摘要:

An approximate equation of state which gives good results at high temperatures is obtained for a general intermolecular potential. The method yields the exact second virial coefficient, and the entire equation of state can be obtained with the same amount of computational work as required for the second virial coefficient. The scheme is also applicable to the quantum correction of orderh2to the equation of state.

ISSN:0031-9171    

DOI:10.1063/1.1692310

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Solutions to the kinetic equation of a steady, homogeneous plasma of arbitrary degree of ionization subjected to strong electric fields are developed. Nonelastic as well as elastic encounters are included in the analysis. Expressions for the current density, electrical conductivity, and electron temperature of the plasma are also presented. Numerical results are illustrated for the case when the nonelastic effects are neglected. Calculations are presented showing the transition of the isotropic partf0of the distribution function from a gas‐temperature Maxwellian at near equilibrium conditions to an electron‐temperature Maxwellian under nonequipartition conditions. It was found that whenever the electron‐electron to electron‐neutral collision‐frequency ratio was much greater than the electron‐to‐heavy‐particle mass ratio,f0is Maxwellian. Whenf0is Maxwellian, the Chapman‐Enskog and Spitzer‐Ha¨rm conductivity expressions developed for the case of weak electric fields are shown to be applicable for strong electric fields providing that in these expressions the electron temperature replaces the gas temperature. An approximate form forf0suggested by Ginzburg is compared with the exact expression. The accuracy of the use of a Maxwellian rather than the nonequilibrium distribution function in the calculation of the electrical conductivity is assessed.

ISSN:0031-9171    

DOI:10.1063/1.1692311

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Experiments have been made on the electrical conductivity of a nonequilibrium, potassium‐seeded argon plasma at atmospheric pressure. The gas is heated uniformly in a vacuum heater up to a temperature of 1700°C. Electric field in the plasma is determined by electrostatic probes as a function of the current density through the plasma, which ranges from 10−5to 2A/cm2. For small current density, the plasma is in thermal equilibrium and the conductivity is independent of the current density. The average momentum transfer cross section between electron and potassium atoms estimated from the equilibrium conductivity is2.3 × 10−14 cm2. As the current density is increased the conductivity decreases, reaches a minimum, and then increases. When the current density is not small, the plasma is not in thermal equilibrium and the distribution function of electrons is not Maxwellian. The decrease of the conductivity is explained by considering inelastic collisions between electrons and potassium atoms and the radiation loss from the plasma. The apparent conductivity at large current density is much higher than the equilibrium value, although the uniformity of the current density was not assured.

ISSN:0031-9171    

DOI:10.1063/1.1692312

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Experimental results on steady magnetically balanced arcs in supersonic external flows are presented and analyzed, along with investigations elsewhere in subsonic flows, to determine the important similarity parameters. The studies indicate that the steady arc has a central core, impervious to the external flow, within which differential Lorentz forces generate a circulation analogous to that generated by gravity forces in nonuniformly heated gas in a horizontal tube. The conservation equations indicate that a “Lorentz convection parameter,” analogous to the Grashof number in free convection phenomena, is an important similarity parameter over a significant range of arc variables. A “characteristic velocity” for the core circulation is indicated. The similarity parameters that provide the interpolation between the properties of subsonic and supersonic balanced arcs indicate the approximations permissible for a first‐order solution to the internal circulation. It is inferred from the results that to a first approximation the thickness of the enthalpy boundary layer varies linearly with the reciprocal of the Reynolds number of the external flow.

ISSN:0031-9171    

DOI:10.1063/1.1692313

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The steady axially symmetric flow of an inviscid incompressible fluid of small conductivity, embedded in a strong magnetic field, past fixed bodies is studied as a problem of finite perturbation. The magnetic Reynolds number is assumed small so that the magnetic field is unperturbed. The flow depends on the parameter&bgr;which is proportional to the product of conductivity and the square of the magnetic field strength. The flow past a semi‐infinite body and a sphere is numerically calculated and the solution indicates that the effect of the body is felt upstream. This upstream influence is convected by the flow and appears as a nondiffusive boundary layer and a wake for the semi‐infinite body and the sphere, respectively. The drag and the various boundary layer and wake characteristics decrease with&bgr;. The classical Bernoulli functionH ( =p + 12 u2)decreases along streamlines and the pressure distribution on the surface of the bodies changes appreciably from the corresponding nonmagnetic value.

