摘要:

We consider the stability of a weakly ionized, low‐density (1010‐1012) plasma in a uniform magnetic field. The plasma is in a finite conducting chamber and there is diffusion across the field lines and streaming to the conducting end walls. The stability analysis is similar to that of Kadomtsev and Nedospasov for the positive column. It is found that instability sets in above a critical field or below a critical background pressure. The driving force is the charge separation produced by the unequal streaming of ions and electrons to the end walls. The unstable mode is helical in space and rotates about the axis of symmetry. Expressions are obtained for the critical field value and for the rotational velocity. These compare favorably with the experiments of Neidigh and Weaver and those of Zharinov.

ISSN:0031-9171    

DOI:10.1063/1.1706650

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

A necessary and sufficient condition for the stability with respect to localized displacements is obtained for arbitrary bounded hydromagnetic equilibria. The use of a natural coordinate system which contains the important properties of the equilibrium configuration facilitates the understanding of the instability.

ISSN:0031-9171    

DOI:10.1063/1.1706651

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The problem of the ac conductivity of a fully ionized plasma is investigated for frequencies embracing the plasma frequency. The finite duration of encounters is taken into account in a self‐consistent fashion which includes collective effects. The concomitant processes of absorption and emission of electromagnetic radiation are investigated and in particular the bremsstrahlung emission and absorption coefficients near the plasma frequency are given. The conversion of longitudinal to transverse waves by scattering from ions is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706652

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Starting with Liouville's equation, a set of equations is derived in the random‐phase approximation for the evolution of the spatial Fourier components of the complete distribution function of a particle in a plasma. A procedure is used which takes account of all the contributions coming from many‐body interactions in the random‐phase approximation. The equations thus describe the collective part of the response of plasma to the particle. The equations which have the structure of the Fokker‐Planck equation describe collisions of electrons carrying an envelope of plasma waves emitted by them. It is shown that in the Markoff approximation this envelope degenerates into a Debye shielding cloud, so that in this approximation the equations describe the collisions of electrons clothed in Debye shielding clouds.

ISSN:0031-9171    

DOI:10.1063/1.1706653

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

A close analogy is found and mathematically investigated between the dynamic behavior of a plasma in a magnetic field and that of a unipolarly charged fluid in an electric field. The general equations and some of their broad consequences are discussed. Unidirectional flow, small disturbances, and stability are compared for the two systems.

ISSN:0031-9171    

DOI:10.1063/1.1706654

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The entry problem in plane laminar magnetohydrodynamic flow is solved numerically for various values of the pertinent parameters describing the flow. The channel configuration is a parallel‐plate channel which has the Hartmann profile for its fully developed velocity flow. The equations are placed in a finite difference form to enable the essential nonlinearities of the principal equations to be used in the solution of the problem. Velocity, temperature, and pressure curves are presented from the results of computational work.

ISSN:0031-9171    

DOI:10.1063/1.1706655

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The flow of an infinitely conducting inviscid gas in the presence of a magnetic field everywhere parallel to the velocity is considered. Such a flow starting from rest and expanding to supersonic velocities has three transitions, across each of which the flow differential equations change type: from elliptic to hyperbolic, or vice versa. The flow velocities at the three transitions are, respectively, the sound speedc, the Alfve´n‐wave speeda, and the speedca/(c2+a2)1/2. A class of those flows is approximately constructed by solving the flow differential equations, with the flow velocity, etc., prescribed on an axis of symmetry. The solution is in the form of a formal power series in a neighborhood of the axis. The resulting streamlines give possible symmetric nozzle contours. Some mathematical investigations are made to determine the acceptable form of the data to be given on the axis. Numerical examples giving nozzle shapes are included and compared with similar nozzles for nonconducting gases. The procedure described is an extension of that of Friedrichs for ordinary gas nozzles.

ISSN:0031-9171    

DOI:10.1063/1.1706656

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The stability of an electrically conductive and incompressible fluid between coaxial rotating cylinders in the presence of a radial density gradient, as well as a circular magnetic field, is studied. The effects of gravity and of the heat generated through viscous and magnetic dissipation is neglected. An eigenvalue problem is formulated for rotationally symmetrical disturbances. Detailed calculations are made for the case of small spacing between the two cylinders. Three dimensionless parameters, each of which contains only one of the three (momentum, thermal, and magnetic) diffusivities, are defined. Parametric equations for surfaces of marginal stability are given, and several planes cutting such surfaces are drawn for the discussions of the roles played by the diffusivities. It is found that both the momentum diffusivity and the magnetic diffusivity are capable of playing the dual role (i.e., the role of stabilization and destabilization simultaneously) in the problem.

ISSN:0031-9171    

DOI:10.1063/1.1706657

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The dimensionless ratiof= &lgr;M/&eegr;Cvrelating the thermal conductivity, molecular weight, viscosity, and constant‐volume molar heat capacity has been determined experimentally for helium, argon, nitrogen, oxygen, and hydrogen in the range 90°–290°K. The experimental method provides a direct determination offby measurement of the subsonic temperature recovery factor. For helium,f= 2.503, and for argon,f= 2.506, in complete accord with the rigorous Chapman‐Enskog kinetic theory for monatomic gases. Data on nitrogen, oxygen, hydrogen, and also carbon dioxide confirm, at least qualitatively, a recent approximate theory which relates deviations from the modified Eucken approximation to the relaxation times of internal energy states. Collision numbers for rotational relaxation derived from the experimental data are: nitrogen, 6.8; oxygen, 6.0; and carbon dioxide, 2.4. These collision numbers are very nearly independent of temperature. The results confirm the fact that the interchange of translational and rotational energy is unusually difficult for hydrogen.

ISSN:0031-9171    

DOI:10.1063/1.1706658

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The stability of an electrically charged droplet with respect to mechanical deformations is studied under the assumptions that the liquid is perfectly conducting, the medium devoid of external fields of force, and the sum of the electrical and mechanical energies in the system conserved. Unlike Rayleigh's case, which dealt with small perturbations of spherical drops, the deformations considered in the present case are allowed to be large in size but confined in shape to ellipsoids of revolution. The energy of the deformed droplet is expressed as a function of a geometrical parameter and the ratio &agr; between the electrical and surface energies of the corresponding spherical shape. Likewise, the dependence of the extremal points on &agr; is investigated. Conforming with Rayleigh, the spherical droplet is shown to be unstable for &agr; > 4 and stable for &agr; < 4. However, for a certain range of &agr; in the latter case, it is found to be only in a metastable state. In addition, both one prolate and one oblate ellipsoid of minimal energy are shown to exist for every &agr; > 4.

ISSN:0031-9171    

DOI:10.1063/1.1706659

出版商:AIP    

年代:1962

数据来源: AIP