Volume 3, Issue 1, January 1996
Index of content:

Suppression of nonlinear interchange mode by zonal counterstreaming flow generation
View Description Hide DescriptionNonlinear evolution of interchange mode produces both vortexflow and shear flow in a scrape‐off layer (SOL) plasma with unfavorable magnetic curvature. When the Rayleigh number becomes the order of 10^{5}, the shear flow exceeds the vortexflow and the zonal counterstreaming flow appears in the perpendicular direction to the ambient magnetic field. Simultaneously, the fluctuation level decreases and the associated cross‐field transport becomes almost classical. However, since reduction of the saturation level weakens the shear flow generation, an intermittent oscillatory behavior appears and continues. Transport due to the vortexflow measured with a Nusselt number may depend on the Prandtl number for a given Rayleigh number.

The magnetic presheath boundary condition with E×B drifts
View Description Hide DescriptionIt is demonstrated rigorously that the effects on a one‐dimensional, collisionless, magnetic presheath with oblique magnetic fieldB of a uniform tangential electric field, causing a drift v _{ D }=E×B/B ^{2}, are equivalent to a transformation to a frame moving tangential to the surface. Therefore, in particular, the Chodura solution with parallel velocityv _{∥}=c _{ s } (the sound speed) is transformed into a solution with v _{∥}=c _{ s }+v _{ D }/tan α, where α is the field angle to the surface.

A new form of the magnetohydrodynamic potential energy
View Description Hide DescriptionIn this Letter a useful and instructive form of the magnetohydrodynamic potential energy is presented. In this form all but one term is positive definite, each term is self‐adjoint, and it can be directly evaluated numerically in nonorthogonal coordinate systems. The product of the local shear and the current parallel to the magnetic field is identified as a significant parameter for current‐driven instabilities.

Force‐free thin flux tubes: Basic equations and stability
View Description Hide DescriptionThe thin flux tube approximation is considered for a straight, symmetrical, force‐free, rigidly rotating flux tube. The derived set of equations describes tube, body sausage, and Alfvén wave modes and is valid for any values of β. The linear waves and instabilities of force‐free flux tubes are considered. The comparison of approximate and exact solutions for an untwisted, nonrotating flux tube is performed. It is shown that the approximate and exact dispersion equations coincides, except the 20% discrepancy of sausage frequencies. An effective cross section is proposed to introduce the removal of this discrepancy. It makes the derived approximation correct for the force‐free thin flux tube dynamics, except the detailed structure of radial eigenfunction. The dispersion of Alfvén torsional waves in a force‐free tubes appears. The valve effect of one directional propagation of waves in rotating twisted tube is revealed. The current and rotational sausage instabilities of a force‐free, thin flux tube are considered.

Statistical mechanics of charged rings
View Description Hide DescriptionStatistical mechanics of massless thin rings carrying electric charge is formulated. The rings are circular, concentric around a common axis, and can undergo axisymmetric deformations. The model is applied to guiding center plasmas confined in a toroidalmagnetic field, where charged rings are identified with flux tubes. It is argued that the steady state of such systems can be viewed in terms of the dynamics of these rings that slide on equipotentials and go through each other. A partial differential equation describing the most probable distribution of charges on the rings is obtained and solved numerically. Solutions corresponding to an ensemble with charges of single species and two species are obtained. The results show that the statistical mechanics of these rings differ in interesting ways from that of line charges.

Stability of force‐free Taylor states in a new version of magnetic flux‐averaged magnetohydrodynamics
View Description Hide DescriptionIt is observed that the recently developed magnetic flux‐averaged magnetohydrodynamics (AMHD) [Phys. Plasmas 1, 2488 (1994)] is incompatible with Taylor’s theorem, which states that the lowest‐energy state of force‐free equilibria based on the conservation of the helicity integral is absolutely stable for vanishingly small resistivity. By a modification of the Lagrangian from which AMHD is derived, a modified version of AMHD that is compatible with Taylor’s theorem is obtained. It also provides an energy principle for examining the linear instability of resistive equilibria, which has a great advantage over resistive MHD.

Asymptotics of the modified plasma dispersion function generalized to real kappa
View Description Hide DescriptionThe modified plasma dispersion function (MPDF), an extension to κ particle distributions of the standard plasma dispersion function (PDF), has been recently generalized to real κ. An analysis of the general form of the MPDF is made to obtain its asymptotic solution for real κ≥2. A recursion relation is derived and applied to calculate the asymptotic expression directly in terms of the PDF. A numerical analysis is made of its error relative to the exact value for a range of integer values of κ from 2 to 5, and the error is found to typically be about 8% for κ=2, 2% for κ=3, 0.4% for κ=4, and 0.2% for κ=5. The precision increases as κ increases, and generally the first four to five terms of the expansion give accurate results. Potential applications for analyzing processes in a variety of space and astrophysical plasmas are discussed.