ISSN:0031-9171    

DOI:10.1063/1.1692314

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

As has been shown previously for the case of a cold plasma, the structure and propagation of hydromagnetic waves of finite but small amplitude can be described by the Korteweg‐de Vries equation. This equation can be derived from the set of the hydromagnetic equations for a collisionless cold plasma, by applying certain scaling relations between the pertinent field variables. For a cold plasma, the hydromagnetic transport equations are equivalent to the Vlasov equations because the distribution functions of the particle velocities are delta functions. In the case of a warm plasma, the initial distribution functions are Maxwellian. Starting from the Vlasov equations for the electron and ion gas of the plasma, the procedure as applied in the case of a zero temperature plasma leads, under known conditions, to a generalized time‐dependent Korteweg‐de Vries equation, with coefficients depending on the temperature of either plasma component and on the angle between the direction of wave propagation and the initial magnetic field. Charge separation effects and displacement currents appear to be negligible to lowest order.

ISSN:0031-9171    

DOI:10.1063/1.1692315

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The initial‐value problem for an unstable electron plasma has been solved by numerically integrating the Vlasov equation in one dimension. The situation chosen is the familiar “bump‐on‐the‐tail” situation of quasilinear theory. The solution is followed well beyond the point at which the electrostatic field energy has reached its maximum value. The electric field spectrum is eventually dominated by the single most linearly unstable wavenumber, which lies in the middle of the allowed range of wavenumbers; it undergoes what appear to be the beginnings of gentle long‐period oscillations characteristic of trapped‐particle periodicities. It is argued that differences from quasilinear predictions may be explained in terms of the level of initial excitations, or “noise,” from which the instability is assumed to proceed.

ISSN:0031-9171    

DOI:10.1063/1.1692316

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Theoretical considerations and previous experimental findings with fast tubular (cylindrical sheet) pinch discharges are reviewed briefly. More recent work with magnetic probes, as well as streak and Kerr cell photography, corroborates that the sheet‐current configuration can be sufficiently stable to survive a fair number of pinch oscillations. It is shown, however, that under conditions of high compression the current layer is likely to break up into a set of individual channels because of a resistive instability. The process involves tearing and reconnection of magnetic field lines. Wavelengths and growth rates seem to be in agreement with rough theoretical predictions. The current channels form separate linear pinches, which under certain circumstances disintegrate subsequently by a secondary instability. A generally turbulent behavior results. Tearing is not prevented by superposition of a strong axial magnetic field, again in agreement with theory, although a slight retardation is noted. When deuterium is used in the discharge, neutrons are emitted. Presumably because of the slow rate of reconnection in most of our studies, the neutrons appear mainly during the secondary instability, rather than at the time of tearing. These findings are of interest both to astrophysics and to controlled‐fusion research.

ISSN:0031-9171    

DOI:10.1063/1.1692317

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

ATM010, time‐resolved, cavity perturbation technique has been used to measure the total number of electronsNein a magnetic mirror compression experiment(Te ∼ 75 keV; ne ∼ 1012−1013 cm−3; plasma length∼ 10 cm; plasma diameter∼ 0.5 cm; cavity length∼30 cm; cavity diameter∼10 cm).Neis measured independently of the plasma density profile and in a high plasma density regime(&ohgr;p > &ohgr;010). High density measurements are possible because the plasma skin depth is greater than the plasma diameter and because the induced charge at the ends of the plasma is small. A swept frequency, raster presentation is used so that the variation ofNewith time can be followed. The measurements show thatNe ∼ 1012−1013at peak compression, and thatNedecays on a time scale∼4 msec. The cavity measurements were in substantial agreement with synchrotron radiation and light measurements, as well as with simple mirror theory.

ISSN:0031-9171    

DOI:10.1063/1.1692319

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

A warm Maxwellian plasma can stabilize velocity‐space instabilities which might otherwise occur in a hot non‐Maxwellian plasma with which it coexists. The relative densities and temperatures of the two species required for stabilization of resonant (&ohgr; ≈ l&OHgr;i, the ion gyroharmonics) loss‐cone modes in a mirror‐confined hot‐ion plasma are evaluated for a model plasma whose density is spatially uniform but whose velocity‐space distribution function simulates the loss‐cone effect of mirror confinement. Marginal stability boundaries are given and compared with several simple but inexact criteria. The dominant features of the stability boundaries are explained on the basis of cutoff of propagation of the unstable waves. Temporal growth rates of the absolutely unstable modes are found to decrease significantly with increasing warm‐plasma density. The resulting transition from absolute to convective growth is demonstrated for the first two gyroharmonics.

ISSN:0031-9171    

DOI:10.1063/1.1692320

出版商:AIP    

年代:1969

数据来源: AIP