Electron acceleration by lower hybrid waves on auroral field lines

ildv. Space Res. Vol.4, No.2—3, pp.515—518, 1984 Printed in Great Britain.

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ELECTRON ACCELERATION BY LOWER HYBRID WAVES ON AURORAL FIELD LINES D. S. Hall, D. A. Bryant and R. Bingham Rutherford Appleton Laboratory, Chilton, Didcot.

Oxon,

OXIJ OQX, U.K. ABSTRACT Particle measurements show that electron acceleration on auroral field lines is a statistical, velocity—dependent, process. It is proposed that the process is stochastic acceleration by waves, and demonstrated that lower hybrid waves seen on auroral field lines have the right properties to account for the electron acceleration. It is further shown that the lower hybrid wave power measured on auroral field lines can be generated by the streaming ions observed at the boundary of the plasma sheet, and that this wave power is sufficient to account for the electron power observed close to the atmosphere. INTRODUCTION In this paper we describe a model in which it is proposed that the streams of electrons thot are associated with discrete aurora are accelerated not by a potential difference but by electrostatic waves /1/. Since the first suggestions that discrete aurora are produced as a result of electrons traversing a magnetic-field-aligned potential difference of kilovolts, it has been pointed out on many occasions that the details of the electron distributions cannot be accounted for by invoking a process as straightforward as one in which all electrons traverse the same potential difference /2,3/. Bryant /4,5/ has summarised the discrepancies between the observed electron distributions and those expected for acceleration through a potential difference of kilovolts. Wave-particle interactions have been invoked to account for some of these discrepancies, such as the flatness of the peak on its low energy side; for the flattening of the peak on its high energy side; and for the production of rrLiltiple peaks. However, the qualifications to the potential difference model have seemed so fundamental to authors such as Bryant /2/, Whalen and Daly /3/, and Hall /6/, that they have suggested an entirely new approach to the problem, in particular suggesting that, in view of the stochastic, velocity dependent, nature of the acceleration, wave-particle interactions may form the observed electron distributions without a magnetic—field—aligned potential difference of kilovolts. ACCELERATION BY WAVES ON AURORAL FIELD LINES The new approach that we adopt to account for the acceleration is to investigate the possibility that the electrons gain energy from those plasma waves which form the broad region of turbulence on aurora] field lines that is as extensive as inverted—Vs. The process we investigate is that electrons are accelerated by those plasma waves which slowly overtake them, the energy gained during each interaction being a small fraction of their final energy. Such a process is stochastic, and is also velocity dependent, because energy transfer only takes place between waves and particles with similar velocities /7/. These are the properties required for the acceleration process that are deduced from the particle distributions. The process is similar to that investigated by Tanaka and Papadopoulos /8/ who showed that interactions between electrostatic waves and electrons can be very efficient in accelerating electrons to produce non—thermal tails. Sturrock /9/ has also shown that high energy tails can be produced through stochastic acceleration by waves of high phase velocity. The effectiveness of electrostatic waves for accelerating electrons has recently been recognised during the search for current drivers for Tokamak fusion devices. Considering aurora] field lines, magnetic—field-aligned electrons are observed within the streams associated with discrete aurora. This indicates that the electron acceleration is directed along the magnetic field. This collimation would occur if electrons were being overtaken by waves with an electric field component parallel to the magnetic field. Both Langmuir (plasma) and lower hybrid waves have this property. However Scarf /10/, Gurnett and Frank /11/, and Mozer et al /12/ have reported that wave energy at the lower hybrid frequency is rrzich higher than that at the Langmuir frequency. In view of these observations we will concentrate our attention on lower hybrid waves. 515

516

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Electron velocity distributions at two locations within an auroral arc /4/ and the associated lower hybrid wave spectra. PROPERTIES OF LOWER HYBRID WAVES

