Index of content:
Volume 4, Issue 5, May 1997

Evolution of paired luminous rings in capacitive radiofrequency hydrogen discharges
View Description Hide DescriptionThe temporal and spatial evolution of paired luminous rings is observed in pulsed capacitive radiofrequency (rf) hydrogen discharges. The timeresolved axial profile of the light intensity indicates that the outermost ring pairs near the electrodes start to appear earlier than the inner ones, and that only the leftside (rightside) rings of ring pairs turn on when the rf voltage applied to the leftside (rightside) electrode is positive. The physical mechanism to create the paired rings seems to be similar to that of the standing striations in dc glow discharges.

Compressible hydromagnetic shear flows with anisotropic thermal pressure: Nonmodal study of waves and instabilities
View Description Hide DescriptionThe evolution of linear magnetohydrodynamic waves and plasma instabilities (firehose and mirror) in a compressible, magnetized plane Couette flow with anisotropic thermal pressure is investigated. In the present study we revealed that the pressureanisotropy brings significant novelty to the effect of coupling and linear reciprocal transformation of the wave modes originally discovered [Chagelishvili, Rogava, and Tsiklauri, Phys. Rev. E 53, 6028 (1996)]. It is found that behavior of the firehose and mirror instabilities is drastically changed due to the presence of shear in the flow. These novel effects are caused by the nonnormality of linear dynamics in shear flows and they have been revealed through use of the nonmodal approach.

Confinement of test particles in a Malmberg–Penning trap with a biased axial wire
View Description Hide DescriptionA nonneutral plasma trap has been constructed in which the radial electric field of a nonneutral plasma column is simulated by a biased wire stretched along the axis of the device. The confinement time of test electrons in this device is found to be comparable in magnitude and scaling with that found in pure electron plasma experiments, in spite of the fact that the test electron density is times smaller than in a typical pure electron plasma. The confinement time is only weakly dependent on the central wire bias. These results may provide useful input to theoretical efforts to explain transport in these traps.

A Lyapunov functional for stability of ideal magnetohydrodynamic systems in arbitrary motion
View Description Hide DescriptionThe stability properties of an ideal magnetohydrodynamic(MHD)fluid (compressible) in an arbitrary state of motion is explored. A stability condition is formulated in general terms based on the concept of a Lyapunov functional for the system which can be taken to be the Hamiltonian. Special consideration is given to stationary systems where the fluid is bounded by a surface on which the normal component of the fluid velocity is zero. For this case a necessary and sufficient condition for stability in terms of an energy principle is formulated. This can be considered to be a generalization of the classic MHD energy principle. A comparison to normal mode solutions is made. Systems being subjected to forced oscillations around a static equilibrium that may be unstable are of prime interest for dynamic stabilization problems. The present theory also includes results relevant to this type of system, although no details of such problems are presented. The emphasis is on general theory, however, one example of an ordinary fluid which is rotating is discussed in order to get a better understanding of the theoretical results.

The evolution of plane current–vortex sheets
View Description Hide DescriptionThe linear and nonlinear evolution of the plane current–vortex sheet, with a basic magnetic field given by and a basic velocity field given by is examined. The discovery of an ideal instability in a large region of parameter space previously found to be stable is reported. In this paper numerical evidence is presented that this parameter regime is in fact highly unstable, with growth rates exceeding those of the modes existing in the region of parameter space previously found to be unstable. An examination of the perturbation energy balance indicates that enhanced energy transfer from the basic velocity field to the perturbed velocity and magnetic fields is responsible for the enhanced growth rate. This occurs due to processes absent from both the resistive and Kelvin–Helmholtz instabilities. Nonlinearly it is found that magnetic reconnection can occur on an ideal time scale in certain cases. These faster instabilities lead to a more violent cascade of excitation in the streamwise direction, as evidenced by the rapid formation of higher harmonics of the initial disturbance. A nonlinear saturation due to increased correlation of the perturbed velocity and magnetic field occurs for all cases.

