Indian Iournal of Radio & Space Physics Vol. 34, February 2005, pp. 1 7-22

Alfven wave in the presence of parallel electric field in the

magnetospheric plasma

J Shrivastava & M S Tiwari

Department of Physics, Dr H S Gour University, Sagar (M P) 470 003, I ndia

Received 14 November 2003; revised 31 May 2004; accepted 12 October 2004 The effect of upward parallel electric field observed along the auroral field l ines on the Alfven wave model of

magnetosphere-ionosphere coupling is examined through the modification of the particle thermal velocity paral lel to ambient magnetic tield. Effects of electron beam generated in the plasma-sheet region and impinging the ionosphere, and temperature anisotropy of the acceleration region have been also considered. The enhancement of the auroral upward field­aligned current in the region of parallel electric field is predicted as observed by S3-3 satel l i te and polar satel l i te data.

Keywords: Alfven wave, Magnetosphere, Electron-beam, Field-al igned currents

PACS No. : 52.35 HI', 94. 10 Rk

1 Introduction

Observations of electric fields in the ionosphere and magnetosphere using various techniques have led to important advances in the understanding of magnetosphere-ionosphere coupling. Paral lel electric field in the auroral acceleration region was observed very early by electron spectra measured on a sounding rocket l •2 • The initial particle evidence was completed by the observation of upgoing ion beams on the S3-3 satel l i te3 and upward acceleration of a barium ion cloud4. The measurement of the S3-3 satellite has provided the existence of parallel electric field of hundreds of mYm- 1 in the auroral acceleration regions. Such measurements had small impact on the field, perhaps because they were not put into context by simultaneous field-aligned current measurements. Alfven waves have been suggested as a possible source of parallel electric fields responsible for accelerating the plasma in the auroral acceleration region6.7 . Recently Mozer and Hull8 analyzing polar satellite data during several hundred passes across auroral zone magnetic field lines at geocentric altitudes of 2-6 RE (Earth radii) have predicted that the appearance of parallel electric fields requires an upward field-aligned current. The parallel electric fields exist where the plasma density is insufficient to carry upward field-aligned currents and these parallel fields are associated with high-altitude electron

acceleration required to carry the imposed current through the low-density region. The parallel electric fields measured in the low altitude region as large as several hundred mYm- l , while higher altitude fields appear to have magnitudes of a few mYm- l . Purpose of this paper is to examine the effects of such parallel electric fields on pre-existing model of auroral acceleration region by Alfven waves9 and their association with the upward field-aligned current. In the polar satellite data the down coming electrons and up going ions are also observed in association with field and current measurements8 . Since distribution of particles is non-Maxwell ian, these parameters are also taken into consideration.

S mall scale intense disturbances of electric field are constantly measured by polar orbiting and Freja satell ites in the altitude range from 900 km to 2 RE above the auroral ionosphere ,o- l 3 . Direct measurements from satel l ites l4- 1 8 and rockets '9 have shown that the discrete flux of keY electrons registered at auroral zone are often correlated with small-scale, localized electromagnetic disturbances, sometimes interpreted as Alfven waves. Because the periods of ULF Alfven wave are compatible with fundamental field line oscillations and the time scale of particle bounce motion along auroral field lines, Alfven waves are considered as powerful agent to explain varIOUS observed phenomena In

1 8 INDIAN J RADIO & SPACE PHYS, FEBRUARY 2005

magnetosphere-ionosphere coupling. The ionosphere­magnetosphere coupling mediated by standing Alfven waves has al�o been treated theoreticall/o.22. Detection of Alfven wave turbulence has been made by Inter-Cosmos-Bulgaria 1 300 satell i tes23,24 as well as more recently with the Freja satellites25 studying the association of auroral particle precipitation and the Alfven wave.

In the recent past, Alfven wave and kinetic Alfven wave are analyzed using particle aspect analysis in view of the auroral acceleration processes26.27. The present paper is attributed to investigate the effects of parallel electric field and · electron beam on the Alfven wave in an anisotropic plasma using particle aspect approach, in view of the recent observations made by Polar satellites8. The results are compared with the observations made by various satellites8.28.29.

