摘要:

The statistical theory of Montgomery, Turner, and Vahala, which determines the most probable ideal magnetohydrodynamic equilibrium compatible with given information on only a few global parameters (e.g., energyE, magnetic helicityH, flux &Fgr;, currentI, ⋅⋅⋅) is extended and investigated for both the tokamak regime (in which experimentally &Fgr;≫&mgr;0aI, withabeing the plasma radius) and the reversed field pinch regime (&Fgr;≪&mgr;0aI). One obtains typical experimentally relevant profiles in the appropriate regimes. Most probable equilibria sequences are investigated as the energy/magnetic helicity ratio is decreased at fixed flux and current: In the tokamak regime (flux≫current) the diamagnetic toroidal fieldBzbecomes less diamagnetic and tends to a uniform field, while in the reversed field pinch regime (flux≪current), field reversal sets inBzwith the radial reversal position moving farther into the plasma and the eventual appearance of hollow pressure profiles. It appears that, in both regimes, the most probable equilibria are becoming more stable as &mgr;0aE/Hdecreases. Linearized analytic force‐free states can also be constructed for certain regimes of the global parameters together with their nonlinear quasi‐force‐free numerical counterparts.

ISSN:0031-9171    

DOI:10.1063/1.863344

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

A simple model of an axisymmetric tandem mirror without thermal barriers is employed to study the stability of ballooning modes which are confined to the central mirror cell. The central cell is treated as long‐thin with isotropic pressure, while the end plug is modeled by a line‐tying boundary condition. The scaling of &bgr;cwith the mirror ratioR*and the connection lengthLcis computed, and the sensitivity of these results to the magnetic field profile chosen is discussed.

ISSN:0031-9171    

DOI:10.1063/1.863345

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The stability of an axisymmetric tandem mirror to ballooning modes is examined including the effect of finite ion gyroradius stabilization. The central cell of the tandem mirror is treated as a long‐thin system with isotropic pressure, while the end plug is modeled by a stabilizing boundary condition. For the particular equilibrium considered, the finite Larmor radius corrections to ideal magnetohydrodynamic theory indicate a strong stabilizing effect on high–nballooning modes even for quite modest values of the gyroradius,k⊥ &rgr;i∼a/L≪1. The dependence of &bgr;conk⊥ &rgr;iis computed, and physical mechanisms associated with this stabilizing influence are discussed.

ISSN:0031-9171    

DOI:10.1063/1.863346

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

A simple model of an axisymmetric tandem mirror is employed to study the stability of global (low‐m) ballooning modes in the central cell. The presence of a perfectly conducting wall in the model gives an estimate of the effect of wall stabilization. The scaling of the critical &bgr; ( = 2p/B2) with mode numberm, connection lengthLcto the end plug, and wall positionwis computed for several magnetic field profiles.

ISSN:0031-9171    

DOI:10.1063/1.863347

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

The motion of a charged particle in a static magnetic field is studied by means of repeated canonical transformations of a Hamiltonian system. Adiabatic invariants are generated based on the assumption that the particle Larmor radius is small compared with the characteristic distance over which the magnetic field varies. Unlike many earlier treatments the transformations presented here preserve the axisymmetry of the dynamics when the magnetic field is axisymmetric. It is assumed that the magnetic field consists of a small nonaxisymmetric part plus the axisymmetric toroidal and poloidal parts. After the introduction of the magnetic moment adiabatic invariant, the motion of the guiding center is studied. The results depend sensitively on the ratio of the poloidal magnetic field to the total magnetic field. In some cases a second adiabatic invariant exists and direct inferences concerning long time particle drifts are possible. In one case where a second adiabatic invariant fails to exist, long term drifts are studied by conventional perturbation expansions. At some points, resonance or lack of resonance phenomena appear and determine the drift effects.

