摘要:

It is noted that a number of theories proposed recently by various authors are actually identical with the theory of polar fluids suggested by Grad in 1952. The relatively close relationship of the recently presented theory of dipolar fluids to polar fluid theory is established. The thermodynamics of polar fluids with heat conduction is sketched. The solved boundary‐value problems of polar fluid theory are summarized and the essential features of these solutions establish a pattern that gives insight into the behavior of polar fluids as well as indicating where the theory might be of practical significance.

ISSN:0031-9171    

DOI:10.1063/1.1692219

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The initial‐value problem is studied for an unbounded gas whose molecules possess internal energy states. A relaxation model is used to approximate the Wang Chang‐Uhlenbeck generalization of the Boltzmann collision integral for a polyatomic gas. The model depends on two adjustable parameters, the elastic and inelastic relaxation times. The problem gives some insight into the behavior of the collective modes of motion of the gas. For linear molecules permitted rotational but not vibrational degrees of freedom the model predicts corrections to the adiabatic sound velocity of(7kT/5m)12in the near continuum limit. The absorption as well as purely dissipative modes are obtained as functions of the elastic and inelastic relaxation times.

ISSN:0031-9171    

DOI:10.1063/1.1692220

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A treatment of the diffusion of a tangential discontinuity in flow velocity is given for the linearized Boltzmann‐Krook equation, with emphasis on the asymptotic behavior for large values of time. The connection with the general asymptotic theory of Grad is also discussed.

ISSN:0031-9171    

DOI:10.1063/1.1692221

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The classical third virial coefficient and its first quantum correction are evaluated analytically for the exponential repulsive potential. The classical integral for the Morse potential is treated approximately. The results are compared with the classical second virial coefficients for these models.

ISSN:0031-9171    

DOI:10.1063/1.1692222

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The virial theorem for a plasma is formulated within a particle framework. The result is applicable to isotropic, anisotropic, and quasirelativistic systems. The form reveals the negative quality of the time derivative of the virial in addition to the structure of the particle‐particle inductance tensor. A tensoral virial theorem is formulated for anisotropic systems. Equations of state for magnetoactive idealized plasma configurations are derived.

ISSN:0031-9171    

DOI:10.1063/1.1692223

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The collision integrals of various kinetic models are compared to those of the Boltzmann binary‐collision operator for gas mixtures. It is found that the Holway ellipsoidal model is unable to reproduce the Boltzmann result for the partial heat‐flow collision integral[&dgr;(12maca2ca)]abwhenma≫ mb. The Gross‐Krook and Sirovich models are found to be in serious disagreement with the Boltzmann operator with regard to the partial traceless‐pressure and heat‐flow collision integrals.

ISSN:0031-9171    

DOI:10.1063/1.1692224

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The Grad 13‐moment method (using separate zero‐order species flow velocities and temperatures) is used to calculate the electron traceless pressurePeand heat flowqefor a weakly ionized gas in a dc magnetic field. Electron‐neutral collisions are assumed to dominate and the “transport approximation” is used to obtain expressions forPeand qeusing arbitrary inverse power interparticle force laws. The results, under most conditions, show terms that are similar to the usual expressions for a simple gas except that the electron viscosity and thermal conductivity involve the electron‐neutral collision frequencyvenrather than the electron self‐collision frequency. In addition, there are terms inqeproportional to any differences in the zero‐order electron and neutral flow velocities and temperatures. Finally, it is noted that the electron‐neutral interparticle force law has very little effect on the form of the results (although it is important in determining the explicit value for&ngr;en).

ISSN:0031-9171    

DOI:10.1063/1.1692225

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

Nonequilibrium plasma states involving nonsmall current densities and/or enhanced electron temperatures are studied by taking 13 moments of the Boltzmann equation and using a new approach. New and nonlinear collisional terms are found for the basic equations. The electrical conductivity is calculated for the fully ionized case under no applied magnetic field: It first decreases slowly from the Spitzer‐Ha¨rm value, then turns sharply around and finally increases as a cubic power in the current density. The sharp turn‐around is located roughly at theelectron sonic point. Regarding the supersonic states it is observed that they can be reached and maintained as steady states if the local electric field is properly reduced below the critical runaway field∈cand is limited to the steady‐state value. Some associated instabilities and ways of stabilization are discussed. It is also observed that unsteady “run‐away” will occur when∈cis exceeded, as emphasized by Dreicer. The possibility of an insurmountable “electron sonic barrier” is indicated. Experimental studies are urged.

ISSN:0031-9171    

DOI:10.1063/1.1692226

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

The dynamic behavior of magnetically driven axisymmetric plasma sheets of negligible thickness is examined by postulating a simplified two‐dimensional plasma sheet model. The equations of motion in the axial and radial directions are derived in Lagrangian form for the general case of time‐varying current. For the case of constant current, the general solution of the equations of motion is obtained. These equations of motion are solved for three different types of small sinusoidal perturbations of a cylindrical implosion. The plasma sheet configurations, particle trajectories, and surface mass density variations are presented for representative examples.

ISSN:0031-9171    

DOI:10.1063/1.1692227

出版商:AIP    

年代:1968

数据来源: AIP

摘要:

A universal relationship is deduced between diffusion coefficients, electric field spectra, and averaged Liouville orbit functions for a turbulent plasma in a magnetic field. This relation is a generalization of a similar relation previously derived by Dupree from completely different considerations. In particular, the solution of the Vlasov equation is avoided. Aside from generality and rigor, the present result differs from Dupree's in that the latter involves Vlasov orbit functions whereas the former involves Liouville orbit functions. The Liouville orbit function is easily evaluated by expanding in terms of the cumulants (semi‐invariants) of the moments of the exact particle orbits. Dupree's results are thus produced without having to solve the nonlinear Vlasov equation. The present results can be viewed as an extension of Spitzer's diffusion formula to strong plasma turbulence. Conditions for the validity of the diffusion expression are determined, and corrections are made for mode frequencies in excess of gyro‐frequencies.

ISSN:0031-9171    

DOI:10.1063/1.1692228

出版商:AIP    

年代:1968

数据来源: AIP