Volume 5, Issue 2, February 1998
 ARTICLES


Coarsegraining and nonlocal processes in proton cyclotron resonant interactions
View Description Hide DescriptionCoarsegrained information from a hybrid simulation show that previously developed quasifluid equations of state capture some aspects of proton cyclotron resonant interactions for parallel propagation in a low plasma. Direct kinetic information is used as a closure for the information exchanged with the higherorder moment quantities. The coarsegraining procedure involves averaging over many protoninertial lengths and looking at long time scales associated with the wave envelopes. By use of the coarsegraining prior to statistical analysis, the anticorrelations predicted by the equations of state are very high for both the single resonantwave case and for a broadband spectrum centered on a resonantwave. These anticorrelations are also consistent with what one expects from a single particle orbitanalysis. A similar analysis, but done without the prior averaging procedures, shows no relevant correlations, and no simple dynamics emerges from the kinetic data in this case. A comparison is made with a model based on quasilinear theory. These results suggest that, in addition to simply taking velocity moments of particle distributions, the proper averaging of kinetic information over space and time scales lying below the range accessible to a fluid model can be essential to its success.

Thermal equilibrium of warm clouds of charge with small aspect ratio
View Description Hide DescriptionGlobal thermal equilibrium computations are presented for nonneutral plasmas whose radial size is much larger than their axial thickness. Axial and radial density profiles are computed for both ideal and nonideal Penning trap fields. Simple results are obtained in the limits of both low and high central density. Comparison is made to the grid calculations of Mason et al. [Phys. Plasmas 3 (5), 1502 (1996)].

Polygon structure of plasma crystals
View Description Hide DescriptionStability and lattice oscillations are studied for polygon structures of plasma crystals under the forces of ion drags, gravitational fields, and sheathelectric fields. Circular lattices of dust grains, trapped in the potential minimum of a wake potential produced in the presence of ion flow, are levitated horizontally under the balance of forces. Positive ions transfer momentum to a negatively charged dust particulate either by scattering due to Coulomb force or by direct capturing due to the finite size of the dust. Resulting drag force on the dust particulates makes a plasma an effective viscous medium and is found to be responsible for the stability condition of the structure. It is shown that the polygon structures of triangle, square, pentagon, or hexagon are stable against spatial perturbations and are accompanied by the oscillations with characteristic low frequency inversely proportional to the effective viscosity.

Global approach to the spectral problem of microinstabilities in a cylindrical plasma using a gyrokinetic model
View Description Hide DescriptionConsidering the spectral problem of microinstabilities in a curved system, methods for solving the global gyrokineticequation are presented for the simple case of a cylindrical plasma. They prove to be efficient for computing the full unstable spectrum of ion temperature gradient(ITG) type modes and have shown to be applicable to the twodimensional integral equation of tokamak configurations.

Parametric instabilities due to relativistic electron mass variation
View Description Hide DescriptionThe stability of an electronic plasma in a largeamplitude dipolar field is analyzed. In such a wave the relativistic electron mass variation must be taken into account and in an overdense plasma an instability arises. The corresponding weakly relativistic theory of Tsintsadze [Sov. Phys. JETP 32, 684 (1971)] is extended to the fully relativistic regime. The growth rate of the instability can attain a significant fraction of the dipolar field frequency. The relevance of this instability to the fast ignitor concept is discussed.

Twodimensional coherent structures of drift waves exhibiting nonBoltzmann relationships in toroidal plasmas
View Description Hide DescriptionThe twodimensional mode equation describing drift waves that exhibit a nonBoltzmann relationship in a toroidal plasma is derived. Three types of solutions are obtained: (1) propagating cell patterns, in particular, triangular and hexagonal cell patterns, (2) a purely growing harmonic function, and (3), an isolated vortex propagating in the ion diamagnetic direction.

Simulation of the electron runaway in a plasma by Langevin equation
View Description Hide DescriptionA rigorous form of Langevin equation for the particleincell simulation of a collisional plasma is obtained. The method is checked by reproducing the known results on the simulation of the electron runaway in a fully ionized uniform plasma with Maxwelliancollisions. The nonMaxwellian effect owing to the electron heat flow on the runaway is explored.

Ponderomotive force in an anisotropic temperature plasma
View Description Hide DescriptionThe paper bridges the need for a theoretical formulation for the ponderomotive force, which is necessary for laboratory regimes where plasmas are thermally anisotropic. The calculations are based on a closed set of moment equations obtained from the Vlasov equation, under the assumption of negligible heat flow, for an arbitrary strength of the external magnetic field. The formulation also results in the inclusion of the finite Larmor radius effect, besides pointing out the limitations in the Chew, Goldberger, and Low [Proc. R. Soc. London, Ser. A 236, 112 (1956)] equations which have been frequently used to describe an anisotropictemperatureplasma.

