Finite Gyroradius Effects Research Articles

Kinetic Theory of Nonlocal Drift Alfvén Instabilities

Kinetic formulation for linear mode analysis of low frequency shear Alfven mode in low-β plasma is presented. Slab geometry is used with density, temperature and flow velocity varying in the x -direction, and the magnetic shear produced by parallel current is assumed to be sufficiently weak. Integral equation representation in wavenumber space is used in order to take full account of the finite gyroradius and Landau resonance effects. The general formulas derived are applied to two lons wavelength instabilities by reducing integral equations to differential equations in real space; one is the localized drift-Alfven mode instability caused by current density and the other the Alfven mode instability due to ion velocity shear. For the former case, our analysis shows necessity of kinetic effects for instability to occur; for the latter, the lowest order finite gyroradius effect on the stability criterion is investigated.

Eigenmode Analysis of the Electromagnetic Wave in the Nonuniform Vlasov Plasma. II. Quantization Condition

A new method for eigenmode analysis of high mode number electromagnetic waves in an inhomogeneous medium is presented. The method is based on an integral equation in the wavenumber srace and is applicable to the case where kinetic effects such as finite gyroradius effects, Landau and cyclotron resonance effects in high temperature magnetically confined plasmas are important. A quantization condition useful to numerically determine the eigenfrequencies is derived which is different from the conventional Bohr-Sommerfeld condition because of the electromagnetic nature of the wave. A systematic computational scheme of the quantization condition is presented and is shown to be highly efficient by a simple example.

Filamentation instability of helicons

Nonlinear interaction of a large amplitude ducted helicon (whistler wave) with slow plasma motion is considered. The low-frequency response accounts for a finite ion gyroradius effect to the usual MHD Alfvén waves. It is found that this coupling leads to a filamentation instability which grows at a rate faster than those reported earlier.

Particle stochasticity due to magnetic perturbations of axisymmetric geometries

The quasi-linear theory of collisionless test particle diffusion in stochastic magnetic fields is extended to include the effects of finite gyroradius ρ and particle drifts (including magnetic trapping). A canonical framework is used, in which both the criterion for onset of stochasticity and the diffusion tensor scale with field-particle coupling coefficients gl. The gl contain all the information about the unperturbed orbit of a given particle and the perturbation fields with which the particle interacts. The modification of transport due to finite ρ and drifts is thus found by comparison of the gl including these effects to their driftless, ρ→0 limit. It is found that runaway electron confinement is substantially improved over earlier, driftless estimates, and that trapped particles in microturbulence ought not be stochastic. The perturbations from proposed ripple injection schemes are large enough to induce stochasticity for certain classes of particles.

Free and forced m=0 oscillations of a sharp-boundary Vlasov-fluid screw pinch

A dispersion differential equation is derived from the linearized equations of the Vlasov-fluid model for a sharp-boundary screw pinch using a very general fast-gyration, small-gyroradius ordering for the ions. Analytic solutions of the dispersion differential equation are obtained. The influence of finite ion gyroradius effects on both free and forced, azimuthally symmetric, small-amplitude oscillations of the plasma column is studied, and the results are compared and contrasted with the asymptotic guiding center plasma description. The forced oscillations are considered for frequencies at and below the first magnetoacoustic resonance. Small, but finite, ion gyroradii can influence the absorption of resonant magnetoacoustic oscillations strongly.

Particle Diffusion by Magnetic Perturbations of Axisymmetric Geometries

The quasilinear theory of collisionless test particle diffusion in stochastic magnetic fields is extended to include the effects of finite gyroradius, particle drifts, and magnetic trapping. Runaway-electron confinement is substantially improved relative to earlier estimates which assumed that particles exactly followed field lines. Trapped particles are not expected to be stochastic.

Particle dynamics in low frequency electromagnetic waves in inhomogeneous plasma

Phase space dynamics of plasma particles in low frequency (ω≪ωci) electromagnetic waves in a low beta inhomogeneous plasma is obtained including the effects of finite ion gyroradius, bounce resonance, and gradient B and diamagnetic drifts. Application of the results to particle flux observations in the magnetosphere is discussed.

