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A stationary theoretical model giving an asymptotic description of the propagation of nonlinear electromagnetic waves in an inhomogeneous plasma is presented. The plasma, considered within the hydrodynamic approximation and assumed to be cold, collisionless, unmagnetized and electroneutral, is described in terms of a nonlinear dielectric function giving the effect of the Miller ponderomotive force. In an infinitely extended slab geometry, a variable transverse density gradient, assumed to be parabolic, is considered in the case when a monochromatic electromagnetic wave is incident upon the slab at an arbitrary angle. The transverse structure of the wave electric field is determined along with the perturbed plasma density profile. The nonlinear wave equation with slowly varying coefficients derived using this model is solved in first and second approximations using an asymptotic multiple-space-scale method due to Bogolyoubov and Mitropolskii. The critical conditions for resonant electrostatic absorption and mode conversion are derived and discussed within these approximations, and some reference numerical calculations are performed.
A self-consistent reductive perturbation analysis for parallel-propagating magnetohydrodynamic waves in warm multi-species plasmas, in which different constituents can have differing equilibrium drifts, leads to a derivative nonlinear Schrödinger equation for the wave magnetic field. Soliton solutions are discussed, including applications to plasmas with two ion species. Such solitons are larger (in amplitude) and wider than in the non-streaming and/or cold-plasma case, other parameters being equal.
A nonlinear treatment is given for MHD waves that propagate parallel to the external magnetic field in warm multi-species plasmas with anisotropic pressures and different equilibrium drifts. Both the wave electric and magnetic fields obey a derivative nonlinear Schrödinger equation. Soliton solutions are discussed, in particular for plasmas with two ion species.
Large-amplitude Alfvén waves, propagating along the magnetic field in an inhomogeneous plasma with non-uniform streaming, are shown to be governed by the DNLS equation modified by the inhomogeneity and the streaming. For weak but arbitrary inhomogeneity this modified DNLS leads to accelerated solitary Alfvén waves. The acceleration is modified further owing to streaming. For certain values of the plasma β, streaming can change the accelerating solitons into decelerating solitons, and vice versa.
Field variables in a slowly varying plasma are solutions of a system of differential and integral equations. To solve these equations, the fields are expanded in the eigenvectors of an algebraic plasma tensor, and the plasma equations can be transformed into a system of transport equations. The expansion becomes singular when eigenvalues coincide (for example in the case of mode conversion). It is shown how this problem can be resolved for an arbitrary system of Maxwell and/or fluid equations in arbitrary dimensions and for every kind of medium. The method is applied to horizontal stratified media as a simple example.
Weakly relativistic electron-acoustic solitons are investigated in a two-electron-component plasma whose cool electrons form a relativistic beam. A general Korteweg-de Vries (KdV) equation is derived, in the small-|ø| domain, for a plasma consisting of an arbitrary number of relativistically streaming fluid components and a hot Boltzmann component. This equation is then applied to the specific case of electron-acoustic waves. In addition, the fully nonlinear system of fluid and Poisson equations is integrated to yield electron-acoustic solitons of arbitrary amplitude. It is shown that relativistic beam effects on electron-acoustic solitons significantly increase the soliton amplitude beyond its non-relativistic value. For intermediate- to large-amplitude solitons, a finite cool-electron temperature is found to destroy the balance between nonlinearity and dispersion, yielding soliton break-up. Also, only rarefactive electronacoustic soliton solutions of our equations are found, even though the relativistic beam provides a positive contribution to the nonlinear coefficient of the KdV equation, describing relativistic, nonlinear electron-acoustic waves.
The Zakharov-Kuznetsov equation is used to describe ion-acoustic wave propagation in a magnetic environment. An initial-value problem is solved for this equation on the basis of a numerical method that uses the fast-Fourier-transform technique for calculating space derivatives and a fourth-order Runge-Kutta method for the time scheme. Numerical simulations show that the disturbed flat (planar) solitary waves can break up into more robust cylindrical ones. Interactions between these two types of wave, and recurrence phenomena, are also studied.
Our study of the relationship between shock structure and evolutionarity is extended to include the effects of dispersion as well as dissipation. We use the derivative nonlinear Schrödinger-Burgers equation (DNLSB), which reduces to the Cohen-Kulsrud-Burgers equation (CKB) when finite ion inertia dispersion can be neglected. As in our previous CKB analysis, the fast shock solution is again unique, and the intermediate shock structure solutions are non-unique. With dispersion, the steady intermediate shock structure solutions continue to be labelled by the integral through the shock of the non-co-planar component of the magnetic field, whose value now depends upon the ratio of the dispersion and dissipation lengths. This integral helps to determine the solution of the Riemann problem. With dispersion, this integral is also non-zero for fast shocks. Thus, even for fast shocks, the solution of the Riemann problem depends upon shock structure.
Plasma sources are used to control spacecraft potentials and, in general, to improve the electrical contact between a charged body and the space plasma. From this point of view, they have been proposed in connection with conducting tethers in space to increase current capability and to allow the use of such tethers for power generation and/or propulsion. In this paper we address the problem of the interaction of a plasma source with the ambient plasma. The source is supposed to be positively charged with respect to the ambient. A self-consistent fluid model is developed to obtain a description of the interaction in the collisionless case. The interaction, which appears to be mainly characterized by the presence of a double layer, is discussed in terms of the ratio between source density and ambient plasma density and the value of the polarizing potential. The current-voltage characteristics of the system are then determined.
The time scales and efficiency of plasma heating by resonant absorption of Alfvén waves are studied in the framework of linearized compressible and resistive magnetohydrodynamics. The configuration considered consists of a straight cylindrical axisymmetric plasma column surrounded by a vacuum region and a perfectly conducting shell. The plasma is excited periodically by an external source, located in the vacuum region. The temporal evolution of this driven system is simulated numerically. It is shown that the so-called ‘ideal quasi-modes’ (or ‘collective modes’) play a fundamental role in resonant absorption, and affect both the temporal evolution of the driven system and the efficiency of this heating mechanism considerably. The variation of the energetics in periodically driven resistive systems is analysed in detail for three different choices of the driving frequency, viz an arbitrary continuum frequency, the frequency of an ideal ‘quasi-mode’, and a discrete Alfvén wave frequency. The consequences for Alfvén wave heating of both laboratory plasmas and solar coronal loops are discussed.
The dispersion equation for parallel whistler-mode propagation in a hot anisotropic plasma is analysed numerically in both weakly relativistic and nonrelativistic approximations under the assumption that wave growth or damping does not influence the wave refractive index. The results of this analysis are compared with the results of an asymptotic analysis of the same equation, and the range of applicability of the latter results is specified. It is pointed out that relativistic effects lead to a decrease in the range of frequencies for which instability occurs. For a moderately anisotropic plasma (T⊥/T‖ = 2) relativistic effects lead to an increase in the maximum value of the increment of instability.