Pages 1025-1035

WHAT DO WE REALLY KNOW ABOUT AURORAL ACCELERATION

M. Temerin

Space Sciences Laboratory, University of California, Berkeley, CA 94720-7450, USA
E-mail: temerin@ssl.berkeley.edu

ABSTRACT

The auroral acceleration region provides an easily accessible region where plasma acceleration processes of solar and cosmic importance can be studied. In addition the auroral acceleration region plays an important role in the magnetosphere. The acceleration of ions in the auroral acceleration region provides an important, and at least during times of large magnetic storms, the dominant source of mass to the magnetosphere while the acceleration of electrons produce beautiful auroral displays. While many of the effects of auroral acceleration are understood since it is relatively easy to measure energetic particles, the mechanisms by which particles are accelerated are less well known since a study of mechanisms requires a combination of measurements of both particles and electric fields, preferably at more that one point, with a theory that describes the creation of such electric fields and the effect of such fields on particle acceleration. Measurements by sounding rockets and satellites dedicated primarily to auroral studies such as S3-3, DE, and Viking have provided much of the in situ observations that are the basis of our current knowledge of auroral acceleration. Currently, Freja, Akebono, and especially the Polar and FAST satellites, together with increasingly more sophisticated sounding rockets are adding to our knowledge of auroral acceleration.

The title of this report and other similar reports was suggested by the main scientific organizer of this session. With the provocative word "really" the title suggests knowledge near the boundary of what we know and do not know. Taking this as hint I have attempted to describe not so much our knowledge of auroral acceleration but the boundary between our knowledge and our ignorance though in some cases this is, no doubt, just my ignorance.

A discussion of auroral acceleration perhaps requires a few remarks of a more general nature. Auroral particle energization is what is usually really meant by auroral acceleration, and the rate of energy gain is given by dW/dt = Fv where W is the energy of the particle F is the force and v is the velocity. Ignoring gravity this becomes dw/dt = qEv where E is the electric field and q the charge of the particle. While this may seem so obvious as not to be worth a remark, explicitly evoking the electric field is not always done in modeling the acceleration of cosmic plasmas. Shock acceleration in the solar wind, for instance, can be treated by invoking first or second order Fermi acceleration, which can be modeled theoretically by invoking pitch angle scattering due to magnetic fluctuations in different reference frames, without explicitly invoking the electric field. Auroral plasmas however are very low beta plasmas which means chat magnetic fluctuations and pitch angle scattering due to magnetic fluctuations are small effects and thus explicitly invoking the electric field is usually necessary.

The velocity of a particle can be divided into parallel motion along the magnetic field and perpendicular motion, which is a nearly circular motion around a magnetic field line with a frequency given by the gyrofrequency (gradient and curvature drifts are typically small, and the E x B drift can be removed by moving into the E x B reference frame). Averaging over a few gyroperiods then gives the result that the important electric fields from the point of view of particle energization are the parallel electric fields and those perpendicular wave fields that have a frequency at the gyrofrequency. Further averaging over a few wave periods gives the result that the important wave electric fields are those that have a parallel phase velocity equal to the particle phase velocity (Landau resonance). Also important are parallel electric fields that don't vary on the time scale of the transit of the particles through them (quasi-static parallel electric fields).

The above discussion while apparently reducing the problem of auroral acceleration to the problem of the creation of the appropriate parallel and perpendicular electric fields really hides several observational and theoretical problems. From the observational point of view the parallel electric field is the most difficult to measure because normally the magnitude of the parallel electric field is at most a very small fraction of the perpendicular electric field (later in this report I show some examples and counter-examples of this from recent measurements on the Polar satellite). Another problem is that the explicit integration of the energy equation requires knowledge of the electric field in the particle frame while measurements are usually in the satellite frame. The satellite frame is always different from the inertial frame which is usually different from the plasma frame (the frame where the E x B velocity is zero) which in turn is different from the particle frame. Consider as an example the perpendicular acceleration of ions to form so-called ion conics or TAI's (transversely accelerated ions). Satellite measurements usually show substantial electric field power at the ion gyrofrequency. However much of this is due to the Doppler shift of short wavelength waves or spatial irregularities due to the satellite velocity in the plasma frame. On the other hand the lack of wave power in the plasma frame at the gyrofrequency is not an absolute barrier to perpendicular ion energization. The gyromotion and parallel motion of the ions can shift even static electric fields which have a perpendicular spatial scale of the order of the gyroradius to the gyrofrequency which may give rise perhaps to perpendicular acceleration by electrostatic shocks (Greenspan, 1984; Borovsky, 1984). Also lower frequency waves effect the ion trajectory. Thus two finite perpendicular waves which add to the gyrofrequency can effectively accelerate ions (Temerin and Roth, 1986). This gives `qEv' the quasistatic component required for effective acceleration as follows: `v' has a frequency component at the gyrofrequency due to gyromotion in the magnetic field and a frequency component at one of the wave frequencies due to perturbative motion in the wave, while E has a frequency component due to the other wave. These three frequencies give several harmonics in the frame of the ion, one of which is quasistatic (that is it doesn't average to zero over the time scale of the wave periods or gyroperiod) and thus energizes the ion.

