Electron trapping and charge transport by large amplitude whistlers

Transcription

1 GEOPHYSICAL RESEARCH LETTERS, VOL. 37,, doi: /2010gl044845, 2010 Electron trapping and charge transport by large amplitude whistlers P. J. Kellogg, 1 C. A. Cattell, 1 K. Goetz, 1 S. J. Monson, 1 and L. B. Wilson III 1 Received 28 July 2010; revised 4 September 2010; accepted 7 September 2010; published 26 October [1] Trapping of electrons by magnetospheric whistlers is investigated using data from the Waves experiment on Wind and the S/WAVES experiment on STEREO. Waveforms often show a characteristic distortion which is shown to be due to electrons trapped in the potential of the electrostatic part of oblique whistlers. The density of trapped electrons is significant, comparable to that of the unperturbed whistler. Transport of these trapped electrons to new regions can generate potentials of several kilovolts. Trapping and the associated potentials may play an important role in the acceleration of Earth s radiation belt electrons. Citation: Kellogg, P. J., C. A. Cattell, K. Goetz, S. J. Monson, and L. B. Wilson III (2010), Electron trapping and charge transport by large amplitude whistlers, Geophys. Res. Lett., 37,, doi: /2010gl Introduction [2] P. J. Kellogg et al. (A search for large amplitude whistlers with wind waves, submitted to Journal of Geophysical Research, 2010, hereafter Paper I) reported large amplitude whistlers observed by the Waves experiment on Wind, similar to those found by Cattell et al. [2008]. Evidence was presented for trapping of electrons by the whistlers. This distortion was shown to be electrostatic as it did not appear in magnetic field measurements. In this paper, this interpretation is further pursued, using data from wave experiments on both STEREO and Wind. It first will be shown, in detail, that these whistlers trap significant numbers of electrons and the trapping mechanism is trapping in the potential energy minima of the electrostatic part of an oblique whistler. These electrons, carried by the whistler into new regions, generate kilovolt electrostatic potentials. 2. Brief Experiment Description [3] The observations reported here were made with instruments on STEREO and on Wind. A full description of the STEREO experiment, S/WAVES, is given by Bougeret et al. [2008] and a description of the Wind experiment, Waves, is given by Bougeret et al. [1995]. Both experiments measure electric field waveforms obtained from cylindrical antennas (6 m long for STEREO, 7.5 to 50 m long for Wind). Wind also carries a search coil for magnetic fields. The Wind spacecraft is spinning, with long electric antennas (X 50 m, Y 7.5 m) in its spin plane. The STEREO spacecraft is 3 axis stabilized, requiring shorter electric antennas. The Wind instrument has two modes, the fast Time Domain Sampler 1 School of Physics and Astronomy, University of Minnesota, Minneapolis, Minnesota, USA. Copyright 2010 by the American Geophysical Union /10/2010GL system (TDSF) measures only two components of the electric field vector, and a slower sampling system (TDSS) measuring four of the six components of the electromagnetic field, The STEREO experiment measured three dimensional electric fields but did not have magnetic measurements. Hence a fuller understanding of the waves can be obtained by combining them. 3. Observations and Analysis [4] In Paper I, we reported results of a search for large amplitude whistlers in data from the Waves experiment on Wind. Five episodes of strong whistlers were found and analyzed. Certain distorted electric waveforms were interpreted as evidence for electron trapping. These distorted waveforms were also observed in data from the S/WAVES experiment on STEREO [Cattell et al., 2008]. As detailed in section 2, each of these experiments has advantages and disadvantages. In particular, magnetic measurements were available from Wind Waves for several events which allows direct determination of the direction of the wavevector, k. In this work we combine the advantages in order to make a more thorough study of the electron trapping phenomenon. It will be shown that the observations are consistent with sheets of electrons trapped in the electrostatic part of the field of an oblique whistler. The trapped electrons are sufficiently cold that they are trapped in a narrow range of phase, thus giving an electrostatic signal rich in harmonics of the fundamental. Figure 1 shows an example, from Wind TDSF data, of the distorted waveform which we discuss. The broad sine wave of the whistler has narrow spikes imposed on it. We show that these are consistent with the (bipolar) electric field of narrow sheets of trapped electrons. Figure 2 shows similar data from STEREO S/WAVES. The top panel shows the entire telemetered event and the lower panels show an expanded view of the data between the black lines in the top panel, detail which is not resolved at the top. The distortion is not as sharp as in the Wind data because the sampling rate is not fast enough to resolve the spikes as clearly. [5] In order to show that the distorting field is due to sheets of electrons trapped at potential maxima of the electrostatic potential, the first step it to show that the field points in just one direction, the normal to the sheet. Figure 3 shows a hodogram of the distorting field in an event from STEREO. In order to make Figure 3, data like that above has been filtered to remove the fundamental frequency part of the waveform; the part remaining then is entirely due to the distortion. Of course it is not a full representation of the distorting electrostatic field, because it is missing its fundamental. Nevertheless, it suffices to establish that the field is unidirectional, consistent with that of a plane sheet. The 1of6

