Further sounding rocket observations of structured whistler mode auroral emissions

Transcription

1 JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 115,, doi: /2009ja015095, 2010 Further sounding rocket observations of structured whistler mode auroral emissions C. A. Colpitts, 1,2 J. LaBelle, 1 C. A. Kletzing, 3 and P. H. Yoon 4,5 Received 16 November 2009; revised 15 March 2010; accepted 29 June 2010; published 26 October [1] Two recent sounding rockets were launched into active auroral substorms from Poker Flat, Alaska: CHARM on 27 February 2007 and SIERRA on 14 January Both payloads included HF wave receivers. As previously reported, the SIERRA HF receiver recorded short lived, periodic, time dispersed features at khz ( stripes ), in which high frequency components precede low frequencies, leading to a nearly linear frequency time signature. These features coincided with a region identified as Alfvénic and dominated by suprathermal electron bursts and ev downward going ions poleward of the main inverted V auroral arc. The CHARM experiment, using different electric field sensors, confirmed the occurrence of the stripe features with characteristics similar to those observed with SIERRA. The most promising mechanism to explain stripes is a cyclotron resonance between downgoing Z mode waves and upgoing electron conics in the topside ionosphere at altitudes of km. These electron conics resonate with successively lower frequency waves as they ascend, leading to emissions in which lower frequencies are delayed relative to higher frequencies; detailed modeling reproduces even fairly subtle nonlinear features of the stripes frequency time signature. The resulting structured Z mode waves then convert to whistler mode waves, which propagate to rocket altitudes. Previous simulations have shown that electron conics can be generated by Alfvénic acceleration and retain the periodicity of the driving Alfvén wave. If this acceleration could be driven by Alfvén waves at the frequency of the periodicity of the stripes, it could explain this periodicity and would be consistent with their correlation with an Alfvénic region. Citation: Colpitts, C. A., J. LaBelle, C. A. Kletzing, and P. H. Yoon (2010), Further sounding rocket observations of structured whistler mode auroral emissions, J. Geophys. Res., 115,, doi: /2009ja Introduction [2] Electromagnetic waves with distinctive frequencytime signatures have long been recognized as valuable tools in space physics, both for providing illuminating tests of plasma physics theory and for remotely sensing space plasma characteristics and processes. Classic examples include atmospheric whistlers (review by Helliwell [1965]) and solar type III bursts (review by Kundu and Vlahos [1982]). [3] The terrestrial aurora is the source of many types of potentially valuable structured electromagnetic signals. Auroral whistler mode waves, known collectively as auroral hiss, often exhibit distinctive frequency time patterns. 1 Department of Physics and Astronomy, Dartmouth College, Hanover, New Hampshire, USA. 2 Now at University of Minnesota, Minneapollis, Minnesota, USA. 3 Department of Physics and Astronomy, University of Iowa, Iowa City, Iowa, USA. 4 Institute for Physical Science and Technology, University of Maryland, College Park, Maryland, USA. 5 Also at School of Space Research, Kyung Hee University, Yongin, South Korea. Copyright 2010 by the American Geophysical Union /10/2009JA For example, Siren [1972, 1975] describes features called hisslers, which consist of impulsive signals sharply decreasing in frequency. Similar features as well as a host of other types are reported by Ungstrup and Carpenter [1974]. More recently, Sonwalkar and Harikumar [2000] call into question Siren s [1975] explanation of hisslers, and the mechanism remains controversial. In addition, Ye and LaBelle [2008] identify and classify a variety of distinctive frequency time patterns characterizing LF auroral hiss observed at South Pole Station, and these similarly remain unexplained. [4] Auroral rocket and satellite wave instruments detect a variety of frequency structured signals in the whistler mode frequency range. For example, with the low Earth orbit Aureole satellite, Beghin et al. [1989] observed distinctive emissions below the electron plasma frequency ( f pe = (ne 2 /4p 2 m e " 0 ) 1/2 ) when auroral electrons are encountered during underdense conditions ( f pe < f ce, where f ce is the electron gyrofrequency given by f ce =qb/2pm e ), which they attribute to conversion of Langmuir waves into whistler mode waves. McAdams et al. [1999] observe the same phenomenon with higher resolution from a sounding rocket, revealing banded emissions below f pe punctuated by intense 1of17

2 Langmuir waves where the frequency of the bands matches the local f pe. [5] The SIERRA rocket experiment, launched from Alaska in 2002, detected several types of structured signals below local f pe and f ce, in the khz frequency range [Samara and LaBelle, 2006a]. The most distinctive, though not the most intense, of these structured emissions were quasi periodic narrowband signals called stripes, which decreased in frequency from 500 khz to 250 khz over about 0.5 s. They occurred intermittently and were restricted to the region dominated by suprathermal electron burst signatures commonly associated with Alfvénically accelerated electrons at the poleward side of the aurora. The lack of one to one correlation with features of the local plasma or auroral electrons suggests that they are nonlocal and therefore electromagnetic waves, and in this frequency range the only electromagnetic (EM) wave mode available is whistler mode; however, no wave magnetic field measurements were available to confirm this. Samara and LaBelle [2006a] suggest a mechanism involving localized upward moving sources of whistler mode signals on the resonance cone at altitudes hundreds to thousands of kilometers above the rocket, but there are many problems with this explanation, and the origin of the stripes remains a mystery. [6] This paper presents confirming evidence of stripe emissions from a recent sounding rocket experiment, using different sensors and antenna orientations from those used in the SIERRA experiment. It also puts forth a plausible explanation for the frequency structure, periodicity, and observed location of these emissions. Section 2 describes the experiment, section 3 presents the experimental results, and section 4 critiques previously proposed stripes generation mechanisms and discusses new ideas for explaining their origin. 