Bäcklund transformations and Painlevé analysis: Exact soliton solutions for the unstable nonlinear Schrödinger equation modeling electron beam plasma
View Description Hide DescriptionIn this paper the Bäcklund transformations technique and Painlevé analysis are used to generate classes of exact solitonsolutions for some nonlinear evolution equations. For the dimensional problem, the unstable system of plasma equations where an electron beam is injected under a highfrequency electric field is reduced to the unstable nonlinear Schrödinger (UNLS) equation. Using the Darboux–Bargmann technique, we obtain the Bäcklund transformations for UNLS equation solvable by the inverse scattering method of Zakharov–Shabat/Ablowitz–Kaup–Newell–Segur (ZS/AKNS) and the ZS/AKNS wave functions corresponding to the solitonsolutions of this equation.

Observation of type1 intermittency caused by currentdriven ion acoustic instability
View Description Hide DescriptionIntermittent chaotic phenomena caused by the currentdriven ion acoustic instability are experimentally observed using a Double Plasma device, in which two mesh grids are installed to excite the instability. When a dc potential is applied to one of the two mesh grids and exceeds a certain threshold, the system suddenly transits from a periodic state to a chaotic state. At the same time, the signals picked up as perturbation components of a current exhibit intermittent turbulent bursts. The calculations of the correlation dimension and the Lyapunov exponent indicate that the system reaches a chaotic state. Furthermore, it is found that the results of mathematical and statistical analysis of observed signals agree with the theoreticalproperties of the type1 intermittency: the occurrence of type lowfrequency noise and the probability distribution of the duration between two bursts. Therefore, it is concluded that the present system reaches a chaotic state via the type1 intermittency.

Strong frequency upconversion by nonlinear Thomson scattering from relativistic electrons
View Description Hide DescriptionThe scattering of laser light by electrons is considered. When the electron is counterstreaming and highly relativistic, and the laser light ultraintense, the scattered light is mainly in the higher harmonics, and the frequency upshift is further enhanced by the Doppler effect. This provides a mechanism for very large frequency upconversion.

Poloidal magnetic field around a tokamak magnetic surface
View Description Hide DescriptionIn this paper a differential equation is obtained for the variation of the poloidal magnetic field along the cross section of the magnetic fieldsurfaces in a tokamak. Toroidal axisymmetry is assumed. The coefficients of the differential equation depend on the curvature of the family of curves orthogonal to the magnetic field lines. Several shapes of magnetic fieldsurfaces have been analyzed in detail as families of nested curves of circular, elliptic, and triangular elliptic shapes. Closed analytic solutions have been obtained in some cases.

Conditions for the existence of steady state stellarators
View Description Hide DescriptionLow collisonality methods developed earlier [Phys. Plasmas1, 3942 (1994)] are extended and applied to the characterization of steady state, toroidally confined nonsymmetric plasmas. A magnetic field is assumed which is a small perurbation of one with exact magnetic surfaces and zero shear. However, exact magnetic surfaces are not required. Two types of conditions on the system are found. In analogy with tokamaks, conditions of energy flux balance and particle flux balance are obtained. The fluxes are of magnitude comparable with those in a tokamak. Another class of constraints relates to properties of the magnetic field In addition to the condition of very small shear [Phys. Plasmas2, 3595 (1995)] and the condition that on a flux surface be a function of [Phys. Plasmas4, 575 (1997)], as extended, a hierarchy of increasingly restrictive conditions on are found. The consequence of these constraints is explored very briefly.

Charged particle confinement in torsatrons and heliotrons with toroidal field coils
View Description Hide DescriptionThe role of a strong and highperiodic toroidal magneticfield ripple (the TF ripple) in charged particle confinement is investigated for the torsatron/heliotron magnetic devices [K. Uo, J. Phys. Soc. Jpn. 16, 1380 (1961)] with discrete toroidal field coils in the helical field period. Caused by currents in these coils, such a ripple involves the appearance of additional toroidal ripple wells along the field line, in which charged particles may be trapped. To analyze the confinement character of the TF rippletrapped particles, the method of a double averaging of their equations of motion is developed. It is shown that the suprathermal particles, which are trapped in the separately located TF ripple wells of the magnetic field, are the most dangerous for confinement because the radial deviations of these particles are times higher than the corresponding values for the helically rippletrapped particles. An additional type of superbanana orbit caused by the TF ripple perturbation of the magnetic field is also found.

Plasma compressibility induced toroidal Alfvén eigenmode
View Description Hide DescriptionFor circular tokamaks, it is demonstrated, both analytically and numerically, that there exists a new frequency gap within the shear Alfvén continuous spectrum around the Alfvén frequency, due to the ion compressibility effect. Here, denotes the Alfvén speed, is the safety factor, and the major radius. The frequency gap width, meanwhile, is proportional to the core ion beta, (ratio between core ion and magnetic pressures), and, correspondingly, the new discrete toroidal Alfvén eigenmode (TAE) inside the gap is referred to as βTAE. Collective excitations of the βTAE by energetic ions are also analyzed.