For lower hybrid waves the wave normal is almost perpendicular to the magnetic field, but there is a non-zero component of the electric field parallel to the magnetic field /1/, and most of the wave energy flows parallel to the magnetic field. The phase velocity parallel to the magnetic field is greater or equal to the electron thermal velocity ‘Te~ On aurora] field will linesresonantly at altitudes of -. with 1-3 RE, vTe is typically — 2 1, so that lower hybrid waves interact electrons of velocities x> io~ 2 x msiO~ms~. The maximum growth rate of the waves is at velocities —2-5 times the electron thermal velocity /13/, so that provided saturation is not reached the spectrum of lower hybrid waves on auroral field lines will be similar to that sketched in the lower panel of figure 1. THE FORM OF THE AURORAL ELECTRON SPECTRUM In figure 1 lower hybrid wave spectra on auroral field lines are compared with observed electron distributions. Because the energy transfer from waves to electrons is a process that takes place most efficiently between waves and electrons with similar velocities /7/, the effect of lower hybrid waves on electrons with velocities < 2 x iO~ ms1 will be negligible. This is in fact what is observed within the electron streams that form the inverted Vs associated with discrete aurora. The relative invariance of electron densities at velocities < 2 x iO~ms1 has been reported by Whalen and Daly /3/, Hall /6/ and Bryant /5/. At higher velocities a flatter spectrum is observed when the peak is at the higher velocity, /4/. Sturrock /9/ and Eichler /14/ have calculated that such high velocity tails would be produced as a consequence of heating by waves, the flatness of the electron distribution reflecting the level of wave energy density. The maximum change in the flatness of the electron distribution takes place at velocities where the wave energy density is greatest, and a plateau forms in the electron distribution at these velocities. ENERGY FLUX PROFILE ON AURORAL FIELD LINES In order to establish whether the observed wave energy flux can account for the electron energy flux observed near the atmosphere, we need to determine the equilibrium level of wave energy flux that would be produced on aurora] field lines as a consequence of the balance between wave generation by a reservoir of free energy, and the damping that results in electron acceleration. Lower hybrid waves can be driven unstable by several mechanisms, cross-field currents due to density, temperature and magnetic field gradients, differential electron-ion drift, or E x ~ drift could all be responsible. In our view the most promising candidate is the earthward streaming ion flow in the boundary plasma sheet /15/.

Electron Acceleration by Lower Hybrid Waves

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Figure 2 Development of the energy flux profile as power is transported from a distance of 10 RE to the atmosphere. Curve (a) is calculated assuming that all the power transferred to electrons is transferred within the atmospheric loss cone, Curve (b) assumes that most of the power is transferred outside the loss cone. Discrete aurora is associated with the boundary plasma sheet /16/ and the power carried by the ion streams at — 2ORE is 2 orders of magnitude higher than that carried by the streams of electrons, associated with discrete aurora, just above the atmosphere. We visualize the process as a continuous evolution of ion, wave and electron power as the ions, waves and electrons flow towards the atmosphere. The wave power observed at any point is then an equilibrium level between production by the ions and loss to the electrons. In order to obtain an estimate of the power budget of the process we have investigated in a simplified and stylized model how power carried initially by an ion stream at geocentric radial distance R might become distributed between ions, waves and electrons as radial distance r decreases. We considered the case where the magnetic field along a line of force 3, ie as a dipole field at very high latitude. We assumed further that there is varies as rbetween power carried in any form into and out of the flux tube, so that such a balance transfer could be neglected. We treated the ion stream, moving towards the earth, as though it is initially isotropic and remains so throughout. The loss of ion power to waves was approximated by assuming that the power transferred per unit distance is proportional to the local power. The loss of wave power to electrons was treated in the same way as the transfer of ion power to waves except that two calculations were made — one for the case in which it was assumed that all electrons having the same velocity parallel to the magnetic field are accelerated in the same way, and one for the case where all of the wave power is transferred to electrons with pitch angles in the atmospheric loss cone. For lower hybrid waves, the obliqueness of the wave front to the magnetic field lines, means that smallerpitchangle electrons are accelerated more efficiently than those with larger pitch angles, so that the second case is more representative. The results of the calculation are shown in terms of energy flux in figure 2 in which the ion, wave, and electron energy fluxes are plotted against radial distance. Also shown in figure 2 are the ion energy flux (1ni4m2) measured by DeCoster and Frank /15/ at radial distances between 10 and 2ORE, the wave energy fluxes (0.01-0.1 rrW m~)estimated from the measurements of wave strength near the lower hybrid frequency between 1-4RE made by Scarf /10/, Gurnett and Frank /11/, and Mozer et al /17/, and the typical electron and ion energy fluxes we have observed just above discrete aurora (10-100 and 0.01 rrt4 nr2 respectively). The comparison of the calculated and measured energy fluxes suggest that there is sufficient power in the observed lower hybrid waves to account for the electron energy flux close to the atmosphere, and that the ion energy flux at >1ORE is sufficient to account for the wave generation.

