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Work on computer simulation of waves and instabilities in magnetized plasmas is reviewed. Included are verification of linear theory. Particular emphasis is given to investigation of nonlinear processes involved in the saturation of instabilities and of wave damping; these include a nonlinear cyclotron resonance and particle trapping in intense waves.
The paper is concerned with a quantitative study of the frequency dispersion characteristics of the ion cyclotron mode in a realistic dipole magnetosphere where the particles are allowed to drift azimuthally. The adopted model assumes that the particles are injected at a constant L shell in an extended region around local midnight. A drift-convoluted distribution function is used to study the spatial and temporal characteristics of the ion cyclotron instability. Two cases are examined: one in which the cold plasma density is constant and the other in which the cold particle density is allowed to vary. The resulting growth rates are presented in both the frequency versus coordinate space and the frequency versus time space. Possible inferences regarding wave emissions such as IPDP (intervals of pulsations of diminishing period) events are discussed. It is shown that the frequency dispersive effects can be produced by either the drift effects or changing the cold plasma density.
The process whereby magnetic island structures tend to merge into larger units is known as magnetic island coalescence. This coalescence process is investigated for the case of a collisionless plasma by means of 2D particle simulations. The pairwise merging of a preformed island chain leads to a gentle redistribution of the density and current density profiles. The nonlinear evolution of the collisionless tearing instability in a long system is found to lead to a much more violent coalescence process resulting in the formation of a vacuum X region. This stage is characterized by enhanced growth rates for the long-wavelength modes that exceed the maximum linear tearing growth rate, super-Alfvenic flows away from the reconnection X line, substantial bulk heating in the parallel direction, and the formation of energetic particle tails in the direction of the inductive electric field.
The problem of the linear stability of collisionless tearing modes in the earth's magnetotail is revisited. It is found that the collisionless tearing mode is linearly unstable with wavelengths of the order of 10 R(E). It is shown that an important feature neglected in earlier theories is a nonzero equilibrium B(y)-field. The physics of the instability is elucidated in the context of a simple slab model and a sheared parabolic model which is representative of the magnetotail in which all three components of the magnetic field are nonzero. The dispersion equation for the instability is obtained by a boundary-layer analysis. The implications of the theory for recent observations on current disruption and diversion during substorms is discussed.
An account is given of the waves and instabilities occurring at collisionless shocks, with attention to the mechanisms responsible for the generation of these waves. The transition region of the shock usually involves an abrupt broadband burst of electrostatic noise that extends from below the lower hybrid resonance to near the electron plasma frequency, and by a broadband burst of whistler mode EM noise below the electron cyclotron frequency. Electrostatic lower hybrid waves are also noted. Upstream of the shock, electron plasma oscillations, ion acoustic waves, and intense ULF MHD waves are often observed. The region downstream of the shock is usually very chaotic; electrostatic waves often extend long distances into the downstream region, together with whistler mode emissions.
Plasma and magnetic field data observed during two ISEE crossing of the plasma sheet boundary layer are studied in conjuction with a linear theory analysis. The plasma distribution functions exhibit three distinct potential sources of free energy: ion/ion relative drifts, electron/ion relative drifts corresponding to nonzero field-aligned current, and large ion temperature anistropies. These observed distributions are used as source functions in a linear Vlasov theory of electromagnetic instabilities at propagation parallel or antiparallel to the average magnetic field. The theory shows that the field-aligned current gives rise to the low frequency kinklike instability, and anisotropies of the flowing ion components give rise to two distinct branches of the ion cyclotron anisotropy instability with spacecraft frame frequencies both below and above the proton cyclotron frequency Omega (p). Analysis of the magnetic field data demonstrates that the appearence of two fast, counterstreaming, anisotropic ion components corresponds to a significant increase in the magnetic fluctuation energy density both below and above Omega(p), in full agreement with the theoretical predictions.
Transverse wave instability of unmagnetized collisionless plasma subjected to shear flow
The electrostatic instabilities in an anisotropic plasma have been studied quite extensively, but the electromagnetic instabilities in high-beta plasmas, where they play an important role, have not been thoroughly investigated. Recently, Davidson and Wu (1970) looked into the ordinary mode electromagnetic instability which can arise in high-beta bi-Maxwellian plasmas. Here, the magnetic instability is discussed in (A, beta) space (A is the anisotropy in the temperature of the plasma species and beta is the ratio of the kinetic pressure to the magnetic pressure), which can occur in generalized non-Maxwellian plasmas with an inverted population of different species.
The mechanisms of electromagnetic instabilities in nonuniform plasmas are analyzed, taking into account the anisotropy in temperature and temperature gradients. It is shown that resonance-type drift instabilities can be produced in nonuniform plasmas by resonant interactions between ions or electrons and plasma drift waves when the temperature anisotropy and temperature gradients vary widely. In contrast, production of off-resonance type instabilities is found to be possible only when the temperature gradients are much greater than the magnetic field gradients. It is pointed out that these findings are applicable to solar wind plasmas with hydromagnetic instabilities and shock transition regions. Attention is given to the occurrence of resonance ion instabilities and off-resonance drift cyclotron instabilities in the solar wind.
Helical instability theory for positive hollow plasma column in magnetic field with shear
An analysis is conducted of the transverse Kelvin-Helmholtz instability in a magnetized plasma for unstable flute modes. The analysis makes use of a two-fluid model. Details regarding the instability calculation are discussed, taking into account the ion continuity and momentum equations, the solution of a zero-order and a first-order component, and the properties of the solution. It is expected that the linear calculation conducted will apply to situations in which the plasma has experienced no more than a few growth periods.
The compressional wave spectrum excited in a fissioning uranium plasma confined in a cavity such as a gas cored nuclear reactor, is studied. Computer results are presented that solve the fluid equations for this problem including the effects of spatial gradients, nonlinearities, and neutron density gradients in the reactor. Typically the asymptotic fluctuation level for the plasma pressure is of order 1 percent.
In the present paper, Liouville's theorem is used in combination with approximate, but extremely accurate, expressions which reflect the invariance of the magnetic moment and the longitudinal invariant to determine analytically the evolution of an adiabatically convecting energetic particle distribution. Features of the convecting distribution, reproduced by this model, include positive pitch angle anisotropy, regions in velocity space where the nonmonotonic perpendicular energy distribution is greater than zero, and the energy dependence of the degree of particle injection. The energy dependence of the injection yields upper and lower cutoffs to the distribution within the plasmasphere, and only an upper cutoff outside. This approach is used to study the evolution of ion cyclotron waves in a convecting particle distribution.
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The lower hybrid drift instability is investigated in nonantiparallel reversed field plasmas, i.e., the magnetic fields on either side of a neutral line are not antiparallel. Such a magnetic field configuration contains magnetic shear, which has a stabilizing influence on the lower hybrid drift instability. It is found that magnetic shear has an inhibiting effect on the linear penetration of the lower hybrid drift mode toward the neutral line. The implications of this result to reconnection processes in the magnetosphere (i.e., the nose and the magnetotail) are discussed.