The characteristics of hiss-like and discrete (rising and falling tones) whistler-mode waves in the lower-band wave frequency range (0.1–0.5 of equatorial electron gyrofrequency) are investigated using waveform data from near-equatorially orbiting multiple THEMIS spacecraft outside the plasmasphere. Statistical results show that wave polarization properties of hiss-like emissions are similar to rising tones, but are significantly different from falling tones. The magnetic wave amplitudes of hiss-like bands and rising tones are generally larger than those of falling tones. Wave normal angles of broadband hiss-like emissions and rising tones tend to be quasi field-aligned, whereas falling tones are very oblique. Importantly, discrete emissions including rising and falling tones are predominantly observed in the region of lowfpe/fce(the ratio of plasma frequency to electron gyrofrequency), whereas hiss-like bands alone preferentially occur in the region of highfpe/fce. These important features of hiss-like and discrete whistler-mode emissions should be considered when evaluating their interactions with energetic electrons.
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 The importance of the wave structure and coherence, i.e., whether it tends to be more discrete or hiss-like, lies in the basic mode of interaction which the wave will undergo with energetic electrons. For example, discrete coherent chorus emissions tend to cause non-linear effects such as phase trapping [Helliwell, 1967; Nunn, 1974a; Bortnik et al., 2008], whereas the interaction between hiss-like emissions and electrons is more akin to a random walk in velocity space, and could be described by quasi-linear theory [Kennel and Petschek, 1966; Horne et al., 2005]. Both the acceleration and precipitation of energetic electrons will reflect this interaction, and could lead to vastly different net effects on the radiation belts [e.g., Albert, 2002; Tao et al., 2012].
 Previous studies showed that wave polarization properties of hiss-like emissions and discrete chorus emissions are somewhat similar [e.g.,Hattori et al., 1991; Santolík et al., 2009, 2010]. The majority of these whistler-mode emissions observed outside the plasmasphere and inside the magnetopause are found to have high polarization ratio, which is defined as the ratio of polarized power to total power. Therefore, these whistler-mode emissions outside the plasmapause are different from “turbulent-like” incoherent plasmaspheric hiss, which typically has low polarization ratio [Thorne et al., 1973; Tsurutani et al., 2011]. It is generally believed that these whistler-mode waves outside the plasmasphere are generated by the cyclotron resonance with energetic electrons (1–100 keV) injected from the plasmasheet [Kennel and Petschek, 1966; Tsurutani and Smith, 1977].
 Although it is generally known that whistler-mode waves outside the plasmasphere exhibit hiss-like or discrete emissions, the conditions and regions in which each type of emission is dominant, have not yet been well documented. Therefore, in the present study we investigate typical properties and preferential regions of each type of emission, which are essential for understanding the generation mechanism of whistler-mode waves and their interaction with electrons.
2. THEMIS Wave Analysis
 We utilized a large dataset of whistler-mode waves observed by the multiple THEMIS spacecraft [Angelopoulos, 2008] in the near-equatorial magnetosphere from June 2008 to May 2012. Three components of wave magnetic field are measured with the Search-Coil Magnetometer (SCM) [Le Contel et al., 2008] on THEMIS with wave frequencies up to 4 kHz. The Electric Field Instrument (EFI) measures the electric field in three orthogonal directions from DC up to ∼8 kHz [Bonnell et al., 2008]. Several waveform bursts with each lasting ∼8 sec are collected per day simultaneously from electric and magnetic fields with a sampling frequency up to ∼16 kHz. Wave bursts have not been triggered completely randomly, but this will not affect our essential conclusion since we investigated the relative occurrence of each type of emission, as discussed in Section 3. Whistler-mode wave frequencies are normalized to the equatorial electron gyrofrequency, which is obtained by mapping the local electron gyrofrequency (calculated based on the background magnetic field intensity measured by the Flux-Gate Magnetometer (FGM) [Auster et al., 2008]) into the magnetic equator using dipole magnetic field model for simplicity. The total plasma density is inferred from the spacecraft potential and the electron thermal speed following the method described by Li et al. .
 Detailed wave polarization properties of whistler-mode waves were analyzed using three components of the wave magnetic field (converted into the magnetic field-aligned coordinates) from the waveform data following the method ofBortnik et al.  (essentially an implementation of Means ). Since we used only magnetic field components, there is a 180° ambiguity in the wave normal determination, and we converted all wave normal directions into values less than 90°. These obtained wave polarization properties have a time resolution of ∼0.016 sec. For waves with sufficiently large values of the polarization ratio (Rp > 0.9), the wave polarization method of Bortnik et al. provides reliable polarization parameters. Since whistler-mode waves outside the plasmasphere are normally highly polarized and have high ellipticity (E), in our analysis we only recorded polarization parameters for waves with Rp > 0.9 and E> 0.7. Here we investigated typical properties of whistler-mode waves in the lower band with wave frequencies of 0.1–0.5fce_eq. Note that the hiss-like emissions with high polarization ratio included in our study are substantially different from plasmaspheric hiss, which has low polarization ratio.
