On the propagation of auroral electron currents by mhd alfvén waves

P/met. Space Sci., Vol. 36, No. 4, pp. 417421, Printed in Great Britain.

1988 0

0032-0633/88 $3.00+0.00 1988 Pergamon Press plc

ON THE PROPAGATION OF AURORAL ELECTRON CURRENTS BY MHD ALFVfiN WAVES J. R. RAN

Geophysical Institute, University of Alaska, Fairbanks, AK 99775, U.S.A.

T. TAMAO

Geophysics Research Laboratory, University of Tokyo, Tokyo 113, Japan (Received 24 September 1987)

Abstract-The dilemma of propagating field-aligned currents by the MHD Alfven waves while the current carriers are super-Alfvenic auroral electrons can be reconciled by neutralizing the current running ahead of the Alfven wavefront. The neutralizing currents are generated by the interaction between the electron beam head and the magnetized background plasma. Thus, the aurora1 electron current is allowed to propagate at the Alfven speed while the electron beam itself propagates at the super-Alfvenic beam speed. Moreover, it is shown that upward field-aligned currents carried by auroral electrons are generated above the aurora1 acceleration region, while those carried by thermal electrons with energy less than 5 eV are most likely generated below the aurora1 acceleration region.

1. INTRODUCTION

Field-aligned currents play an important role in transferring energy from the solar wind to the magnetosphere and the ionosphere. In this paper we wish

to address a fundamental issue on the propagation of field-aligned currents carried by the kiloelectronvolt aurora1 electron beam. It has been shown that the field-aligned currents with scale length much greater than the ion gyroradius must propagate exclusively by Alfven waves in MHD plasmas (Siscoe, 1983). Even when the scale length is comparable to the ion gyroradius, the field-aligned currents are still carried predominantly by Alfven waves as shown by Cao and Kan (1987) based on the two-fluid plasma equations. Propagation of field-aligned currents by Alfven waves means that the current must propagate behind the Alfven wavefront (e.g. Goertz and Boswell, 1979). This means that the electron streaming speed or the electron current speed must be sub-Alfvtnic. The electron thermal speed can be greater than the AlfvCn speed as long as the electron streaming speed does not exceed the Alfven speed. Since the streaming speed of the aurora1 electron beam is much greater than the Alfven speed, the electron beam will inevitably overtake the Alfven wave. Therefore we are faced with the dilemma of propagating the field-aligned current by Alfven waves at the AlfvCn speed while the current is carried by the aurora1 electrons streaming at superAlfvenic speeds.

The objectives of this paper are : (1) to call attention to the dilemma of propagating super-Alfvenic aurora1 electron currents along field lines by Alfv&n waves ; and (2) to propose a plausible solution to the dilemma on the basis of neutralizing the field-aligned current which overtakes the AlfvCn wave. The neutralizing current ahead of the Alfven wavefront can be generated by the interaction between the electron beam head and the ambient plasma. Thus, the aurora1 electron current can propagate at the Alfven speed while the aurora1 electron beam itself and the associated kinetic energy flux propagate at the super-Alfvenic beam speed.

2. NEUTRALIZING

THE CURRENT

ALFVtN

AHEAD

OF THE

WAVEFRONT

Field-aligned currents can be written as

Jllk 0 = Jldr) + JIIAk0

(1)

where Jl10 is the steady-state current and JllA is the increment currents propagating by Alfven waves. The steady-state current is carried by magnetospheric electron flux supplied by a source region on aurora1 field lines. The current speed of the steady-state current Jl10 is allowed to exceed the Alfven speed because the current is not required to be carried by Alfven waves. The current speed of the transient current J,, is not allowed to exceed the Alfven speed because it must 417

J. R. KAN and T. TAMAO

418

propagate by Alfvtn waves. The propagation of JllA in a uniform MHD plasma can be written from the Alfven wave solution as (e.g. Kan and Sun, 1985) J,,, N f f&&V. E,

