摘要:

It is shown that an appropriate choice of variables can greatly simplify the discussion of equilibrium and stability of low‐pressure plasma in arbitrary mirror fields. One specifies by &agr; and &bgr; the line of force on which a particle is moving and also specifies its adiabatic invariants &mgr;,J; the energy of the particle is then determined as a functionK(&mgr;,J, &agr;, &bgr;) which plays the role of a Hamiltonian. Any equilibrium distribution can then be written in the formF{&mgr;,J, K(&agr;, &bgr;, &mgr;,J)} and it is shown that a sufficient criterion for such distributions to be stable against interchanges is (∂F/∂K)&mgr;J< 0. Necessary and sufficient criteria are also derived. When approached in this way, the exact form of the field configuration only enters the problem through the determination of the functionK, which may be easily calculated. In general a comprehensive view of plasma behavior, convenient for the discussions of equilibrium, confinement and stability, can be obtained from the structure of theK(&agr;, &bgr;, &mgr;,J) = constant contours. An example of the application of this approach to a Ioffe stabilized mirror is described. This confirms the existence of stable plasma equilibria in this field configuration.

ISSN:0031-9171    

DOI:10.1063/1.1711283

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

It is shown that the Penrose criteria for the existence of unstable electrostatic oscillations of a Vlasov plasma can be derived simply from the energy‐momentum conservation laws applied to marginally unstable modes. These criteria also are obtained variationally as necessary conditions for instability by extremizing the possible motions which can convert kinetic energy into electric field energy.

ISSN:0031-9171    

DOI:10.1063/1.1711284

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The effect of an isotropic pressure on longitudinal nonlinear plasma waves is investigated. Two distinct types of solitary wave solutions are found, one similar to the nonlinear zero pressure wave and a new type which is best described as a solitary wave within a solitary wave. The order of magnitude of the width of the first type of wave and the outer part of the second is the geometric mean of the gyroradii of the ions and electrons when moving with the Alfve´n speed. It is found that the isotropic pressure shortens the width of the first type of wave. Both cases of unequal and equal ion and electron temperatures are investigated for the two types of waves.

ISSN:0031-9171    

DOI:10.1063/1.1711285

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The method of expansion in instantaneous eigenfunctions is used to obtain approximate solutions to the linearized Vlasov equation when the unperturbed function is time‐dependent. The method is useful when the time‐dependence of the unperturbed function is slow compared with the plasma frequency. The general results are used to obtain the growth of wave energies in the quasilinear limitation of weak two‐stream instabilities. Deviations from previous results for this problem are found.

ISSN:0031-9171    

DOI:10.1063/1.1711286

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

An approximation scheme is developed for calculating the equilibrium properties of a system containing both short‐range and weak long‐range interactions. The results are applied to the calculation of the pair correlation and equation of state for an electron gas in a neutralizing background. Although the starting point is the Bogoliubov‐Born‐Green‐Kirkwood‐Yvon hierarchy, the short‐range divergence usually encountered in the ``dynamic'' approach is avoided, and the results (calculated through second order in the plasma parameter) are found to be in agreement with previous calculations by diagrammatic methods.

ISSN:0031-9171    

DOI:10.1063/1.1711287

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The influence of non‐Maxwellian free electron energy distributions on the steady state de‐excitation radiation of not completely stripped impurity ions persisting in homogeneous spherical plasmas is investigated. A formulation of the source function for arbitrary free electron energy distributions is given. Numerical examples which emphasize the importance of the effect discussed are presented.

ISSN:0031-9171    

DOI:10.1063/1.1711288

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The exchange of energy between a plasma, and a test particle in a time‐independent potential, has been studied. The motion of the test particle and the plasma interactions are treated quantum mechanically. A general formula, obtained for the energy transfer, is applied to the problems of the free particle and to the linear harmonic oscillator in the dipole approximation. Contributions to the energy transfer are separated into parts associated with friction and with thermal agitation or velocity diffusion. The results are compared with the classical limits. For the free particle, the corrections to the classical results are logarithmic, whereas for the harmonic oscillator the corrections are very important, when the oscillator transition energies exceed the random electron energies in the plasma. The frictional contribution to the energy loss by the oscillator is related to the electrical conductivity.

ISSN:0031-9171    

DOI:10.1063/1.1711289

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The correlation function between the electrostatic field at pointaand the electrostatic field at pointbin a fully ionized hydrogen plasma is computed. The correlation function is shown to be a long‐range function of the distance between pointsaandb. This result has significance in the treatment of transport properties in a plasma.

ISSN:0031-9171    

DOI:10.1063/1.1711290

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The nonlinear theory has been extended to spatially growing plasma oscillations in a bounded plasma, and it is shown that at large distances this leads to a stationary turbulent electrostatic spectrum. A novel feature appears in that the gradient of the longitudinal radiation pressure leads to a charge separation and consequently to a dc electrostatic field in the region in which the turbulence is growing.

ISSN:0031-9171    

DOI:10.1063/1.1711291

出版商:AIP    

年代:1964

数据来源: AIP

摘要:

The flow of an infinitely conducting plasma past a two‐dimensional magnetic dipole oriented parallel to the flow has been considered by Hurley, among others. The problem consists of finding a vacuum magnetic field such that along a bounding field line whose location is to be found, the magnetic pressure balances the Newtonian dynamic pressure appropriate to the local slope of the boundary. A related problem has been solved by Cole and Huth; in their case there is no flow, but an isotropic static plasma surrounding the magnetic field region which exerts a constant pressure on the boundary. In the actual flow problem we would expect there to be a stagnant (trapped) region near the front. The stagnant flow would be at nearly constant pressure. Away from this region the Newtonian pressure would again be applicable. This problem, which is a mixture of those cited above, has been solved by an approximate technique due to Cockcroft. The solution is shown to have features of both the cited problems, as appropriate.

ISSN:0031-9171    

DOI:10.1063/1.1711292

出版商:AIP    

年代:1964

数据来源: AIP