Volume 5, Issue 4, April 1998
 ARTICLES


Kinetic Alfvén waves driven by velocity shear
View Description Hide DescriptionConsidering the effect of the finite ion gyroradius, the kinetic Alfvén wave in an anisotropic medium driven by a parallel velocity flow was investigated and the full dispersion relation was given. In deducing the dispersion relation, the coupling between electrostatic and electromagnetic oscillations, effects of the resonant electrons and the longitudinal motion of ions are considered. Based on the analytical and numerical calculations, two instability boundaries are found. They are and Resonant electrons serve as the main energy source in these two regimes, while the ion longitudinal motion only suppresses the mode in the second regime. In the boundary layer of the magnetopause, the temperature anisotropy also modifies the instability by lowering the frequency and reducing the growth rate. The above results show that the lowfrequency Alfvén waves with the scale of perpendicular wavelengths greater than the ion gyroradius in the magnetopause can be efficiently driven by a velocitysheared flow.

Explicit reduction of body dynamics to selfconsistent particle–wave interaction
View Description Hide DescriptionThe onedimensional (1D) spatially periodic system of classical particles, interacting via a Coulomblike repulsive longrange force, is studied using classical mechanics. The usual Bohm–Gross dispersion relation for the collective modes is obtained in the absence of quasiresonant particles. In the presence of quasiresonant particles, the evolution equations for longwavelength modes are coupled to the particles’ motion through a selfconsistent wave–particle Hamiltonian. The wave–particle Lagrangian is derived from the full body Lagrangian. The derivation relies on an explicit scale separation argument and avoids the use of kinetic theory and continuous medium formalism.

Electron surface waves in a plasma slab with uniform ion density
View Description Hide DescriptionElectron surface waves in a metal bound plasma slab have been detected and analyzed. In this work it is shown that the presence of a matrix sheath between the central quasineutral region and the metal walls allows for the propagation of surface waves analogous to those found in dielectric bound plasmas.Measurements of the dispersion relations and eigenfunctions of asymmetric and symmetric, electrostatic,surface, and body waves are made via particleincell simulation of a plasma slab with sheaths. The plasma slab has finite temperature electrons and fixed ions of uniform density. The sheaths consist of electron free, fixed, uniform ion regions (“matrix sheath”) of thickness A linearized Vlasov theory is developed for comparison with the simulation. It is shown that the long wavelength approximation is not valid even for long wavelengths in the propagation direction. Collisionless damping of both surface and body waves is measured which compares well with theoretical estimates.

Electron surface waves in a nonuniform plasma slab
View Description Hide DescriptionElectron surface waves in a nonuniform, metal bound, thermal plasma slab have been analyzed and detected. Measurements of the dispersion relations of these waves, as well as the eigenstructure of the perturbed electron density, reveal a spectrum of waves with frequencies above and below the peak electron plasma frequency in the slab. These waves are analogous to the Gould–Trivelpiece and Tonks–Dattner waves found in dielectric bound plasma columns. Measurements have been made using particleincell simulation of an argon plasma and are compared with linear fluid theory in which the adiabatic approximation is made for the perturbed pressure. The presence of the metal boundary leads to regions near the plasma sheaths in which the fluid theory breaks down; we explore the differences between theory and measurement in this region.

Kinetic description of cyclotronrange oscillations of a nonneutral plasma column
View Description Hide DescriptionThe kinetic analysis introduced by Prasad, Morales, and Fried [Prasad et al., Phys. Fluids 30, 3093 (1987)] is used to derive damping conditions and a differential equation for azimuthally propagating waves in a nonneutral plasma column in the limits and (where is the Larmor radius, is the wave number, and is the density scale length). The predictions of the kinetic analysis are verified using a twodimensional particleincell simulation of Bernstein modes in a thermal rigidrotor equilibrium. Differences between modes in a strongly magnetized limit and near the Brillouin limit are studied in the simulation.

Refraction of the ordinary wave near the electron cyclotron fundamental
View Description Hide DescriptionDetailed ray tracing, of wave propagation in a plasma near electron cyclotron resonances, suggests that refraction can lead to reduced absorption, in some cases. By studying the full wave equation for the ordinary wave near the fundamental, in a slab model, it is shown that such refraction does indeed reduce absorption, for this particular case, but that wave energy tunnelling can significantly modify the result.

Dynamic screening effects on antiscreening excitations for ion–ion collisions in dense plasma
View Description Hide DescriptionIn dense plasmas, dynamic plasma screening effects are investigated on antiscreening channels for excitation of a oneelectron ion target by a oneelectron ion projectile. The ion–ion interaction potential is considered by the introduction of the longitudinal plasmadielectric function. A semiclassical straightline trajectory method is applied to the ion projectile path in order to visualize the dynamic plasma screening effects on the transition probabilities in dense plasmas as a function of the impact parameter and the collision energy. The transition probabilities including the dynamic plasma screening effects are found to always be greater than those including the static plasma screening effects. When the projectile velocity is greater than the electron thermal velocity, the interaction potential is almost unshielded. The difference between the dynamic and static plasma screening effects is more significant for lowenergy projectiles. It is also found that the quadrupole transitions (dipolequadrupole and quadrupole–quadrupole) show the double peaks due to the node of the radial wave function.

