M. N. Rosenbluth

A general method, suitable for fast computing machines, for investigating such properties as equations of state for substances consisting of interacting individual molecules is described. The method consists of a modified Monte Carlo integration over configuration space. Results for the two-dimensional rigid-sphere system have been obtained on the Los Alamos MANIAC and are presented here. These results are compared to the free volume equation of state and to a four-term virial coefficient expansion.

The stability of a plane current layer is analyzed in the hydromagnetic approximation, allowing for finite isotropic resistivity. The effect of a small layer curvature is simulated by a gravitational field. In an incompressible fluid, there can be three basic types of ``resistive'' instability: a long-wave ``tearing'' mode, corresponding to breakup of the layer along current-flow lines; a short-wave ``rippling'' mode, due to the flow of current across the resistivity gradients of the layer; and a low-g gravitational interchange mode that grows in spite of finite magnetic shear. The time scale is set by the resistive diffusion time τR and the hydromagnetic transit time τH of the layer. For large S = τR/τH, the growth rate of the ``tearing'' and ``rippling'' modes is of order τR−3/5τH−2/5, and that of the gravitational mode is of order τR−1/3τH−2/3. As S → ∞, the gravitational effect dominates and may be used to stabilize the two nongravitational modes. If the zero-order configuration is in equilibrium, there are no overstable modes in the incompressible case. Allowance for plasma compressibility somewhat modifies the ``rippling'' and gravitational modes, and may permit overstable modes to appear. The existence of overstable modes depends also on increasingly large zero-order resistivity gradients as S → ∞. The three unstable modes merely require increasingly large gradients of the first-order fluid velocity; but even so, the hydromagnetic approximation breaks down as S → ∞. Allowance for isotropic viscosity increases the effective mass density of the fluid, and the growth rates of the ``tearing'' and ``rippling'' modes then scale as τR−2/3τH−1/3. In plasmas, allowance for thermal conductivity suppresses the ``rippling'' mode at moderately high values of S. The ``tearing'' mode can be stabilized by conducting walls. The transition from the low-g ``resistive'' gravitational mode to the familiar high-g infinite conductivity mode is examined. The extension of the stability analysis to cylindrical geometry is discussed. The relevance of the theory to the results of various plasma experiments is pointed out. A nonhydromagnetic treatment will be needed to achieve rigorous correspondence to the experimental conditions.

Kelvin isotherm, lattice vibrations, fluid degrees of freedom, thermal electronic excitation and ionization, and molecular vibrational and rotational degrees of freedom. Two options are available for computing EOS for multicomponent systems from separate EOS for the individual species and phases. The phase transition model is used for a system of immiscible phases, each having the same chemical composition. In the mixture model, the components can be either miscible or immiscible and can have different chemical compositions; mixtures cab be either inert or reactive. PANDA provides over 50 commands that are used to define the EOS models, to make calculations and compare the models to experimental data, and to generate and maintain tabular EOS libraries for use in hydrocodes and other applications. Versions of the code available for the Cray (UNICOS and CTSS), SUN (UNIX), and VAX(VMS) machines, and a small version is available for personal computers (DOS). This report describes the EOS models, use of the commands, and several sample problems. 92 refs., 7 figs., 10 tabs.

Formulas for the electron thermal conductivity have been derived in the collisional and collisionless limits for the case of destroyed magnetic surfaces.Received 26 September 1977DOI:https://doi.org/10.1103/PhysRevLett.40.38©1978 American Physical Society

The contribution to the Fokker-Planck equation for the distribution function for gases, due to particle-particle interactions in which the fundamental two-body force obeys an inverse square law, is investigated. The coefficients in the equation, $〈\ensuremath{\Delta}\mathrm{v}〉$ (the average change in velocity in a short time) and $〈\ensuremath{\Delta}\mathrm{v}\ensuremath{\Delta}\mathrm{v}〉$, are obtained in terms of two fundamental integrals which are dependent on the distribution function itself. The transformation of the equation to polar coordinates in a case of axial symmetry is carried out. By expanding the distribution function in Legendre functions of the angle, the equation is cast into the form of an infinite set of one-dimensional coupled nonlinear integro-differential equations. If the distribution function is approximated by a finite series, the resultant Fokker-Planck equations may be treated numerically using a computing machine. Keeping only one or two terms in the series corresponds to the approximations of Chandrasekhar, and Cohen, Spitzer and McRoutly, respectively.