3. Observational Results
 Whistler-mode waves exhibit either hiss-like or discrete structure when viewed in the frequency-time spectrogram.Figures 1a–1cshow representative examples of a hiss-like band, a rising tone, and a falling tone respectively. Hiss-like emissions exhibit a banded structure and discrete rising (falling) tones show a clear increase (decrease) in frequency with time. Hiss-like emissions and rising tones are quasi field-aligned with wave normal angles that are mostly less than 20°, whereas falling tones are very oblique, as shown inFigure 1. A flag was used to identify whether the whistler-mode emissions are hiss-like, rising or falling tones (Figure 1, top). The flag is equal to 1 for rising tones, and −1 for falling tones, and 0 for emissions that are ambiguous. At each recording time, the frequency at which the magnetic field spectral density maximized (over the lower-band wave frequency range of 0.1–0.5fce_eq) was recorded after smoothing over the adjacent three points and is shown as the black solid line in Figure 1 (middle). Subsequently, the sweep rate at each point was calculated using the adjacent 7 points on the black line. If a positive (negative) sweep rate is maintained for longer than ∼0.1 sec, the flag is set to 1 (−1); otherwise it is equal to 0.
 Over the period from June 2008 to May 2012, ∼10000 wave bursts were recorded from THEMIS A, D, and E in the region between 5 and 10 RE, after excluding the data inside the plasmapause or outside the magnetopause according to the criteria by Li et al. . The majority of the data were collected in the near equatorial region with magnetic latitude less than 15°. The number of wave bursts regardless of the presence of whistler-mode waves in the L-MLT domain is shown inFigure 2a. Here one wave burst is defined as one recording lasting ∼8 sec, as shown in Figures 1a–1c. Figure 2bshows the number of wave burst, during which whistler-mode waves were observed. In each wave burst which recorded whistler-mode waves, we also calculated the ratio of plasma frequency to local electron gyrofrequency (fpe/fce) and the statistical results of the mean value in each bin is shown in Figure 2c. The value of fpe/fceis relatively smaller at lower L-shells and 03-12 MLT and larger in the noon-dusk sector where the plume preferentially forms.
 For each wave burst that recorded whistler-mode emissions, we categorized it into a hiss-like band, a rising tone, or a falling tone according to its frequency-time spectrogram using the flag (Figure 1, top) and further confirmed it by visual inspection. Note that closely packed rising (falling) tones were classified into the rising (falling) tone category. For an event where discrete emissions and a hiss-like band coexist, which is quite often, it was categorized into discrete rising or falling tone, since the wave amplitude of discrete elements is typically stronger than that of the hiss-like band. Therefore, a whistler-mode emission categorized into hiss-like band in our study is purely a hiss-like band without clear discrete elements, as shown inFigure 1a. At each data point with Rp > 0.9 and E > 0.7, we recorded parameters potentially distinctive for each type of emission, including the value of wave normal angle, wave amplitude (integrated over 0.1–0.5 fce_eq), and fpe/fce. After collecting these parameters from the wave burst data over the period from June 2008 to May 2012, we investigated their distribution in each category, as shown in Figure 3. Note that in each categorized event, the flag was used to select wave polarization properties for the corresponding wave category. This means that the polarization properties of rising (falling) tones were recorded during the time interval when the flag is equal to 1 (−1) and those of hiss-like emissions were recorded when the flag is equal to 0. Wave amplitudes of hiss-like emissions peak in the range of 30–100 pT, which is slightly weaker than those of rising tones peaking at 30–300 pT. However, the amplitudes of falling tones are much weaker, with >50% having wave amplitudes less than 30 pT. The wave normal angle of hiss-like emissions tends to peak at <20° with a small second peak at large angles (60°–80°). Similarly, wave normal angles of rising tones are preferentially smaller than 20°. In sharp contrast, falling tones are very oblique with the peak occurrence rate at 70°–80°, which is consistent withLi et al. [2011a]. Interestingly, hiss-like emissions alone tend to occur in the region with high values offpe/fce (>4), whereas discrete emissions of rising and falling tones are preferentially observed in the region with low values of fpe/fce (<6). Compared to rising tones, falling tones prefer to occur in the region of even lower values of fpe/fce.
