摘要:

Knowing that short-time propagators for Fokker–Planck equations are Gaussian, and based on a path-sum formulation, an efficient and simple numerical method is presented to solve the initial-value problem for electron kinetics during rf heating and current drive. The formulation is thoroughly presented and discussed, its advantages are stressed, and general, practical criteria for its implementation are derived regarding the time step and grid spacing. The new approach is illustrated and validated by solving the one-dimensional model for lower-hybrid current drive, which has a well-known steady-state analytical solution. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872626

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

An analysis of ion cyclotron resonance heating in a plasma containing two ion species is given. Particular emphasis is placed on the important case of comparable concentrations of the two species. The properties of ion-Bernstein waves in such a plasma are discussed. A summary of the cutoff–resonance (Budden) and cutoff–resonance–cutoff (triplet) configurations is given and an analytic expression obtained for the Budden transmission coefficient (relevant also to the triplet case), which is valid for any concentration ratio of the two-ion species. A formula for the damping coefficient of the ion hybrid wave is obtained and a ray tracing code is used to illustrate the absorption of this mode by electrons close to the two-ion hybrid resonance. The reduced, second-order fast wave equation is solved numerically, illustrating the transition from strong electron heating through mode conversion at the two-ion hybrid resonance to direct electron damping of the fast wave in a high beta plasma.

ISSN:1070-664X    

DOI:10.1063/1.872369

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The paper analyzes low-frequency waves in a plasma model that is made up of two thermally anisotropic magnetohydrodynamic components, by means of wave-front diagrams, a useful tool that has not attracted the desired attention. The wave-front diagrams of the fast propagating suprathermal mode, besides the usual fast, slow, and Alfve´n modes, have been plotted for a variety of situations. These diagrams are used to bring out the physical significance of the anisotropic modelvis-a`-visthe isotropic model. The question of stability that has been completely ignored so far in the plasma models based on two magnetohydrodynamic components has also been addressed. Analogues of the firehose and mirror instabilities, which are supported by this model, are examined. Their comparison with single-component anisotropic plasma results suggests the possibility of suppressing the mirror instability. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872370

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The time-dependent flux-surface-averaged Fokker–Planck equation for the distribution function of minority ions during ion cyclotron resonant heating introduced by Stix in a classic paper [T. H. Stix, Nucl. Fusion15, 737 (1975)] is solved keeping two dimensions (2-D) in velocity space (speed and pitch-angle). An analysis of the applicability of the method of expansion of the distribution functionfin Legendre polynomials of the pitch-angle, a method suggested by Stix and subsequently used by others, is given. A full numerical 2-D solution is also calculated. It is shown that the convergence of the Legendre polynomial expansion is very slow and non-uniform with respect to both particle energy and pitch-angle, making the method impractical whenfis required at energies much higher than the background plasma thermal energy. However, the iterative sequences for the moments offare found to converge very fast. In particular, a good approximation to the pitch-angle average of the distribution function is obtained already with two terms kept in the expansion, for a wide range of heating parameters. The validity of Stix’s analytical one-dimensional approximations is analysed in detail. ©1997 American Institute of Physics. 

ISSN:1070-664X    

DOI:10.1063/1.872371

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

Measurements have been made of nonlinear sawtooth oscillations of the displacement of a magnetized electron column in a cryogenic, cylindrical trap. First reported 7 years ago, these oscillations occur when the displacement is destabilized by a resistive wall and damped by a temperature-dependent collisional viscosity. A typical evolution can last for thousands of seconds. Measurements show that oscillations of the plasma displacement are accompanied by oscillations in the plasma temperature. A simple predator-and-prey model of the temperature and displacement gives rise to a limit cycle solution due to the nonmonotonic dependence of the viscosity on temperature. These limit cycles are in good quantitative agreement with the measured sawtooth oscillations. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872372

