摘要:

Equilibrium properties of a two‐dimensional guiding center plasma are reinvestigated in detail by means of the BBGKY hierarchy. A new equation of state is presented and compared with the results of the Monte Carlo simulation and the correlation energy is computed. A heuristic generalization of the the dispersion relation is investigated by means of different truncation schemes of the hierarchy. Analytical and numerical results support the appearance of periodic states for a neutral system in an unbounded domain at a moderately high value of the coupling parameter &ggr;c∼8.

ISSN:0031-9171    

DOI:10.1063/1.864111

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The integral equation technique previously developed for electrostatic drift waves to study low‐frequency electromagnetic perturbation is extended. When &sgr;e≫&sgr;i(as is the case for tearing modes) the problem can be reduced to the simultaneous solution of an integral and a differential equation. Using a Fourier representation for &fgr;˜(x), a differential equation is derived from Ampere’s law for a modified Green’s function that contains the magnetic effects. This equation is solved simultaneously with an integral equation (corresponding to the quasineutrality condition inkspace) to obtain the eigenvalues and corresponding eigenfunctions. When applied to the study of microtearing modes this method gave, for the same values of the parameters, larger growth rates than those of the usual differential approximation.

ISSN:0031-9171    

DOI:10.1063/1.864112

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

Nonlinear gyrokinetic equations are derived from a systematic Hamiltonian theory. The derivation employs Lie transforms and a noncanonical perturbation theory first used by Littlejohn for the simpler problem of asymptotically small gyroradius. For definiteness, only electrostatic fluctuations in slab geometry are considered; however, there is a straightforward generalization to arbitrary field geometry and electromagnetic perturbations. An energy invariant for the nonlinear system is derived, and several limiting forms are considered. The weak turbulence theory of the equations is examined. In particular, the wave kinetic equation of Galeev and Sagdeev can ony be derived by an asystematic truncation of the equations, implying that this equation fails to consider all gyrokinetic effects. The equations are simplified for the case of small but finite gyroradius and put in a form suitable for efficient computer simulation. Although it is possible to derive the Terry–Horton and Hasegawa–Mima equations as limiting cases of our theory, several new nonlinear terms absent from conventional theories appear and are discussed. The resulting theory is very similar in content to the recent work of Lee. However, the systematic nature of our derivation provides considerable insight into the structure and interpretation of the equations.

ISSN:0031-9171    

DOI:10.1063/1.864113

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The problem of energy conservation for the renormalization of the drift wave instability in a sheared magnetic field is considered. It has been suggested previously that there is a connection between a certain constraint on the nonlinear term in the drift kinetic equation and energy conservation. Arguments are presented to dissolve this connection; and in turn, energy conservation is formulated in the physically meaningful statistically averaged sense. Finally, energy conservation is proven for the system of nonlinear equations, renormalized by the normal stochastic approximation, describing the drift wave instability.

ISSN:0031-9171    

DOI:10.1063/1.864114

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

Relaxation of compressible plasmas to an equilibrium with flows is studied. The magnetohydrodynamic (MHD) equations with large parallel thermal conductivity and ergodic field lines show that ∫v⋅Bis an invariant even with compression. Also,S=∫&rgr; ln( p/&rgr;&ggr;) is the only entropy‐like invariant of the MHD equations with infinite parallel thermal conductivity;Sincreases in time with finite thermal conductivity. The other invariants are energy, helicity ∫A⋅B, mass ∫&rgr;, and possibly angular momentum. Equilibria are found by extremizing energy while conserving these invariants or by maximizing entropy with the energy and other invariants as constraints. These invariants are complete in the sense of generating all equilibria that form after relaxation with ergodic field lines. For parallel flows, there are three classes of solutions characterized by the sign ofd&rgr;/dB2and the mirror mode parameter. A sufficient condition for stability is derived. This condition is never satisfied by the class withd&rgr;/dB2>0, indicating the possibility of unstable resistive interchanges. The class withd&rgr;/dB2<0 is stable if generalizations of the local firehose and mirror criteria are satisfied, and if generalized Taylor helicity eigenvalues exceed those of the equilibrium. A comparison of these conditions with those of Frieman and Rotenberg is discussed.

