摘要:

The problem of Landau damping in plasma oscillations is studied in a relativistic gas and the asymptotic forms of the dispersion relation and the damping coefficient are obtained in the non‐relativistic as well as in the relativistic limits. In the relativistic limit it is found that while the damping is very strong in the case where the phase velocity is small compared to the velocity of light, it is absent when the phase velocity exceeds the velocity of light. Moreover, in the former case, in the extreme relativistic limit the damping becomes independent of the plasma temperature.

ISSN:0031-9171    

DOI:10.1063/1.1706486

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Transverse electromagnetic oscillations in a gyrotropic plasma exhibit Landau damping when the wave is not monochromatic. The dependence of the damping on the equilibrium distribution and the boundary (or initial) values is investigated. The resulting dispersion relation is interpreted by examining the response of a single free electron to an incident wave. It is shown that the damping mechanism is associated with the Doppler shift caused by the thermal distribution, so that some particles are in cyclotron resonance for any laboratory frequency. The correlation of whistler data with this complex dispersion relation can be used to evaluate electron temperatures at several earth radii; a specific numerical example givesT≈ 105°K atR≈ 4Re(geocentric).

ISSN:0031-9171    

DOI:10.1063/1.1706494

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

An instability that consists of a bunching transverse to the directed motion of an infinitely thin layer of electrons is investigated theoretically. The initial model is a plane sheet, infinite in extent, and neutralized by positive ions. This configuration is found to be unstable if all electrons travel with the same relativistic velocity. If the electrons are monoenergetic, but have a small angular spread in velocities, a criterion for stability is obtained that places a lower limit on the spread. This limit is directly proportional to the wavelength of the perturbation. The theory is also applied to a thin cylindrical sheet inside a perfectly conducting cylinder. The system is infinite in the axial direction, and the electrons move in the azimuthal direction. In the absence of axial velocity, the instability is present as in the plane sheet. Considering a spread in axial velocity leads to a stability criterion independent of perturbation wavelength. A numerical example, employing the proposed parameters of the Astron device, indicates that an angular spread of about 60° is necessary for stability.

ISSN:0031-9171    

DOI:10.1063/1.1706485

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

It is known that the positive column is unstable in a strong longitudinal magnetic field. The correct explanation of this phenomenon has been given by Kadomtsev and Nedospasov. However, the instability mechanism is not fully interpreted in their work. In this contribution, the main features of Kadomtsev and Nedospasov's stability criterion are derived from simple physical arguments, and the mechanism responsible for instability is thus shown in a quantitative way. In particular, the perturbed radial potential distribution can be related to the perturbed density distribution, and hence need not be assumed. It turns out that this screw instability is a new and important type of instability hitherto not considered. The instability mechanism is not very sensitive to the degree of ionization, and hence may also be expected to be operative in highly ionized plasma columns. Possible connections with the instabilities observed in the Stellarator and the Zeta machine are discussed. An attempt is also made to explain regular oscillations observed in a toroidal discharge in terms of the present theory.

ISSN:0031-9171    

DOI:10.1063/1.1706487

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Dispersion of waves propagated at frequencies near the ion cyclotron frequency in collision‐dominated plasmas subjected to axial magnetic fields is investigated. Radial and axial propagation constants, satisfying Maxwell's equations, and including the contributions of binary elastic ion‐ion and ion‐electron interparticle forces to an ion conductivity tensor, are calculated. Elements of the ion conductivity tensor are found analytically by expressing the ion distribution function in the Boltzmann equation as a series of orthogonal Laguerre polynomials in velocity space with time‐dependent expansion coefficients. Right‐handed and left‐handed elliptically polarized waves are found from a numerical solution for a range of values of the ion cyclotron frequency about the fixed wave frequency of 7.62 Mc. The axial wavelengths &lgr;zL, &lgr;zR, and damping lengths &lgr;DL, &lgr;DRare calculated as functions of the magnetic field for a plasma density of 1021m−3, and temperature of 104, 105and 106°K. Enhanced dispersion occurs with increasing temperature. Stronger dispersion is associated with the left‐handed elliptically polarized wave; for 105° and 106°K, above resonance &lgr;DL≫ &lgr;zL, whereas below &lgr;DL≈ &lgr;zL. Ion‐ion collisions broaden the resonance width and decrease absorption at resonance.