Stationary modes in a nonneutral plasma
View Description Hide DescriptionIn a nonneutral plasma column of constant density it is shown that, for certain parameter values, an infinitely degenerate internal mode, which has no variation in the axial direction, can be stationary in the laboratory frame. However, this mode cannot be driven resonantly by stationary electric or magnetic field asymmetries. When the plasma density is nonuniform the possibility of resonance of stationary field asymmetries with the continuous spectrum is pointed out.

Continuum plasma flow past a sphere
View Description Hide DescriptionFlow of a collisiondominated weakly ionized gas over a solid sphere is investigated in the limit where is the mean free path, is the Debye length, and is the sphere radius. Such flow is encountered in plasma heating of metallic/ceramic powders in rf plasmaaided manufacturing processes. The flowReynolds number (Re) based on sphere diameter is in the intermediate range The continuity, the momentum conservation, and the energy conservation equations for the neutrals and those for the charged particles are simultaneously solved with the Poisson’s equation for the selfconsistent electric field. A model for production and recombination of the charged particles is incorporated in the formulation. The surface of the sphere is considered as a sink for the charged particles and is at the floating potential. A finite difference method is employed to solve the governing equations. The flow field, the temperature distributions, the charged particle number density variations are obtained and the heat transport to the sphere surface is determined for a range of flowReynolds number. The effects of Reynolds number, the far field temperature, and the surface temperature on the electric sheath around the sphere surface and on the heat transport to the sphere, are delineated.

Constraints on finitetime current sheet formation at null points in twodimensional ideal incompressible magnetohydrodynamics
View Description Hide DescriptionIt is shown rigorously that, under the conditions of twodimensional ideal incompressible magnetohydrodynamics, finitetime singularity formation (including finitetime collapse to a current sheet) cannot occur at a magnetic null point of any type unless driven by a pressure singularity occurring outside a neighborhood of the null point. The proof is based on the depletion of nonlinearity at a twodimensional magnetic null point.

Effect of finite magnetic moment on threshold amplitude of electrostatic waves in nonlinear dynamics
View Description Hide DescriptionAn ensemble of electrostatic waves propagating obliquely to the external uniform magnetic field accelerates the plasma electrons, giving rise to a mechanical energy in terms of finite magnetic moment (μ). In nonlinear analysis, this magnetic moment modifies the resonances among the harmonics and the overlapping parameter leading to stochasticity. It is shown that the threshold amplitude of electrostatic waves at the onset of chaos increases slowly for harmonics and sharply for higher harmonics owing to the effect of magnetic moment. A sharp decrease of threshold amplitude with wave vector (k) pertaining to the ensemble of waves for higher harmonics is also delineated. The findings may have astrophysical and cosmological signatures in the high energy particle regimes.

Parametric interaction of selflocalized upper hybrid states in quantized plasma density irregularities
View Description Hide DescriptionA theoretical model of the interaction between slow transport and rapid ponderomotive processes of upper hybrid (UH) oscillations driven by a homogeneous pump electric field is presented. The selflocalization of UH oscillations in quantized plasma density depletions due to a thermal nonlinearity is described. The threshold for the parametric decay of the primary localized UH state into a secondary UH state and lower hybridwaves is calculated, as well as the amplitudes of the nonlinearly stabilized UH states. These selflocalized UH states constitute a complex response of the plasma to the imposed energy flux, which may be an important source of electromagnetic radiation, such as the electromagnetic emissions stimulated in high frequency pumping of the ionospheric plasma.

Modification of Langmuir solitons due to ion sound dispersion
View Description Hide DescriptionThe modifications of Langmuir solitons caused by the dispersion of the ion sound are investigated. They include the solitonresonant radiation, soliton deformation, and the decrease of the soliton amplitude and velocity because of the radiation. The results of the previous paper [Karpman and Schamel, Phys. Plasmas 4, 120 (1997)] are confirmed and completed.

Dynamics and control of internal transport barriers in reversed shear discharges
View Description Hide DescriptionTransitions to an enhanced confinement regime in tokamakplasmas with negative central magnetic shear have been observed in a number of devices. A simple model incorporating the nonlinear coupling between the turbulent fluctuations and the sheared radial electric field is added to a transportmodel in order to investigate the dynamics of the transition to this enhanced confinement mode. In this model, by incorporating both the instability growth rate profiles and particle and/or power deposition profiles, a rich variety of transition dynamics is uncovered. Transition dynamics and their concomitant thresholds are examined within the context of these models. In the course of investigating these transitions, potential methods for triggering and controlling these enhanced confinement regimes have been discovered and are discussed.