Selffocusing dynamics of nonlinear waves in media with parabolictype inhomogeneities
View Description Hide DescriptionThe possibility of accelerating the selffocusingdynamics of light beams in nonlinear and dispersive media with either a constant or a weakly oscillating parabolic density profile is investigated. It is shown that the selfcompression of wave packets, that freely selffocus in homogeneous media, can be enhanced by the action of appropriate parabolic inhomogeneities, whose lensing influence shortens the focal time of the wave. A similar property also occurs when the scalar envelope of a nonlinear waveform interacts with a uniform external magnetic field. The motion of light beamlets, originating from the filamentation instability of an incident beam, is analytically described for inhomogeneous media with focusing and defocusing density profiles.

Orbital resonances and chaos in a combined rf trap
View Description Hide DescriptionThe rf combined trap for confining a nonneutral plasma by a combination of rf fields and a uniform magnetic field is introduced. The particle motion is studied in such a trap in which the rf fields are given by the mode. The aim is to determine limits on a focus at the center for low angular momentum particles. Such a focus allows densities in excess of the local Brillouin limit. The motion is described in terms of an effective potential consisting of the ponderomotive potential plus a radial potential due to the magnetic field plus a centrifugal potential Near the origin the equations reduce to a pair of Mathieu equations for the and motions. For certain parameters the system is quasispherically symmetric, i.e. the effective ponderomotive frequencies in and are equal. In this case the Brillouin limit for a uniform density plasma is shown to equal the usual cylindrical limit. Numerical integration of the ponderomotive equations is shown for parameters near those giving quasispherical symmetry. There is resonance for giving islands. The islands limit the size of the focus at the origin, even for For particles with large effective energy there can also be chaos, depending on the elongation of the rf cavity. It is found that the deleterious effect of islands and chaos on the focus is minimized by having the elongation close to unity and having particles trapped deeply in the ponderomotive well.

Threewave processes in a turbulent nonstationary plasma
View Description Hide DescriptionThe contribution of plasma turbulence to the decaytype coupling of three regular waves is derived and discussed. The effect is due to the nonlinear interaction of the waves with the turbulence as well as the plasma nonstationarity induced by the turbulence. The conservation relations for the wave occupation numbers, energy, and momenta are considered. It is shown that for the interactions of three regular waves in a closed system, the ManleyRowe relations are valid (i.e., there is no exchange of the number of quanta with the plasma turbulence). However, the turbulence causes phase shifts of the interactingwaves, and affects the energy balance via the nonstationarity of the system.

Fluid models for kinetic effects on coherent nonlinear Alfvén waves. II. Numerical solutions
View Description Hide DescriptionThe influence of various kinetic effects (e.g., Landau damping, diffusive and collisional dissipation, and finite Larmor radius terms) on the nonlinear evolution of finite amplitude Alfvénic wave trains in a finite environment is systematically investigated using a novel, kinetic nonlinear Schrödinger (KNLS) equation. The dynamics of Alfvén waves is sensitive to the sense of polarization as well as the angle of propagation with respect to the ambient magnetic field.Numerical solution for the case with Landau damping reveals the formation of dissipative structures, which are quasistationary, polarized directional (and rotational) discontinuities which selforganize from parallel propagating, linearly polarized waves. Parallel propagating circularly polarized packets evolve to a few circularly polarized Alfvén harmonics on large scales. Stationary arcpolarized rotational discontinuities form from obliquely propagating waves. Collisional dissipation, even if weak, introduces enhanced wave damping when is very close to unity. Cyclotron motion effects on resonant particle interactions introduce cyclotron resonance into the nonlinear Alfvén wave dynamics.

Velocity–space drag and diffusion in a model, twodimensional plasma
View Description Hide DescriptionThe quasilinear fluctuation integral is calculated for a twodimensional, unmagnetized plasma (composed of charged rods), and is expressed in terms of Fokker–Planck coefficients. It is found that in two dimensions, the enhanced fluctuationsgenerated by fast electrons lead to anomalously large transport coefficients. In particular, the effect of a small population of fast electrons is only weakly dependent on their density. In three dimensions, the effect of fast electrons is masked by the dominant approximation, but higherorder terms describe processes similar to those in two dimensions, and these terms can become significant for weakly stable plasmas. The differences between two and three dimensions arise from the fact that both emission and damping of plasma waves are retained to lowest order in two dimensions, while the threedimensional dominant approximation effectively includes only wave emission by test particles. An understanding of the differences between two and three dimensions is crucial to the interpretation of twodimensional particle simulations.

