摘要:

A previously developed perturbation‐theory‐to‐all‐orders formalism is applied to the oscillations of a ``collisionless'' electron plasma which is bounded by perfectly reflecting walls. The long‐time damping rate is the same for thenth order electric field as for the first order. This result generally doesnotapply to the unbounded plasma.

ISSN:0031-9171    

DOI:10.1063/1.1706869

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

Theory of nonlinear stationary longitudinal waves in relativistic plasmas is treated by solving a relativistic Boltzmann equation without the conventional approximation of linearization. It is proved here that in plasmas of physically reasonable electron velocity distributions, stationary waves of arbitrary amplitude can be propagated and obey a dispersion equation. If the velocity of propagationVis less than the velocity of lightc, the amplitude of these waves will generally be limited; if the velocity of wave propagation is greater thanc, however, there is no amplitude limitation. The nonlinearity in the Boltzmann equation causes a decrease of frequency of oscillation for a given wave velocity in addition to the distortion in waveform from pure sinusoidal waves. Detailed solutions for plasmas with Maxwellian electron velocity distribution and relativistic electron beams are given. In the former case, a dispersion equation including nonlinear effect is derived through a series expansion to an order higher than that used in the linearized theory. In the latter, a complete analytic solution in terms of elliptical integrals is given. In both cases dispersion characteristics for several parameters are computed and plotted. The agreement between these nonlinear dispersion equations in the limit of vanishing amplitudes and those of the linearized theory published in literature is indicated.

ISSN:0031-9171    

DOI:10.1063/1.1706870

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The problem of the plane wave oscillation of a one‐dimensional plasma is considered. It is shown that for stable plasmas with unperturbed distribution functions in a general class which includes Maxwellians as a special case, the electric field does not damp exponentially fast, as predicted by Landau. Instead, the electric field tends to zero as some reciprocal power of time, where the exact power depends on the smoothness of the initial data. To obtain a more conventional result it is assumed that all distribution functions vanish for particle speed greater than some constant, as they must relativistically. Then for wavenumber less than a certain constant the plasma oscillations do have an undamped part corresponding to a conventional normal mode with a phase speed greater than the fastest particle speed. For wavenumbers larger than that constant the oscillations tend to zero as some reciprocal power of time.

ISSN:0031-9171    

DOI:10.1063/1.1706871

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The fluctuation longitudinal electric field,Ek, is studied for a two component plasma immersed in a uniform, external electric fieldE0. Since the time dependence of the space‐averaged part of the distribution functions precludes the usual Laplace transform approach, computational techniques are developed to solve the integral equation forEkdirectly in the time domain. Solutions are given for the case whereE0is large compared to the critical field for runaway and compared with the familiar constant‐drift solutions. Growth in the vicinity of resonance (vdrift≈ &ohgr;p/k) is observed, followed by Landau damping at longer times.

ISSN:0031-9171    

DOI:10.1063/1.1706872

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The usual kinetic equation derived from the B‐B‐G‐K‐Y hierarchy for a plasma with Coulomb interparticle forces breaks down for plasmas with distribution functions which the linearized Vlasov equation would predict to be unstable. As the first step towards deriving a kinetic equation for an unstable plasma in this paper the equation for the two‐particle correlation function is solved for times for which the distribution function may be regarded as time independent. Part of the correlation function is shown to grow exponentially in time; thus the Bogoliubov adiabatic hypothesis breaks down. Taking only the fastest growing part of the correlation function, a velocity space diffusion equation is obtained for the distribution function with a time‐dependent diffusion coefficient.

ISSN:0031-9171    

DOI:10.1063/1.1706873

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The influence of four basic relaxation mechanisms on two‐component plasma waves is examined. The analysis stems from a set of generalized macroscopic equations that include two self‐relaxation mechanisms in addition to terms which dampen difference in temperatures and difference in flows between the gases. The emergent dispersion relation is diagonal with respect to longitudinal and transverse components of the state vector. The longitudinal relation is linear in the temperature coupling parameter while the transverse relation is independent of the self‐relaxation rates and the difference in velocity relaxation rates. The longitudinal determinant yields well‐known roots in the limit of long temperature relaxation times, while in the opposite limit new relations are obtained.