2. Instrumentation [7] The data presented in this paper come from two independent rocket experiments launched into the auroral F region from Poker Flat, Alaska. The SIERRA rocket was launched 14 January 2002, at 0823 UT (2056 magnetic local time (MLT)) into an active substorm and reached an apogee of 735 km. The CHARM rocket was launched 27 February 2007, at 0839 UT (2112 MLT) also into an active substorm and reached an apogee of 733 km. Both rockets included high frequency electric field wave receivers as well as a host of electron, ion, DC magnetic field, and DC and lowfrequency electric field measurements, but the sensors used in the two high frequency electric field measurements differed, as described below. The data from the CHARM experiment were limited because of a payload system failure. [8] The SIERRA sounding rocket experiment consisted of a main payload and two subpayloads. This investigation includes only data from the main payload, which included electron and ion detectors covering the energy spectrum from thermal energies up to 14.5 kev and ev, DC and extra low frequency (ELF)/very low frequency (VLF) electric field measurements using two perpendicular antennas, and the Dartmouth high frequency electric field receiver (HFE) which performed continuous waveform measurements of 100 khz to 5 MHz electric fields (for details see Klatt et al. [2005], MacDonald et al. [2006], and Samara and LaBelle [2006a]). [9] The HF electric field on SIERRA was obtained from measurements of the voltage difference between two 3 m boom stacer elements of cylindrical 6 m tip to tip Weitzmann booms with diameters of 2 cm. These booms acted as a wire dipole antenna of an approximate effective length of 3 m at frequencies greater than 100 khz. The booms lay in a plane perpendicular to the payload axis, which was aligned perpendicular to the ambient magnetic field, and which rotated in so called cartwheel mode with a spin rate of 0.33 Hz, so that the antenna and the component of the wave electric field to which it is most sensitive were alternately parallel and perpendicular to this magnetic field. The input capacitance of the sensor/preamplifier system has been estimated to be C in 40 pf [Samara and LaBelle, 2006b], which implies a correction factor of approximately 10% for the measured HF electric fields. [10] The HFE receiver made continuous full waveform measurements from 100 khz to 5 MHz and transmitted them to the ground via broadband analog telemetry where they were initially recorded on tape media and later digitized at a 10 MHz sample rate. The dynamic range of the analog telemetry link was limited because of the broad 5 MHz bandwidth, requiring that the receiver employ automatic gain control (AGC) to ensure full modulation of the transmitted signal. The receiver also employed a high pass filter with a corner frequency at about 100 khz to ensure that the gain level of the AGC would not be set by intense VLF signals such as auroral hiss. The AGC level was recorded on a separate, lower time resolution telemetry channel, and the full waveform was recovered later by recombining the HF signal and the AGC signal. Similar receiver systems were previously flown on the PHAZE II, AT II, RACE, and HIBAR rockets, as described by, for example, McAdams et al. [1999] and Samara and LaBelle [2006b]. [11] The CHARM sounding rocket consisted of a single payload equipped with a variety of particle and electric field detectors. Because of a failure of the attitude control system, all booms were deployed at much higher than intended spin rates, the rocket went into a flat spin, and large quantities of nitrogen were released into the payload environment. As a result, all of the particle detectors and most of the field detectors recorded no usable data. The Dartmouth HFE electric field instrument and the science magnetometer were the only instruments that recorded useful data. [12] In contrast to SIERRA, on CHARM the HF electric field was measured using the difference in voltage between two spheres of a diameter of 6 cm located 30 cm apart on an axial fiberglass boom. This boom was intended to be on the spin axis, parallel to the Earth s magnetic field, but as the rocket went into a flat spin this axis instead rotated roughly around the Earth s magnetic field, taking on a range of angles with respect to the ambient magnetic field but chiefly perpendicular to it. [13] The CHARM HFE receiver was essentially identical to that flown on SIERRA and described above, employing the AGC and high pass filter in the same way and was transmitted on similar telemetry links. Unfortunately, because of the payload system failure, the AGC level was not recorded, and only relative amplitudes could be obtained from the receiver. However, these data suffice to provide 2of17

3 Figure 1. A khz spectrogram of a 5 s interval ( s) of the SIERRA data, illustrating several closely spaced examples of dispersed features called stripes, visible at khz and lasting s with distinct linearly descending signature. qualitative spectra and confirm wave phenomena observed in the data from the previous SIERRA flight. 3. Data Presentation [14] Figure 1 shows a khz spectrogram of a 5 s interval of SIERRA data, s after launch. Peaks at regular intervals of 50 khz represent interference from onboard rocket system electronics, and the apparent roll off below 100 khz is due to the instrumental high pass filter. The AGC has been accounted for in this spectrogram, which therefore effectively shows the relative power spectral densities of various emissions. The most intense waves are bursty features near khz. However, the waves with the most distinctive frequency time structure are the stripelike emissions at khz, with s durations and approximately 10 khz bandwidths. They are distinguished by their approximately linear frequency time signatures whereby the highest frequencies arrive at the detector first, with lower frequencies progressively more delayed. The typical delay over the frequency range khz is s, implying a frequency time slope of 1000 khz/s. The slope is nearly linear but exhibits occasional kinks or variations in slope. The features are quasiperiodic, with several to several hundred emissions occurring in sequence, separated by time intervals of about 0.05 s. As a result, at any instant up to 4 5 features coincide. As shown by the absolute spectral density scale in Figure 1, their amplitude is highly variable, but their power spectral density averages V 2 /m 2 Hz, implying net root meansquare field strength of mv/m. Samara and LaBelle [2006a] first described these features and labeled them stripes. [15] Figure 2 shows an overview of the wave and particle data recorded on the SIERRA (left) and CHARM (right) rocket experiments. In all panels the horizontal axes represent time after launch, s for SIERRA and s for CHARM, approximately the durations of the flights. For reference, SIERRA reached an apogee of 735 km at 492 s and crossed 500 km altitude at 245 s and 739 s. CHARM reached an apogee of 733 km at 497 s and crossed 500 km at 247 s and 747 s. [16] Figure 2a shows khz spectrograms of HFE data. For both SIERRA and CHARM, the color scale represents relative wave electric field intensity on a 40 db scale (blue to red). In these spectrograms the AGC is not folded in. For reference the SIERRA spectrogram can be seen along with the corresponding AGC level in Figure 1 of Samara and LaBelle [2006a]. For CHARM the AGC level was not recorded because of the payload system failure; however, if the uniform background noise is generated in front of the AGC, this suggests that the spectrogram is a good representation of the relative power. Both spectrograms show the presence of several distinct plasma wave modes. Unstructured broadband whistler mode waves, called broadband auroral hiss, occur up to 500 khz at approximately s in the SIERRA data and up to 600 khz at s in the CHARM data. In both cases the apparent lower cutoff at 100 khz is due to the instrumental high pass filters described in section 2. The other clearly identifiable wave modes occurring on both flights are Langmuir waves and waves just above the plasma frequency on the Langmuir upper hybrid mode, also known as the slow Z mode. These occur at 1 2 MHz and s in the SIERRA data and at khz and s in the CHARM data. In both flights these waves are characterized by a sharp cutoff (a lower cutoff on SIERRA where f pe > f ce 3of17

