摘要:

Physical processes involved in collisionless damping of the fast hydromagnetic mode are investigated by considering the stochastic heating of electrons by a random spectrum of fast waves. We take as a model a weakly damped fast wave, propagating in a direction such that the damping is mainly due to electron heating; allowance is made for the possibility of a small component of electric field parallel to the unperturbed field. To estimate the damping we consider an ensemble of electrons accelerated (1) by magnetic‐moment magnetic‐field‐gradient interaction and (2) by the parallel electric field. Electron heating is calculated from a Fokker—Planck type of equation; the damping decrement is obtained by equating the electron heating rate to the wave energy loss rate, and agrees with the damping decrement obtained from the appropriate asymptotic limit of the general dispersion relation. Some general aspects of this method for obtaining wave‐damping decrements are discussed.

ISSN:0031-9171    

DOI:10.1063/1.1762053

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The instability induced by external gravitational forces in an infinite, stratified, anisotropic plasma with a magnetic field has been studied using the Chew, Goldberger, and Low approximation. A plasma whose equilibrium properties vary with height in a horizontal variable magnetic field and a vertical gravitational field is considered. Three stability criteria are derived from the energy principle, two of which lead to the ``firehose'' and ``mirror'' instabilities found in a uniform anisotropic plasma while the third criterion is for the convective instability arising from gravity. In contrast to the isotropic case, it is found that the convective criterion depends explicitly upon the magnetic field. An increase of the magnetic field by a constant quantity shows that the plasma is more stable. The growth rates of the unstable displacements in the least stable regions are calculated using a normal mode analysis.

ISSN:0031-9171    

DOI:10.1063/1.1762054

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The minimum‐Bmagnetic field, provided by the superposition of a tranverse quadrupole‐cusp field and a uniform axial field, suppressed certain of the low‐frequency oscillations spontaneously present in the thermal cesium plasma of the TOPSYQ‐device with the uniform axial field alone, in conjunction with a sharp increase in the center‐line equilibrium plasma density of up to two orders of magnitude. However, measurements of the transverse plasma flux immediately prior to and immediately after oscillation suppression failed to detect any change in the radial plasma transport; the ``anomalous diffusion'' observed in the TOPSY plasma in a uniform magnetic field is still present in the absence of low‐frequency potential oscillations. Rather than being a function of plasma‐column oscillations, the observed cross‐field plasma transport isquantitativelyexplained in terms ofE/Bdrifts due to azimuthal ionizer‐plate temperature gradients. The sharp density increase which accompanied oscillation suppression must thus be ascribed to changes in the ionizer sheath conditions leading to an increased ``source'' flux of plasma into the column from the ionizer, rather than to a decrease in the radial plasma ``loss'' flux. These results have serious implications for the study of transport processes in plasmas and, in particular, call into question the use ofQ‐devices for the experimental study of ``anomalous diffusion'' in complex magnetic field geometries.

ISSN:0031-9171    

DOI:10.1063/1.1762055

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Exact (quasi‐neutral) one‐dimensional static pinch solutions are obtained when the distributions functions are allowed to have two perpendicular temperatures. The solutions can simulate plasma‐magnetic field interfaces, single sheet pinches, and periodic pinches.

ISSN:0031-9171    

DOI:10.1063/1.1762056

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A power supply consisting entirely of coaxial lines was used to produce a current pulse of 100 nsec duration in a thetatron coil, the plasma inside the coil being preionized. Measurements were made of the magnetic field, using magnetic probes, and of x rays produced. These measurements showed that, under suitable conditions, shock waves were produced and the electrons were heated to a temperature of several thousand electron volts. A necessary condition for producing an electron temperature approaching that required by shock theory was that the magnetic field outside the plasma should be in the opposite direction to the magnetic field inside the plasma.

ISSN:0031-9171    

DOI:10.1063/1.1762057

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

The fundamental solution of the linear Boltzmann equation in the two‐dimensional steady case is presented. The linear Boltzmann equation governs the perturbed distribution functionfin a steady flow over a point source. The point source is represented in the equation by a singular inhomogeneous term involving a delta function. The fundamental solution is split into three parts,f = f&dgr;+ fa+ fb. Bothf&dgr;andfaare explicit. They are singular at the origin and decay exponentially for large r. The ``remainder''fb, which satisfies an inhomogeneous linear Boltzmann equation, is bounded at the origin and behaves fluid‐dynamically like a macroscopic flow for larger. At smallr, the series expansion offbconsists of terms of integral powers ofrand integral powers ofrmultiplied by lnr, with the zeroth power ofrbeing the leading term. At intermediate and larger, fbis expressed in terms of the Euler fluid components.

ISSN:0031-9171    

DOI:10.1063/1.1762058

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

An initially discontinuous density distribution (the shock‐tube configuration) is studied analytically as an initial value problem for the Boltzmann equation. The distribution function is expressed in an infinite series of orthogonal polynomials in velocity space. The early time behavior is dominated by a collisionless interaction; the weight function for the orthogonal polynomials is, therefore, taken as the distribution function corresponding to the collisionless evolution of the density discontinuity. Moment equations are developed for Maxwell molecules. Truncation of the series for the distribution function leads to a determinate system of six quasilinear partial differential equations for the first six moments. For sufficiently small initial number density ratio the system is totally hyperbolic with the characteristics determined from the known collisionless solution. Numerical solutions are obtained for initial number density ratios of 5, 10, and 100. Early time results show the departure from collisionless behavior; moreover, after a sufficient time, the shock, contact, and expansion regions become evident as in the classical case. The shock region evolves into a steady‐state shock wave with structure similar to that obtained by steady‐state theories. The contact and expansion regions also assume their expected asymptotic character.

ISSN:0031-9171    

DOI:10.1063/1.1762059

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Using the Boltzmann equation, the initial filling rate of the high-energy tail of the distribution function is calculated for the case where the distribution function is zero above, and Maxwellian below a cutoff point. A general expression is obtained for the filling rate, as well as for the depletion rate of the distribution function below the cutoff point. The results are applied to hard sphere molecules, for which they can be evaluated analytically in terms of error functions. The resulting growth rate is compared with the corresponding one obtained using the Bhatnagar—Gross—Krook collision term. The latter rate correctly shows a number of aspects of the qualitative behavior, but is quite different numerically. The general result is also applied to Coulomb molecules, and the character of the resulting divergencies is exhibited. Relaxation of the distribution function in time is studied with the aid of a high-speed computer. It is concluded that under all conditions of physical interest, the characteristic filling time for the tail of the distribution function is of the order of the mean time between collisions.

ISSN:0031-9171    

DOI:10.1063/1.1762060

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

Applications of couple stress and micropolar theories to the problems of Couette and Poiseuille flows between two parallel plates are discussed and the results are compared.

ISSN:0031-9171    

DOI:10.1063/1.1762061

出版商:AIP    

年代:1967

数据来源: AIP

摘要:

A variational formulation is presented for the slow motion of viscous, heat‐conducting liquids whose viscosity and conductivity are realistic functions of temperature. The formulation reduces to previous results as special cases.

ISSN:0031-9171    

DOI:10.1063/1.1762062

出版商:AIP    

年代:1967

数据来源: AIP