ISSN:0031-9171    

DOI:10.1063/1.1706874

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The most general form of hydromagnetic Kelvin‐Helmholtz discontinuity in ideal incompressible fluids has been considered. The presence of surface tension on the surface of discontinuity and gravity is also assumed. The stability of the hydromagnetic flow of two uniform infinite streams with planar interface exhibiting this type of discontinuity, has been analyzed in detail. Two necessary and sufficient criteria for its stability have been obtained, in contrast to only one that is usually given. The stabilizing effect of magnetic field is strongly dependent on its discontinuity at the interface and its orientation relative to that of streaming. The consideration of the stability to a single mode of perturbation leads to the conclusion that this is dependent on the above mentioned factors, as well as the following ones. The effect of surface tension and gravity is dependent on the wavelength, while that of the magnetic field is dependent on the direction of propagation of perturbation.

ISSN:0031-9171    

DOI:10.1063/1.1706875

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

Electromagnetic propagation through an infinite circular cylindrical traveling wave tube in which a conducting fluid of constant conductivity is moving axially with uniform speed is studied. Asymptotic solutions valid for |&agr;R0|«1 and |&agr;R0»1, where &agr; is the complex separation constant andR0the tube radius, are obtained and analyzed. Concentrating specifically on the axial body force per unit tube length induced in the fluid, the |&agr;R0|»1 solution indicates, fixing the current sheet input and geometry, that the magnitude of the induced axial force is a marked function of the dimensionless parameter &bgr;, equal to the magnetic Reynolds number based on wavespeed and wavelength multiplied by the slip. The body force rises linearly with &bgr; for small &bgr;, reaches a peak and then, because of the inability of the electromagnetic field to penetrate into the conductor with increasing &bgr; (skin effect), falls like &bgr;−1/2for large &bgr;. From the practical viewpoint, the results suggest the adjustment of the electrical and fluid mechanical parameters so that operation occurs at that value of &bgr; which optimizes the force. It is further indicated, especially for moderate to high &bgr; operation, that for efficient utilization and conservation of working fluid mass and electrical energy, injection and acceleration take place in an annulus close to the coils rather than throughout the entire cross section.

ISSN:0031-9171    

DOI:10.1063/1.1706876

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The effect of electrical resistivity on hydromagnetic instabilities is studied with special emphasis on interchange instabilities. A ``stellarator'' expansion is utilized to reduce the stability problem to one of solving two coupled second‐order ordinary differential equations. This expansion enables one to treat a general geometry in a simple manner. A low‐pressure strongly stabilized pinch is one special case. Further expansions are made in which perturbations vary rapidly in a thin layer the width of which is related to the resistivity. Highly localized interchange instabilities are found with growth rates which are independent of the resistivity in the limit as it goes to zero. These exist whenever the pressure decreases outwards. Interchanges with eddies of finite length grow more slowly, as the cube root of the resistivity. A stability criterion for king modes, which are characterized by vanishing pressure gradients in the resistive layer, is obtained. It depends on the entire plasma configuration and is identical to the one that would be obtained from the energy principle if the resistive layer were replaced with a vacuum. Gyration radius effects which are not included may significantly affect these resistive instabilities because they have slow growth rates and vary rapidly in a localized region.

ISSN:0031-9171    

DOI:10.1063/1.1706877

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

It is shown that a weakly ionized plasma column in an axial magnetic field and an inward‐directed radial electric field—a Penning discharge at higher pressures—is unstable against a macroscopicm= 1 perturbation. The instability is analyzed by dimensional analysis. The applicability of this method is discussed. A steady‐state model of some experimental Penning discharges is developed. On the basis of this model, the critical magnetic field for the onset of instability as predicted by the theory agrees well with the values observed. The instability discussed here is caused by the presence of a third fluid, the neutrals, in an electron‐ion plasma. The same mechanism is also applicable to the initial phase of some rotating plasmas of the homopolar type.

ISSN:0031-9171    

DOI:10.1063/1.1706878

出版商:AIP    

年代:1963

数据来源: AIP