4 Figure 2. Overview of wave and particle data recorded on the (left) SIERRA and (right) CHARM rocket experiments. (a) The khz spectrograms of HFE data; the color scale represents relative wave electric field intensity on a 40 db scale (blue to red). (b) The 7 ev to 14.5 kev energy spectrograms of electrons. (c) The ev energy spectrograms of (top) hydrogen and (bottom) oxygen ions. (d) Occurrence rate measurements for stripes. (e) Time histories of the electron plasma (solid line) and cyclotron (dashed line) frequencies. and an upper cutoff on CHARM where f pe < f ce ) that has been interpreted as the local electron plasma frequency. (For a brief period from 395 to 445 s on SIERRA, where f pe < f ce, the waves exhibit an upper cutoff.) Waves at or near the upper hybrid frequency appear in the CHARM data at khz during two intervals, s and s. Upper Hybrid waves also occur intermittently in the SIERRA data, for example at roughly 550 and 575 s after launch. [17] Figure 2b shows 7 ev to 14.5 kev energy spectrograms of electrons. As discussed earlier, no electron data are available for CHARM. As the SIERRA payload headed north from Poker Flat (65 invariant magnetic latitude), it first encountered the upward current region at 230 to 530 s after launch, characterized by inverted V electron signatures typical of downgoing electrons associated with discrete auroral arcs [MacDonald et al., 2006]. From 530 to 690 s the payload encountered a region of suprathermal electron burst signatures commonly associated with Alfvénically accelerated electrons in the downward or mixed current region on the poleward side of the aurora [Samara and LaBelle, 2006a; Klatt et al., 2005]. Some smaller inverted Vs are mixed within this region, for example at s. Klatt et al. [2005] confirm the presence of Alfvén waves throughout this time period and through comparisons of de/db and the Alfvén speed show that these Alfvén waves dominate the region and are responsible for the electron acceleration. Onboard magnetometer data show mixed currents rather than unambiguous downward currents, although this is a typical signature as the downward current region is difficult to detect with magnetometers at rocket altitudes. After about 690 s the payload penetrated the polar cap region with its weak flux of low energy electrons. [18] Figure 2c shows ev spectrograms of hydrogen (top) and oxygen (bottom) ions; again, because of the payload system failure, no ion data are available from CHARM. 4of17

5 Figure 3. The khz spectrograms of 1 s intervals of both the (left) SIERRA and (right) CHARM HFE data ( s in the SIERRA data and s in the CHARM data), illustrating examples of stripes visible at khz lasting s. Several parameters that can be scaled off of the plots are indicated: slope, upper frequency bound, and spacing. On SIERRA, relatively low ion fluxes occur from the time the detectors turn on ( 230 s) until about 550 s. However, during s, oxygen and hydrogen ions are observed at energies up to about 110 ev. This time interval corresponds to the Alfvénically accelerated electrons described above, and the presence of downgoing ions reinforces the premise that the rocket penetrates an Alfvénic region at this time [Samara and LaBelle, 2006a; Klatt et al., 2005]. [19] Figure 2d shows histograms of the observations of the stripe features. For each rocket data set, 1 s spectrograms have been generated for the entire flight with 40 db intensity range; a total of 840 (800) spectrograms were generated with frequency range of khz from the SIERRA (CHARM) waveform data. From manual inspection of these spectrograms, counts are accumulated of the number of stripe features defined by the following criteria: amplitude exceeding the noise level by 5 db, duration s, dispersion time (total time from the arrival of the highest frequency at the detector to the arrival of the lowest frequency) exceeding 0.2 s, and a dispersion slope of 1500 to 200 khz/s. Several hundred stripes are observed confined to a roughly 200 s interval on each flight. In the SIERRA observations, approximately 300 stripes are observed during s. Interestingly, this period coincides closely with that for which the payload is in a region of ev oxygen ions and Alfvénically accelerated electrons. On CHARM, the stripe emissions are also restricted to a relatively short time period, s, during which approximately 180 stripes were observed. [20] Figure 2e displays the time histories of the electron plasma (solid line) and cyclotron (dashed line) frequencies. The cyclotron frequencies are calculated from magnetic fields measured directly with onboard magnetometers, and the plasma frequencies are determined from the observed HF wave cutoffs described above. The SIERRA payload spends most of its flight in an overdense plasma (f pe > f ce ) region, except for a short period, s, when it passes through a region of underdense plasma. In contrast, the CHARM payload is in an underdense region throughout its flight. During the time of the stripe observations, SIERRA is in overdense plasma and CHARM in underdense plasma, so these emissions are not restricted to one region or the other. [21] Figure 3 shows khz spectrograms of 1 s intervals of both the SIERRA (left) and CHARM (right) rocket data, showing examples of stripes observed in each experiment, with power in color scale from 170 (black) to 130 (orange) 10 log V 2 /m 2 Hz for the SIERRA spectrogram (unfortunately no AGC data is available for CHARM, but the power is also on a 40 db scale for this spectrogram). Several parameters can be scaled from such spectrograms. Since the stripes are nearly linear, they are characterized by a slope determined from the intersection of the stripe feature with two fixed frequencies, for example 300 khz (460 khz) near the bottoms (tops) of the features, as shown in Figure 3 (left). This parameter measures the approximate slope of the stripes, averaging over slight departures from linearity. Stripes are also characterized by a spacing determined from the intersections of two consecutive stripe features with a fixed frequency, for example 400 khz near the middle of the features, as shown in Figure 3 (right). A third characteristic scaled from such spectrograms is the upper frequency bound defined as the frequency at which the power spectral density of the stripe drops to the background level, as shown in Figure 3 (right). Since these emissions often are obscured by the more intense auroral hiss at their lower frequencies, it is not generally possible to determine their lower frequency bound. [22] Figure 4 shows the results of scaling these parameters manually from 1 s spectrograms, for the SIERRA (left) and CHARM (right) data sets. Figure 4a shows scatterplots and histograms of the upper frequency bound. In the scatterplots, the altitude range km is on the x axis, frequency is on the y axis, and each point plotted represents an upper frequency bound measurement. The histogram shows the number of measurements for each frequency value, accumulated over the entire altitude range. The range of upper 5of17