Magnetohydrodynamic simulation on co and counterhelicity merging of spheromaks and driven magnetic reconnection
View Description Hide DescriptionA magnetohydrodynamic relaxation process of spheromak merging is studied by means of an axisymmetric numerical simulation. As a result of counterhelicity merging, a fieldreversed configuration is obtained in the final state, while a larger spheromak is formed after cohelicity merging. In the counterhelicity case, a clear pressure profile of which isosurfaces coincide with flux surfaces is generated by thermal transport of a poloidal flow induced by driven reconnection. It is also found that a sharp pressure gradient formed in the vicinity of a reconnection point causes a bouncing motion of spheromaks. According to the bounce motion, the reconnection rate changes repeatedly. As shown by the Tokyo University Spherical Torus No. 3 (TS3) experiments [M. Yamada, et al., Phys. Rev. Lett. 65, 721 (1990)], furthermore, strong acceleration of a toroidal flow and reversal of a toroidal field in the counterhelicity merging were observed.

A model of ions interacting with neutrals in high electric field and the application to presheath formations
View Description Hide DescriptionA model of interactions between ions and neutrals in the high electric field is proposed and the exact solution to the Boltzmann equation with the interaction terms is derived. It is shown that the solution produces the known dependence of the ion drift velocity and the mobility on the parameters of the plasma and neutrals in the high electric field. Experimental results on mobilities of ions in the parent gas are studied by using the formula of the drift velocity obtained in our model. As an application, the presheath formation at the plasma–wall boundary is discussed and a comparison with experimental measurements of sheath potential profiles has been performed.

Deuteriumtritium simulations of the enhanced reversed shear mode in the Tokamak Fusion Test Reactor
View Description Hide DescriptionThe potential performance, in deuteriumtritium plasmas, of a new enhanced confinement regime with reversed magnetic shear [enhanced reversed shear (ERS) mode] is assessed. The equilibrium conditions for an ERS mode plasma are estimated by solving the plasmatransportequations using the thermal and particle diffusivities measured in a short duration ERS mode discharge in the TokamakFusion Test Reactor [F. M. Levinton et al., Phys. Rev. Lett. 75, 4417 (1995)]. The plasma performance depends strongly on and neutral beam penetration to the core. The steadystate projections typically have a central electron density of and nearly equal central electron and ion temperatures of keV. In timedependent simulations the peak fusion power, 25 MW, is twice the steadystate level. Peak performance occurs during the density rise when the central ion temperature is close to the optimal value of keV. The simulated pressure profiles can be stable to ideal magnetohydrodynamic instabilities with toroidal mode number and for up to 2.5; the simulations have . The enhanced reversed shear mode may thus provide an opportunity to conduct alpha physics experiments in conditions similar to those proposed for advanced tokamak reactors.

Partial reconnection in the nonlinear internal kink mode
View Description Hide DescriptionThe effect of the electron pressure gradient in Ohm’s law on the nonlinear development of the internal kink mode is investigated. While pressure fluctuations have a destabilizing effect, the average pressure gradient giving rise to diamagneticflows is stabilizing. If the latter is strong enough, it leads to saturation at finite island size. The relevance of the results for the sawtooth phenomenon in tokamak plasmas is discussed.

Generalized ballooning and sheath instabilities in the scrapeoff layer of divertor tokamaks
View Description Hide DescriptionThe stability of the scrapeoff layer to high toroidal mode number ballooningtype instabilities is considered. The equilibrium includes a simple model of the Xpoint geometry, and parallel (as well as crossfield) equilibrium variations of temperature, density, and potential. The latter are computed numerically from the Braginskii form for Ohm’s law. The stability analysis includes the effects of curvature, resistivity, parallel variation of the drift frequency, and sheathboundary conditions at the divertor plate. Importantly, the equilibrium model assures consistency among the possible instability drives; i.e., the pressure weighting of the curvature, the plasma potential ( drift), and the conditions at the divertor plate are coupled by the equilibrium model. Numerical solutions indicate two modes: (i) the curvaturedriven mode with growth rate enhanced by the sheaths; and (ii) the shear mode driven by equilibrium variations in the region between the X point and the plate. The latter mode is shown to be partly driven by the Xpoint geometry. The effect of finite Larmor radius, resistivity, and electron inertia on these modes is investigated.

