ Wpredicted

byFormula

(33)

in[W

olfet

al.,

2012a],dam

pingfactor

α

asafraction

oftheoscillationan

gularfrequency

ω=

2π/τ

,THEMIS

footprints’geographic

latitudean

dlongituderanges

predictedbythetheAM-03model

Kubyshkinaet

al.[2011],ob

served

periodof

Pi2

pulsationsat

THEMIS

footprints’ranges

τ Pi2,dam

pingfactor

ofthePi2

pulsationsαPi2

asafraction

oftheoscillationan

gularfrequency

ωPi2

=2π

/τPi2,THEMIS

probe(s)

usedto

calculate

theAlfven

traveltimeτ A

(thetimerequired

foran

Alfven

waveto

travelfrom

theequatorialplasm

a

sheetto

thecorrespon

dingionospheric

footprint),an

d4τ

A.

Ndate

start

end

ττ W

αGeoLats

GeoLon

sτ P

i2αPi2

probe

4τA

yyymmdd

hhmm

hhmm

[min][m

in][rad/m

in]

[deg]

[deg]

[min][rad/m

in]

[min]

12008

0225

0950

1030

2,0

1.4

0.24

62-75

180-230

0.8

0.19

P5

1.7

22008

0309

0350

0420

6.6

6.5

0.14

48-60

250-285

4.0

0.10

P1

2.7

32008

0313

0625

0700

5.6

3.7

0.12

58-64

230-255

1.6

0.15

P3

2.9

42008

0313

0700

0820

5.1

3.8

0.23

59-66

225-250

1.7

0.31

P4

2.5

52008

0317

0905

0930

4.3

4.1

0.09

64-69

200-230

2.2

0.15

P2

4.0

62008

0317

1020

1040

2.3

3.4

0.14

67-72

190-220

2.0

0.18

P2

2.7

72009

0207

0400

0500

6.1

4.0

0.13

59-64

285-300

3.1

0.14

P5

1.1

82009

0210

0900

1030

4.7

5.6

0.04

60-71

200-260

3.7

0.02

P4

2.8

92009

0211

0200

0300

4.7

4.3

0.16

59-68

300-320

1.9

0.08

P5

0.5

102009

0217

0330

0430

2.3

4.1

0.08

59-65

270-300

2.2

0.10

P4

2.0

112009

0217

0700

0800

3.9

6.2

0.08

58-69

240-270

2.6

0.06

P4

3.3

122009

0223

0300

0330

2.8

4.3

0.12

58-66

280-310

3.1

0.11

P3

1.5

132009

0225

0530

0600

6.6

3.4

0.38

58-67

250-280

2.4

0.23

P2

3.5

142009

0301

0810

0900

4.7

4.6

0.10

57-72

220-260

2.9

0.14

P4

2.3

152009

0305

0240

0305

3.6

6.3

0.20

58-64

270-305

2.4

0.14

P3

1.7

162009

0305

0305

0350

6.1

5.3

0.29

58-64

270-305

2.4

0.15

P4

2.0

172009

0309

0900

1000

7.9

4.7

0.07

62-79

190-250

3.1

0.06

P3

4.5

182009

0315

0810

0840

4.3

2.8

0.12

57-64

243-250

1.7

0.11

P4

2.6

192009

0315

0840

0920

4.3

4.0

0.13

60-65

235-250

1.7

0.17

P2

2.6

202009

0317

0540

0610

4.7

4.0

0.20

59-78

230-270

1.9

0.20

P5

2.9

212009

0319

0800

0930

4.3

4.0

0.05

60-67

230-250

2.4

0.04

P4

2.4

222009

0323

0600

0640

3.3

2.8

0.08

56-62

255-270

2.0

0.06

P4

3.7

232009

0330

0110

0210

8.6

8.1

0.11

58-72

245-300

3.7

0.08

P3

2.7

242009

0331

0820

0900

2.8

3.5

0.16

61-65

230-245

2.9

0.11

P4

3.3

252009

0408

0650

0750

4.7

4.6

0.12

58-65

235-260

3.4

0.07

P4

3.3

c⃝2014 American Geophysical Union. All Rights Reserved.