Particle distributions often provide a better guide to electric fields that are important for particle acceleration than direct measurements of electric fields do. Particle distributions integrate the effect of electric fields over large distances. For instance, the monoenergetic peak in electron distributions measured in inverted-V electron events provides good evidence for the existence of quasi-static parallel fields. In general, measurements of particles and fields together with theory provide the basis for understanding auroral acceleration processes.

The auroral acceleration region accelerates electrons both upward and downward along magnetic field lines, though the downward acceleration dominates and is, of course, better known because it creates the visible aurora. Ions, on the other hand, with a few but interesting exceptions, are mostly accelerated upwards. Ions that do precipitate into the atmosphere are due predominately to the direct injection of ions into the loss cone in regions above what I here consider the auroral acceleration region. Ions precipitate into the ionosphere in the cusp by direct entry from the magnetosheath due to reconnection or by pitch angle scattering from the ring current. The average properties of precipitating electrons has been well established in several studies by Newell et al. (e.g., 1996) on the basis of data from the DMSP satellite. The average properties of upgoing ions as seen by the DE-1 satellite were described by Yau et al. (1985). Upgoing electrons seen near the equator have been described by Klumpar (1993). The reason for this asymmetry between ions and electrons has to do with the different kind of auroral acceleration that occurs in upward and downward current regions as described below.

Though auroral acceleration processes occur to some extent along the whole field line, measurements from S3-3, Viking and DE satellites have established that a large portion of the particle acceleration that occurs on auroral field lines occurs in an altitude range of about 1000 km to about 10000 km The simple explanation (perhaps overly simple) for this is that it is in this region that the relative drift velocities between ions and electrons are maximum since the field-aligned currents increase in proportion to the magnetic field but the plasma density is still small. Thus acceleration is required either to maintain the current or the large relative drift of particles can lead to instabilities and waves which heat the plasma.

In this region auroral acceleration processes can be divided by their region of occurrence into those that occur in regions of upward field-aligned current and those that occur in regions of downward field-aligned current. Auroral acceleration can be also divided physically into processes that are due to wave-particle interactions and those that are due to quasi-static electric fields. Upward and downward field-aligned currents are the mechanism by which the stresses of the magnetosphere are transferred to the ionosphere and are the proximate causes of the processes that lead to auroral acceleration, but I do not consider in this report the origin of these field-aligned currents as this involves treating the dynamics of magnetosphere as a whole. The most characteristic particle acceleration feature of the upward current region is the inverted V electron distribution and upward going ion beams while the most characteristic features of the downward current region are ion conics and field-aligned counters/reaming electron beams. Figure 1, compiled from data taken on the S3-3 satellite and taken from Redsun et al. (1985) shows the strong association between electric fields and particle signatures. The figure shows that most large electric fluctuations (i.e. `electrostatic shocks') are associated either with ion conics, a signature of wave heating, or ion beams, a signature of acceleration through quasi-static parallel electric fields.

Fig. 1.The magnetic local time and invariant latittude locations of large electric fields defined as greater than 90 mV/m and their associations with ion conics and ion beams. This figure demonstrates the close connection between electric fields and particle signatures of acceleration.

The upward current region is perhaps the better understood of the two regions. The model is that in this region electrons are accelerated downward and ions are accelerated upward predominately by quasi-static electric fields that are parallel to the magnetic field. The potential drops associated with these electric fields are typically a few hundred volts up to as much as 40 kV. These parallel potential drops are related to parallel currents since the upward current is mainly carried by magnetospheric electrons whose temperature is typically one keV and whose density is less than one cm-3. Under these conditions the magnetic mirror of the converging magnetic field lines prevents most of the magnetospheric electrons from precipitating into the ionosphere. To carry more current it is necessary to drive more electrons into the ionosphere which requires a parallel potential drop which lowers the mirror points of the magnetospheric electrons. This leads to a simple voltage-current relation that is a function of the density and temperature of magnetospheric electrons (e. g., Knight, 1973; Lyons, 1980).

