Waves In Collisionless Plasma Research Articles

Nonlinear Dispersion of Stationary Waves in Collisionless Plasmas

A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a nondifferential form expressed in terms of a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift Δω is found analytically as a function of the wave amplitude a. Smooth distributions yield Δω ∼ a(1/2), as usual. However, beamlike distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation.

Nonlinear Stage of Alfvén Ion-Cyclotron Instability

A model describing nonlinear saturated state of Alfvén ion-cyclotron instability is presented. Spirally symmetric exact solutions of Vlasov – Maxwell equations describing nonlinear Alfvén waves in collisionless plasmas are presented. On their basis the equation describing ion distribution function in non-linear equilibrium of a weak-collision plasma with the wave is obtained, taking into account an uniform fast ion injection, ion drag caused by electrons and neglecting ion angle scattering. A solution of this equation and relations of the wave parameters with the injection parameters are obtained analytically in the case of the infinitely narrow velocity distribution of the injected ions

Resolution of a shock in hyperbolic systems modified by weak dispersion

We present a way to deal with dispersion-dominated "shock-type" transition in the absence of completely integrable structure for the systems that one may characterize as strictly hyperbolic regularized by a small amount of dispersion. The analysis is performed by assuming that the dispersive shock transition between two different constant states can be modeled by an expansion fan solution of the associated modulation (Whitham) system for the short-wavelength nonlinear oscillations in the transition region (the so-called Gurevich-Pitaevskii problem). We consider both single-wave and bidirectional systems. The main mathematical assumption is that of hyperbolicity of the Whitham system for the solutions of our interest. By using general properties of the Whitham averaging for a certain class of nonlinear dispersive systems and specific features of the Cauchy data prescription on characteristics we derive a set of transition conditions for the dispersive shock, actually bypassing full integration of the modulation equations. Along with the Korteweg-de Vries (KdV) and modified KdV (mKdV) equations as model examples, we consider a nonintegrable system describing fully nonlinear ion-acoustic waves in collisionless plasma. In all cases our transition conditions are in complete agreement with previous analytical and numerical results.

Undular bore transition in bi-directional conservative wave dynamics

A complete set of conditions describing the transition across the dissipationless undular bore (dispersive shock) is derived for nonlinear weakly dispersive conservative systems that generally are not integrable by the inverse spectral transform method. In the absence of integrable structure, we postulate modulation description of the undular bore with the aid of the averaged Whitham equations complemented by the Gurevich–Pitaevskii type natural boundary conditions. The main assumption used is that of the hyperbolicity of the Whitham system. The undular bore transition conditions are obtained in a general form by finding a set of integrals available for the similarity reductions of the Whitham systems regardless of the existence of the Riemann invariants. The obtained set of conditions can be viewed as a “dispersive” replacement for the classical shock conditions and allow one to fit an unsteady undular bore into the solution of the ideal dispersionless equations. We apply the obtained general conditions to the (integrable) Kaup–Boussinesq shallow-water system and to the (non-integrable) system describing fully nonlinear ion-acoustic waves in collisionless plasma. A complete agreement with previous analytical and numerical solutions is demonstrated.

Electrostatic Radiative Waves in Collisionless Plasma

Electrostatic Radiative Waves in Collisionless Plasma

Current drive in a high beta Tokamak using magnetic pumping

The RF current drive by magnetic pumping of a single wave in collisionless plasma is calculated by using an adiabatic method on the Vlasov equation. The self-consistent field effect on this current is also calculated by the adiabatic invariant method, and the relation between the efficiency and the external pumping wave amplitude is obtained. Calculations are made, appropriate to an experimental test in a small high beta Tokamak.

Computer simulations of collisionless shock waves

A review of the contributions of particle computer simulations to the understanding of the physics of magnetic shock waves in collisionless plasmas is presented. The emphasis is on the relation between the computer simulation results, spacecraft observations of shocks in space, and related theories, rather than on technical aspects of the numerics. It is shown that much has been learned from the comparison of ISEE spacecraft observations of the terrestrial bow shock and particle computer simulations concerning the quasi-perpendicular, supercritical shock (ion scale structure, ion reflection mechanism and ultimate dissipation processes). Particle computer simulations have also had an appreciable prospective role in the investigation of the physics of quasi-parallel shocks, about which still little is known observationally. Moreover, these numerical techniques have helped to clarify the process of suprathermal ion rejection by the shock into the foreshock, and the subsequent evolution of the ions in the foreshock.

The instability and damping of standing Langmuir waves in collisionless plasma

Describes the numerical experiments on the instability and damping of one-dimensional standing Langmuir waves. These experiments were performed in the region of initial wave parameters Eo2/8 pi nT>m/m>(kord)2 in a wide range of initial wave amplitudes Eo2/8 pi nT approximately 4.10-2-102 and phase velocities Vph/VT approximately 16-48.

Resonant interactions between fast particles and collision-dominated MHD waves

The theory of resonant interactions between particles and MHD waves (in collision-dominated plasmas) is shown to be equivalent to the corresponding theory for waves in collisionless plasmas provided that the wave properties are described in a suitable way. Slow-mode waves (as well as fast mode waves and Alfven waves) might contribute to the scattering of cosmic rays in the interstellar medium.

Investigation of ion acoustic waves in collisionless plasmas

The Green's functions for the linearized ion Vlasov equation with a given boundary value are derived. The propagation properties of ion acoustic waves are calculated by performing convolution integrals over the Green's functions. For Te/Ti less than about 3 it is concluded that the collective interaction is very weak and that the propagation properties are determined almost completely by freely streaming ions. The wave damping, being due to phase mixing, is determined by the width of the perturbed distribution function rather than by the slope of the undisturbed distribution function at the phase velocity as concluded from normal mode calculations.