Measuring from electron temperature fluctuations in the Tokamak Fusion Test Reactor
View Description Hide DescriptionA method is developed for determining directly from experimental data the classical tearing mode stability parameter Specifically, an analytical fit function is derived for the electron temperature fluctuations in the vicinity of a magnetic island. Values of determined from the fit function parameters for and modes ( and are poloidal and toroidal mode numbers) are obtained using the high resolution profile data from major radius shift (“jog”) experiments on the TokamakFusion Test Reactor (TFTR) [D. Meade et al., Proceedings of the International Conference on Plasma Physics and Controlled Nuclear Fusion. Washington, District of Columbia, 1990 (International Atomic Energy Agency, Vienna, 1991), Vol. I, pp. 9–24]. It is found that the modes have

Geometrical influences on neoclassical magnetohydrodynamic tearing modes
View Description Hide DescriptionThe influence of geometry on the pressure drives of nonideal magnetohydrodynamic tearing modes is presented. In order to study the effects of elongation, triangularity, and aspect ratio, three different machines are considered to provide a range of tokamak configurations: TokamakFusion Test Reactor (circular) [Fusion Technol. 21, 1324 (1992)], DIIID (Dshaped) [Plasma Physics and ControlledNuclear Fusion Research 1986 (International Atomic Energy Agency, Vienna, 1987), Vol. 1, p. 159], and Pegasus (extremely low aspect ratio) [Fonck et al., Bull. Am. Phys. Soc. 41, 1400 (1996)]. For large aspect ratio tokamaks, shaping does very little to influence the pressure gradient drives, while at low aspect ratios, a very strong sensitivity to the profiles is found. In particular, this sensitivity is connected to the strong dependence on the magnetic shear. This suggests that at low aspect ratio it may be possible to stabilize neoclassical tearing modes by a flattening the profile near low order rational surfaces (e.g., ) using a combination of shaping and localized current drive, whereas at large aspect ratio it is more difficult.

Nonlinear tearing modes in the presence of resistive wall and rotation
View Description Hide DescriptionNonlinear simulations of tearing modes with a resistive wall and plasma rotation in a twodimensional (2D) incompressible slab are presented. The regimes of interest include cases (1) in which a tearing mode is unstable even for a perfectly conducting wall; (2) in which a resistive wall tearing mode is unstable but may be stabilized by rotation. In (1), the mode can lead to a wall locking process, in which both the flow and the mode’s phase velocity are slowed, allowing flux diffusion through the wall and a wider island. There is a bifurcation with hysteresis between locked and unlocked states. If the decay of total momentum is large, the range with multiple states is smaller. In (2) resistive wall modes grow and lock for all parameters with linear instability. And even if rotation gives linear stability, there is nonlinear instability. The bifurcation diagram is similar to that for case (1), but in which the zero island width state takes the place of the unlocked state. Results are shown for case (2) giving the critical field error to drive nonlinear instability and begin locking.

Complete integral suppression of Pfirsch–Schlüter current in a stellarator plasma in Heliotron E
View Description Hide DescriptionThe poloidal magnetic field was measured to detect the plasma boundary position. It was found that the pressureinduced plasma shift, an observable characteristic of the Pfirsch–Schlüter current, depends strongly on the initial position of the magnetic axis. When the axis was moved by the vertical field inside the torus, the finiteβ shift became smaller. Complete suppression of the finiteβ plasma shift was achieved in a deeply inward shifted configuration: 7 cm from the standard position This effect is explained by magnetohydrodynamic(MHD) equilibrium theory for stellarator toroidal plasmas with a large magnetic hill and deep inward shift.

Fundamental heating with stellarator wave modes
View Description Hide DescriptionA perturbation method is developed to find the structure of Alfvén wave modes in a cylindrical waveguide filled with a cold, collisional, uniform plasma with a vacuum layer between the plasma and a conducting wall when the magnetic field is a superposition of a uniform and an inhomogeneous field created by helical windings. The influence of the helical field on the wave mode structure is treated as a perturbation. It is shown that the azimuthal component of a modified fast Alfvén wave is lefthand polarized in the central part of the plasma. This implies a coupling between the fast (righthand polarized) wave and slow (lefthand polarized) waves due to the inhomogeneity of the fields. The coupling efficiency is examined for different plasma parameters. Results demonstrate that efficient coupling between the modes occurs for appropriate plasma parameters in this model, indicating that efficient plasma heating at the fundamental ion cyclotron frequency is possible in stellarators.