While a parallel electric field may be required by the boundary conditions that impose currents the exact way the electric field is distributed along the magnetic field and the way it interacts self-consistently with the ions and the electrons, is one of the main unanswered questions in the upward current region. Almost all the plasma must be very close to charge neutrality as a simple calculation of any large scale deviation from charge neutrality would show a resulting enormous electric field. The plasma in the acceleration region can be divided into four components: ionospheric electrons and ions and magnetospheric electrons and ions. The density of each of these components and especially the densities of the ionospheric components changes greatly due to the parallel potential drop. For instance, the ionospheric electrons are mostly excluded from the parallel electric field region since they are reflected by the potential drop while the density of ionospheric ions drops in the parallel electric field region as these ions are accelerated by the electric field.

Despite the fact that to first order these two changes are in the same direction under most circumstances there does not appear to be a simple way to preserve charge neutrality under the assumption that ions and electrons are accelerated solely through a large parallel potential. [The model of Chiu and Shultz (1978) preserves charge neutrality in the presence of a parallel electric field by assuming different pitch angle distributions for magnetospheric electrons and ions. However, pitch angle distributions are due to wave-particle interactions near the equatorial region while the parallel potential is mainly determined by the large scale convection and pressure gradients that result in parallel currents and potentials, and it is unlikely that nature will arrange the pitch angle distribution to match the requirements imposed by the forces that drive the large scale convection of the magnetosphere.] Such considerations lead some to the conclusion that there must be a small-scale region of large parallel electric fields called a strong `double layer' where the plasma is not neutral. While such large double layers have not been seen, large electric fields which are mostly perpendicular but may have a component parallel to the magnetic field have been seen. These structures, called `electrostatic shocks' (Mozer et al., 1977) have an electric field chat points toward the region of parallel acceleration and the potential drop through the large electric field is closely related to the potential inferred from the energy of the associated ion beam (Figure 2).

Fig. 2. Correlation between the ion energy and the potential through the associated electrostatic shock.

Similarly, the potential drop can be inferred from the electron spectrum (Evans, 1974). Figure 3 shows a typical differential electron spectrum as measured below the inverted V acceleration region by an electron detector on a rocket together with a simulated Monte Carlo spectrum. The simulated spectrum assumes that electrons with a temperature of 1 keV exist above a potential of 7 kV located at altitude of 1 RE. In the simulation all the electrons below the energy of the potential drop (7 keV) are due to backscattered and secondary electrons created by the interaction of the electrons with the atmosphere. The good agreement between data and expectation strongly supports the primary role of quasi-static parallel electric fields in accelerating electrons and ion beams in the upward current region. Comparisons made by DE-1 and DE-2 (Reiff et al., 1988) of upgoing ion beam energies also are in agreement with the primary role of quasi-static parallel electric fields.

Fig. 3. A measured (a) and simulated (b) electron spectrum within an inverted V for different pitch angles. The measured spectra were made by the Bidarca rocket payload. The simulated spectrum assumes that electrons with 1 keV temperature fall through a 7 kV potential drop.

This simple theoretical argument can be contrasted with observations which show that the acceleration region can be far more complicated. In addition to the hypothesized strong double layers, electrostatic shocks which are regions of large but mostly perpendicular electric field, along with weak double layers, and a variety of waves have been observed in the upward current region. It may well be that under many circumstances there is no quasistatic way to accommodate the requirements imposed by the magnetosphere. The observation of flickering aurora suggests that under some circumstances the whole potential structure oscillates. It has been shown that flickering aurora is due to a field-aligned electron component with energies below the peak energy of the inverted V superimposed on the inverted V electron flux (Temerin et al., 1986; McFadden et al., 1987). To be visible, the electron fluxes need to oscillate at less than 10 Hz which corresponds to the O+ gyrofrequency in the acceleration region. However, Temerin et al. predicted that electron fluxes corresponding to the H+ gyrofrequency should also be seen since waves at these frequencies occur in the auroral acceleration region (Gurnett and Frank, 1972; Temerin and Lysak, 1984) and, in fact, such fluxes were subsequently seen (Temerin et al., 1993). (In fact, waves corresponding to He+ cyclotron frequency have also been observed (Gustafsson et al., 1990).)