2 Figure 1. Wind. A typical whistler event showing the distortion due to trapped electrons, as seen on the X and Y antennas of next step is to show that only oblique whistlers show the distortion. Figure 4 displays observation of two events taken from the Slow Time Domain Sampler (TDSS) on Wind. For these events, TDSS was in a mode where signals from 3 orthogonal search coils were transmitted, so that the direction of the wavevector could be determined from the minimum variance of the magnetic field, the direction of the eigenvector of the variance matrix with the least eigenvalue. The sampling rate was too slow to clearly resolve the distorting characteristic, but sufficient to show that there is a strong harmonic component. For the event on the left in Figure 4, the angle between k and B was 48 degrees, so that this is an oblique whistler, and there is a strong harmonic signal. For the event on the right, the k B angle is 4 degrees and there is no harmonic signal, thus no trapped sheet. [6] If there is an electron sheet at constant phase, then its field points along the wavevector. From this, the change of wavevector direction during an event has been determined for several events, utilizing the maximum variance directions of short samples of about two cycles each. All of the Figure 2. A typical whistler event as seen on the three antennas of STEREO, converted to an orthogonal coordinate system. 2of6

3 Figure 3. Hodograms showing linear polarization of the harmonic signal, i.e., the non whistler part. STEREO events (there were 24 in all in an episode lasting only four minutes), had nearly the same obliquity which changed little during an event, with the event averaged angle k to B varying only from 46.3 to 51.2 deg. The Wind events of Paper I showed a greater range of obliquity, determined from the minimum variance of the magnetic field, from nearly zero to 48 degrees. [7] If the fields are transformed to a coordinate system with one axis along k, then the field in the other two orthogonal components should not contain the field of the trapped electron sheet and should be only the sinusoidal induction field. This coordinate system was used in Figure 2, where the z component is along k. It will be seen that the transverse components are purely the sinusoidal induction field. [8] The electric field can be integrated to find the potential and can be differentiated to find the charge density. These require transforming from a time series to a spatial series, so that it is necessary to know the velocity of the waveform relative to the spacecraft. As we are primarily concerned with the relative phases of the potential and the electron density, the magnitude of the velocity is not so important, but the sign is essential. At the time of the STEREO observations, on 12 December 2006, the spacecraft was at a GSM system latitude of 24 deg. From observation of a drop in electron density immediately preceding the whistlers, to about 2 cm 3, it is just outside the plasmasphere. For a whistler traveling parallel to the magnetic field, the electrostatic component is in phase with one of the transverse components, and for one traveling anti parallel, the electrostatic component is 180 degrees out of phase. These whistlers are found to be moving away from the magnetic equator. Their velocity has been taken from the dispersion relation for normal whistlers. As the whistlers are fast, the trapped electrons are energetic and must follow the magnetic field lines. The potential is therefore calculated by integrating the component of electric field along B. The trapped electron density is calculated by differentiating the electric field in the k direction. [9] Figure 5 completes the demonstration that the electrons are trapped in potential maxima of the electrostatic component of the whistler. The bottom panel shows the electric field measurements, the black curve being the electric field in the k direction and the green curve is the electric field of that transverse component which would be in phase with the longitudinal component in a normal whistler. This is in order to show the effect of the trapped electrons. The upper panel shows the results calculated from these data. The black curve is the potential and the red curve is the electron density, calculated as described above. The green curve is a Figure 4. Two events from Wind data, to show that (right) parallel propagating whistlers do not have the distorting signal characteristic of (left) trapped electrons. 3of6