Trajectories of Charged Particles in Radial Electric and Uniform Axial Magnetic Fields

The trajectories of charged particles were determined over a wide range of parameters characterizing the motion in cylindrical low-pressure gaseous discharges and plasma-heating devices which have steady radial electric fields E perpendicular to uniform steady magnetic flelds B. Three radial distributions of E were considered: E ? r, constant E, and E ? r-1. These distributions are characteristic of the fields measured in a modified Penning discharge, in two NASA Lewis Bum-out-type plasma-heating devices, and that estimated for the Ixion device, respectively. The plasmas of such ? × B? devices are often characterized by their high ratios of drift energy to mean particle energy, finite gyroradius effects, and sizeable electric field changes in the distance covered by a cyclotron radius. Such particle motions are not amenable to simple guiding center theory. From numerical calculations of the actual trajectories it was concluded that the differences between cyclotron frequency and qB/m, and between azimuthal drift and a guiding center approximation (including ? × B? and centrifugal force terms) are appreciable. The net cyclotron motion obtained by subtracting the actual drift from the trajectories, however, has a nearly circular contour over which the speed is quite constant.

Electron Beams Generated in Foilless Diodes

The operation of a foilless diode to generate a hollow relativistic electron beam has been performed on the FX-25, a Van de Graaff charged 3 MV device. The diode consists of a cylinder of carbon (graphite) supporting either a cathode tip of larger diameter or a right circular cylinder of equal diameter and a coaxial anode guide wall having either an abrupt discontinuity in wall diameter or a smooth wall. Six configurations were employed to explore the emitted electron behavior in the crossed electric and magnetic fields. Finite gyroradius effects limit the transmitted current at low applied axial magnetic field strengths. The transmitted current increases with increasing field strength until a critical field is reached, when further increase in field strength results in a decrease to a plateau in transmitted current. This critical field produces an electron gyroradius equal to the gap between cathode guide wall (anode) and is found to satisfy ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> > 2 ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> where ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> is the electron gyro-frequency and ω <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b</sub> is the beam plasma frequency. At high applied field strengths a very thin beam is transmitted and bounded by the space charge limited current. These features agree qualitatively with recent computer simulations of Jones and Thode.

Influence of ion-ion collisions and kinetic effects on minidisruptions of confined plasmas

Resistive m=1 modes associated with minidisruptions of current carrying plasmas are shown to be strongly influenced simultaneously by the effects of finite ion gyroradius, finite drift wave frequency, and ion-ion collisions in the plasma regimes of interest. The modes acquire finite frequency of oscillation and, for low β, the reduction in their growth rates is due mainly to the drift wave frequency, the effect of ion-ion collisions being slight (less than 10% effect); but, even for low β, ion-ion collisions significantly alter the radial structure of the modes. As a result, the reconnecting mode, which tends to lose its radial localization above a threshold temperature, remains well-localized when ion-ion collisions are included.

Ogo 5 magnetopause structure and classical reconnection

The observations made during one unusual crossing of the magnetopause by the satellite Ogo 5 are compared with the classical reconnection model developed by Levy, Petschek, and Siscoe. The magnetic field observations appear to be generally consistent with this MHD model, although allowance must be made for the fact that the estimated magnetopause thickness was no more than 3.5 ion gyrodiameters. The nature of the finite gyroradius effects in such thin structures is discussed.

Energy anisotropy instabilities in high-beta plasmas: A comparison of various kinetic and fluid descriptions

The Vlasov-fluid model is employed to study linear perturbations of a particular class of magnetized, infinite, homogeneous equilibria. The dispersion properties of waves and anisotropy driven instabilities with frequencies at or below the ion cyclotron frequency are used to compare and contrast the Vlasov-fluid model with other well-known models of a high-beta plasma. Although the various models differ widely in physical content and in the manner in which the dispersion equation is derived, the results obtained from any one of them agree with appropriate limits of all the others. The results illuminate the nature of the anisotropy driven fluid-like instabilities and illustrate their connection to kinetic descriptions that include dispersion due to finite gyroradius effects. For the simple equilibria that have been considered, no reason has been found not to regard the Vlasov-fluid model as an acceptable model of a high-beta plasma.

Linearized gyro-kinetics

In preceding work on plasma gyro-kinetics magnetic coordinates were introduced prior to making the transformation to the guiding centre variables. It is the transformation from the particle variables to the guiding centre variables which permits finite gyroradius effects to be retained in lowest order. The present treatment avoids the substantial mathematical complications inherent in these prior treatments by introducing the transformation to the guiding centre variables and performing the guiding centre gyrophase average before specifying the magnetic coordinates to be employed. In this way the unperturbed, gyro-averaged Vlasov operator which retains finite gyro-effects is obtained in the most convenient manner for arbitrary unperturbed magnetic fields.