(2)

where “ +” and “ - ” signs are for waves propagating “parallel” and “antiparallel” to B,, respectively, ZA = (p,, VA)- ‘, and V, = B,/&, The head of JllA is located in the Alfven wavefront ; the closure of JllA is due to the ion polarization current flowing along the wavefront. The AlfvCn wavefront is sufficiently thin compared with a typical spatial scale length along aurora1 field lines so that (2) is applicable to aurora1 field lines. Figure 1 illustrates the relationship on the field-aligned current, the closure current, the electric field and the direction of wave propagation relative to the background magnetic field as described in (2). Consider a field-aligned electron beam propagating into an ambient plasma. The electron beam carries with it a field-aligned current. Because field-aligned currents must propagate at the Alfven speed, it is natural to discuss the propagation of an electron beam and the beam current based on the beam speed relative to the Alfven speed. The Alfven speed in the magnetosphere ranges from 1000 to 2000 km s-’ which is the speed of 5 eV electrons. If the beam speed is equal to the Alfvtn speed, the head of the field-aligned current coincides with the head of the beam itself. If the beam speed is less than the AlfvCn speed, the head of the current propagates ahead of the beam. The field-aligned current ahead of the beam is carried by ambient electrons driven by the polarization electric field across the Alfvin wavefront. If the beam speed is greater than the Alfvtn speed, the head of the beam overtakes the Alfven wave. The beam current (Js) ahead of the wave must be neutralized by the ambient plasma because no field-aligned currents can propagate ahead of the Alfven wave. Figure 2 illustrates the proposed scenario of an upward current carried by aurora1 electrons propagating downward into an ambient plasma. The speed of a kiloelectronvolt aurora1 electron beam is 20,000 km s-r which is much faster than the Alfvtn speed (2000 km s-l). The super-Alfvenic aurora1 electron beam can propagate ahead of the Alfven wave, but the field-aligned electron current cannot do so because it must propagate by the Alfven wave. To reconcile this dilemma, we propose that the beam current ahead of the wave must be neutralized. Electrons at the leading edge of the beam penetrate into the ambient plasma creating a negative charge layer and leaving behind a positive charge layer to set up a polarization field as shown in Fig. 2. The induced polarization field at the head of the beam accelerates

ambient electrons to produce the neutralizing current in the region between the wavefront and the head of the beam. The neutralizing current (J,,) is generated at the expense of the beam energy. The reduction in the beam speed can be estimated as follows. The current neutralization Jb + J, = 0 leads to N,V,-N,V,

= 0

(3)

where Nb and V, are the beam density and beam speed, while No is the ambient plasma density and V, is the neutralizing current velocity. The conservation of energy leads to NJ&-NbV;

= N,V,Z

(4)

where V,,,, is the beam speed when the neutralizing current vanishes. From (3) and (4), the reduction of the beam speed due to the generation of the neutralizing current is given by (VW- V,)l V, = :N,IN,

(5)

for Nt,/NO << 1. The above discussion showed that upward field-aligned currents propagating downward by Alfven waves along aurora1 field lines can indeed be carried by kiloelectronvolt aurora1 electrons. Now we need to determine the carriers of upward currents propagating upward along aurora1 field lines. Figure 3 illustrates the scenario of an upward current propagating upward. Before the wavefront propagates across the acceleration region, the upward current is carried by thermal electrons without any complication. When the wavefront propagates across the acceleration region, the accelerated electrons carry the upward current by launching a downward propagating Alfven wave. The upward current behind the downward propagating wavefront is now carried by aurora1 electrons. The upward current carried by auroral electrons ahead of the wavefront is neutralized. Thus the thermal current is replaced by the aurora1 beam current behind the downward propagating wavefront. The duration for the thermal current to persist is 2S/ VA in each bounce period 2L/V, of Alfven wave where S is the altitude of the acceleration region and L is the distance between the ionosphere and the magnetopause or the plasma sheet. Therefore, the probability of observing the coexistence of thermal and aurora1 currents is S/L which is about 5-10% of the transient period during which the field-aligned currents are increasing or decreasing. The concept of the neutralizing current (or the back current) induced near the head of an electron beam propagating into an ambient plasma has been discussed extensively in the literature on relativistic electron beam physics (e.g. see a review by Benford and Book, 1971). However, theoretical treatment of the

419

Propagation of aurora1 electron currents (A) Incident (Downgoing)

Wavefront

(B) Reflected

(Upgoing)

I I

I I

0 I I

Wavefront

FIG.