ISSN:0031-9171    

DOI:10.1063/1.1706488

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The acceleration of a plasma by a capacitor discharge between coaxial electrodes is studied for (1) a shock tube having an initially uniform gas distribution and for (2) a plasma gun which accelerates a constant mass into a vacuum. Differential equations written for the first case for a simple snowplow model and solved by analog computer, are found to closely predict peak plasma velocities for a certain range of pressures. However, experimental study by means of a ``difference'' magnetic probe shows that the actual current distribution in the space between the electrodes is rather complex. Near the time when peak plasma velocity is reached, the first pulse splits into two pulses and persisting loop currents form in the plasma. An efficient mode of plasma acceleration which produces faster and more sharply defined shock waves is observed at low pressures when the center electrode is initially positive. Computer solutions are also obtained for the plasma gun, which seems to be intrinsically capable of greater efficiency than the shock tube.

ISSN:0031-9171    

DOI:10.1063/1.1706489

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

The increase in Doppler temperature with charge number, found in stellarators, has been remeasured with improved precision for observation parallel to the lines of force. No dependence on position was found, and the results are ascribed tentatively to positive‐ion waves parallel to the magnetic field.

ISSN:0031-9171    

DOI:10.1063/1.1706490

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

Three‐dimensional gravity waves on the surface of an inviscid incompressible fluid of finite depth are considered. The waves are assumed to be periodic in time and in two perpendicular horizontal directions. The surface profile, potential function, pressure, and frequency of the motion are determined (to second order) as series in powers of the amplitude divided by the wavelength in one direction. As in the two‐dimensional case previously considered by Tadjbakhsh and Keller, it is found that the frequency increases with amplitude for depths less than a critical value and decreases with increasing amplitude for greater depths. The critical depth depends upon the wavelengths in the two horizontal directions. The three‐dimensional results do not reduce to the two‐dimensional ones when one of the wavelengths becomes infinite. This is because the motion remains three dimensional.

ISSN:0031-9171    

DOI:10.1063/1.1706491

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

If a body does not rotate uniformly it suffers differential rotation. Under certain conditions the existence of differential rotation of a body is a consequence of quite general properties of dissipative processes. LetEbe the kinetic energy of rotation,AandIthe angular momentum and the moment of inertia along the axis of rotation; then the body cannot rotate rigidly unless the positive semidefinite formK=E‐A2/2Ivanishes. If this condition is not satisfied, the motion of the system can still be specified provided the relaxation time for establishing a steady state corresponding to a given value of the energy and angular momentum is much less than the relaxation times of the energy and angular momentum. If this be the case, the steady state of the system can be approximated with a state in which the dissipation is a minimum subject to the constraints thatEandAhave fixed values. This leads to the investigation of states of least dissipation subject to auxiliary conditions. The resulting eigenvalue problem is solved for several simple models in which the dissipation is due solely to viscous friction. If the values ofEandAspecified through the auxiliary conditions do not makeKvanish, the models exhibit differential rotation.

ISSN:0031-9171    

DOI:10.1063/1.1706492

出版商:AIP    

年代:1962

数据来源: AIP

摘要:

An analysis is made for the motion of a gas bubble rising steadily in a quiescent liquid of infinite extent. The disturbed layer of the fluid, due to viscosity, on either side of the interface is thin when the Reynolds number is sufficiently large and thus makes possible a considerable simplification of the governing equations of motion. Simultaneous solutions of the boundary‐layer equations for the flow outside and inside of the bubble are obtained by considering that the tangential velocity components and the shear stresses on both sides of the interface are equal. From the calculated external stress field, the drag of a spherical bubble with negligible flow separation is evaluated. Good agreement is obtained with published data for spherical air bubbles in four different organic liquids. The experimental drag curve due to Haberman and Morton for air bubbles rising in filtered water deviates from that predicted from the present theory. The theoretical results are applicable to any fluid sphere moving steadily in a substantially immiscible, viscous liquid provided that the internal circulation is complete, the flow separation is negligible, and the Reynolds number is sufficiently large.

ISSN:0031-9171    

DOI:10.1063/1.1706493

出版商:AIP    

年代:1962

数据来源: AIP