Abstract
A theoretical study is presented of the electrostatic electron cyclotron instability involving Bernstein modes in a magnetized plasma. The presence of a tenuous thermal ring distribution in a Maxwellian plasma decreases the frequency of the upper hybrid branch of the electron Bernstein mode until it merges with the nearest lower branch with a resulting instability. The instability occurs when the upper hybrid frequency is somewhat above the third, fourth, and higher electron cyclotron harmonics, and gives rise to a narrow spectrum of waves around the electron cyclotron harmonic nearest to the upper hybrid frequency. For a tenuous cold ring distribution together with a Maxwellian distribution an instability can take place also near the second electron cyclotron harmonic. Noise-free Vlasov simulations are used to assess the theoretical linear growth-rates and frequency spectra, and to study the nonlinear evolution of the instability. The relevance of the results to laboratory and ionospheric heating experiments is discussed.
Highlights
The interest in cyclotron harmonic phenomena in magnetized plasma [1,2,3,4,5,6,7,8,9] were triggered by the observation of emissions, absorption, and resonances at harmonics of the electron cyclotron frequency in laboratory experiments and satellite sounding experiments [10, 11]
Recent laboratory experiments [27, 28] using a mirror confined plasma have shown a number of different instabilities and emissions, including oscillations near the second electron cyclotron harmonic attributed to the presence of thermal ring distributions [12]
We have carried out a theoretical study of the electron cyclotron instability due to the sum of a Maxwellian core distribution and a thermal ring or deltafunction ring electron distribution
Summary
The interest in cyclotron harmonic phenomena in magnetized plasma [1,2,3,4,5,6,7,8,9] were triggered by the observation of emissions, absorption, and resonances at harmonics of the electron cyclotron frequency in laboratory experiments and satellite sounding experiments [10, 11]. Maser instabilities due to loss-cone or ring-like electron distributions give rise to excitations in the Z (slow X) mode or upper hybrid mode branch for ωpe ωce [13], while radiation in the fast X mode branch near ωce dominates in the opposite limit The latter has been studied extensively in the framework of auroral kilometric radiation [21], solar and stellar radio bursts [22], etc, and via simulations and laboratory experiments [23,24,25]. The aim of this paper is to carry out a theoretical and numerical study of the electrostatic electron cyclotron instability and to discuss its relevance to spectral features of stimulated electromagnetic emissions escaping the plasma in laboratory [27, 28] and ionospheric heating [14] experiments. A parallelized Vlasov code [38, 39] in two spatial and two velocity dimensions (x, y, vx, vy), plus time, is used to carry out noise-free simulations to assess the theoretical results and to study the nonlinear saturation of the instabilities
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