Beam-excited whistler waves at oblique propagation with relation to STEREO radiation belt observations

Abstract

Abstract. Isotropic electron beams are considered to explain the excitation of whistler waves which have been observed by the STEREO satellite in the Earth's radiation belt. Aside from their large amplitudes (∼240 mV/m), another main signature is the strongly inclined propagation direction relative to the ambient magnetic field. Electron temperature anisotropy with T e⊥ > T e , which preferentially generates parallel propagating whistler waves, can be excluded as a free energy source. The instability arises due to the interaction of the Doppler-shifted cyclotron mode ω = − e + kV b cosθ with the whistler mode in the wave number range of kc/ω e ≤ 1 (θ is the propagation angle with respect to the background magnetic field direction, ω e is the electron plasma frequency and e the electron cyclotron frequency). Fluid and kinetic dispersion analysis have been used to calculate the growth rate of the beam-excited whistlers including the most important parameter dependencies. One is the beam velocity (V b ) which, for instability, has to be larger than about 2V Ae , where V Ae is the electron Alfvén speed. With increasing V Ae the propagation angle (θ) of the fastest growing whistler waves shifts from θ ∼ 20 • for V b = 2V Ae to θ ∼ 80 • for V b = 5V Ae . The growth rate is reduced by finite electron temperatures and disappears if the electron plasma beta (β e ) exceeds β e ∼ 0.2. In addition, Gendrin modes (kc/ω e ≈ 1) are analyzed to determine the conditions under which stationary nonlinear waves (whistler oscillitons) can exist. The corresponding spatial wave profiles are calculated using the full nonlinear fluid approach. The results are compared with the STEREO satellite observations.

Whistler-Langmuir oscillitons and their relation to auroral hiss

“…Subsequent kinetic simulations by Sydora et al (2007) have shown that during the nonlinear saturation of the temperature anisotropy instability a significant wave number shift (from large k values) to the Gendrin point (where phase and group velocity coincide) takes place accompanied by the formation of whistler oscillitons. As discussed in a recent paper by Sauer and Sydora (2010), a similar process happens during beam excitation of obliquely propagating whistler modes. The importance of whistler Gendrin modes has also been pointed out recently by Verkhoglyadova and Tsurutani (2009) showing that the measured propagation direction of a chorus event in the Earth's magnetosphere agrees well with the calculated Gendrin angle.…”

“…4 to study this mechanism of instability. As suggested by other whistler wave studies (Sydora et al, 2007;Sauer and Sydora, 2010), results of particle-in cell (PIC) simulations are presented in Sect. 5 which show that WL oscillitons are formed in the quasi-stationary saturated state of the beam-plasma interaction.…”

“…The dispersion relation for high-frequency waves in a cold plasma in which the electron cyclotron frequency is larger than the electron plasma frequency ( e > ω e ) is derived using the same tensor formalism as described in the recent paper by Sauer and Sydora (2010). The only difference is that the displacement current has to be taken into account and therefore, the ratio between electron cyclotron frequency and electron plasma frequency (G = e /ω e ) appears as an additional parameter.…”

“…4) belongs to the phase velocity maximum of the whistler mode at kc/ω e > 1, like in a plasma with G<1 (see Fig. 7 in Sauer and Sydora, 2010), and will not further be considered here.…”

Multipoint observations of plasma phenomena made in space by Cluster

“…Hwang et al (2014a), using both Cluster observations and linear theory, further explored wave enhancements behind DFs and found that two wave modes: a high-frequency beam mode and a low-frequency whistler mode, are associated with a localized electron beam. The generation of whistlers is associated with the electron beam components that can persist for a significant time before being quickly thermalized (Sauer and Sydora 2010). Considering the earthward motion of the DF flux tube, Fermi acceleration related to a shortening of the magnetic field lines contributes to preventing such electron beams from being rapidly thermalized, which can generate whistlers that can in turn energize particles, possibly leading to ion bulk heating.…”