The model suggested that these potential fluctuations propagate as electromagnetic ion cyclotron waves. Such waves have a small but finite parallel electric field component and an increased velocity as they propagate towards the ionosphere which allows them to resonantly accelerate low energy ionospheric electrons to keV energies. The one problem with the model was that the required wave amplitude was larger than had been observed. The inferred waves should have a perpendicular amplitude of a few hundred mVm-1. Now (I come to the real reason that I am writing about this) such waves have been observed in data from the EFI instrument on Polar. Figure 4 shows 100 Hz waves with an amplitude of about 200 mV/m detected in the southern auroral oval at an altitude of about 1 RE The frequency is slightly below the local H+ gyrofrequency. Additional waves can be seen at frequencies that correspond to the He+ and O+ frequencies. In my opinion such waves are not due to an instability in the electron beam distribution but rather they are due to an oscillation of the potential structure. The theory for this has not been developed. One interesting application of these waves is to solar physics. We have suggested (Temerin and Roth, 1992) that such waves could explain the observations of 3He enhancements by up to four orders of magnitude with respect to 4He seen in the ions accelerated from impulsive solar flares at MeV energies. In many ways the flare plasma is similar to auroral plasmas. This is one example where in situ observations in the magnetosphere can lead to increased knowledge of plasma physics processes applicable to solar physics and astrophysics. Additional electric field data showing the parallel and one of the perpendicular electric field components surrounding the interval of the intense 100 Hz waves is shown in Figure 5. The data is preliminary in that finding the parallel component requires knowledge of the direction of the magnetic field. Here the direction of the magnetic field was guessed based on the assumption that on the average it should be the direction where the electric field is least. One can see that the parallel (or strictly speaking, chat there exists a direction where the electric field is small) electric field is much smaller than the perpendicular field.

Fig. 4. Large amplitude electromagnetic ion cyclotron waves observed by the EFI experiment on the Polar satellite. Such amplitudes have not been seen before but were predicted on the basis of the observed electron flux modulations.

Fig. 5. A larger time interval (8 s) surrounding the intense waves shown in Figure 4. The parallel electric field and one of the perpendicular electric field components is shown. This demonstrates the large electric field fluctuations in the auroral acceleration region and the difficulty of measuring the much smaller parallel component of the electric field.

Additional complications can be inferred from the upgoing ion beam. Observations of upgoing ion beams, which are ionospheric ions accelerated through a potential, show an energy difference between the highest and lowest energy ion in the beam that is a few times larger than the mean energy of the beam. This implies that on the ion transit time scale the oscillating parallel electric field component in the acceleration region is larger than the average component. Typically small-amplitude double layers or solitary waves or electrostatic ion cyclotron waves are found in association with ion beams (Temerin et al., 1982; Bostrom et al., 1988). Figure 6 shows some examples of solitary waves taken from recent Polar satellite data near perigee in the southern auroral oval. These are, to my knowledge, the biggest and fastest solitary waves yet seen with a parallel electric field amplitude of 180 mVm-1 and a parallel velocity based on the time delay of the signal between two probes of about 100 kms-1. Such parallel fields may be responsible, if not for accelerating the ions, at least for heating them. The inverted V electrons also show the effects of wave interactions. Even such a `normal' inverted V spectrum as the one in Figure 3 shows the effect of waves. The simulated spectrum shows a steep drop at 7 keV while the data shows a gentler drop so as to avoid a positive slope in the electron distribution function. Some of the higher energy electrons fill in this area. The energy lost by the electrons probably goes into generating whistler waves in the form of V-shaped hiss, which are normally found in association with inverted V electron distributions, or perhaps other waves also.

Fig. 6. Some examples of solitary waves showing the parallel electric field component. These are the largest parallel electric fields that have been seen.