Plasma convection instability in an inhomogeneous magnetic field

A convection instability characteristic of plasmas in an inhomogeneous azimuthal magnetic field is treated in the linear stage and in nonlinear saturation. The analysis is done in such a way that collisional and collisionless limits can be taken, and these limits are displayed along with the more general intermediate result. The instability, known previously in the literature in its collision‐dominated form, is shown to be a ’’flute’’ instability with collisional modifications to the growth rate. The nonlinear saturation is analyzed by examining a finite amplitude restoring‐force term in the differential equation that describes the instability. This term is due to the fact that the instability convects plasma into striations of the plasma column surface, modifying the density gradient driving force. The effects of finite ion gyroradius are displayed, and applications of this study to convection cells in a thermal plasma and to exploding wire plasmas are discussed.

Moment equations treatment of the reconnecting mode

A mode with azimuthal wave number m = 1 can be excited in a resistive plasma column as a result of reconnection of the magnetic field lines under conditions for which the ordinarily known internal kink mode given by the ideal MHD theory would be stable. In the absence of resistivity, magnetic reconnection would not be allowed and the relevant mode would be singular at a specified radius within the plasma column as in the case of the resistive tearing modes that are found for m ≥ 2. The analysis presented here is based on a set of moment equations that are appropriate for relatively high-temperature and low collisionality regimes. In these regimes, the mode growth rate tends to weaken considerably as the temperature increases and the mode acquires a frequency of oscillation with phase velocity close to the electron diamagnetic velocity, as a result of the effects of finite ion gyroradius and finite drift wave frequency, even in the absence of an equilibrium radial electric field.

On propagation direction of ring current proton ULF waves observed by ATS 6 at 6.6RE

From June 11 to September 16, 1974, the NOAA low-energy proton detector on board the ATS 6 satellite observed 71 cases of ultralow-frequency oscillations of proton flux intensities. The oscillation periods varied from 40 s to 6 min, and the events were observed most frequently during moderate geomagnetic conditions. The flux oscillations occurred at various local times, yet almost two thirds of the events were detected in the near-dusk region of the magnetosphere. For a majority of the events in this set a substantial phase shift in flux oscillation was detected between different energy channels and/or between two oppositely oriented detector telescopes. The phase shift is mainly due to the finite gyroradius effect of the protons gyrating in the geomagnetic field. By examining this finite gyroradius effect on the perturbed particle distribution function associated with the wave in a nonuniform magnetic field, the propagation direction of the wave from particle observations made by a single spacecraft is determined

Finite-gyroradius effects on m = 1 and m = 2 instabilities of sharp-boundary screw pinches

Recent numerical and analytical investigations of finite-ion-gyroradius effects in the context of the Vlasovfluid model are in good agreement with results of high-beta stellarator experiments. MHD-unstable m = 2 modes in near-theta-pinch devices, such as Scyllac, appear to be stabilized at an ion temperature at least four times smaller than believed previously. This conclusion makes wall stabilization of m = 1 modes more feasible.

Finite- stabilization of flute-like microinstabilities

The stability of a finite- beta plasma with density and temperature gradients located in a cylindrically symmetric azimuthal magnetic field is investigated using the Vlasov-Maxwell set of equations. The frequency is assumed to be low but finite gyroradius and wave-guiding centre resonance effects are retained. It is found that beta can both stabilize and destabilize the fast flute mode depending on the gradients, but has no effect on the temperature gradient mode. The interchange mode is essentially unaffected by beta . This latter result is in agreement with results from fluid models, as one might expect.

Stationary Equilibrium and Diffusion in a Toroidal Plasma with Helical Magnetic Field

A theoretical study of the equilibrium and diffusion in a stellarator field with the helical winding l =3 has been carried out. It is shown that a stationary equilibrium exists even when finite inertia and finite ion gyroradius effects are taken into account. The plasma loss flux consists of two parts; one is determined by the averaged magnetic field and the other is due to the perturbed components with helical structure of the electrostatic potential and of the density distribution. The latter term will become appreciable when a marked anisotropy in electron pressure presents.

Flute oscillations in bounded plasmas and the effect of incoherently precessing ions

Flute oscillations in bounded, non-uniform plasmas are considered from the guiding centre point of view. The effects of field curvature are replaced by generalized forces that are proportional to the parallel and perpendicular components of the particle energy. A perturbation analysis, covering all density regimes and including the finite gyro-radius effects, is carried out in cylindrical co-ordinates. It is shown that the final equation can always be solved by a variational method. Explicit solutions in terms of confluent hypergeometric functions are also presented for a special class of density distributions. For a monoenergetic plasma, in which all ions precess coherently, there can be stable regions at both very low and very high densities. If the ions precess incoherently, due to a spread in the energy, then a new over-stability emerges in the above stable regions. This over-stability, whose growth rate is very small compared to its oscillation frequency, is shown to be in agreement with the observations made in neutral injection experiments.