1. A

SKETCH OF THE RELATIONSHIP

THE ELECTRIC

FIELD ASSOCIATED

(B)

FIG.

2. A SKETCHOF

ANI JPWARD CURRENT

A DOWNGGING

&PVhl

PASSING THROUGH ERATION

REGION.

WAVE

UPGOING

CARRYING

AN AURORAL

ACCEL-

WITH

ALET&

FIG.

OF THE CURRENT

(A)

DOWNGGING

AND AND

WAVES.

3. A SKKEH OF AN

AN UPWARD

CURRENT

UPGOING

ALWI?N

PASSING THROUGH ERATION

REGION.

WAVE

CARRY ‘ING

AN AIJXORAL AC( ZL-

J. R.

420

KAN and

neutrali~ng current problem is still lacking. Particle simulation can be a powerful tool for studying the propagation of the aurora1 electron beam and the propagatiodof the beam current along field lines. The simulation must be performed using a two-dimensional full particle magneto-inductive or electromagnetic code. The boundary condition must be open to allow the injection and escape of a finitedimension electron beam propagating along the external magnetic field of a magnetized plasma. Unfortunately, simulations of electron beam propagation to date are electrostatic which are not applicable to the propagation of field-ali~ed currents carried by auroral electrons. Nevertheless, it is instructive to learn from the electrostatic simulation results (e.g. Okuda and Kan, 1987). In the electrostatic approximation, the electron beam is found to propagate into the background plasma at a speed smaller than the injection beam speed while the beam current is practically fully neutralized. The complete current neutralization is to be expected in an electrostatic simulation. The beam speed is reduced because part of the beam energy is used to drive the neutralizing current and to excite electrostatic waves via beam-plasma instability. The almost complete neutralization of the beam current is consistent with the MHD results that the field-aligned currents propagate only by Alfven waves. Since the Alfven speed is zero in such a plasma, the beam current simply cannot propagate in the simulation model. Thus, the beam must propagate without beam current, i.e. the beam current must be completely neutralized by the ambient plasma. The simulation results also show that the neutralizing current is modulated by the large-amplitude electrostatic waves excited by the beam-plasma interaction. 3. RATIO OF THERMAL

TO AURORAL

FIEL~~IG~D

CURREXTS

Field-aligned current measurements by Hoffman et al. (1984) indicate that the thermal electrons of 5 eV energy or less can carry up to 50% of the upward field-aligned current. This is a puzzling feature of the upward field-aligned current which deserves greater attention than has been given so far. Assuming the field-aligned currents are generated above the aurora1 acceleration region, the ratio of thermal to total fieldaligned current densities can be estimated as follows. During each bounce of Alfven waves, the maximum thermal current occurs right after the Alfven wave is reflected from the ionosphere. The thermal current decreases to zero at T, + 2S/V,, where T, is the time of mth reflection from the ionosphere. The total current density just after the mth reflection is given by

T. TAMAO J,,(T,)=C,V-(E’,-E;+..-+E~-Em).

(6)

The thermal current just after the mth reflection from the ionosphere is given by Jllth(Tm) = -&V-E&.

(7)

The reflected wave field is given by E:, = R,E’,

(8)

and the incident wave field at the mth bouncing given by EL = l&E&_ t.

is (9)

The ionosphere reflection coefficient R, for a uniform conductivity is given by (e.g. Mallinchrodt and Carlson, 1978) R, = (CA -Z&E,+&) where XCA is the wave conductance and Zp is the Pedersen conductance. The magnetospheric reflection coefficient RM has been discussed by Kan and Sun (1985). They showed that RM N - 1 on open field lines ; - 1 < RM ( + 1 on closed field lines. The value of R, on closed field lines increases from > - 1 on boundary layer field lines to + 1 as one moves towards the inneredge plasma-sheet field lines. The maxima ratio of thermal to total current densities on aurora1 field lines can be estimated from (Q-(9) as

