摘要:

An approximate, linearized equation for the pair correlation function, containing a Debye potential instead of the Coulomb potential, is used to derive by direct integration a solution for the pair correlation function for the case of long‐wavelength plasma oscillations in a fully ionized gas without a magnetic field. The correlation function is then applied to describe the effect of collisions in a linearized Boltzmann equation for the single‐particle distribution function, which again is integrated directly. By substituting the integral of the single‐particle function over the velocity space (so as to obtain the number density of the particles) into Poisson's equation for the electric field, a dispersion equation is constructed for the oscillations. From this dispersion equation the damping of the oscillations can be found. The result combines the Landau damping with the collisional damping.The purpose of the paper is to show what can be done with direct integration in coordinate space, without introducing Fourier and Laplace transforms and without integrations in a complex plane. Only the most interesting terms have been considered. The results obtained are not essentially different from those derived by means of other methods.

ISSN:0031-9171    

DOI:10.1063/1.1706843

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

Hamilton's principle with a Lagrangian density consisting of kinetic energy minus the sum of internal and magnetic energy is used to derive the momentum equation and the pressure jump condition for a compressible nondissipative plasma continuum. This is done for a system consisting of fluid, vacuum and prefectly conducting solid parts by varying the fluid particle paths subject to conservation of mass, conservation of entropy and the Gallilean invariant form of Maxwell's equations. This is done also in Eulerian form for a purely fluid system using Lin's additional constraint.

ISSN:0031-9171    

DOI:10.1063/1.1706844

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The interchange instability is studied in an equilibrium similar to that of a stellarator with helical windings, on the basis of the combined Maxwell and Vlasov equations in the limit of small particle gyration radii. However, the first correction in the size of these radii and its effect on the stability criterion is studied. It is found that, just as in the work of Rosenbluth, Krall, and Rostoker, the stability criterion may be expressed in terms of the growth ratesHof the zero‐gyration‐radius theory. The stability is always improved by this correction and the new stability criterion is given bysH/&OHgr; <ma2/R2, where &OHgr; is the ion gyration frequency,athe ion gyration radius,Rthe radius of the plasma, andmthe azimuthal wavenumber. The zero‐gyration‐radius normal mode equation and growth rates are then found and these are applied to the special case of helical windings with trefoil symmetry. It is shown that even when the gyration radius is small its effect may be significant, in many cases increasing the plasma pressure which may be stably confined by a factor of 2 or more.

ISSN:0031-9171    

DOI:10.1063/1.1706845

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

Additional measurements of the transmission of a burst of plasma through a 90° bend in magnetic field include a mass and energy analysis of the incident and transmitted plasma. Under certain conditions of input density and bend magnetic field, tenfold reductions in plasma contaminants (atomic mass > 3) may be realized. Some further results on the source of neutralization of the polarization field are presented and discussed.

ISSN:0031-9171    

DOI:10.1063/1.1706846

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The configuration consisting of a dielectric rod, surrounded by a plasma shell and a concentric outer conducting cylinder, is investigated theoretically and experimentally for its propagation characteristics. It is predicted from the theory that such a configuration will support propagation in a backward wave mode (oppositely directed phase and group velocities). These backward waves were observed in experiments using a configuration essentially identical to the above (the dielectric rod had an air space down the center used to insert a probing antenna), with the plasma provided by a cesium discharge. Agreement between these observations and calculations is excellent. A forward wave was also observed at low frequencies, and is attributed to the influence of the sheath at the plasma‐conductor interface. The observed dispersion curve for this forward wave is also in good agreement with that calculated using the expected sheath size of the cesium plasma‐metal interface.

ISSN:0031-9171    

DOI:10.1063/1.1706847

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A torsional hydromagnetic wave is induced by application of an oscillatory radial electric field to one end of a cylindrical deuterium plasma located in a magnetic mirror field. The wave propagates in the axial direction to the center of the device, where a resonance occurs between the hydromagnetic wave frequency and the local ion cyclotron frequency. Wave magnetic‐field measurements indicate that transfer of power from the 1‐MW, 8.3‐Mc oscillator to the hydromagnetic wave is about 65% efficient, and that more than 90% of the wave energy is transferred out of the wave at the resonance region.