Electrodynamics as a problem of eigenvalues. I. Maxwell operator and its properties. Momentum‐energy tensor
View Description Hide DescriptionA new method of formulation of problems in macroscopic electrodynamics is proposed. Maxwell equations are written in the abstract‐operator form. A solution to the formal problem of eigenvalues and eigenfunctions of the introduced Maxwell operator allows us to use the well‐developed mathematical technique of linear operator theory for various electrodynamical problems. In particular, calculation of the momentum‐energy tensor, wave generation, perturbation theory, and variational approach can be applied for electrodynamical systems (cavities, waveguides, free space) filled with media of arbitrary dispersion. In the first part of the paper we deal with a formal foundation of the method and calculation of the momentum‐energy tensor.

Electrodynamics as a problem of eigenvalues. II. Variational method of calculation of electromagnetic field oscillations in dispersive medium
View Description Hide DescriptionThis part of the paper deals with a variational approach. The general scheme is given and two examples are presented: free oscillations of an electromagnetic field in a cavity filled with an inhomogeneous dispersive resonant medium and wave propagation in a longitudinally homogeneous plasma cylinder in an infinitely strong magnetic field. A comparison shows good agreement of results of a variational approach with results of an exact numerical solution. Possible ways of improving accuracy are discussed.

Electrodynamics as a problem of eigenvalues. III. Maxwell operator and perturbation theory
View Description Hide DescriptionThis part of the work deals with perturbation theory. The standard technique permits us to solve problems of volume disturbances in free space, waveguides, and cavities, of disturbances of boundary conditions caused by finite conductivity of walls, and of disturbances of the boundary shape. Expressions for frequency and wave number shifts caused by the perturbation are obtained by the unified method. Several examples are presented: wave amplification in the waveguide filled with a resonant medium like an electron beam in a longitudinal magnetic field, the frequency shift (and increment/decrement) of a cavity loaded by an electron beam, and the field disturbance in the waveguide caused by finite conductivity of the walls.

Second harmonic generation in collisionless plasma in parallel plate guide
View Description Hide DescriptionAn analysis of second harmonic power generation in collisionless, unmagnetized plasma bounded by parallel plates is presented, which predicts much higher yield under appropriate plate separation and input energy than the maximum reported yield for unbound plasma. One can therefore look for optimization of second harmonic power by choosing suitable parameters.

Linear‐conversion theory of energetic minority‐ion Bernstein‐wave propagation across gyroresonance in nonuniform magnetic field
View Description Hide DescriptionAn energetic minority‐ion population, such as neonatal fusion alphas, can support a Bernstein wave whose frequency is a harmonic of their gyrofrequency. The sign of the wave energy depends on the local wave vector, whose rate of change is proportional to the magnetic‐field gradient. As a result of the field nonuniformity, the wave crosses the gyroresonance layer and its energy flips sign. This results in energy transfer to a gyroballistic mode (which exists only in the resonance layer), with a conversion coefficient exactly equal to 2.

Analytical calculation of Boozer magnetic coordinates for axisymmetric magnetohydrodynamic equilibria
View Description Hide DescriptionA new analytical technique for extracting the Boozer magnetic coordinates in axisymmetric magnetohydrodynamic equilibria is described. The method is based upon the correspondence between the expansion of the flux function in toroidal multipolar moments and the expansion in toroidal axisymmetric harmonics of the magnetic scalar potential χ_{0}, which appears in the covariant representation B=∇χ_{0}+β ∇ψ_{ T } of the magnetic field. An example of calculation of Boozer magnetic coordinates is given for an experimental highly shaped high β equilibrium of DIIID [Plasma Physics Controlled Nuclear Fusion Research, 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. I, p. 159].

Changes of plasma potential induced by ion‐beam injection
View Description Hide DescriptionIt is experimentally clarified that injection of a stationary ion beam always changes the background plasma potential in a beam–plasma system. In this experiment, a technique of ion energy analysis is adopted to determine the plasma potential in the system. Results show that the plasma potential changes sensitively depending on the beam‐to‐plasma density ratio, even if other parameters are not allowed to vary. Finally, all the results obtained here are tentatively explained with the help of a Boltzmann relation.