2 Basic assumptions

The wave electric field considered along the x­axis is of the form27

Ex = E, cos (kll Z - lilt) . . . ( 1 )

Here kll is the component of wave vector k along magnetic field Bo and W the wave frequency, which is real . Considering the equation of motion for the charged particles, the detai led calculations of particle trajectory in the presence of Alfven wave have already been performed by Shrivastava and Tiwari27 which are used for further analysis.

3 Distribution function

To evaluate the dispersion relation and current one can hereafter take the zeroth order distribution N(V), of the form26.27

N(V) = No f.1 (V.1) fll ( VII)

m

f.1 (V.1) = [ -- ] exp { - --

2rrT.1

m m( VII - vof fll ( VII) = [ __ ] 1 /2 exp { - ---- I

2rr7l1

where Til ce = 7Ile [ 1 + e Eo I kll 711 0]

. . . (2)

. . . (3)

Here 7Ile and T.le are the parallel and perpendicular temperatures of electrons with respect to the ambient magnetic field, Vo the beam velocity and No the background plasma density.

Here we fol low the technique of Pines and Schrieriffer30, Bers and Brueck3 ' , where a change in the zeroth order distribution function is due to the result of change in the temperature parallel to the parallel electric field Eo. This method was further considered by Misra et al. 32 for the investigation of whistler mode instability and Dwivedi et al.26 for the investigation of kinetic Alfven wave. The existence of parallel electric fields in the presence of Alfven wave on auroral field l ines may be due to double layers, electrostatic shock, anomalous resistivity and the non­l inear plasma effects3 ' .

4 Current

The perturbed current per unit wavelength in the presence of parallel electric field and electron beam is evaluated fol lowing the method of Shrivastava and Tiwari27 as

k 2 2 2 V 2 2 V 2 3e II E, Wpe He Wpi Hi }z = - ---- [---- + ]

8me w Qe4 Qi4(m/me) . . . (4)

Here, Wpi.e = (4nNoe2/mi,e) 1/2 is the plasma frequency, VT.li.e = (2 T.1i.e1mi,e) 1 /2 the perpendicular component of thermal velocity, where the temperature T is expressed in unit of energy. Also Qi.e is the cyclotron frequency .

5 Dispersion relation

With the help of the wave equation27, the dispersion relation for the Alfven wave in the presence of parallel electric field and electron beam is obtained as

w = kll VA [ 1 - - ----- - --

e2

2 VA2 8VA4

{ VTlle4 ( 1 - - X ---) + V04 + 2 VTllc2V02 } ] . . . (5) 2 2 4 m kll VTlle

In the anisotropic plasma the dispersion relation can be further written as

SHRIV AST A V A & TIWARI: ALFVEN WA VE IN MAGNETOSPHERIC PLASMA 19

1 Tile VT ol/ 1 c.o = kll VA [ l - -- { ( -- ) -- + V02 } - --

2 V / Tole 2 8 VA 4

7Jle e2 E02 VUe4

X { ( __ )2 ( 1 - -- -- ) -- + V04 Tol e kll2 TII/ 4

Tile + ( -- ) Vue2 Vo2 } ] . . . (6)

Tole

Here, VA= BoI(4 7t No m i) 1 /2 is the Alfven speed and VA « c (c is velocity of light). Also Vll1e = (7Jle/me) 112 is the electron thermal velocity parallel to the magnetic field. In this model also the evaluation of dispersion relation is based on real quantities and concept of imaginary quantity in various expressions has not been adopted. It is noticed that the dispersion relation of Alfven wave is modified due to thermal and beam velocities of electron in the presence of parallel electric field. In case these terms are zero, the dispersion relation reduces to the well known form c.o = kll VA'

6 Result and discussion

In the numerical evaluation of the wave frequency and associated current per unit wave length, we have used the following plasma parameters suitable for auroral acceleration region8,9,26.29.

Bo = 4300 nT; Qi = 4 1 2 S-I; No = 5 ,Ox l03/m3,

EI = 50 mY/m; VUi = 3.5 X 1 04 rnls; c.op;lQi = 10;

K7Jl i = I keY; K7Jle = 1 0 keY.