Submarginal profiles and turbulent transport: An exactly solvable model
View Description Hide DescriptionThe possibility that linearly stable (“submarginal”) profiles can support turbulent transport in the absence of external noise is considered in the context of a onedimensional, realizable stochastic model of “almost passive” advection that includes a stability threshold dependent on a critical gradient. The important limits of zero and infinite Kubo number (dimensionless autocorrelation time) are solved analytically. When the stability threshold is linear, it is proven rigorously that, within the context of the model, submarginal profiles do not carry any turbulent flux. A generalization to include a nonlinear stability threshold reminiscent of a subcritical bifurcation supports submarginal profiles.

Direct observation of potential profiles with a 200 keV heavy ion beam probe on the Compact Helical System
View Description Hide DescriptionIn this paper we present space potential profiles directly observed in a toroidal helical plasma of the Compact Helical System (CHS) [K. Matsuoka et al., Proceedings, 12th International Conference on Plasma Physics and Controlled Nuclear Fusion, Nice, 1988 (International Atomic Energy Agency, Vienna, 1989), Vol. 2, p. 411], using a 200 keV heavy ion beam probe. The potential profiles exhibit widely varied characteristics, including positive and negative polarities for electron cyclotron and neutral beamheated plasmas, respectively. The behavior of highenergy particles in the CHS plasmas are deduced from loss cone diagrams evaluated from the observed potential profiles.

Testing the scaling of thermal transport models: Predicted and measured temperatures in the Tokamak Fusion Test Reactor dimensionless scaling experiments
View Description Hide DescriptionTheoretical predictions of ion and electron thermal diffusivities are tested by comparing calculated and measuredtemperatures in low (L) mode plasmas from the TokamakFusion Test Reactor [D. J. Grove and D. M. Meade, Nucl. Fusion25, 1167 (1985)] nondimensional scaling experiments. The DIIID [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] Lmode scalings, the transportmodels of RebutLalliaWatkins (RLW), Boucher’s modification of RLW, and the Institute for Fusion StudiesPrinceton Plasma Physics Laboratory (IFSPPPL) model for transport due to ion temperature gradient modes are tested. The predictions use the measured densities in order to include the effects of density profile shape variations on the transportmodels. The uncertainties in the measured and predicted temperatures are discussed. The predictions based on the DIIID scalings are within the measurement uncertainties. All the theoretical models predict a more favorable dependence for the ion temperatures than is seen. Preliminary estimates indicate that sheared flow stabilization is important for some discharges, and that inclusion of its effects may bring the predictions of the IFSPPPL model into agreement with the experiments.

Effects of orbit squeezing on ion transport processes close to magnetic axis
View Description Hide DescriptionIt is shown that ion thermal conductivity close to the magnetic axis in tokamaks is reduced by a factor of if Here, is the orbit squeezing factor, is the ion (electron) mass, and is the ion (electron) temperature. The reduction reflects both the increase of the fraction of trapped particles by a factor of and the decrease of the orbit size in units of the poloidal flux ψ by a factor of

Electron transport processes close to magnetic axis in tokamaks
View Description Hide DescriptionElectron transport fluxes valid in the region close to magnetic axis in tokamaks are derived from the moment equation approach. It is found that bootstrap current does not vanish on the axis, electrical conductivity is reduced from its classical value, and particle and heat fluxes are enhanced over those in the conventional neoclassical theory. The reason for the deviation from the conventional theory is because the fraction of the trapped particles is finite in the region close to the magnetic axis. The existence of the bootstrap current on the magnetic axis may reduce or eliminate the need of the seed current.