摘要:

A linear relaxation equation for the heat flux in a fluid, proposed by Vernotte as a generalization of Fourier's law, is shown for liquids to be consistent with the assumption that thermal energy is carried by elastic waves of very high frequency which may be envisaged as being propagated in a continuum. The elastic constants and the velocity of the waves are obtained from the infinite frequency limits of viscoelastic equations, derived in earlier papers to describe the relaxation of compressional and shearing strains, and from these, the relaxation time and thermal conductivity are calculated for several nonassociated liquids with the aid of a theory of Debye. It is shown that the Vernotte equation may be viewed formally, from the point of view of irreversible thermodynamics, as a force‐flux equation linking two irreversible processes, and this interpretation makes it possible to calculate terms in the pressure and internal energy which are nonlinear in the temperature gradient.

ISSN:0031-9171    

DOI:10.1063/1.1706020

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The Montroll‐Ward‐Lee‐Yang approach to quantum statistics is generalized to multicomponent systems. It is also generalized so as to include external fields. The formalism is constructed in a volume‐dependent manner, and includes internal coordinates, such as spin, from the beginning. It is rigorously proved that the quantum‐mechanical volume‐dependent cluster integral may be expressed in terms of connected diagrams only. The rules for drawing these diagrams are given. By simply generalizing the meaning of the word ``determinant,'' all arguments are made to apply to both Fermi‐Dirac and Bose‐Einstein statistics simultaneously. A statistics factor, &ggr; = ±1, for bosons (fermions) is introduced, in terms of which single formulas apply to both statistics. Rules are stated, by means of which the &ggr; dependence of the contribution to the pressure for any diagram is given in terms an elementary topological property of the diagram.

ISSN:0031-9171    

DOI:10.1063/1.1706021

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The starting point is the Liouville equation for the density in phase space of a system of charged particles and a denumerably infinite set of field oscillators. By integrating out the coordinates of all but a finite number of particles and oscillators one obtains a chain of equations relating the reduced distribution functions. A complete solution to the chain is obtained by a generalization of the expansion method of Rosenbluth and Rostoker. In lowest order, a coupled set of self‐consistent field equations in the one‐particle and one‐oscillator distributions is obtained. These are partially decoupled to give the usual Vlasov equation and a companion equation for the oscillator distribution. In first order one obtains a similar set of equations for the two‐particle and the particle‐oscillator correlation functions. An entirely similar pair of equations then relates the first‐order distribution functions themselves. It appears that the general solution is obtained by the steady unfolding of higher correlation functions in terms of higher and higher self‐consistent field equations. The first‐order equations can be regarded as a ``Fokker‐Planck'' equation for particles and a ``Fokker‐Planck'' equation for radiation.

ISSN:0031-9171    

DOI:10.1063/1.1706022

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The Vlasov equations have been derived previously by Harris by starting from the Liouville equation and treating both plasma particles and electromagnetic field statistically. A byproduct of this derivation was an equation forf&lgr;(q&lgr;,p&lgr;), the probability density in the phase space of one of the radiation field oscillators. These functions are now used to define an entropy for the electromagnetic field. If the phases and amplitudes of all electromagnetic waves are precisely defined (coherent radiation), the field entropy is negatively infinite. Any incoherence increases the entropy. A direct consequence of thef&lgr;equation is that the field entropy is a constant of the motion. This is analogous to Newcomb's proof that the particle entropy is constant. It follows that incoherent radiation cannot be calculated from the Vlasov equations.

ISSN:0031-9171    

DOI:10.1063/1.1706023

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

A stability criterion is obtained starting from Vlasov's collision‐free kinetic equations. Possible instabilities propagating parallel to an arbitrary unit vectoreare related to a functionF(u)≡&Sgr;j&ohgr;j2∫d3vgj(v) &dgr;(e·v−u), wheregi(v) is the normalized unperturbed distribution function, and&ohgr;j≡(4&pgr;njej2/mj)12the plasma frequency, for thejth type of particle. By using a method related to the Nyquist criterion, it is shown that plasma oscillations growing exponentially with time are possible if and only ifF(u) has a minimum at a valueu= &xgr; such that∫−∞∞du(u−&xgr;)−2[F(u)−F(&xgr;)]>0. A study of the initial‐value problem confirms that the plasma is normally stable if no exponentially growing modes exist; but there is an exceptional class of distribution functions (recognizable by means of an extension of the above criterion) for which linearized stability theory breaks down. The method is applied to several examples, of which the most important is a model of a current‐carrying plasma with Maxwell distributions at different temperatures for electrons and ions. The meaning of the mathematical assumptions made is carefully discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706024

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The particle treatment is applied to a study of the structure of the wake behind a charged body moving supersonically through a low‐density plasma. For the case of a body whose dimensions are considerably smaller than a Debye length, a solution is obtained which is very similar in structure to the solution obtained by using the linearized fluid dynamics equation. For the case of a disk whose radial dimensions are much larger than a Debye length, two conical regions are found in the wake. At the surface of each of these cones, over thicknesses of the order of a Debye length, the ion and electron densities are increased over their ambient values. Formulae for the electrohydrodynamic drag on a wire, and on a large disk are obtained.

ISSN:0031-9171    

DOI:10.1063/1.1706025

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The problem of the stability of the nonlinear plasma oscillations of Bernstein, Greene, and Kruskal is discussed. The eigenvalue equation for the perturbed distribution function possesses an expansion in powers of a parameter proportional to the maximum value of the equilibrium electrostatic potential. The stability of any given distribution can be inferred from consideration of the zeroth order alone.

ISSN:0031-9171    

DOI:10.1063/1.1706026

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

A dispersion relation is derived and analyzed for the case where the equilibrium velocity of an incompressible, nonresistive, cylindrical plasma has a spiral motion along magnetic field lines. The symmetric hydromagnetic equations are used to derive the plasma hydromagnetic pressure. The dispersion relation is found by matching plasma and outer‐region hydromagnetic pressures across a sharp‐moving interface. The zeros of the dispersion relation are obtained by a sequence of mappings between three complex planes. The presence of flow introduces overstable modes. Form= 0 the time‐divergences are removed by flow. Form= 1 the divergences are enhanced by flow such that the growth rates and oscillation frequencies increase linearly with the flow velocity. The smaller is the wavelength of the disturbance in thezdirection, the larger are the overstable eigenvalues.

ISSN:0031-9171    

DOI:10.1063/1.1706027

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

A theory is developed for a Langmuir‐type probe consisting of a collecting electrode placed at the stagnation point of a blunt body immersed in a supersonic partially ionized stream. It is shown that under certain conditions, the stagnation‐point boundary layer equations and the probe sheath equations can be solved together to yield potential vs current relationships which permit the free stream ion and electron densities and temperatures to be measured by such a probe. It is shown also that the stagnation‐point heat transfer will vary with probe potential, thus providing additional information useful in plasma jet diagnostics.

ISSN:0031-9171    

DOI:10.1063/1.1706028

出版商:AIP    

年代:1960

数据来源: AIP

摘要:

The solution of the equation for the current in an ideal plasma, when the electric field, in a direction perpendicular to a constant magnetic field, is abruptly increased from zero to a constant value, is obtained using Laplace transforms. An exact solution and approximate solutions for some simple cases are obtained and discussed. An expression and the corresponding RLC network are found for the specific impedance of the plasma.

ISSN:0031-9171    

DOI:10.1063/1.1706029

出版商:AIP    

年代:1960

数据来源: AIP