摘要:

A variational principle of Hamilton's type is constructed for stationary, bounded magnetohydrodynamic flows, also known as stationary equilibria. The chief object is to find how much information must be given in order to have a well‐posed problem. The results indicate, but do not rigorously prove, that five suitably chosen functions of a single variable and the location of a rigid conducting boundary defined a unique stationary flow. Comparison is made with other variational principles.

ISSN:0031-9171    

DOI:10.1063/1.1692520

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An equation of motion for the amplitude of the perturbation of the interface of two incompressible fluids is obtained under the specification of small viscosities and small electrical conductivities. This equation describes the motion of a damped harmonic oscillator with the effects of the electric field given as: (1) a forcing function proportional to the displacement, and (2) a forcing function proportional to the time integral of the displacement. A stability analysis of this equation shows how the electrical conductivity, surface charge, frequency of the applied field, viscosity, surface tension, electric permittivity, fluid depth, and density affect the stability of the fluid interface. The destabilizing effect of the surface charge and the stabilizing effect of the viscosity are illustrated for dc and ac applied fields. It is shown that the minimum dc destabilizing voltage can be lower than the value given by Taylor and McEwan, and that instability can result with an ac field that is about 0.2 the strength of the destabilizing dc field.

ISSN:0031-9171    

DOI:10.1063/1.1692521

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The edge effect problem for a flush electrostatic probe is modeled by the flow of a weakly ionized compressible gas past a discontinuous wall potential. The basic flow is a Couette flow and the potential jump is applied at the lower wall which is thus divided into positive and negative current collectors. For a sufficiently small applied potential discontinuity the problem may be linearized about a basic state whose characteristics are known numerically. The linear problem retains the full coupling and ellipticity of the nonlinear one. Results are presented for the total current collected by each electrode, the magnitude of the jump in current density at the junction of the electrodes and the dependence of this quantity on Reynolds number, the first‐order moments of the current density, and the upstream and downstream length scales for the current collection. For conditions investigated here, these length scales are several channel thicknesses. Thus, the operation of a flush electrostatic probe may be completely dominated by edge effects.

ISSN:0031-9171    

DOI:10.1063/1.1692522

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

An approximate method especially suited to near‐continuum flows is developed. The method is applied to the case of Couette flow with arbitrary specular and diffuse reflection. The result is in very close agreement with all known limits. In the case of purely diffuse reflection the approximate theory leads to a slip coefficient which is within112%of the exact value. The analytical behavior in the neighborhood of the walls is exactly described. The limit of purely specular reflection is exactly described by the approximation method. The method only involves elementary calculations.

ISSN:0031-9171    

DOI:10.1063/1.1692523

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

A theory is developed which treats the coupled equations of the various hierarchies as simultaneous equations in time. This scheme proceeds by successive approximations rather than a power series expansion in the small parameter ([n&lgr;d3]−1in a plasma,nr03in a Boltzmann gas). The theory is suitable for the derivation of equations for nonuniform and force driven systems. Examples are given for a plasma and a Boltzmann gas.

ISSN:0031-9171    

DOI:10.1063/1.1692524

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The role of ballistic term in the turbulence that occurs in plasma shock waves is discussed. For electrostatic turbulence these terms are shown to give rise to a wake behind a shock wave in which the energy density in the fluctuating fields decays spatially asx−3for a class of distribution functions including resonance functions. The importance of the ballistic transport of turbulent fields inside shocks is also pointed out. This occurs because in such structures there is usually not enough length scale for these fields to phase mix away. Thus, the use of conventional quasilinear theory (which neglects these effects) will often be inadequate to describe even weak turbulence in a shock wave.