6 Figure 4. Scatterplots and histograms of several stripe parameters for the (left) SIERRA and (right) CHARM data sets. Scatterplots and histograms of (a) the upper frequency bound, (b) slope, and (c) spacings. In the scatterplots, the altitude range km is on the x axis, frequency (slope/spacing) is on the y axis, and each point plotted represents an upper frequency bound (slope/spacing) measurement. The histogram shows the number of measurements for each frequency (slope/spacing) value, accumulated over the entire altitude range. frequency bounds observed in the two experiments is similar and mostly overlaps, although the frequency upper bounds observed in the SIERRA experiment tend to be slightly lower than those observed in the CHARM experiment. The occurrence rate peaks at 420 khz on SIERRA and at 540 khz on CHARM. The example case shown in Figure 3 also illustrates this difference. [23] Figures 4b and 4c show the distributions of frequency slopes and temporal spacings in the same format as Figure 4a. The ranges of these two parameters observed in the two experiments are nearly identical: khz/s and s, respectively. In the SIERRA experiment a large number of shorter spacings, around 0.05 s, are measured, whereas the spacings measured in the CHARM experiment are more evenly distributed over the range s. The similarity of these characteristics in the two experiments conducted 5 years apart in different auroral events using electric field sensors with different probe spacings and antenna configurations suggests that these emissions occur in a wide range of plasma conditions. Furthermore, the distribution of these parameters over a range suggests that they are natural emissions and not instrumental. [24] Figure 5a shows khz spectrograms of two trains of stripe emissions, observed in the SIERRA experiment at s (left) and s (right). The grayscale again shows electric field wave power, but for these spectrograms the AGC has been folded in, so the power is in absolute units, from (white) to (black) V 2 /m 2 Hz for the first example and from to V 2 /m 2 Hz for the second example. The stripes in the first example are distinct and show a clear periodicity, while the periodicity of the emissions in the second example is less obvious. The stripes in the second example illustrate a case of extreme variability in the stripe emission intensity, with intensity variations exceeding 10 db. [25] Figure 5b shows time series of the logarithm of the wave power integrated over the selected frequency bands in which the stripes are relatively unobscured by other emissions: khz (left) and khz (right), as indicated by white horizontal lines in each panel, with.0065 s cadence. The time series show that the variations in the power associated with the stripe occurrences are quasiperiodic. Fast Fourier transform (FFT) analysis confirms this: Figure 5c shows averages of three consecutive 128 point FFTs starting at 590 s (left) and s (right). Both spectra show a peak in the ELF frequency range, at Hz and indicated by vertical dashed lines. These time series and spectra represent the best examples out of several dozen 6of17

7 Figure 5. (a) Spectrograms of two different examples of stripe emissions, with frequency from 200 to 700 khz on the y axis and time from (left) 590 to s and (right) to s on the x axis. The frequency bands from which we calculate power spectral density are indicated. (b) Log of the time series of the average power spectral density in the indicated frequency band, with the same x axis as Figure 5a and with relative power in db on the y axis. (c) Average of three 128 point Fast Fourier transforms, which exactly covers the time shown in Figure 5a, with frequency from 0 to 50 khz on the x axis and relative power in db on the y axis. There is a very clear peak visible in the ELF frequency range, at Hz, in both examples. FFT analyses attempted. Typical spectra are broader and less distinctly peaked, although most of the power lies in the ELF range in every case. [26] The distribution of the stripe parameters across the broad range of values seen in Figure 4, in particular the variation in periodicity and slope of the stripes, provides evidence that these are in fact natural phenomena and not due to interference. This interpretation is reinforced by the correlation between the stripe features and the region of Alfvénically accelerated electrons associated with downward or mixed currents on the SIERRA flight, indicating a physical connection of these emissions to this region. The interpretation is further bolstered by the observation of these emissions on two distinct sounding rockets launched 5 years apart, with different probe spacings and antenna configurations. The stripe features on the two flights have similar but not identical characteristics, in both cases having a range of spacings, frequency bounds, and frequency time slopes, and occurring within a relatively narrow region of the aurora. [27] At first it seems curious that these signals appear to persist in this region but have not been reported by other auroral sounding rockets and satellites. However, in hindsight this is not unexpected, given that the sounding rockets discussed here were equipped with HFE receivers, which performed continuous full waveform measurements. Previous experiments detected HF waves with a variety of techniques, e.g., spectral analyzers [Pfaff et al., 1997; Beghin et al., 1989], broadband power analyzers [Boehm, 1990; Ergun et al., 1991], and waveform snatchers [Kintner et al., 1995; Bonnell et al., 1997]. These techniques are not suitable for detecting short duration, nonstationary features such as stripes. For example, broadband power monitors have no frequency resolution and would not see the characteristic slope and periodicity of the emissions, while waveform snatchers would typically only capture one measurement over the time of a stripe and so would also be unable to observe the characteristic time variation of these features. Furthermore, any waveform snatcher tuned to archive only the strongest signals would be biased against detecting stripes, which are typically not the strongest signals. [28] Satellite experiments such as those on FAST, Polar, Freja, Viking, and Aureol 1 suffer from further disadvantages because of their ten times higher speed. In the rocket data, the stripes tend to form clusters lasting a 1 3 s (a little over 2 s in the example of Figure 1), corresponding to1 3 kmif 7of17