Ion plateau transport near the tokamak magnetic axis
View Description Hide DescriptionConventional neoclassical transport theory does not pertain near the magnetic axis, where orbital variation of the minor radius and the poloidal field markedly change the nature of guidingcenter trajectories. Instead of the conventional tokamak bananashaped trajectories, nearaxis orbits, called potato orbits, are radially wider and lead to distinctive kinetic considerations. Here it is shown that there is a plateau regime for the nearaxis case; the corresponding potatoplateau ion thermal conductivity is computed.

Sheared slab instability in tokamak plasma with negative magnetic shear
View Description Hide DescriptionThe sheared slab instability is reconsidered in tokamak plasma with negative magnetic shear. A modified sheared slab model is presented to include both the magnetic shear and its variation with the magnetic surface. The results show that the slow variation of magnetic shear can aggravate the sheared slab instability in the region near the minimum magnetic surface and that it has a weak stabilizing role in the plasma core near the axis. However, when the effect of the variation of magnetic shear increases, it can give rise to a stronger slab instability. In addition, a linear mode coupling mechanism could be mediated by the variation of magnetic shear with a magnetic surface.

Feasibility experiments for electron ripple injection on current drive experimentupgrade
View Description Hide DescriptionIn search of a method to generate a radial electric field in tokamak plasmas, an experimental study has been performed to investigate the possibility of inducing radial electrical current. An external coil array has been used to create a local magnetic ripple well and the electron cyclotron resonance heating(ECH) has been used to trap some electrons that will then be subject to rapid vertical drifts into the plasma. Using a simplified experimental arrangement with only a toroidalmagnetic field, an ECHdriven radial electrical current has been observed. The ECHdriven elecron temperature anisotropy, which is necessary for ripple trapping and electron drifts, has been determined by several different methods. The perpendicular temperature can be shown to be as large as 11 times the parallel temperature, which should yield a significant amount of ripple trapping and radial current.

Noncircular, finite aspect ratio, local equilibrium model
View Description Hide DescriptionA tokamak equilibrium model, local to a flux surface, is introduced which is completely described in terms of nine parameters including aspect ratio, elongation, triangularity, and safety factor. By allowing controlled variation of each of these nine parameters, the model is particularly suitable for localized stability studies such as those carried out using the ballooning mode representation of the gyrokinetic equations.

Flux buildup in field reversed configurations using rotating magnetic fields
View Description Hide DescriptionRotating magnetic field (RMF) current drive is a very attractive method for both increasing the flux and sustaining the current in field reversed configurations (FRC). It has been demonstrated in low temperature, low field rotamaks, and will now be applied to a new translation, confinement, and sustainment (TCS) experiment attached to the LSX/mod (Large fieldreversed configuration Experiment) facility [Hoffman et al. Fusion Technol. 23, 185 (1993)]. Previous RMF calculations have been concerned primarily with the plasma currents and particle orbits produced in onedimensional cylinders with the rotating field strength of near equal magnitude to the confining axial field. Both fluid current and particle orbits are calculated here in the more interesting regime appropriate to TCS and reactors where the confinement field far exceeds the rotating field strength. New insight is gained into both the flux buildup requirements for twodimensional equilibria and into the limits on ion rotation in this high confinement field regime.

Flowshear stabilization of ion temperature gradientdriven instability in a tokamak: Slab theory
View Description Hide DescriptionA simple physical model for the flowshear stabilization of ion temperature gradient (ITG)driven instability in the presence of dissipative trapped electrons is presented. Reduced fluid equations and magnetic sheared slab geometry are adopted. From analytical analyses and numerical calculations, it was found that the coupling between the sheared flows and nonadiabatic electrons will result in the stabilization of both toroidal sheared flow and poloidal sheared flow on hybrid dissipative trapped electronITG mode. This implies that the confinement improvement in tokamaks can be obtained not only through the poloidal sheared rotation in the edge region of tokamaks for the Hmode(highconfinement mode), but also through the toroidal sheared rotation in the core region for further confinement improvement associated with internal transport barrier(ITB) and negative shear (or reversed magnetic shear). When the poloidal and toroidal sheared flows are simultaneously considered, it was found that in the presence of poloidal sheared flow, the toroidal sheared flow is a stabilizing or destabilizing effect on hybrid dissipative trapped electronITG mode according to the relative sign of the poloidal and toroidal sheared flows. However, for sufficiently large value of the toroidal sheared flow, the toroidal sheared flow is always destabilization on the hybrid dissipative electronITG mode regardless of the relative sign of these sheared flows. These conclusions are consistent with the experimental observations on the Japanese Tokamak60U (JT60U) [Y. Koide et al., Phys. Rev. Lett. 72, 3662 (1994)], where large toroidal rotation shear or jump was observed across the surface (the internal transport barrier location). Toroidal sheared flow stabilization therefore appears to offer favorable prospects for high confinement operation of future fusion reactor.