ISSN:0031-9171    

DOI:10.1063/1.1692525

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The matrix elements describing nonlinear effects in a weakly unstable plasma are interpreted by means of Feynman diagrams involving the shielded Coulomb potential, given byVs(q, &ohgr;) = 4&pgr;e2/q2&egr;(q,&ohgr;), where&egr;(q, &ohgr;)is the dielectric response function. The quasiparticles or plasmons are obtained from the poles ofVs, but effects of the nonresonant parts ofVsare also retained. All the matrix elements describing interactions of Langmuir oscillations in a strong magnetic field through second order in the quasiparticle numbers are found explicitly and shown to yield the correct classical results in the limitℏ → 0. In particular, the equations of Walters and Harris for three‐wave scattering in a cold plasma are extended to finite temperatures, and the shielding or dressing of the electrons is included in the equations for the nonlinear Landau damping. The self‐energy of a plasmon is also represented by diagrams and the optical theorem is used to compare the self‐energy with the scattering matrices. It is found that the quantum method provides a relatively simple way of deriving and interpreting equations for the time development of the wave spectrum and particle diffusion.

ISSN:0031-9171    

DOI:10.1063/1.1692526

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

A calculation of mode‐mode coupling for collisional drift waves demonstrates several inherently nonlinear phenomena, namely, amplitude saturation, harmonic generation, frequency shift, wave‐associated transport across the magnetic field, and parametric excitation of subharmonics. There is qualitative agreement with published experiments; the introduction of some additional damping mechanism into the theory could narrow the broad quantitative discrepancy between theory and experiment. The analysis uses the nonlinear ion and electron fluid equations in which ion inertia, finite ion gyroradius, perpendicular ion viscosity, and resistivity terms have retained. No cross‐B transport is produced by the large‐amplitude steady‐state oscillations in the absence of ion viscosity; non‐ambipolar transport in the pump‐out direction appears when ion‐ion collisions are introduced. A byproduct of the calculations is a single nonlinear scalar wave equation for the collisional drift wave. Solutions to this equation show limit‐cycle behavior, i.e., periodic but nonsinusoidal finite‐amplitude oscillations which are stable (or unstable) against changes of oscillation amplitude. These nonlinear solutions are described by dispersion relations containing the oscillation amplitude as one of the parameters.

ISSN:0031-9171    

DOI:10.1063/1.1692527

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

Continuing experimental studies of beam‐plasma interactions in a magnetic field have shown an assortment of nonlinear effects to be present during a well‐developed instability. Observations have been made of: the vanishing of the spatial growth rate; electron cross‐field diffusion in synchronism with the unstable electric field; generation of harmomics of the fundamental interaction frequency up to the seventh; similarities in the spatial behavior of all seven harmonics; and the existence of a wavenumber power spectrum whose average behavior over the domain of the harmonic peaks is proportional tok−5±0.5, in agreement with certain theories of plasma turbulence. The data suggest that the large‐amplitude fundamental electric field is the driving force for the nonlinearity that generates the harmonics, and that the fundamental, and the harmonics as well, represent waves traveling with a phase velocity equal to that of the slow space‐charge wave on the electron beam. An interpretation is offered in terms of an approach to stationary plasma turbulence through a linear beam‐plasma interaction, followed by harmonic generation, wave‐wave coupling, and ultimate broadening of the emission peaks into a continuous spectrum.

ISSN:0031-9171    

DOI:10.1063/1.1692528

出版商:AIP    

年代:1969

数据来源: AIP

摘要:

The one‐dimensional problem of electrons confined in a quadratic potential is solved in the WKB approximation. The unique feature of the problem is that, since particle bounce time is independent of energy, resonant particles that normally cause Landau damping periodically interact with the wave and regenerate all phase information. Because of the efficiency of the regeneration mechanism, the dielectric properties governing the system change and give rise to “regenerative modes” associated with harmonics at twice the bounce frequency. The eigenvalues calculated in this WKB approximation are in agreement with previous numerical calculations.

ISSN:0031-9171    

DOI:10.1063/1.1692529

出版商:AIP    

年代:1969

数据来源: AIP