摘要:

A study is made of the collisionlessE‐layer equilibria which are formed by the injection and trapping of a relativistic electron beam in a cylindrical conducting vessel. Assuming axisymmetry, information about the generalE‐layer equilibria is derived from the conservation of canonical angular momentum. Of particular interest for the design of experiments is the range of radial thicknesses and the average radius of the layers as a function of layer strength&zgr;. Under certain conditions there is shown to be a maximum radial thickness&Dgr;rmax, dependent only on&zgr;. For a number of practical cases&Dgr;rmax/r ≈ &zgr;1/2, whereris the average radius. The balance of axial pressures and over‐all energy conservation are imposed as constraints on the general equilibria. For most of the cases studied these constraints are incompatible with the assumption of a radially thinElayer. In such cases the thin‐layer equilibria are inaccessible, but it is expected that the thick‐layer equilibria are accessible.

ISSN:0031-9171    

DOI:10.1063/1.1694666

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

Equilibrium properties of intense relativistic nonneutralElayers are studied within the framework of the steady‐state Vlasov‐Maxwell equations. The analysis is carried out for an infinitely longElayer aligned parallel to a uniform magnetic fieldB0eˆz, assuming that theElayer is thin (radial thickness is small in comparison with the mean radiusR0) and&ngr;/&ggr;0 ≪ 1(&ngr;is Budker's parameter, and&ggr;0mc2is the electron energy). Equilibrium properties are calculated for the class of thinE‐layer equilibria in which all electrons have the same canonical angular momentumP&thgr;, but an arbitrary distribution in energyH, i.e.,fe0 (H, P&thgr;) = R0F (H + e&phgr;) &dgr; (P&thgr; − P0), whereR0, &phgr;0, andP0are constants. One of the most important features of the analysis is that the influence of equilibrium self‐fields on the radial thickness of theElayer can be large, even though&ngr;/&ggr;0 ≪ 1is assumed and the self‐field corrections to the mean radius of theElayer are small.

ISSN:0031-9171    

DOI:10.1063/1.1694667

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

Experimental investigations on the RECE‐Berta device at Cornell show that weak gradients in the applied magnetic field do not influence the stability of strong relativistic electron rings for field differences across the rings of up to 0.8%. The main effect of such gradients is a radial displacement of the equilibrium position of the rings toward the low‐field region of the tank. The magnitude of this displacement depends on the field gradient, and the strength and geometry of the electron ring. A theory for the displaced electron ring equilibria is presented which assumes a balance of the forces due to the external field and the image fields arising from currents in the conducting tank wall. The theory shows good quantitative agreement with the observed ring movement. From these results it appears that the final “dump” of the rings can be explained by the existence of a gradient in the basic mirror field.

ISSN:0031-9171    

DOI:10.1063/1.1694668

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

The theory of the rf plugging of a magnetically confined plasma in an open‐ended system is presented; it takes explicit account of the collective effect brought about by the dynamic screening action of the plasma. The theory predicts a maximum efficiency of the rf plugging at an optimum frequency corresponding to a zero of the longitudinal dielectric constant. The plugging efficiency is calculated as a function of the plasma density, the strength of the rf field, and the intensity of the magnetic field. These theoretical predictions are compared with experimetal observations, demonstrating satisfactory agreement in over‐all features. The results provide a useful scaling law associated with the concept of the rf confinement. The theory also offers an explanation for the discrepancy between the experimental values of the optimum frequency and those predicted by a conventional theory based on an individual‐particle model.

ISSN:0031-9171    

DOI:10.1063/1.1694669

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

The methodology for the computation of the conductance of a confined arc discharge has been established. A limiting case which describes the capillary argon ion laser at a filling pressure near 0.2 Torr, at a discharge tube radius of 1 mm, and at a discharge current of 7 A has been treated. The theoretical method utilizes a variational principle which resembles the standard approach of Robinson and Bernstein and Nighan. The derivation is carefully explained and applies to the case where the electron mean‐free‐path for momentum transfer is much larger than the radius of the discharge tube. The variational principle formulation has provided a convenient way of deriving computationally simple upper and lower bounds for the electron conductance of the discharge tube. These bounds are particularly important in light of the computation time now required for an accurate calculation.

ISSN:0031-9171    

DOI:10.1063/1.1694670

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

It is shown experimentally that the turbulent shear layer of a circular jet having a bell‐shaped velocity profile cannot support a wave disturbance. The spatial growths of the axisymmetric pressure waves decay rapidly downstream from the nozzle exit for a wide range of forcing frequencies investigated.

ISSN:0031-9171    

DOI:10.1063/1.1694671

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

The hydrodynamic stability of the flow between two plane porous plates with velocity slip at the plates is examined using a finite difference scheme. Results in the form of critical Reynolds number as a function of cross flow with velocity slip as a parameter are given.

ISSN:0031-9171    

DOI:10.1063/1.1694672

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

For a wide class of flows, limits on the effective bulk and shear viscosities of a polar fluid are obtained. It is shown that, under circumstances which cause the effective shear viscosity to increase, the effective bulk viscosity decreases.

ISSN:0031-9171    

DOI:10.1063/1.1694673

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

Dispersion relations for self‐gravitating systems are obtained using the direct duality with space charge coupled systems by taking electrohydrodynamic results and replacing the charge density with the mass density, the electric field with the gravitational field, and the permittivity by−1/4&pgr;G.

ISSN:0031-9171    

DOI:10.1063/1.1694674

出版商:AIP    

年代:1974

数据来源: AIP

摘要:

A well‐known sufficient condition for magnetohydrodynamic stability of toroidal equilibria with closed field lines is improved by taking into account the compressive energy in the energy principle. As a result, the condition also becomes necessary for stability in special cases.

ISSN:0031-9171    

DOI:10.1063/1.1694675

出版商:AIP    

年代:1974

数据来源: AIP