摘要:

The stability of an electrically conducting fluid flowing between parallel planes subject to a transverse magnetic field is investigated for infinitesimal three‐dimensional disturbances. Primary interest is in the effect of the magnetic field on the critical point of the neutral stability curves. The governing stability equations include perturbations for both the velocity and magnetic fields and result in a sixth‐order coupled set of linear differential equations. The results indicate a strong dependence of the critical eigenvalues on both the magnetic field strength and a fluid property, the magnetic Prandtl number. The effect of both is to stabilize the flow.

ISSN:0031-9171    

DOI:10.1063/1.1694224

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

An analysis was performed on the incompressible, unsteady, magnetohydrodynamic boundary layer on a semi‐infinite flat plate mounted in a duct. The stream unsteadiness was composed of a small sinusoidally oscillating component superimposed on a constant value, while the constant magnetic field was normal to both the stream and the plane of the plate. Solutions to the momentum and energy equations were obtained by numerical integration for the unsteady magnetic interaction effects, including dissipation, using a product series expansion in the Strouhal numbersand a Hartmann‐Reynolds number parameter&khgr;. A time and distance dependent boundary condition at the edge of the thermal layer was properly satisfied using this expansion procedure. The results show that, while increases in skin friction and heat transfer occur both with the steady magnetic case(s = 0,0 < &khgr; ⩽ 0.2)and with the unsteady nonmagnetic case(0 < s ⩽ 0.6, &khgr; = 0), the full unsteady magnetic interaction produces amplitude increases in these quantities withs, but a conteracting decrease with&khgr;. Other results presented include the unsteady magnetic interaction effects on the phases of the skin friction and heat transfer.

ISSN:0031-9171    

DOI:10.1063/1.1694225

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The stability of a special three‐dimensional shearing boundary layer with imbedded shearing magnetic fields is studied. Boundary layer solutions are obtained for a finitely, electrically conducting fluid, and then the sixth‐order differential equations describing the instability are solved numerically. It is found that the flow is always unstable and that the neutral stability curves pass through the origin of the&agr;‐Rdiagram, where&agr;is the wave number andRis the Reynolds number. An increase of the magnetic field tends to stabilize the flow when the conductivity is small or extremely large. An increase of resistivity has a stabilizing effect at moderate magnetic Prandtl number and a destabilizing effect at high magnetic Prandtl number.

ISSN:0031-9171    

DOI:10.1063/1.1694226

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The effect on magnetohydrodynamic equilibria of conducting wall shape in a straight plasma current multipole, or doublet, is studied by examination of two extreme longitudinal current models. For the first of these models, the current is concentrated in two filaments which are symmetrically located in the cross section of the device. In the second model, the current density is uniform over the cross section. If the neck size is appropriately chosen, the two‐filament case is excluded and the proper doublet equilibrium is obtained. For a neck size which allows both models, the poloidal magnetic fields at the wall are compared.

ISSN:0031-9171    

DOI:10.1063/1.1694227

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The three‐dimensional plasma model of Montgomery, Lin, and Vahala [Phys. Fluids15, 815 (1972)] is extended to include the effects of the fluctuating electric field on the particle motion along constant, uniform magnetic field lines. The particles are assumed to move across the field lines with the guiding‐centerE × Bdrift. The thermal equilibrium coefficient of spatial diffusion across the magnetic field is calculated and exhibits both a Bohm‐like1 / Bdependence and a1 / B2dependence on the magnetic field. The1 / B2term is independent of the plasma volume. The1 / Bterm contains a multiplicative factor which goes to zero as the plasma volume becomes infinite.

ISSN:0031-9171    

DOI:10.1063/1.1694228

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The collisional regime of neoclassical transport theory is investigated, using a moment equation approach as well as a method based on the drift kinetic equation. Allowing for both density and temperature gradients, and an externally induced toroidal electric field, the transport coefficients describing particle and energy flux perpendicular to the magnetic field of an axisymmetric confinement system are derived. Relations between the parallel and perpendicular fluxes, which are exact in the collisional regime, are also derived. Charge neutrality is used to obtain the electrostatic potential variation on a magnetic surface.

ISSN:0031-9171    

DOI:10.1063/1.1694229

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The instability induced by a vertical external gravitational field in a stratified plasma permeated by a uniform horizontal magnetic field is investigated by means of an expansion method. Dissipative processes arising from finite electrical and thermal conductivities are considered. It is found that a new unstable mode exists and a new condition, in addition to the Schwarzschild condition, must be satisfied for stability. The new stability condition is associated with the modes which exist in the nondissipative plasma, but are modified by dissipation. The net effect of this new condition is to destabilize the system.

ISSN:0031-9171    

DOI:10.1063/1.1694230

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

An analysis is presented, in a cylindrical approximation, of the nonlinear behavior of them = 1magnetohydrodynamic kink instability that occurs in a tokamak when the “safety factor”q(r) = rBz / RB &thgr;(r)falls below unity on axis. A kinked neighboring equilibrium is found, which is accessible from the initial straight equilibrium in the sense of satisfying the flux‐conservation constraints. Owing to the singular nature of the fundamental, all harmonics are excited in a singular region near whereq (r) = 1. The nonlinear amplitude is moderate. It is shown that growing modes of this type should produce negative voltage spikes and inward shifts in major radius, as are seen in the experiments. The predicted magnitudes of these two effects are, however, much smaller than those observed.

ISSN:0031-9171    

DOI:10.1063/1.1694231

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

The resistive tearing mode is analyzed in the nonlinear regime; nonlinearity is important principally in the singular layer aroundk·B = 0. In the case where the resistive skin time&tgr;sis much longer than the hydromagnetic time&tgr; H, exponential growth of the field perturbation is replaced by algebraic growth liket2at an amplitude of order(&tgr; H / &tgr; S )4/5. Application of the theory to the unstable tearing modes of a tokamak with a shrinking current channel yields good agreement with the observed amplitudes of them ≥ 2oscillations. The analysis excludes the very long wavelength mode, andm = 1in the tokamak, for which the “constant‐&PSgr;” approximation is invalid.

ISSN:0031-9171    

DOI:10.1063/1.1694232

出版商:AIP    

年代:1973

数据来源: AIP

摘要:

A toroidal, circular cross section, sharp‐boundary model of a high‐pressure tokamak with currents confined to the surface, is tested for stability against kink modes. It is shown that for&bgr; > 0.21 &egr;, where&egr;is the inverse aspect ratio, the model is unstable to then = 1kink mode (nis the mode number the long way) for all values of the safety factor above and below the Kruskal‐Shafranov limit. Along then = 1marginal stability linem = 2(mis the mode number the short way) is found to be the dominant harmonic.

ISSN:0031-9171    

DOI:10.1063/1.1694233

出版商:AIP    

年代:1973

数据来源: AIP