摘要:

Approximate expressions describing the Tonks‐Dattner and Buchsbaum‐Hasegawa resonances (at the second electron cyclotron harmonic) in a warm nonuniform plasma are derived by means of a fairly easy analytic continuation technique. Connection formulas are developed for third‐order electric field differential equations derived from kinetic theories and show the coupling of slow and fast waves in the vicinity of a linear turning point. The relatively simple field expressions predict traveling longitudinal waves possessing outwardly directed phase velocities. Internal plasma fields appreciably larger than the excitation field are found when the density nonuniformity supports even mode resonances. The field equations and expressions for the associated impedance variation are compared to numerical integration solutions and show striking similarity to experimental observations.

ISSN:0031-9171    

DOI:10.1063/1.1694465

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The characteristics of two low‐frequency electrostatic flute instabilities of a low‐pressure hollow cathode arc discharge are reported. Mode I has azimuthal mode numberm = 1, and occurs when the radial electric field is negative (directed inward) while mode II hasm = −1and occurs when the field is positive. The radial electric field is controlled by varying the potential of a secondary anode cylinder located close to the outer discharge radius. A linear perturbation analysis, based on the two‐fluid equations, is given for a low‐&bgr;, collisionless, cylindrical plasma column, immersed in a uniform axial magnetic field, having a Gaussian density profile and an arbitrary radial electric field profile. Reasonable correlation between theory and experiment is demonstrated for both modes, by comparing the calculated and measured frequencies, mode numbers, and also the eigenfunctions of the density and potential fluctuations. The instabilities are basically centrifugal flute modes, driven byE × Bdrift in the presence of a density gradient and modified by the velocity shear due to nonuniformE × Brotation.

ISSN:0031-9171    

DOI:10.1063/1.1694466

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

Detailed computational results are presented on the stability and radial distribution of linear tearing modes in cylindrical tokamaks of various radial profiles. In the case of a skin‐current profile, a “double tearing mode”, with two points of discontinuity in the radial magnetic field perturbation is found. An analytical method is also derived for comparison of the stability of different radial profiles. It is further shown that the tearing mode can be driven by finite electron viscosity, as well as by the usual finite resistivity mechanism.

ISSN:0031-9171    

DOI:10.1063/1.1694467

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

Experiments on the spatial instability of a beam‐plasma system led to the observation that the instability is quenched when irradiated by high power microwaves. It is conjectured that this effect is due to a local decrease in plasma density in the irradiated region. A theoretical model is detailed that explains the salient features of the observed effect. Auxiliary measurements on a system with a controlled density gradient are presented that give strong support for the proposed mechanism.

ISSN:0031-9171    

DOI:10.1063/1.1694468

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

An analysis of the stability of the kink mode of a relativistic charged‐particle beam propagating in a toroidally confined plasma is presented. The essential feature is the treatment of the beam as a distinct component of the system having finite velocity and inertia in addition to its current. To simplify the analysis, the plasma background is assumed to be a pressureless, uniform fluid obeying the laws of perfect magnetohydrodynamics while the beam is treated as a cold, rigid body. To simulate toroidal geometry, periodic boundary conditions are imposed in the axial direction of a straight, cylindrical volume. The walls of the cylinder have perfect conductivity. A strong solenoidal field is externally imposed, but the beam is the only source of the poloidal field. It is found that a modification of the stability condition of Kruskal and Shafranov applies; the onset of instability corresponds to the appearance of closed particle orbits rather than the more severe condition of closed field lines. The maximum rotational transform consistent with stability is&igr;/ 2&pgr; = 1 + (&bgr;z &ggr;mc2) / (e R 0 Bz).

ISSN:0031-9171    

DOI:10.1063/1.1694469

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

Observations of direct nonlinear coupling between electromagnetic waves and electrostatic waves in the bulk volume of a plasma are reported and compared with the predictions of an accompanying physical theory. The experimental configuration consists of a cylindrical resonant cavity partially filled with a coaxialQ‐machine plasma column. Experimental verification of the predicted interaction resonances is presented. The finite interaction length defined by the cavity modifies the theoretical wave number selection rule, imparting a “lineshape” to the resonance which is consistent with observations. Two of the three interacting waves are externally excited and their interaction causes a third wave to grow with distance. The direction of growth depends upon the resonance conditions and choice of excitation, while the rate of growth depends upon the pump level, coupling strength, and linear wave damping. Indirect measurements of the mode power levels are presented which verify in magnitude the theoretically predicted coupling.

ISSN:0031-9171    

DOI:10.1063/1.1694470

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

It is shown that cross‐field gradients of guiding‐center drift velocities can excite several high‐frequency(&ohgr; > &ohgr;ci )electrostatic instabilities. The instabilities can enhance effective interelectron and/or electron‐ion collisions which in turn destory the velocity gradients. In pulsed, turbulent heating experiments, this effect is expected to appear as anomalously rapid current penetration (anomalous skin effect).

ISSN:0031-9171    

DOI:10.1063/1.1694471

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The laminar interaction of counterstreaming plasmas in the presence of a magnetic field was studied by numerical simulation. The model is one‐dimensional and is based on the Vlasov equation with straight orbits for ions(&OHgr;i t ≪ 1). Electrons are treated as a massless, zero‐termperature fluid maintaining charge neutrality with the ions, and a finite resistivity is assumed. Magnetic field and density profiles are determined for different Mach numbers, density ratios, and resistivities. Effects of various finite initial density profiles in the streaming plasma are investigated. The distribution function is examined to determine whether microinstabilities would develop in a turbulent model. The relevance of these results to the formation of magnetic pistons is discussed.

ISSN:0031-9171    

DOI:10.1063/1.1694472

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A new formulation of the quasilinear theory of weakly turbulent plasmas is presented, which explicitly separates resonant and nonresonant wave‐particle interactions from the outset. This is achieved by making a canonical transformation to “oscillation center variables” before attempting to solve the Vlasov equation. A systematic method of constructing the generating function to any order in the wave amplitude is presented, based on a variant of Hamilton‐Jacobi perturbation theory. Momentum and energy split naturally into a wave and a particle component. The results are generalized to apply to weakly inhomogeneous plasmas, and verified by demonstrating momentum and energy conservation.

ISSN:0031-9171    

DOI:10.1063/1.1694473

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

In order to investigate the effect of toroidal curvature on magnetohydrodynamic modes in tokamak configurations, stability criteria are derived by means of an expansion in the inverse aspect ratio. For a low‐pressure system,&bgr;&thgr; ∼ 1, with a nearly constant safety factor,q = qa(0) + …, the well known stability criterion for kink modes, relatingqato the ratioa / bof the plasma radius to that of a conducting wall, is determined in second order. Here, it is shown that toroidal effects modify this criterion favorably in fourth order when the vacuum region does not extend too far. Typically, it is found that improvement is achieved whenb / ais less than 1.25 to 1.5. Interchange and ballooning effects are incorporated in the stability criteria.

ISSN:0031-9171    

DOI:10.1063/1.1694474

出版商:AIP    

年代:1973

数据来源: AIP