The most interesting region in the upward current region is probably at the lower boundary of the acceleration region at the interface of the colder ionospheric plasma with the hotter magnetospheric and accelerated plasma. At this boundary the parallel potential reflects most of the ionospheric electrons while the ion density decreases to conserve flux as the upward ion velocity increases. The effect is an abrupt decrease in density (the auroral plasma cavity). It is here perhaps that most of VLF hiss and other waves associated with the upward current region are generated. We know very little about this region because of the lack multipoint measurements that could determine the distance from the boundary. Measurements at altitudes between 3000 km and 10000 km imply an extensive acceleration region since when particle signatures indicating acceleration below a satellite located in this region are seen (upflowing ion beams, enlarged electron loss cone, few ionospheric secondaries) often particle signatures indicating acceleration above are also seen (accelerated electrons, reflected loss cone (that is, `electron hole')). However, though the prevalence of ion beams increases with altitude in the 3000-10000 km altitude range the average observed ion energy does not. This suggest to me that the potential drop (i.e. parallel electric field) is relatively concentrated near the bottom of the acceleration region, followed at higher altitudes by a weaker but larger in extent parallel field. But this is speculation: observations from a single spacecraft only show that particles have been accelerated somewhere. It is only when one can compare observations from relatively nearby spacecraft that one can be confident of the location.

The downward current region is even more complicated. It is in the downward current region that a majority of the ion conics and counters/reaming electron beams together with the greatest turbulence in the low frequency electric fields is seen. Particle acceleration extends to lower altitudes in the downward current region. ISIS-2 measurements at 1400 km altitude (Klumpar and Heikkila, 1982) showed both TAI's and upgoing field-aligned electron beams, as have recent measurements by Freja (Boehm et al., 1995). In contrast the parallel electric field in the upward going current region rarely extends below 3000 km. It is not clear whether quasi-static parallel electric fields play an important role in this region. If they do their effects are masked by the effects of waves. There are perhaps three general models for the origin of the turbulence. In one model the turbulence is generated by the downward current. The current is carried by upward moving ionospheric electrons. Since some plasma instabilities due to the drift of one species relative to others depend on the ratio of drift velocity to the thermal velocity it may be that the drift of ionospheric electrons can be unstable at relatively low drift velocities. In another model the waves are due to propagation of waves along the field line from above. For instance, turbulent fields on cusp field lines are sometimes thought to propagate to the ion conic generation region along the magnetic field from perhaps the reconnection region on the dayside. A third model is that at least some of the turbulence is generated by the ion conics and electron beams. In this model, another mechanism, perhaps quasistatic parallel fields must then generate at least some of the electron beams.

The typical electron spectrum in this region is in stark contrast with that of inverted V's. It shows an enhanced field-aligned electron component and much larger flux of lower energy electrons. These features are an indication that ionospheric electrons have been heated mostly in the direction parallel to the magnetic field. In the ionosphere the typical signature of the field-aligned electrons are probably suprathermal electron bursts (Johnstone and Winningham, 1982) which are generally not very energetic. However sometimes the same kind of electron spectra become much more energetic. Figure 7 shows an electron spectrum from the Bidarca rocket experiment shortly before entry into the auroral oval. The rocket payload was probably crossing an auroral arc near the polar cap boundary (a so-called `traversing arc' that tend to occur after substorm expansion). The interesting point is that the downward electron energy flux is about 100 ergs/s-cm2, larger than that of a typical inverted electron spectrum and so capable of producing a bright aurora. This intense electron flux lasted for less than a second corresponding to a ground track of three quarters of a kilometer. Temerin et al. (1994) have modeled the spectra by assuming stochastic heating (as would occur from a broad spectrum of waves but no explicit wave modes were assumed) of upgoing cold ionospheric electrons above the payload and, of course, the self-consistent backscattered and secondary electrons. In this case a parallel potential drop of about 5 kV was assumed above the heating region to prevent most of the electrons from escaping (this parallel field is really an ambipolar field based on a temperature of a few keV: sudden heating of electrons must produce electric fields to confine the electrons in order to insure charge neutrality) and to help reflect the heated electrons. There is good agreement between the data and the model (Figure 8) suggesting that electron heating by waves can produce discrete auroral arcs which is in contrast to the usual assumption that discrete auroral arcs are related to inverted V electron fluxes.

This is perhaps a good place to finish. I have come to the point where I can say that we still don't really know what causes the discrete aurora, which is, after all, one of the main goals of this field of research.

Fig. 7. An electron spectrum for various pitch angles that shows enhanced downgoing field-aligned electrons and a large flux of lower energy electrons extending to higher energies. This kind of electron spectrum is indicative of wave heating.

Fig. 8. An simulation of the electron spectrum in Figure 7. The simulation assumes stochastic heating, mostly in the parallel direction, of ionospheric electrons.

ACKNOWLEDGMENTS

The author would like to acknowledge NASA contract NAS5-30367 and grant NAG5-3182 for support for this research.

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