ISSN:0031-9171    

DOI:10.1063/1.1706848

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A current‐carrying plasma confined in a smooth toroidal magnetic field tends to expand due to the nonuniformity of the field and the self‐interaction of the current. This expansion can be nullified, in the absence of externally imposed rotational transform, by means of a vertical magnetic field (perpendicular to the plane of the toroid). Macroscopically considered, such a vertical magnetic field interacts with the Ohmic heating current to supply an inward ponderomotive force. This paper derives the magnitude of the plasma expansion tendency and of the vertical field required to achieve steady state conditions. It is also demonstrated that if the plasma configuration is determined by an aperture limiter, helical fields are equivalent to an applied vertical field, insofar as the plasma equilibrium is concerned.

ISSN:0031-9171    

DOI:10.1063/1.1706849

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

A series of experiments with the Model C stellarator showed that a previously detected asymmetry in the device could be removed by applying such a magnetic fieldBT, transverse to the main confining magnetic field, that an inherent lack of closure of the flux lines of the confining field was removed. The symmetrized stellarator was then used to demonstrate that an equilibrium (discussed theoretically elsewhere) could be achieved in the plasma by applying a uniform magnetic field transverse to the plane of the stellarator. With currentIOHflowing toroidally in the plasma, the tendency for the toroid to expand, due to the hoop force and the U‐bend drift, is counterbalanced by theIOH× BTforce. The observed transverse field required for equilibrium is in good agreement with the value predicted theoretically. Improvement at equilibrium of such plasma parameters as electron temperature, particle confinement time, and energy replacement time is demonstrated.

ISSN:0031-9171    

DOI:10.1063/1.1706850

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

The two‐dimensional problem of the interaction of a hypersonic flow with the field of a current carrying wire is analyzed. The electrical conductivity behind the normal shock is taken to have an arbitrary finite value, while the free stream conductivity is zero. It is found that the magnetohydro‐dynamically supported shock wave follows the magnetic field lines closely and that the hot flow is confined to a narrow region behind the shock at all values of conductivity. For low conductivities the shock position is determined by setting the interaction parameter based on the velocity behind the normal shock and a distance of &egr; times the shock radius equal to ⅓[1 + (2&egr;)½] where &egr;(≪1) is the density ratio across the shock. The high conductivity case is reached when the magnetic Reynolds number, based on the above parameters, exceeds unity. The shock position is then determined by equating the dynamic and magnetic pressures. The thickness of the current sheet in this case is of the order of the shock radius divided byRm½&egr;−¾. For low conductivities the case of a wire embedded in a solid cylinder has also been considered, and it is shown that the heat transfer is reduced sharply when the shock wave is lifted off of the surface of the cylinder.

ISSN:0031-9171    

DOI:10.1063/1.1706851

出版商:AIP    

年代:1963

数据来源: AIP

摘要:

Hartunian's theory for the curvature of a shock wave progressing into quiescent gas near a wall is extended to the cases of two parallel walls, of a rectangular tube and of a circular tube. Shock curvature is considered as caused both by laminar and by turbulent boundary layers along the walls behind the shock. For a completely laminar boundary layer, the axial extent of the curved shock in the cases of two parallel walls and of a circular tube is found to be 0.760 and 0.783, respectively, of Hartunian's single wall result. The correction arising from the finite length of the boundary layer is calculated. This correction is found to be negligible provided the boundary layer length is larger than approximately one‐half the distance between the walls. An estimate is presented for the correction arising from the flow behind the foot of the shock. This correction is of some importance at very low initial pressures. An approximate method is given to find the curvature of shock fronts which are followed by a relaxation region. The results obtained are in good agreement with the available experimental data.

ISSN:0031-9171    

DOI:10.1063/1.1706852

出版商:AIP    

年代:1963

数据来源: AIP