8 interpreted as spatial. This implies that a satellite traverses the structure in s, which is marginal for recognizing the temporal signature of the stripes. Moreover, the resolution of satellite borne HF receivers is generally insufficient to resolve such short lived features. A possible exception is the burst mode of, for example, the FAST wave receiver, but even in this case the signature of the stripes would not be obvious: in burst mode FAST measures the HF electric field with 8 khz resolution at 30 sweeps per s and would therefore be able to marginally resolve these emissions in this mode, but the instrument is only in burst mode for 0.1% of the time in the auroral zone. The FAST burst mode also includes 0.25 s waveform snatches, which are also marginal for detecting stripes, especially if they are biased to favor large signals. The FAST waveform snatcher probably represents the best existing opportunity to confirm the stripes with an alternate instrument and platform, provided the stripe features occur at altitudes of a few thousand kilometers. Incidentally, no FAST data are available from the time of the SIERRA rocket experiment, and at the time of the CHARM rocket experiment FAST was at a distant location ( 73 geographic latitude and 262 geographic longitude). 4. Stripe Generation Mechanisms [29] Samara and LaBelle [2006a], who first reported the stripe features, suggested a model for their generation involving a localized source moving upward along the magnetic field at altitudes far above the rocket and generating oblique downward going whistler waves on the whistler wave resonance cone. Because the ray velocity of resonance cone whistler waves is more oblique for higher frequencies, the upward moving pattern of emitted waves would appear as decreasing frequency versus time at a spacecraft well below the emission region, regardless of which side of the source field line the spacecraft lies on. The proposed mechanism is similar to that which is generally accepted for explaining VLF whistler mode saucers, except that in the saucer case the source is relatively stationary and the satellite flies rapidly through the emission pattern, whereas in Samara and LaBelle s [2006a] stripes model, the rocket is relatively stationary and the pattern moves rapidly past it. Ray tracing analysis showed that such waves would reach the rocket with the observed stripe pattern for source altitudes 1300 (2600) km and source speeds 5000 (1000) km/s. The inspiration for this model was simulations showing that electron phase space holes emit resonance cone whistler mode waves as they decay [e.g., Oppenheim et al., 2001]. Electron phase space holes are prevalent at high altitudes along auroral field lines corresponding to the downward current region, and furthermore, in that region the phase space holes move upward as required by the model [e.g., Mozer et al., 1997; Ergun et al., 1998; Franz et al., 1998]. [30] As Samara and LaBelle [2006a] make clear, the connection between phase space electron holes and the stripe features is tenuous for several reasons. First, the altitudes and velocities of the electron holes necessary to produce the stripes are at the extremes of their known ranges. Second, while the stripes are observed to coincide with the region of Alfvénically accelerated electrons, which may be associated with downward current, there is no time delay between when the stripes turn on (and off) and when the electron precipitation pattern changes. Such time delay is expected from the model since the stripes propagate at an angle with respect to the magnetic field while the electrons propagate directly down the field line. Assuming a source region 1000 km above the rocket, an offset of 2 magnetic latitude associated with the propagation of these waves from the source region to the rocket location is expected [Samara and LaBelle, 2006a]. Of course, density structure such as a density enhancement in this region could result in ducting of the waves, which would reduce this offset, but no large density structures are observed at the rocket location. Finally, two dimensional simulations of electron holes show that the emitted electrostatic whistler mode waves have nearly perpendicular wave normal angles, whereas nearly parallel wave normal angles are required for the whistler waves to produce the stripe signature by propagation to lower (rocket) altitudes. [31] These shortcomings of the previously proposed generating mechanism for these emissions, together with new CHARM rocket observations confirming the stripes, motivate an investigation of other possible mechanisms. One promising possibility stems from the altitude dependence of the electron plasma and electron cyclotron frequencies in the topside ionosphere. Specifically, consider the conditions for a wave to Landau (cyclotron) resonate with upward going electrons in the topside ionosphere. For wave frequencies matching the plasma (cyclotron) frequency, an upward going electron of a given energy will resonate with successively lower frequency waves as it ascends. The different frequency waves would then arrive at the rocket at different times, with the time delay dependent on the speed, and therefore the energy, of the electron. In some cases, wave frequency dispersion may also be a factor, though typically this dispersion is far less than that because of the electron motion. There may be one particular electron energy for which the delay times for the various frequency waves exactly matches that of the observed stripe features. For the generation of the stripe emissions, the electrons would have to be accelerated in a series of pulses rather than a continuous beam in order to explain the periodicity of the emissions. One possible method for the acceleration of electrons to these energies with this periodicity is Alfvénic acceleration through the Alfvén resonator Landau Resonance With a Monoenergetic Upward Electron Beam [32] The observation of ev downgoing ions in the SIERRA experiment, coincident with the stripe emissions, suggests that a volt potential drop may exist on the field line of the emissions above the rocket. This potential drop would also give rise to a ev upward electron beam. Such an electron beam can generate Langmuir waves via Landau resonance. Since the resonant frequency f pe decreases with altitude in the topside ionosphere, lower frequencies would be excited at more delayed times, which agrees qualitatively with the dispersion of the stripe features. This scenario is illustrated in Figure 6. [33] To address whether the stripe emission frequencytime pattern can be explained by Langmuir wave emission 8of17

