Nonlinear Stabilization of High‐Frequency Instabilities in a Magnetic Field
TL;DR: In this paper, it was shown that the broadening of wave-particle resonances by the random motion of particles in a turbulent electric field may determine the saturation level of a variety of high-frequency instabilities.
Abstract: It is shown that the broadening of wave‐particle resonances by the random motion of particles in a turbulent electric field may determine the saturation level of a variety of high‐frequency instabilities. Secular changes of the guiding center positions, cyclotron radii, and phase angles give rise to resonance broadening and diffusion, similar to that produced by collisional scattering. The field dependent broadening is expressed in terms of resonance functions which replace the familiar resonant denominators of the linear theory. Resonance functions are derived in a simple manner from the solution of a Brownian motion problem, leading to an expression in terms of diffusion coefficients. The close resemblance of the theory to quasilinear theory and the linear theory including collisions allows one to start from a linear stability analysis and then assess the importance of nonlinear effects. This method is illustrated by the determination of the saturation level of cyclotron instabilities from the condition of vanishing nonlinear growth rate.
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TL;DR: In this article, the motion of an ion in a coherent lower hybrid wave (characterized by ω≳≳Ωi) in a tokamak plasma is studied.
Abstract: The motion of an ion in a coherent lower hybrid wave (characterized by ‖k∥‖<<‖k⊥‖ and ω≳≳Ωi) in a tokamak plasma is studied. For ions satisfying v⊥≳ω/k⊥, the Lorentz force law for the ions is reduced to a set of difference equations which give the Larmor radius and phase of an ion on one cyclotron orbit in terms of these quantities a cyclotron period earlier. These equations exhibit stochastic behavior when the wave amplitude exceeds a threshold. The stochasticity threshold is given a simple physical interpretation. In addition, the difference equations are used to derive a diffusion equation governing the heating of the ions above the stochasticity threshold. Far above the stochasticity threshold, ion Landau damping is recovered. By including the effects of collisions, the heating rate for the bulk ions is obtained.
325 citations
TL;DR: In this paper, the dynamics of magnetosphere-ionosphere coupling were investigated by means of a two-dimensional two-fluid MHD model including anomalous resistivity, and the system evolved toward an electrostatic structure, with the perpendicular electric field having a shorter scale than the field-aligned current.
Abstract: The dynamics of magnetosphere-ionosphere coupling has been investigated by means of a two-dimensional two-fluid MHD model including anomalous resistivity. When field-aligned current is generated on auroral field lines, the disturbance propagates toward the ionosphere in the form of a kinetic Alfven wave. When the current exceeds a critical value, microscopic turbulence is produced, which modifies the propagation of the Alfven wave. This process is modeled by a nonlinear collision frequency, which increases with the excess of the drift velocity over the critical value. The system evolves toward an electrostatic structure, with the perpendicular electric field having a shorter scale than the field-aligned current. The approach to a steady state is strongly dependent on the presence or absence of the turbulence and on the boundary conditions imposed in the generator. As current is increased or scale size is decreased, the turbulent region reflects and absorbs most of the Alfven wave energy, decoupling the generator from the ionosphere.
314 citations
TL;DR: In this paper, a general review of anomalous resistivity with emphasis on its applicability in space and more specifically on ionospheric plasmas is presented, addressed to the general ionosphere community rather than the specialist.
Abstract: This is a general review of anomalous resistivity with emphasis on its applicability in space and more specifically on ionospheric plasmas. It is addressed to the general ionospheric community rather than the specialist. Therefore a substantial amount of rigor has been sacrificed in favor of simplified physical pictures. However, several prescriptions are presented, on the basis of which one can compute the anomalous resistivity resulting from each specific mechanism. Following a conceptual discussion of resistivity a general formalism is presented for its computation on the basis of the spectrum of electric field fluctuations. On the basis of this it is shown that stable nonthermal plasmas can at most enhance resistivity by a few percent. The same is true for collisionally driven instabilities. From the current-driven instabilities, only the ion acoustic instability can produce a steady state anomalous resistivity. The rest result in transient resistivity and the appearance of hot electron or ion spots. A more satisfying picture emerges when the low-frequency turbulence that produces resistivity is excited parametrically by a high-frequency instability. The case where such a driver arises from the interaction of precipitating electrons is discussed in detail. Finally, the relevance of the various resistivity mechanisms and their importance in ionospheric electron acceleration is discussed. Although a large number of physical notions are well understood, the efforts toward their incorporation into a gross modeling picture remain embarrassingly small.