4 Figure 5. Potential, electron density and other relevant quantities in a whistler with trapped electrons, showing trapping in potential maxima. (bottom) Field components as measured, and (top) quantities derived from them. (pseudo) density calculated from the green curve in the lower panel, in order to show which of the peaks in the electron density are the normal peaks and which are due to the trapped electrons. The trapped electron peaks are then the peaks which are not coincident with the green peaks and show clearly that electrons are trapped in the electric potential maxima. [10] The electric field of the trapped electrons distorts the field in the plane perpendicular to the magnetic field, B. The ellipticity of the fields in this plane has been one way to determine the angle between the wavevector and B. A hodogram of the field in this plane is shown in the work by Cattell et al. [2008, Figure 1D] where it can be seen that the distortion is not only very large, the hodogram is like a figure 8, which makes it difficult to estimate the propagation direction using only the ellipticity. Determination of the angle between k and B from the direction of the harmonic field provides a more accurate way to determine the wavevector angle. [11] In addition to the high frequency signals discussed heretofore, here is a low frequency component of the potential which is not easily seen in short sections of the waveforms, as in Figure 5. This low frequency potential can only be calculated from the STEREO data as the Wind TDSF had poor response below about 140 Hz, while the STEREO TDS had response useable down to 15 Hz [Bougeret et al., 1995, 2008]. In Figure 6 shown are four examples of this potential obtained by integrating whole events. Again, as discussed for the upper panel of Figure 5, the black lines are the potentials, the unresolved red and green lines are the electron densities and pseudo densities, the latter to distinguish the density of the trapped electrons from the normal (not loaded by trapped electrons) whistler density. Potentials of several kilovolts are generated by the charges of the trapped electrons, carried into regions other than where they were trapped. The y axis scale refers only to the potentials. The electron density and pseudo density are only relative, and the (rel) refers to them. The potentials are absolute, at least to the extent that the velocity is correct. The topmost panel shows a typical event, with potentials of only about 3000 Volts. The second panel shows an abrupt rise to about 6500 volts due to a narrow electron bunch. The next two panels show nearly periodic modulations of kv potentials with a frequency of about 19 Hz. We have not been able to identify this frequency in terms of characteristic frequencies of a plasma. The lower hybrid frequency in this plasma is from about 70 to 200 Hz, depending on the assumed oxygen concentration. [12] It will be seen that there is little relation between the low frequency potential and the whistler frequency waveforms. It is likely that there are two effects here, first that trapped electrons are being carried into a region and adding to the ambient electron population, and second that the ambient population is being reflected and evacuated by the large low frequency potentials. We think that these effects, whose ratio cannot be easily determined, account for the lack of clear correlation. [13] The kilovolt potentials seem quite impressive. However, if these whistlers obey the normal dispersion relation, then their phase velocity along B is.33 c, so the energy of the trapped electrons is about 29 kev in the plasma frame. The group velocity of such a whistler packet, again in the B direction, would be.36 c. An electron at rest in the plasma frame would have an energy of 34 kev in the wave packet frame, so would not be reflected by the few kv potential, though of course, the density will be strongly affected. 4. Summary and Conclusions [14] We present observations of unusual waveforms of whistler waves observed by STEREO and Wind. It is shown that these waveforms are distorted by sheets of electrons trapped in the electrostatic potential of oblique whistlers. This is shown by (1) the distorting part of the electric field is linearly polarized, (2) this distorting component is not present for whistlers which are propagating nearly parallel to the magnetic field, and (3) the excess electron density is 4of6

