Stabilization of the fan instability: Electron flux relaxation

Abstract

This paper presents some relevant simulation results on the interaction between electrostatic waves and suprathermal electron fluxes at anomalous cyclotron and Landau resonances. In particular, the case of a dense and continuous wave spectrum is studied. It is shown that, after the waves excited by the fan instability at anomalous cyclotron resonances have reached a first saturation stage due to particle trapping, the process of “dynamical resonance merging” takes place, which leads to a strong amplification of the waves’ amplitudes. The Landau resonances do not play an essential role in the total energy exchange between the particles and the waves, as they mainly help to smooth the peaks rising during the evolution of the electron parallel velocity distribution and contribute to damping. Moreover, the paper shows that at the asymptotic stage of the interaction, when the waves’ amplitudes are saturated and the electron flux is relaxed, some physical features clearly do not fit the predictions of the well-known quasilinear theory. The careful examination of a huge number of trajectories of particles moving in the effective field of the wave packet allows to state that most of the particles involved in the resonant interactions are trapped by several waves simultaneously. In this so-called “multitrapping” process, the particles perform complex oscillatory motions which are far from what is expected from the quasilinear theory, where the diffusive behavior of the particles in the velocity space results from small successive random steps.

Loss-cone instability: Wave saturation by particle trapping

“…The numerical simulation results and the analytical developments discussed below are all based on a threedimensional theoretical model [19][20][21][22] that describes the quasilinear evolution of electrostatic waves resonantly interacting with particles in a magnetized plasma ͑nonlinear wave-wave interactions are neglected compared to wave-particle ones͒. In this model, we suppose that the plasma electrons can be divided in two groups: a thermal bulk of density n 0 and a suprathermal flux of resonant particles with a much smaller density: n res Ӷ n 0 .…”

“…As one can separate the Hamiltonian ͑1͒ as H = H 1 + H 2 , where H 1 = ͚ p=1 N ͓P p + eA 0 ͑r p ͒ / c͔ 2 / 2m e , the symplectic operator 23,24 L͑⌬t͒ = L 1 ͑⌬t / 2͒L 2 ͑⌬t͒L 1 ͑⌬t / 2͒ + o(͑⌬t͒ 3 ) of order 2 in time step can be used for advancing the Hamiltonian H; L 1 and L 2 are canonical transformations applying to H 1 and H 2 , respectively. 21,22 The model allows one to choose arbitrary sets of waves ͑k , k ͒ for which the periodicity conditions have to be verified, i.e., k x,y,z L x,y,z / 2 = ± 1 , ± 2. . ., where ͓L x , L y , L z ͔ is a three-dimensional spatial simulation box of volume V = L x L y L z .…”

“…[16][17][18] This paper is aimed to investigate the interaction at normal cyclotron resonances − n c = k z v z ͑n ജ 1͒ between lower hybrid waves and electron distributions presenting loss-cone type features. This study is performed by means of a theoretical Hamiltonian model and a corresponding numerical symplectic code, which have already provided new and interesting results [19][20][21][22] in what concerns the linear and nonlinear stages of the fan instability at the anomalous cyclotron resonance.…”

Nonturbulent stabilization of ion fluxes by the fan instability

“…It assumes that the plasma particle velocity distribution can be split into (i) a thermal bulk containing almost all ions and supporting the waves' dispersion and propagation, and (ii) the resonant ions, which are involved in intense energy exchanges with the waves [27]. Whereas the oscillations of the nonresonant ions of the bulk in the waves' potentials can be considered using the linear approach, the motion of the resonant particles is essentially nonlinear and described by the Newton-Lorentz equations.…”

“…Then, the anisotropic character of the parallel velocity distribution is the cause of the resonant wave generation at the anomalous cyclotron resonances. Note that fan instability due to electron distributions [20][21][22][23][24][25][26][27] physics as well as in tokamak plasmas [28], where suprathermal tails of electrons can be created during the current drive [29,30]. Some authors [31] explain the perpendicular heating of ion beams observed above the auroral terrestrial acceleration region by the excitation of ion acoustic waves generated by the ion distributions owing to the fan instability; performing calculations in the frame of the quasilinear theory of weak turbulence, they obtain an estimate of the heating rate, which is consistent with satellite observations [9,19] and that they compare with numerical simulations performed in 1D geometry, all waves propagating in the same quasiperpendicular direction (see also [32]).…”