9 Figure 6. Depiction of the scenario where an electron beam generates waves by Landau resonance with different frequencies at different altitudes (acceleration region is assumed to be above the rocket altitude, where the downgoing ion beam is observed). For wave frequencies less than the plasma frequency, an upward beam of fixed energy will resonate with successively lower frequency waves as it ascends. The different frequency waves would then arrive at the rocket at different times, with the time delay dependent on the speed, and therefore the energy, of the electron. There may be one particular electron beam of energy for which the delay times for the various frequency waves exactly matches that of the observed stripe features. by an upward electron beam, consider a range of typical ionospheric density profiles, derived from Lysak and Hudson s [1987] model: z zo nz ðþ¼n 0 e ð Þ=h þ n 1 z 1:55 ; ð1þ where z is the altitude in kilometers above Earth s surface,the ionospheric parameters n 0, z 0,andh take on typical values (n 0 = , z 0 = , and h = ) [Kletzing,1994; Kletzing et al., 1998],andn 1 = , as given by a published fit to S3 3 data[lysak and Hudson, 1979]. The density model determines the difference in altitude between points where the plasma frequency exactly equals the upper and lower bound frequencies of the stripe emission. In this investigation, these frequencies are taken as 500 and 250 khz, respectively, as scaled from an example stripe emission observed at s after launch in the SIERRA experiment (Figure 3). This altitude difference together with the observed time delay (0.4 s) then determines the velocity, and therefore the energy, of the causative electron beam. [34] Applying this method, simulated frequency time signatures for Landau resonant waves associated with upgoing electron beams have been generated for density profiles of the form (1). For electron beam energies of 5 50 ev, the simulated frequency time signatures approximately match the frequency time signatures of the observed stripe features. This energy range approximately coincides with that of the downward ions observed in coincidence with the stripe emissions in the SIERRA experiment (Figure 2) and with that of upward electrons typically observed in the downward current region [Paschmann et al., 2003]. Since these emissions are generated as Langmuir waves at the plasma frequency, a mode conversion is required in order for them to propagate to the rocket in the whistler mode. For f pe < f ce, as occurs where these emissions would be generated, the Langmuir mode and whistler mode waves are connected, allowing efficient mode conversion between these modes [André, 1985]. For the resulting whistler waves to reach rocket altitudes, their frequency need only remain below the plasma frequency, which is true for any realistic density profile. [35] However, Landau resonance with upgoing electrons results in Langmuir waves with an upward directed k vector, and hence, if the whistler waves result from linear conversion, they would also have upward directed k vector. The waves could reach rocket altitudes if either (1) an unusual density gradient above the source reflects the whistler waves, or (2) the conversion mechanism between Langmuir and whistler waves is nonlinear, resulting in whistler mode waves with downgoing k vector. In the former case, the wave energy would become either considerably displaced or spread out from the field lines of the beam. The latter case seems significantly less probable than the linear conversion mechanism. Therefore, Landau resonance with a monoenergetic upgoing electron beam is an unlikely mechanism for the generation of the stripe emissions Cyclotron Resonance With Electron Conics [36] Just as with the generation of Langmuir waves via Landau resonance, electron cyclotron resonance can generate waves of decreasing frequency with increasing altitude, so that an upward moving source results in decreasing frequency with time as observed in the stripes emissions. However, the electron cyclotron mechanism requires a perpendicular anisotropy in the electron distribution, as opposed to the bump on tail in the parallel velocity of an 9of17

10 Figure 7. (a) An example of VIKING electron data showing a conic observed at 10,000 km altitude at auroral latitude [André and Eliasson, 1992, Figure 1]. (b) The results of test particles injected into a model of Alfvén waves in the auroral Alfvén resonator [from Thompson and Lysak, 1996, Figure 4]. The distribution shown is at the top of the ionosphere (2 R E altitude). (c) Model conic distribution at 3500 km, for a reflection height of 2500 km, with the resonant ellipse of the most unstable mode at this altitude superposed. upgoing monoenergetic electron beam. Electron conic distributions having the required perpendicular anisotropy have been observed along the auroral field lines [André and Eliasson, 1992; Chaston et al., 2002]. Figure 7a shows an example of VIKING electron data showing a conic observed at km altitude at auroral latitude [André and Eliasson, 1992, Figure 1]. André and Eliasson [1992, p. 1073] report that such conics are frequently observed by the Viking satellite at all magnetic local times, at altitudes from a few thousand kilometers to 13,500 km (apogee). Thompson and Lysak [1996] proposed a mechanism to explain these electron conics, whereby electrons accelerated downward by Alfvén waves at the bottom of the Alfvén wave resonator reflect in the converging magnetic field and appear as upgoing conics, because the parallel propagating electrons in the loss cone are lost and are not reflected. Figure 7b shows the results of test particles injected into their model of Alfvén waves in the auroral Alfvén resonator [from Thompson and Lysak, 1996, Figure 4]. The distribution shown is at the top of the ionosphere (2 R E altitude) and hence directly comparable to the VIKING observations shown in Figure 7a. [37] The conic feature survives to high altitudes despite the adiabatic evolution of the electron distribution, which converts perpendicular to parallel energy as the electrons ascend in the diverging magnetic field. Significantly, Thompson and Lysak s [1996] test particle simulations predict that Alfvénically generated conics generated in this fashion can be modulated according to the period of the Alfvén waves standing in the resonator, 1 Hz in the case reported [Thompson and Lysak, 1996, Figure 6]. This frequency can be in the ELF range depending on the parameters of the resonator. In this frequency range such waves are often called Alfvén ion cyclotron waves [Temerin et al., 1986] or just ion cyclotron waves, as their frequency is typically close to the oxygen cyclotron frequency, in this case 19 Hz at 2500 km and 9 Hz at 5000 km. Temerin et al. [1986] show that these Alfvén ion cyclotron waves in the resonator act in the same way as the lower frequency waves and similarly accelerate electrons, which are modulated by the frequency of the waves. Hence, waves associated with