5 Figure 6. The potentials of some longer sections, showing the large potentials generated by the transported electrons. localized at maxima of the electrostatic potential, obtained by integrating the electric field in the magnetic field direction. In addition, it was shown (Paper I) that the distorting field is electrostatic and is not present in magnetic measurements. Two kinds of electron trapping by whistlers have been discussed in the literature. One [Matsumoto and Omura, 1981; Omura and Matsumoto, 1982] is trapping at a fixed phase of the whistler in a cyclotron resonance. These electrons are moving through the whistler, but see an electric field which rotates in synchronism with the electron s velocity. This type of trapping is not the trapping responsible for the waveforms discussed here. The second, the responsible mechanism here, is trapping in the electrostatic potential of an oblique whistler [e.g., Kumagai et al., 1980]. [15] The trapped electron density is being carried into new regions where the changed density generates electrostatic potentials of several kilovolts. This is a new feature of the interaction of whistlers with electrons which, to our knowledge, has not previously been taken into account. [16] It is to be supposed that the whistlers trap electrons while they are growing, as there do not seem to be electrons of the trapped energy available in the region we observe. In neither this paper nor in Paper I do we think we are reporting whistlers in the region where they are generated. Their generation remains uncertain, but it may be that they come from regions where the phase velocity of whistlers is much slower, i.e., regions of higher density, where they might find a population of electrons whose speed is not greatly different from the whistlers. We note that the density is changing rapidly with position in the observed region, and that the whistlers are propagating away from the magnetic equator, where other work has suggested that whistlers are generated [LeDocq et al., 1998; Parrot et al., 2003]. 5of6

6 [17] Acknowledgments. This work was supported by the National Aeronautics and Space Administration under grants NNX07AF23G.(STEREO) NESSF grant NNX07AU72H, and NNX07AM97G and NNX08AT81G (Wind). L. B. Wilson was partially supported by a Dr. L. Burlaga/Arctowski Medal Fellowship. We thank R.Lepping, GSFC and C. T. Russell, UCLA, and CDAWeb for the magnetic field and density data, and R.Lin, UCBerkeley for the ion density data. References Bougeret, J. L., et al. (1995), WAVES: The radio and plasma wave investigation on the Wind spacecraft, Space Sci. Rev., 71, 231, doi: / BF Bougeret, J. L., et al. (2008), S/WAVES: The radio and plasma wave investigation on the STEREO mission, Space Sci. Rev., 136, , doi: /s Cattell, C., et al. (2008), Discovery of very large amplitude whistler mode waves in Earth s radiation belts, Geophys. Res. Lett., 35, L01105, doi: /2007gl Kumagai, H., K. Hashimoto, I. Kimura, and H. Matsumoto (1980), Computer simulation of a Cerenkov Interaction between obliquely propagating whistler mode waves and an electron beam, Phys. Fluids, 23, 184, doi: / LeDocq, M., D. A. Gurnett, and G. B. Hospadarsky (1998), Chorus source location from VLF Poynting flux measurements with the Polar spacecraft, Geophys. Res. Lett., 25, 4063, doi: /1998gl Matsumoto, H., and Y. Omura (1981), Cluster and channel effect phase bunchings by whistler waves in the nonuniform geomagnetic field, J. Geophys. Res., 86, 779, doi: /ja086ia02p Omura, Y., and H. Matsumoto (1982), Computer simulations of basic processes of coherent whistler wave particle interactions in the magnetosphere, J. Geophys. Res., 87, 4435, doi: /ja087ia06p Parrot, M., et al. (2003), Source locations of chorus observed by Cluster, Ann. Geophys., 21, 473, doi: /angeo C. A. Cattell, K. Goetz, P. J. Kellogg, S. J. Monson, and L. B. Wilson III, School of Physics and Astronomy, University of Minnesota, 116 Church St., SE, Minneapolis, MN 55455, USA. (pauljkellogg@gmail.com) 6of6