 In each wave burst, during which whistler-mode waves were recorded, we calculated the root mean square (RMS) of wave amplitude during the intervals with the corresponding flag. For example, in each wave burst of rising tone category, RMS wave amplitudes were calculated for the intervals during which the flag is equal to 1. In each category, we further sorted them by various RMS magnetic wave amplitude ranges.Figures 4a–4cshow the relative occurrence rate, which in each bin is defined as the ratio of total number of wave bursts in the corresponding emission category and wave amplitude ranges to the total number of wave bursts which recorded whistler-mode emissions regardless of the emission type and wave amplitude. Note that the relative occurrence rate (rather than the absolute occurrence rate) is shown in order to focus on the dominance of each type of whistler-mode emission in the L-MLT domain. Modest hiss-like emissions alone preferentially occur in the noon-dusk sector and at higher L-shells in the postmidnight-noon sector. However, extremely strong hiss-like emissions are predominantly observed from the premidnight to the postdawn sector. In contrast, rising tones preferentially occur at lower L-shells from the midnight to the afternoon sector. Strong rising tones are confined toL< 7 on the nightside and extend to slightly higher L-shells on the dayside. Extremely strong rising tones (Bw≥ 300 pT) are confined to even lower L-shells (<6) in the midnight-noon sector. The relative occurrence rate of falling tones is generally smaller than that of hiss-like emissions or rising tones especially for strong wave amplitudes (>50 pT). Falling tones with modest wave amplitudes (10–50 pT) preferentially occur in the dawn-noon sector atL < ∼8. Interestingly, the preferential region of discrete emissions including both rising and falling tones is roughly consistent with the region with lower fpe/fce, that is at lower L-shells from postmidnight to noon, as shown inFigure 2c. In contrast, the dominant region of modest hiss-like band alone generally agrees well with the region of higherfpe/fce, that is in the noon-dusk sector and at relatively higher L-shells in the postmidnight-noon sector. In the region of modest values offpe/fce, events of both hiss-like band alone and discrete elements are likely to occur. Since the events, in which both hiss-like and discrete emissions were observed, were sorted into rising or falling tone category, the actual relative occurrence rate of hiss-like band is higher than that shown inFigure 4a in the region where discrete emissions are also observed.
4. Summary and Discussion
 In the region between the plasmapause and the magnetopause, particularly at 5–10 RE, whistler-mode emissions exhibit either hiss-like bands or discrete elements (rising or falling tones). We investigated the characteristics of hiss-like bands and discrete rising and falling tones and the preferential region where each type of emission occurs. The typical amplitude of hiss-like emissions and rising tones is generally larger (a few tens of pT to a few hundreds of pT) than that of falling tones (< tens of pT). The wave normal angle of hiss-like bands and rising tones tends to be quasi field-aligned (<30°), whereas falling tones are very oblique with a peak occurrence rate at 70°–80°. Discrete rising or falling tones preferentially occur in the region with lower values offpe/fce, at lower L-shells from postmidnight to noon. However, hiss-like emissions alone are predominantly observed in the region with higher values offpe/fce.
 Our statistical results show that wave polarization properties of hiss-like bands and rising tone chorus are very similar, consistent withHattori et al.  and Santolík et al. [2009, 2010]. This similarity suggests that the generation mechanism of the hiss-like band and discrete chorus may have a close relationship. Previous studies [e.g.,Nunn, 1974b; Koons, 1981; Hattori et al., 1991; Trakhtengerts et al, 2001] suggested that a wavelet existing near the upper edge of the hiss-like band may be able to generate a discrete chorus emission.Omura and Nunn  and Hikishima and Omura  showed that in order to trigger rising tones the triggering wave amplitude should be larger than the threshold wave amplitude but should not deviate much from the optimum wave amplitude. We suggest that the generation of rising tone chorus may need an initial wave amplitude (produced by linear wave growth) close to its optimum value, but further investigation of this relationship is beyond the scope of this paper.
 Previous statistical studies on the global distribution of chorus wave intensity [e.g., Meredith et al., 2003; Li et al., 2011b] include both hiss-like and discrete emissions. Previous studies of whistler-mode wave-particle interactions obtained diffusion coefficients by applying quasi-linear diffusion theory assuming the waves as incoherent broadband emissions [Kennel and Petschek, 1966; Horne et al., 2005]. However, for coherent, discrete narrowband emissions, the usual quasi-linear diffusion may not provide an accurate description of the wave-particle interaction and nonlinear wave-particle interaction becomes crucial [Inan et al., 1978; Albert, 2002; Omura and Summers, 2006; Omura et al., 2007; Bortnik et al., 2008; Tao et al., 2012]. Therefore, the typical features of hiss-like and discrete whistler-mode emissions should be considered and the interaction may need to be treated differently. Our analysis provides characteristics of those distinctive emissions, which are important for evaluating the effect of whistler-mode waves on energetic electrons.
 This research was funded in part by NASA grants NNX11AD75G, NNX11AR64G, NNX08AI35G, and NAS5-02099, and NSF grant AGS-0840178. The authors acknowledge O. Le Contel and A. Roux for use of SCM data; J. W. Bonnell and F. S. Mozer for use of EFI data; and K. H. Glassmeier, U. Auster, and W. Baumjohann for the use of FGM data provided under the lead of the Technical University of Braunschweig and with financial support through the German Ministry for Economy and Technology and the German Center for Aviation and Space (DLR) under contract 50 OC 0302.
 The Editor thanks David Nunn and an anonymous reviewer for assisting in the evaluation of this paper.