electron conics generated by Alfvénic acceleration followed by reflection show promise to explain naturally the quasi periodicity of the stripes emissions. This scenario is illustrated in Figure 8 and is the basis for the analysis in sections and [38] The cyclotron resonant condition, the energy of an electron cyclotron resonant wave with frequency f, is given by E ¼ 1 = 2 m e c 2 f 2 ðf f ce Þ 3 ; ð2þ ðf f ce Þ f f 2 where f ce is the electron cyclotron frequency and f pe is the electron plasma frequency [Parks, 2004; Kennel and Petschek, 1966]. Unlike the Landau resonance, cyclotron resonance with upgoing electrons results in downgoing waves, which allows for the propagation of these waves to rocket altitudes. In sections and we investigate the frequency time signatures of waves resulting from electron cyclotron resonance at different altitudes and frequencies by an upward electron beam of fixed energy, using a variety of possible density profiles and making two different assumptions for the wave mode. In all cases we model the electron cyclotron frequency as a decreasing function of altitude: 4: f ce ¼ r 3 ; ð3þ where f ce is in khz and r is in km. This model decreases as 1/r 3 and matches the measured magnetic field at the rocket altitude Cyclotron Resonance Into Whistler Mode Waves [39] The requirement that the cyclotron resonant waves connect to the whistler mode at the high source altitudes where f ce = khz implies that the electron plasma frequency must be greater than or equal to the cyclotron resonant frequency at those altitudes. This requires considering somewhat unrealistic electron density profiles. The electron cyclotron resonant frequencies at each altitude for electron beams of various energies were calculated for a range of such density profiles. Given the altitude at which the different frequencies are resonant for a particular electron energy, one can calculate the time delay between the frequencies using the speed of the electron and the differ- pe 10 of 17

11 Figure 8. Depiction of the scenario where an electron conic generates waves by cyclotron resonance with different frequencies at different altitudes. As with the Landau resonance depicted in Figure 6, for wave frequencies less than the plasma frequency, an upward beam of fixed energy will resonate with successively lower frequency waves as it ascends. The different frequency waves would then arrive at the rocket at different times, with the time delay dependent on the speed, and therefore the energy, of the electron. ence in distance the electron had to travel to reach the source region from the acceleration region, which is assumed to be at the same altitude for all the electrons. The time delay resulting from the propagation of the waves from the source region to the rocket is negligible because for all frequencies the waves travel much faster than the electrons. [40] The calculated frequency time signature based on 100 ev electrons is nearly identical to that of the observed stripes. The upper and the lower frequency bounds of the calculated frequency time signature are set by the density profile as expected because whistler mode waves with f < f pe < f ce are bounded above by the electron plasma frequency. These results suggest that if cyclotron resonance into whistler mode is responsible for the stripe emissions, the sharp upper frequency bound observed on many of the emissions could be set by the local plasma frequency in the region in which they are generated. Therefore, observations of the stripes at rocket altitudes could provide a means of remotely sensing the plasma density at much higher altitudes in the topside ionosphere. [41] However, the density profiles necessary to generate the emissions in the whistler mode by cyclotron resonance are unusually high for the topside ionosphere, requiring f pe f ce up to 5000 km altitude. Typical values of f pe at 5000 km are roughly an order of magnitude lower [Kletzing et al., 1998], and the measured value of f pe at the SIERRA rocket location is consistent with the nominal value. In extraordinary cases, such as one example encountered by the IMAGE satellite, the required conditions occur (R. F. Benson, personal communication, 2008), but the extreme rarity of the necessary conditions casts strong doubt on the cyclotron resonance into the whistler mode as a candidate mechanism for the stripe emissions Cyclotron Resonance Into Z Mode Waves [42] For typical conditions at km the cyclotron resonant frequency is considerably higher than f pe.in this regime the whistler mode is inaccessible, but the cyclotron resonance can generate Z mode waves. Downward propagating Z mode waves can then reach altitudes where f pe becomes greater than the wave frequency, where they can mode convert to whistler mode waves, which propagate down to rocket altitudes [Oya et al., 1985; Budden, 1985; Santolík et al., 2001]. Such a mechanism was proposed by Oya et al. [1985], who called it leaked auroral kilometric radiation ( leaked (AKR) ) and reported relevant observations from the low Earth orbiting EXOS C satellite. If such a mode conversion and propagation to low altitudes is possible, the stripe emissions could result from cyclotron resonance with upgoing electrons even in the presence of a realistic density profile for which f pe < f ce at altitudes where f ce = khz. [43] To test the plausibility of this mechanism we start with an electron population that includes both the background isotropic distribution and the upgoing electron conic distribution generated by downgoing Alfvénically accelerated electrons reflected from the ionosphere. We then calculate the growth rate of Z mode waves due to cyclotron resonance with these electrons at various altitudes to determine if Z mode waves can be generated by such electrons. Finally, we calculate the time delay of the different frequencies on the basis of the resonant altitude and the parallel velocity of the electrons, which changes with altitude according to the conservation of the second adiabatic invariant m, and compare the resulting frequency time signature with that of the observed stripes. 11 of 17