ISSN:0031-9171    

DOI:10.1063/1.864115

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

An energy principle is used to obtain the solution of the magnetohydrodynamic (MHD) equilibrium equationJ×B−∇p=0 for nested magnetic flux surfaces that are expressed in the inverse coordinate representationx=x(&rgr;, &thgr;, &zgr;). Here, &thgr; are &zgr; are poloidal and toroidal flux coordinate angles, respectively, andp=p(&rgr;) labels a magnetic surface. Ordinary differential equations in &rgr; are obtained for the Fourier amplitudes (moments) in the doubly periodic spectral decomposition ofx. A steepest‐descent iteration is developed for efficiently solving these nonlinear, coupled moment equations. The existence of a positive‐definite energy functional guarantees the monotonic convergence of this iteration toward an equilibrium solution (in the absence of magnetic island formation). A renormalization parameter &lgr; is introduced to ensure the rapid convergence of the Fourier series forx, while simultaneously satisfying the MHD requirement that magnetic field lines are straight in flux coordinates. A descent iteration is also developed for determining the self‐consistent value for &lgr;.

ISSN:0031-9171    

DOI:10.1063/1.864116

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

Equilibrium and stability properties of high‐beta torsatrons are investigated using numerical and semianalytical techniques based on the method of toroidal averaging. The averaged equilibria are compared with those obtained using full three‐dimensional codes. Good agreement is obtained, thus validating the averaged method approach. The stability of plasmas for configurations with different aspect ratios and numbers of field periods is studied. The role of the vertical field is also studied in detail. The main conclusion is that for moderate‐aspect‐ratio torsatrons (Ap≲8), the self‐stabilizing effect of the magnetic axis shift is large enough to open a direct path to the second stability region.

ISSN:0031-9171    

DOI:10.1063/1.864117

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The stability of short‐wavelength, low‐frequency modes in a hot electron plasma is investigated. Particular attention is devoted to the effect of the dependence of perturbed quantities along the equilibrium magnetic field lines. Two types of modes in a bumpy torus are considered: modes which are nearly flutes in each mirror cell but vary in phase from cell to cell, and modes which have significant variation in each cell. Generally speaking, allowing perturbations to vary along the field lines is destabilizing. However, sufficiently large hot electron gyroradii can stabilize all short perpendicular wavelength modes.

ISSN:0031-9171    

DOI:10.1063/1.864118

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

The high‐frequency precessional mode of a hot‐electron‐stabilized magnetic configuration has previously been shown to be stable in a window of core‐plasma mass. Under conditions of frequency matching, the resulting stable negative‐energy precessional wave can be destabilized by coupling to positive‐energy shear‐Alfve´n waves. Coupling is avoided when the hot‐electron precession frequency exceeds the core‐plasma ion gyrofrequency.

ISSN:0031-9171    

DOI:10.1063/1.864119

出版商:AIP    

年代:1983

数据来源: AIP

摘要:

Axisymmetric merging of spheromaks is studied extensively by means of a magnetohydrodynamic code. Merging simulations of identical and different spheromaks created by the Princeton slow induction method have revealed that (1) the total magnetic energy decreases rather quickly through reconnection while the magnetic helicity is reasonably conserved; (2) a hollow structure appears in the radialqprofile when two different spheromaks merge, while theqprofile is doubled when the identical spheromaks merge; and (3) the postmerging toroidal flux becomes the sum of the premerging fluxes, while the postmerging poloidal flux remains the same as the larger of premerging fluxes. It is also observed that kinetic energy once converted from the magnetic energy through reconnection is returned back to the agnetic energy near the end of the merging process, this indicating a relaxation toward a lower‐energy force‐free equilibrium.

ISSN:0031-9171    

DOI:10.1063/1.864120

出版商:AIP    

年代:1983

数据来源: AIP