Model equations from gyrokinetic theory for a non‐neutral plasma to include temperature effects and applications to a plasma of infinite length
View Description Hide DescriptionGyrokineticequations are derived for applications to non‐neutral plasmas in constant, straight magnetic fields wherein E×B drift velocities are of the same order as thermal velocities. The ratio of the E×B rotation frequency to the cyclotron frequency and the ratio of the gyroradius to a plasma scale length are assumed to be of order ε and terms are retained in the gyrokineticexpansion to second order to include finite‐Larmor‐radius (FLR) effects. A mode equation is obtained for a non‐neutral plasma in the infinite‐length approximation. The singularities of this equation are compared and contrasted with the familiar mode equation from the cold‐fluid approximation. A numerical investigation of m=1 perturbations for a pure electron plasma with parameters chosen to closely approximate those in the report by Driscoll [Phys. Rev. Lett. 64, 645 (1990)] reveals no exponentially unstable modes with significant growth rates and strongly suggests that finite temperature is not the source of the exponential growth seen in the experiments.

Another paradox involving the second law of thermodynamics
View Description Hide DescriptionRecently a paradox has been posed that appears to challenge the second law of thermodynamics in a plasma blackbody environment [D. P. Sheehan, Phys. Plasmas 2, 1893 (1995)]. In this paper another, related paradox is posed in an unmagnetized Q plasma. Laboratory experiments simulating some necessary conditions for the paradoxical system corroborate theoretical predictions and fail to resolve the paradox in favor of the second law.

Comparison of Zakharov simulation and open boundary Vlasov simulation of strong Langmuir turbulence
View Description Hide DescriptionBoth Zakharov equations and Vlasov equations are solved numerically to study the strong Langmuir turbulence developed in a plasma driven by an external pump field oscillating at the plasma frequency. A steady state turbulence in Vlasov simulations is reached by using open boundary conditions under which hot particles generated by strong caviton fields are replaced by initial cold Maxwellian particles when they cross the boundaries of simulation domain. A similar steady turbulent state in Zakharov simulations is easily achieved by implementing a phenomenological damping model and using periodic boundary conditions. Simulation results of these two different models are compared and investigated.

Langmuir field structures favored in wave collapse
View Description Hide DescriptionStudy of Langmuir collapse thresholds shows that they have little polarization dependence and that moving packets have the lowest thresholds in the undamped case. However, incorporation of damping into the density response inhibits collapse of packets moving at more than a small fraction of the sound speed. Investigation of energy transfer to packets localized in density wells—the nucleation process—shows that at most a few trapped states can exist and that energy transfer is most effective when there is a single barely‐trapped state. Coupled with an argument that closely packed wave packets have lower collapse thresholds, this argument yields an estimate of the number density of localized nucleating states in a turbulent plasma. It also leads to a simple and direct semiquantitative estimate of the collapse threshold. All these results are in accord with previous numerical simulations incorporating ion‐sound damping, which show a preponderance of slow‐moving or stationary packets with little or no intrinsic polarization dependence of thresholds. Likewise, the number densities obtained are in good agreement with simulation values, and the simple estimate of the threshold is semiquantitatively correct. The extent of the agreement supports the nucleation scenario with close‐packed nucleation sites in the turbulent state.

Lower‐hybrid wave collapse
View Description Hide DescriptionThe formation, collapse and arrest of lower‐hybrid wave packets are investigated analytically. The three‐dimensional structure of the wave packet is incorporated in the analysis and its polarization is studied for the first time. Nonlinear collapse thresholds are obtained via a Hamiltonian formulation and are used in calculating the probability distribution of collapsing wave packet structures as a function of their polarization. Transit‐time interaction theory is then used to calculate the arrest scale at which collapse is halted as the waves are damped. It is found that collapse thresholds are lowest for circularly polarized packets, but that nearly linearly polarized ones predominate in collapse because of their greater numbers in the linear phase of the evolution. It is argued that subsonic collapse persists until very near arrest, in accord with recent numerical simulations. Time scale analysis shows that the parallel field structure has difficulty in attaining its self‐similar form in the available collapse time, also in accord with simulations. Transit‐time theory implies that electrons travelling roughly parallel to the ambient magnetic field can arrest collapse at a scale comparable to that previously estimated for ions; which process dominates depends on the electron and ion temperatures and packet geometry. The resulting arrest scales are found to be in accord with the simulations.

Weakly relativistic solitons in a cold plasma with electron inertia
View Description Hide DescriptionIon‐acoustic solitons have been investigated in a cold plasma in the presence of electron inertia through the derivation of the Korteweg–de Vries (KdV) equation taking into account of weakly relativistic effects. Interestingly, relativistic solitons of both compressive and rarefactive characters are found to exist at the negligible difference of u _{0}/c and v _{0}/c (u _{0}, v _{0} being the initial speeds of streaming electrons and ions respectively, and c, the velocity of light) of the order 1×10^{−7}.