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

This is an extension of a study of electric currents and force balance orthogonal to a unidirectional magnetic field of induction (B) in a collisionless plasma [K. D. Cole, Phys. Plasmas3, 2717 (1996)]. All quantities are assumed to vary only in one direction orthogonal toB. Two new concepts are introduced, which are not in conventional plasma physics. First a magnetic polarization effect corresponding to electric polarization is found. This defines a contribution to the magnetic moment per unit volume of−&rgr;mc2E2/B3.Second the conduction current is defined in terms of the curl of the magnetic field intensityH, in accordance with Maxwell. In this scheme, when there is no electric field,(1/4&pgr;)(∂H/∂z)B+(∂p⊥/∂z)=0,instead of the conventional equation withB/&mgr;0in place ofH.In both schemes,j×B−&bnabla;p⊥=0.Though this makes no difference to the electric current intensity calculated in the two schemes, and no difference to the force balance equation, it makes a significant difference to the relationship betweenBandp⊥in many plasma conditions of interest. When the electric field is nonzero, the situation is more complex. It is shown that the new diamagnetism of this paper and the dielectric current of the earlier one are consistent with special relativity. Some applications of the theory are discussed. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872373

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

The stabilization of cylindrical plasmas by resistive walls combined with plasma rotation is analyzed. Perturbations with a single mode rational surfaceq=m/nin a finitely conducting plasma are treated by the “resistive kink” dispersion relation of Coppi &etal; [Sov. J. Plasma Phys.2, 533 (1976)]. The possibilities for stabilization of ideal and resistive instabilities are explored systematically in different regions of parameter space. The study confirms that an ideal instability can be stabilized by a close-fitting wall and a rotation velocity on the order of resistive growth rates [J. M. Finn, Phys. Plasmas2, 3782 (1995)]. However, the region in parameter space where such stabilization occurs is very small and appears to be difficult to exploit in experiments. The overall conclusion from the cylindrical plasma model is that resistive modes can readily be wall stabilized, whereas complete wall stabilization is hard to achieve for plasmas that are ideally unstable with the wall at infinity. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872374

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

For a single particle species confined by a uniform magnetic fieldB, the Bogema–Davidson inversion theorem determines a self-consistent rigid-rotor equilibrium distribution functionF(H⊥−&ohgr;rP&thgr;)as the derivative of the given radial density profilen(r)with respect to the corresponding generalized potential&psgr;(r).Aside from the quadratic density profile, most forms one can choose forn(r),even if integrable, yield potentials&psgr;(r)that cannot be inverted. The functionFcan be found parametrically, however, by writing the derivative ofnwith respect to &psgr; as the ratio of the radial derivatives ofnand &psgr;. Several nontrivial examples of physical interest are studied. Numerical methods for calculatingFare presented, its asymptotic form and integration are investigated, and applications to experiment are discussed. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872375

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A three-dimensional nonlinear Kadomtsev–Petviashvili (K–P) wave equation is derived to discuss the solitons in multicomponent plasma contaminated with negative ions. A new formalism of the simple wave solution method is developed for finding the soliton behaviors caused by the presence of negative ions in plasmas. It is seen that the nonlinear wave equation leads, in some cases, to an ordinary differential equation and a straight way for solving the soliton propagation in plasmas. The overall observations describe the natures of compressive and rarefactive solitons along with the shock-like wave caused by the interaction of negative ions. Also discussed are the possible controls of the scenarios of soliton behaviors. Moreover it is believed, from present investigations, that the observations of collapses or explosions in solitons could enhance the understanding of the soliton phenomena in laboratory and space plasmas. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872545

出版商:AIP    

年代:1997

数据来源: AIP

摘要:

A generalized Fokker–Planck equation is developed in the pattern of a well-known collision operator [Beliaev and Budker, Sov. Phys. Dokl.1, 218 (1957)] and solved for a relativistic singly charged electron–ion plasma under the impact of crossed electric and magnetic fields. Using the differential form of the collision operator and the modified Rosenbluth potentials appropriate for the relativistic plasma various cross-field transport coefficients are derived analytically in the limit of nonrelativistic, moderately relativistic and ultrarelativistic temperatures. ©1997 American Institute of Physics.

ISSN:1070-664X    

DOI:10.1063/1.872396

出版商:AIP    

年代:1997

数据来源: AIP