12 Figure 9. Local temporal growth rate at selected altitudes, plotted versus propagation angle and normalized frequency f/f ce. Angles greater than 90 correspond to downgoing waves. [44] The electron population is modeled as a relatively cold isotropic background distribution superimposed with an electron conic distribution. The background electron density is given by the same Lysak and Hudson [1987] model used for the Landau resonance calculations in section 4.1 (equation (1)), with typical values for the ionospheric parameters: n 0 =6 10 4, z 0 = 318, and h = 383 [Kletzing, 1994]. The electron conic distribution is modeled after the Viking observations [André and Eliasson, 1992], shown in Figure 7a, and the test particle calculations of reflected Alfvénically accelerated electron conics [Thompson and Lysak, 1996] shown in Figure 7b. The model starts as a ring distribution at a selected reflection altitude, for example 2500 km. The distribution at this altitude is perpendicular to the Earth s magnetic field. The distribution then evolves with altitude in order to conserve the magnetic invariant m. The electron conic density is set to be 0.01% of the electron density at the source and constant at all altitudes above the source height, the background electron density is set by (1), and the cyclotron frequency is set by (3). Figure 7c shows an example model conic distribution at 3500 km, for a reflection height of 2500 km. [45] Evaluating the stability of Z mode waves under these conditions requires use of the full dispersion relation for Z mode waves to calculate the index of refraction and the temporal growth rate. Appendix A describes the basis of numerical calculations of the temporal growth rate. Figure 9 shows the local temporal growth rate at selected altitudes, plotted versus propagation angle and normalized frequency f/f ce. Angles greater than 90 correspond to downgoing waves. The most unstable waves have nearly perpendicular propagation, but there is a significant amount of growth of downward directed waves. Figure 9 shows that Z mode waves are unstable over a wide range of altitudes, from the source altitude of 2500 km up to 4500 km, despite the adiabatic folding up of the electron conic. Above 4500 km, the cyclotron resonant frequency becomes lower than the lowest observed stripe frequencies. These calculations include the folding up of the electron conic because of the conservation of m but not the feedback of the waves on the electron distributions. For reference, Figure 7c shows the resonant ellipse of the most unstable mode at 3500 km, superposed on the electron conic distribution. The ellipse represents the parallel and perpendicular velocities for which the cyclotron resonance condition (2) is met, for frequency f = 452 khz, f/f ce = , and wave propagation angle = [46] Provided that the Z mode to whistler mode conversion occurs relatively quickly, or equally quickly for all frequencies, the frequency time signature the waves exhibit at rocket altitudes depends primarily on the electron travel time rather than the wave travel time. The time delay for the different frequencies can thus be calculated in the following manner. The upward distance that the electrons travel before 12 of 17

13 Figure 10. (left) A khz spectrogram of SIERRA data, from 620 to 621 s after launch, showing several observed stripes. (right) Simulated frequency time signature resulting from a 300 ev electron reflected at a source altitude of 2000 km. emitting a wave of a given frequency is determined by the reflection altitude and the magnetic field profile, which determines both the altitude of cyclotron resonance for that frequency and the altitudinal variation of the upward electron speed due to the conservation of m. The density profile also affects the cyclotron resonance altitude dependence, but only weakly. The reflection altitude can be selected to optimize the resulting frequency time signature, but must be above the rocket location ( 700 km) and below the altitude where the highest observed stripe frequency matches the cyclotron resonant frequency ( 3000 km). Because the electron s energy is perpendicular where it reflects, the parallel velocity of the electron as a function of altitude above the reflection height is determined by the electron s total energy and the conservation of m. The total electron energy can also be selected to optimize the results, within the expected energy range of Alfvénically accelerated auroral electrons ( 1 ev 5 kev). For each 1 km step in altitude above the reflection height, the time required for the electron to cover that step is calculated by averaging the parallel velocity at the top and bottom of the 1 km interval and multiplying by 1 km. The total time delay is determined by summing the time delays for each 1 km interval between the reflection height and the altitude of cyclotron resonance for a selected frequency. Stepping up in altitude as in these calculations assumes that the field line is roughly linear and vertical in this region. As a check on the viability of this assumption, the arc length of the L = 8.54 (70 ) field line between the altitude of 2000 and 5000 km was calculated and is equal to 3003, or 0.1% greater than the 3000 km length assuming a linear field line. The polar angle increases over this distance from to 27.20, which results in a magnetic field strength slightly less than that calculated assuming a constant angle of 20 (vertical propagation along the 70 field line): 3.0% lower at 2000 km and 7.1% lower at 5000 km. [47] Figure 10 (left) shows a 1 s khz spectrogram of the SIERRA data, from 620 to 621 s after launch, showing several observed stripes, with power in grayscale from 170 (white) to 110 (black) 10 log V 2 /m 2 Hz. Figure 10 (right) shows the simulated frequency time signature resulting from a 300 ev electron reflected at a source altitude of 2000 km, with the same frequency and time scale as Figure 10 (left). The simulated emission matches the frequency time signature of the observed stripe emissions, lasting 0.4 s and decreasing roughly linearly from 500 to 300 khz. The slope of the simulated emission depends primarily on the electron energy; the resulting signature from a 300 ev electron matches this observed stripe emission most closely. For the range of observed stripe slopes ( khz) the electron energy range required is ev, within the typical energy range of Alfvénically accelerated electrons. In addition, there is a departure from linearity in many of the observed stripe emissions, particularly those shown in Figure 10 (left), in which there is a kink in the middle of the stripes at 400 khz before and after which they decrease in frequency approximately linearly. Interestingly, the simulated stripe also shows a small kink near the middle frequencies and is more linear above and below this kink. The kink in the observed stripe emissions is more pronounced, but many of the observed stripes have more subtle departures from linearity similar to that of the simulated stripe. [48] It is promising that the simulated stripe emission matches not only the frequency range and frequency time slope of the observed emissions but also the departures from linearity, and it is important to investigate how these departures arise. The inflection, or kink, in both the observed and simulated stripe emissions is a result of the interplay between two conflicting effects, both arising from the magnetic field, changing as a function of altitude. Figure 11 (left) shows the cyclotron frequency as a function of altitude. The cyclotron frequency is directly proportional to the magnetic field, and thus decreases as r 3. This leads to a gradient in f ce which decreases with altitude, and the effect of this on the stripe frequency time signature is to cause the slope to decrease with decreasing frequency. If the parallel velocity of the electrons is kept constant with altitude, the 13 of 17