Since the acceleration region is reported to lie between I and 3 RE8•9, the authors estimate their results at 2 RE, where Bo = 4300 nT. The simultaneous observations of parallel electric fields and upward field-aligned current are recently reported8,28 by polar satellite data in the density depletion region, where the plasma density varies from - 0.0 1 to 10 particles­cm·3 , Therefore, we have taken the density No - 5 .0 x I 0.3 particle-cm·3 in order to sustain the parallel electric fields. In higher density side the magnitude of parallel electric field is observed8 to be negligible. The quantitative estimates from the model of Kolesnikova et a/.33 gives a small value of the order

of 10 /-lV/m, which is taken in the present Alfven wave model effective in accelerating superthermal electrons downward into the ionosphere29. The wave amplitude is taken as 50 mY/m according to the observations of Mozer et at.5 and justification for that is given in Tiwari and Rostoker9.

Figure 1 shows the variation of real frequency c.o with kll for different values of parallel electric field Eo and the fixed value of beam velocity Va corresponding to energy of a few keY. It is seen that frequency c.o increases with kll as the basic characteristic of Alfven wave and that the upward parallel electric field along the magnetic field is more effective towards the higher wave numbers. Furthermore, it is observed that the wave frequency c.o is decreasing at the higher values of kll due to the parallel electric field. The effect of the parallel electric field at the fixed electron beam velocity is to enhance the phase velocity of the wave. The increased phase velocity from the particle velocity may cause the acceleration of the charged particles by the wave­particle interaction mechanism. Therefore, the wave­particle interaction may be important and parallel electric field in the auroral magnetosphere may contribute towards the acceleration of charged particles through the wave, which is same as suggested by Mozer and Hu1l8, Hull et at. 28, Mozer and Kletzing34, Ergun et al.35 and Hull et al.36. It is also observed that the lower values of electric field affect the wave frequency much more as the electrons are evacuated by the higher electric fields as predicted by Kolesnikova et at.33 based on FAST observations. The signatures of higher electric fields in the lower density regions are reported by the satellite observations8. Thus, to built up a discrete arc in diffuse aurora, the time required is of the order of time period of the Alfven wave ( 1 0- 15 min). The energy source is located at a distance > 1 00 RE in the

2�r-----------------------------------�

Eo II: 3.04,iV/m

ofoL-----,-------4.------,6,------.8------�IO -IZ all • 10 lem

Fig. 1 - (() versus kit for different Eo at fixed Vo

20 INDIAN J RADIO & SPACE PHYS, FEBRUARY 200S

distant magnetotail , i n order that Alfven waves have propagated a single wavelength. The effect of parallel electric field i s to control the arc formation process by reducing i ts required time.

Figure 2 predicts the variation of field-aligned current per unit wave length with kll for different values of paral lel electric field Eo. It is observed that the current is in the reverse direction (upward) as predicted by the observations of Mozer and Hu1l8 and Hull et al.28 and approaches a constant value with the increase of electric field at higher kll' The effect of parallel electric field along the magnetic field is to decrease the upward current by diverging it into the perpendicular current for maintaining the current continuity condition. Thus the perpendicular currents may be constituted towards the ionosphere, as the wave is propagating towards the ionosphere and the field-aligned current reversal may occur during the auroral acceleration processes. These findings support the observations of parallel electric fields in the density depletion region and i ts effect on field-aligned currents as reported by Mozer and Hul l8 and Hul l et a/28• The strength of field-aligned current i s determined by parallel electric fields in Alfven wave model of auroral acceleration process in comparison with satell i te observations.

1000 ,..------- -�:<" ·;··,:·=;-l 800

. E o = 6 uV/m I ;;".'�- ::: I � 400

3

200 �\tl ; 2.5 1( 1�9cm/"C

'10 ;2.0 l 10 em/sec

o���-.------�------.------.------� o 10

Fig . 2 - ill versus kll for d ifferent Eo at fixed Vo

-10

Eo = 6 uV/ m

- 30

- 40

o:!----�-------,.-------�-----.-------.j 10

- 1 2 FIll x 1 0 fern

Fig. 3 - w versus kll for di fferent Vo at fixed Eo

Figure 3 shows the variation of real frequency w with kll for different values of electron beam velocity Vo (in the energy range of a few keY) at the fixed value of electric field Eo. Recently Hull et al.28