ISSN:0031-9171    

DOI:10.1063/1.863348

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

For a two‐degree‐of‐freedom dynamical system in which the dynamics depends on a parameter &mgr;, the effect of an externally imposed random variation (e.g., collisions) of &mgr; is considered. In particular, mapping equations in conjunction with particle conservation are used to directly derive transport coefficients. The analytic method and nature of the results depend on a stochasticity parameterKwhich describes the nonlinearity of the collision‐free dynamics and a collisionality parameter &sgr;. For largeKor &sgr;, Rechester, Rosenbluth, and White’s method of diagrams in Fourier space is used to calculate stochastic diffusion. For smallKand moderate &sgr;(≳K3/2), an expansion in powers ofKis used to solve the map equations and thus obtain plateau transport coefficients. For smallKand small &sgr;, an expansion in powers of &sgr; leads to banana transport coefficients. The results are applied to the calculation of radial resonant transport coefficients for tandem mirrors; the plateau and banana particle and energy fluxes are equivalent to those previously obtained from drift‐kinetic theory, and the stochastic fluxes, not directly calculable in the drift‐kinetic approach, are given explicitly.

ISSN:0031-9171    

DOI:10.1063/1.863349

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Finite Larmor radius effects are incorporated into near theta pinch magnetohydrodynamic theory following the method of Pearlstein and Freidberg. By a straightforward solution of the eigenvalue problem with finite Larmor radius effects included, the stability of various diffuse profile configurations has been investigated. The results differ qualitatively, as well as quantitatively, from sharp boundary theory, and it is not true, in general, that the stabilizing effect is absent form= 1. It is found that fat plasmas can be completely stabilized by finite Larmor radius effects.

ISSN:0031-9171    

DOI:10.1063/1.863350

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Stimulated Brillouin scattering of CO2laser radiation from a pre‐ionized gas target is observed and studied with the following parameter changes: (1)f/7.5 focusing versusf/2 focusing, (2) nitrogen plasma versus hydrogen plasma, (3) pure nitrogen versus nitrogen with a hydrogen impurity, and (4) single line operation of the laser versus multiline operation. Thef‐number dependence is found to be weak because the increased intensity with the smallerfnumber is offset by the shorter interaction length for the Brillouin instability. The instability growth in nitrogen is found to be more severe than in hydrogen because the nitrogen plasma has a higherZTe/Tiresulting in a lower damping rate for the ion‐acoustic wave. In all the above cases the Brillouin reflectivity reaches saturation and the inferred saturation amplitudes of the ion‐acoustic waves are consistent with ion trapping being the saturation mechanism. Addition of a small amount (≃6%) of a light ion impurity (hydrogen) to a heavy ion plasma (nitrogen) virtually extinguishes the Brillouin instability. Finally, multiline operation of the CO2laser pump, with the line separation &Dgr;&ohgr; and the instability growth rate &ggr; such that &Dgr;&ohgr;/&ggr;≫1, is seen to reduce the Brillouin reflectivity as if each line were acting independently, as expected.

ISSN:0031-9171    

DOI:10.1063/1.863312

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

Brillouin backscatter is calculated in an inhomogeneous laser‐produced plasma. Equations for the spatial dependence of the incident reflected and sound waves are numerically integrated through the underdense plasma. Effects investigated are those stabilizing ion heating or nonlinear sound wave dissipation, flow velocity magnitude and gradient, electron heating, and broadband incident laser light. It is found that the effect of velocity gradient and broadband light can be very important in reducing the backscatter.

ISSN:0031-9171    

DOI:10.1063/1.863313

出版商:AIP    

年代:1981

数据来源: AIP

摘要:

A simple three‐fluid model has been developed to describe the critical surface structure for cases in which an abrupt density jump causes resonant absorption to be the dominant absorption mechanism. In this model, ions, thermal electrons, and superthermal electrons interact in a rarefaction wave induced by the three‐temperature equation of state and the ponderomotive force of the laser beam. Scaling laws from particle‐in‐cell calculations are used to simulate the effects of resonant absorption. The three temperatures characterizing the problem result in four distinct laser intensity regimes. Simple expressions are derived for the induced static potential, ion velocity, density, and temperature in three of these regimes. It is shown that these results agree with recent two‐dimensional simulation studies. The model provides a critical surface momentum flux condition well‐suited for implementation in a one‐dimensional implosion code.

ISSN:0031-9171    

DOI:10.1063/1.863314

出版商:AIP    

年代:1981

数据来源: AIP