518

D. S. Hall, D. A. Bryant and R. Bingham

CONCLUSION We have shown that the streams of accelerated electrons (inverted-V’s) that are associated with discrete aurora are produced as a result of a continuous evolutionary process along an auroral flux tube, in which streaming ions generate lower hybrid waves that accelerate electrons. Lower-hybrid waves appear to have the properties, and are observed in sufficient strength, to account quantitatively for the electron acceleration which results in discrete aurora, and qualitatively for the details of the observed electron distributions. The streaming ions observed within the boundary plasma sheet carry sufficient power to account for the observed wave and electron power. REFERENCES 1.

Bingham, R., Bryant, D.A., and Hall, D.S., 1984, A wave model for the aurora, Geophys. Res. Lett., 11, 4, 327.

2.

Bryant, D.A., 1978, Particle acceleration, spatial structure, and pulsations in the aurora, Proc. ESA symposium on European sounding rocket, balloon, and related research, ESA SP-135, p.53.

3.

Whalen, B.A., and Daly, P.W., 1979, Do field-aligned auroral particle distributions imply acceleration by quasi-static parallel electric fields, J. Geophys. Res., 84, 4175.

4.

Bryant, D.A., 1981, Rocket studies of particle structure associated with auroral arcs, in : “Physics of Auroral Arc Formation”, Geophysical Monograph 25, American Geophysical Union, Washington, p.103.

5.

Bryant, D.A., 1983, The hot electrons in and above the auroral ionosphere observations and physical implications, in : “High Latitude Space Plasma Physics’, Plenum, New York, p.295.

6.

Hall, 0.5., 1980, The influence of energy diffusion on auroral particle distributions, Proc. Vth ESA symposium on European rocket and balloon programmes, ESA SP-152, 285.

7.

Hall, D.S., 1983, Acceleration of auroral electrons by waves, Rutherford Appleton report, RL83-02B. Tanaka, M., and Papadopoulos, K, 1983, Creation of high energy electron tails by means

8.

of the modified two—stream instability, Phys. FL., 26, 1697. 9.

Sturrock, P.A., 1966, Stochastic Acceleration, Phys. Rev., 141, 186.

10.

Scarf, F.L., Fredericks, R.W., Russell C.T., Kivelson, M., Neugebauer, M., and Chappell, C.R., 1973, Observations of a current-driven plasma instability at the outer zone plasma sheet boundary, J. Geophys. Res., 78, 2150.

11.

Gurnett, D.A., and Frank, L.A., 1977, A region of intense plasma wave turbulence on aurora] field lines, J. Geophys. Res., 82, 1031.

12.

Mozer, F.S., Cattell, C.A., Temerin, M., Torbert, R.B., von Glinski, S., Woldorft, M., and Wygant, J., 1979, The dc and ac electric field, plasma density, plasma temperature and field—aligned current experiments on the S3-3 satellite, J. Geophys. Res., 84, 5875.

13.

Mcbride, J.B., Ott, E., Jay, P.B., and Orens, J.H., 1972, Theory and Simulation of turbulent heating by the modified two-stream instability, Phys. Fl., 15, 2367.

14.

Eichler, D., 1978, Jnl., 224, 1038.

15.

DeCoster, R.J., and Frank, L.A., 1979, Observations pertaining to the dynamics of the plasma sheet, J. Geophys, Res., 84, 5099.

16.

Bryant, D.A., Courtier, G.M., and Bennett, G., 1972, Electron intensities 41. over auroral arcs, in : “Earths Magnetospheric Processes”, D. Reidel, Dordrecht, p.1 Mozer, F.S., Cattell, C.A., Hudson, M.K., Lysak, R.L., Temerin, M., and Torbert, R.B., 1980, Satellite measurements and theories of low altitude auroral particle acceleration, Sp. Sci., Rev., 27, 155.

17.

Electron

acceleration by strong

plasma turbulence, Astrophysics