observed the existence of parallel potential at altitude below the spacecraft, which prevents electrons of ionospheric origin with energies below - 1 -3 keY from accessing this altitude. Enhancements in the electron beam energies just outside the cavity (e.g., 23 :47 :45-2348:00 hrs UT) relative to those within the cavity are consistent with parallel acceleration by a - 1 -3 keY potential28 . The electron beam generates the reflected wave as evidenced by negative phase velocity of the wave. The higher beam velocity decreases the phase velocity of the reflected wave as W i s decreasing with the beam velocity . These reflected wave may lead the downward (towards the ionosphere) current as observed by polar satel l ite data8.

Figure 4 demonstrates the variation of field -aligned current per unit wave length with kll for different values of electron beam veloci ty in the presence of parallel electric field. The reflected wave also generates the field -aligned current towards the ionosphere as exhibited in Fig. 4. This current may be contributed by the divergence of perpendicular current caused by incoming waves. Enhancement of current i s also observed with the decrease of phase velocity.

Figure 5 predicts the behaviour of the wave in anisotropic plasma. Mechanisms, such as electron i nertia37 and the effect of mirroring magnetic fields on . 38 b ' anIsotropy may e Important to explain the existence of smal l ampl i tude paral lel electric fields. The temperature anisotropy is selective for the particular wave number at which the phase velocity i s maximum. However, the h igher anisotropy IS

1000',-----------------------------------------,

800

-11)4. 600 -IQ � 400

200

° 0��---.2------�------�----�--------4 10

Fig. 4 - i" versus k" for di fferent Vo ar fixed Eo

SHRIV AST A V A & TIWARI : ALFVEN WAVE IN MAGNETOSPHERIC PLASMA 2 1

40

30

I -� IQ 20

3 10

0

\b ' \0 9cm /stJe Eo c 6 ol1,Vlm

0 2 , 4 6

-12 - I tulC 10 e m

Fig. 5 - (j) versus kll for different TIlITJ. and fixed Vo, Eo

l 10

decreasing the phase velocity of the wave at the particular wave number. The decrease in phase velocity at higher wave number may be due to Landau damping of the wave. The effect of temperature anisotropy on the field-aligned current is seen in Fig. 6. The temperature anisotropy generates the upward current and enhances the current due to the increase of kll as well as the temperature anisotropy. The converging magnetic field towards the ionosphere may lead the anisotropic distribution, which also controls the field-aligned current and frequency of the magnetic field oscillations as suggested by Schiver39.

It is reported that for the existence of parallel electric fields and discrete auroras in the auroral acceleration region, all that is needed is an imposed, uniform, upward field-aligned current and a decreased density, such that the particle acceleration is required to carry the imposed currents. In the present investigation, for the first time, the effect of d.c . parallel electric field has been considered in the presence of electron beam and temperature anisotropy on the Alfven wave model for the magnetosphere­ionosphere coupling. Observations have indicated, however, that microscale wave-particle interactions play an active role in dissipating and transferring energy in the auroral zone from beam kinetic energy to the thermal energy via plasma waves40A l . Most theoretical work in this area assumes the existence of electron or ion beams and then examines the waves and wave-particle interactions that resu1t

39A2.43. Our findings are compared with the satel l ite observations and that support the view of Alfven wave model for magnetosphere-ionosphere coupling.

The present model incorporates most of the observational features of the polar8 and FAST satellites28 . However, this has excluded the effect of

E

0=-------

-200 • Vo "" l tQ emil � Eo· 6 .. Vim

.ct - 400 'Q -r

- 600

----_._ .. _---

-12 tt .. 11 10 fern

Fig. 6 - 111 versus kll for different 7i1TJ. and fixed Vo, Eo

upgoing ion beams and higher electric fields due to l imitations of the present theoretical model. The major finding of model is the development of field­aligned currents by the parallel electric fields rather than vice-versa. The effect of parallel electric field is significant to control the process. However, the electron beam velocity and temperature anisotropy of the acceleration region also contribute to the system. The study may be applicable to the experimental plasma also in heating devices.

Acknowledgment

Financial assistance by Indian Space Research Organization, Bangalore, India, is thankfully acknowledged.

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