304 citations
TL;DR: In this paper, a comparative study of upstreaming energetic ions in the kilovolt energy range and electrostatic hydrogen cyclotron (EHC) waves has been made using the ion mass spectrometer and plasma wave receiver data sets for the first 1200 orbits of the S3-3 spacecraft.
Abstract: A comparative study of upstreaming energetic ions in the kilovolt energy range and electrostatic hydrogen cyclotron (EHC) waves has been made using the ion mass spectrometer and plasma wave receiver data sets for the first 1200 orbits of the S3-3 spacecraft. The upstreaming energetic ions and EHC waves are found to coincide in over 90% of the events studied. In addition, both EHC waves and upstreaming ions with energies greater than 500 eV exhibit a lower border in their altitude distribution near 5000 km. The nearly exact correlation suggests either that the upstreaming ions are producing the EHC waves or that the EHC waves are heating the ions. One example of EHC waves and upstreaming energetic ions is analyzed to test the two hypotheses. Evidence that EHC waves are heating ions is presented in the form of conic ion distributions which some theories predict are the consequence of this process. Perpendicular ion heating to at least 6 keV is found to coincide with EHC waves. Evidence that the upstreaming ions are the source of free energy for the EHC waves is presented in the form of an ion distribution function with ∂f/∂ν > 0. However, the stability of that ion distribution function is considered and found to be stable unless other conditions such as filamentation or electron drift are invoked. There also exists the possibility that the source of free energy for EHC waves is drifting thermal electrons. For the one example studied the drifting electron process is consistent with data from the S3-3 magnetometer. However, it is inconsistent with the S3-3 electron spectrometer which indicates that the current is carried by keV electrons, not thermal electrons. Consequently, the source of free energy for EHC waves is not yet unambiguously determined.
278 citations
TL;DR: In this paper, the authors present a systematic parameter study of the spatial growth rates of electrostatic waves in an electron plasma consisting of a cold component and a hot component with a weak "loss cone" perpendicular velocity distribution.
Abstract: We present a systematic parameter study of the spatial growth rates of electrostatic waves in an electron plasma consisting of a cold component and a hot component with a weak ‘loss cone’ perpendicular velocity distribution. The cold electron density controls which harmonic band can be excited. When the upper hybrid frequency based upon the cold electron density alone is between 1 and 2 times the electron cyclotron frequency, only the first harmonic band is unstable; when the upper hybrid frequency is between 2 and 3 times the cyclotron frequency, the first and second harmonic bands are unstable; and so on. Sufficiently large cold density eventually stabilizes the low harmonic bands. The cold electron temperature Tc controls the spatial amplification; when 0 < Tc/TH < a few times 10−2, where TH is a characteristic energy of the hot electrons, the instability is nonconvective. The first and second harmonic bands can be simultaneously nonconvective. The nonconvective property has been found for a wide range of hot and cold electron densities. It persists even when the hot electron loss cone is almost completely filled. Sufficiently large Tc/TH changes the instability from being nonconvective to being convective. Since cold electrons which come from the ionosphere would be confined to the loss cone if they were not turbulently scattered, the ionospheric source velocity distributions induce a nonconvective instability. However, cold electrons can be heated by electrostatic wave turbulence. Until Tc/TH = 5 × 10−2, nonresonant, quasilinear diffusion heats the cold electrons more rapidly than resonant diffusion heats or scatters the hot electrons into the loss cone. We propose that cold electron heating removes the nonconvective property, so that the spatial amplification of the instabilities can be reduced to a magnitude consistent with their hot and cold electron sources in steady state.
275 citations
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