C. Nonlinear Wave Modulation of Electrostatic Waves

Nonlinear wave modulation of electrostatic waves in collisionless plasma is examined by applying the reductive perturbation method to the one dimensional Vlasov-Poisson equations. It is shown that the nonlinear wave-particle resonant effect leads to the modified nonlinear Schrödinger equation with a nonlocal-nonlinear term, where φ(ξ, τ) is the small but finite complex potential amplitude, and τ and ξ are stretched variables in the reductive perturbation theory. L denotes a Cauchy principal part. Besides giving rise to the nonlocal-nonlinear term, the contribution of the resonant particles having the group velocity of the wave modifies the local nonlinear coupling coefficient q. The effect of the nonlocal-nonlinear term is described explicitly by investigating the modulation instability of the electrostatic waves.

On collisionless damping of ion acoustic waves

Exact theoretical treatments show that the damping of ion acoustic waves in collisionless plasmas does not vanish when the derivative of the undisturbed distribution function at the phase velocity equals zero.

Nonlinear Hydromagnetic Waves in a Collisionless Plasma with Isothermal Electron Pressure. I. Wave Train Propagating across a Magnetic Field

Nonlinear hydromagnetic waves in a hot collisionless plasma are investigated, on the basis of a two-fluid model of plasma composed of cold ions and isothermal electrons. In this paper (Part I), wave trains propagating across a magnetic field are studied analytically. An existence condition for solutions is exactly obtained, and the typical wave profiles are given graphically. These waves are qualitatively similar to those in a cold plasma. The width of the wave is of the order of the geometric mean between the Larmor radii of the electron and of the ion. As limiting cases, they include two special solutions which have already known, that is, (i) solitary wave solutions in a hot plasma, (ii) wave train solutions in a cold plasma.

Interactions of Solitary Waves –A Perturbation Approach to Nonlinear Systems–

An approximate method of studying interactions between two solitary waves which propagate in opposite directions is presented. In the first approximation, the solution is described by s superposition of two solitary waves which are governed by their respective Korteveg-de Vries equation. The second order approximation gives a small correction where the two waves overlap one another. The method is extended to the system, in which there exist n “quasi-simple” waves (the simple waves under the effects of higher derivative terms, such as dispersions of dissipations). The possibility that n “quasi-simple” waves can be superposed to describe nonlinear systems is studied. Applications to ion acoustic waves in collisionless plasmas and shallow water waves are discussed.

Shock Waves in Collisionless Plasmas

Book on shock waves in collisionless plasmas covering basic equations and classification of shock structures, magnetosonic waves, shocks and solitons, electrostatic shocks and solitons, etc

Investigation of ion shock waves in collisionless plasma: S G Alikhanov et al, Zh Eksper Teor Fiz, 60 (3), 1971, 982–992 (in Russian)

Investigation of ion shock waves in collisionless plasma: S G Alikhanov et al, Zh Eksper Teor Fiz, 60 (3), 1971, 982–992 (in Russian)

Nonlinear Collisionless Plasma Waves and Intensity of the Electric Field of the Ionospheric Irregularities

An exact longitudinal wave solution of nonlinear equations for a cold and collisionless one‐fluid magneto plasma has been obtained. The wave is found to be anharmonic (non‐sinusoidal) in form and its amplitude involves an arbitrary parameter. By means of a pseudo‐potential well, the domain of nonlinear oscillations is defined and the maximum amplitude up to which a nonlinear wave can grow is determined. Intensity of the equatorial sporadic‐E irregularities is computed and the coherent energy density is found to be of the order of 10−9 erg/cm3.

Quasilinear Theory of Hydromagnetic Waves in Collisionless Plasma

A quasilinear theory of hydromagnetic waves in nonrelativistic collisionless plasma (with no superthermal “tail”) is derived. It is shown that the time evolution of the space-averaged velocity distribution function of each species is described by a diffusion equation in velocity space, and that this “diffusion” can be split into resonant and nonresonant parts. The resonant diffusion determines the heating of the (finite-β) plasma by damping hydromagnetic waves; such heating enhances electron and ion kinetic temperatures parallel to the average magnetic field, and does not affect transverse temperatures. Quasilinear quenching of the hose instability is discussed as an example.

Evolutionary conditions for shock waves in collisionless plasma and stability of the associated flow

The evolutionary condition for transverse and normal shock waves, and the fire- hose and mirror instability conditions for the associated flow, in a collisionless, anisotropic plasma having a strong magnetic field are determined using the theoretical representation of Chew, Goldberger & Low (1956) for such a medium. The results are expressed in terms of the Mach number, Alfvén Mach number, and the ratio of the temperatures parallel and perpendicular to the magnetic field in the flow approaching the shock wave, and applied to ascertain in what range of these parameters various types of instabilities may occur. The effect of the heat flux, which does not vanish generally in a collisionless plasma, on the shock stability is discussed.

Magnetic-Compression Waves in Collisionless Plasma—Oblique Ambient Magnetic Field

Numerical analysis is made of the structure of one-dimensional unsteady magnetic compression waves propagating into collisionless plasmas when the ambient magnetic field is oblique to the wave direction. Integration of the equations of motion is carried out by dividing the flow field into discrete elements or slabs of plasma and following their motion on a digital computer. Results from these calculations show that both the sub- and supercritical solutions change continuously from one limiting situation to the other. A similarity rule is found for correlating the subcritical cases so that the two-parameter family of solutions in mass ratio and field angle are reduced to a single set.