Jllth(Tm) JII(T,)=

-

Ii;”R$- 1

(I-R,)(l-FR”,)/(l-R,R,)’

(lo)

It can be shown that for R, = -0.8 and RM = -0.5 the ratio in (10) is about 0.8 during the first bounce, but falls off rapidly to about 0.1 during the third bounce. Combining this result with the 5-10% observability discussed earlier, we conclude that field-aligned currents generated above the aurora1 acceleration region must be carried by the aurora1 electrons. By process of emanation, the thermal currents on auroral field lines (e.g. Hoffman et al., 1984) are most likely generated by the upward electric field supported by Coulomb collisions of the background electrons and ions below the aurora1 acceleration region. Finally, the kinetic energy flux of the aurora1 electrons can be estimated by employing a linear currentvoltage relation, J,, = Jb = KG,,,

(11)

which is an approximation of the result derived from the loss-cone effect. The downward kinetic energy ffux of the auroral electron beam is given by h$,V,W, = (K~~/e)~~

= Jz/K

(12)

if W,, N edD,,>> W, which is the initial kinetic energy

Propagation of aurora1 electron currents of electrons before passing through the aurora1 acceleration region.

421

most likely generated below the aurora1 acceleration region. Acknowledgements-This

4. CONCLUSIONS The dilemma on the propagation of field-aligned currents by Alfven waves, while the currents are carried by the super-Alfvenic aurora1 electrons, is of fundamental importance in aurora1 physics. To reconcile this dilemma, we proposed that the aurora1 electron current getting ahead of the Alfvtn wavefront is neutralized by the return current generated at the head of the electron beam. Since the aurora1 electron beam speed is much faster than the Alfven speed, the beam will overtake the wave, but the current will not. This is made possible by the neutralizing current spontaneously generated to nullify the beam current ahead of the Alfven wave. The proposed plausible solution to the dilemma needs to be verified either by a suitable simulation model or by a quantitative theoretical model of neutralizing current generated at the beam head propagating along the magnetic field of a magnetized plasma. We have also shown that field-aligned currents on aurora1 field lines are carried mainly by the aurora1 electrons in the kiloelectronvolt energy range if the currents are generated above the acceleration region. If thermal currents exist on aurora1 field lines as suggested by observations (Hoffman et al., 1984), they are

work was in part supported by an NSF Grant ATM-8521194. Cooperative study between T. Tamao and J. R. Kan was in part supported by the Toray Science Foundation of Japan. REFERENCES

Benford, G. and Book, D. L. (1971) Relativistic beam equilibrium, in Advances in Plasma Physics, 4 (Edited by Simon. A and Thomnson. W. B). Interscience Publishers. John Wiley, New York ’ Cao, F. and Kan, J. R. (1987) Finite-Larmor radius effect on field-aligned currents in hydromagnetic waves. J. geophys. Res. 92, 3397. Goertz, C. K. and Boswell, R. W. (1979) Magnetosphereionosphere coupling. J. geophys. Rex 84, 7239. Hoffman, R. A., Sugiura, M. and Maynard, N. C. (1984) Current carrier for the field-aligned current system, in Magnetospheric Currents (Edited by Potemra, T. A.). Geophys. Monograph 28, AGU. Kan, J. R. and Sun, W. (1985) Simulation of the westward traveling surge and Pi2 pulsations during substorms. J. geophys. Res. 90, 10911. Mallinchrodt, A. J. and Carlson, C. W. (1978) Relations between transverse electric fields and field-aligned currents. J. geophys. Rex 83, 1426. Okuda, H. and Kan, J. R. (1987) Injection of an electron beam into a plasma and spacecraft charging. Physics Flui& 30,209.

Siscoe, G. L. (1983) Solar system magnetohydrodynamics, in Solar-terrestrial Physics (Edited by Carovillano, R. L. and Forbes, J. M.). D. Reidel, Dordrecht.