Volume 5, Issue 3, March 1998
 LETTERS


Alpha effect of Alfvén waves and current drive in reversedfield pinches
View Description Hide DescriptionCircularly polarized Alfvén waves give rise to an αdynamo effect that can be exploited to drive parallel current. In a “laminar” magnetic the effect is weak and does not give rise to significant currents for realistic parameters (e.g., in tokamaks). However, in reversedfield pinches(RFPs) in which magnetic field in the plasma core is stochastic, a significant enhancement of the α effect occurs. Estimates of this effect show that it may be a realistic method of current generation in the presentday RFP experiments and possibly also in future RFPbased fusion reactors.
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 ARTICLES


Energy related conservation law for fluids and multifluid plasmas with equilibrium flow
View Description Hide DescriptionWithin the framework of dissipationless multifluid theory for plasmas, all nonlinear perturbations of a stationary equilibrium that could be created from the equilibrium without breaking local entropyconservation are considered. Describing the fluid perturbations by Eulerian displacement vectors reveals a general symmetry and through Noether’s theorem leads to a conservation law. Its relation to the law of energy conservation is discussed since it will be important for the generalization of the energy principle known for static equilibria in magnetohyrodynamics to an energy principle of stationary equilibria in the framework of a multifluid theory.

Power coupling to helicon and Trivelpiece–Gould modes in helicon sources
View Description Hide DescriptionThe effects of finite electron mass on the helicon mode and the role of the TrivelpieceGould (TG) mode in helicon sources are considered. In an unbounded plasma these waves are commonly referred to as whistler waves. A simple cold plasma antennawave coupling code gives results which compare favorably with experimental observations of the whistler wave resonance cone. The connection between these cones and the TrivelpieceGould eigenmodes of bounded plasmas is discussed. The theory is applied to the study of antennawave coupling in helicon sources. It reveals that finite electron mass effects do not significantly improve antennawave coupling for It is also suggested that, because of the resonance cone dispersion, eigenmode cavity resonances of the TrivelpieceGould mode could be difficult to excite in practice. This precludes geometric resonances of the antenna impedance due to the existence of the TG mode as an explanation for the high plasma production efficiency of helicon sources.

Characterization of helicon waves in a magnetized inductive discharge
View Description Hide DescriptionThe propagation of helicon waves and the plasma density has been measured in a cylindrical, magnetized plasma for a range of magnetic fields and input power levels. A transition in the coupling mechanism from electrostatic (E mode) to inductive (H mode) coupling is evidenced by a sharp change in the plasma density coinciding with a change in the wave fields from a linearly polarized standing wave, with highest amplitude close to the antenna to a righthand elliptically polarized traveling wave with a phase velocity of about extending into the downstream region. An explanation of the transition to the H mode is put forward in terms of the conductivity across the magnetic field and an associated skin depth for power deposition. The polarization of the wave fields in the H mode is interpreted in terms of the interference between and −1 modes (where is the azimuthal mode number).

Collisionless plasma modeling in an arbitrary potential energy distribution
View Description Hide DescriptionA new technique for calculating a collisionless plasma along a field line is presented. The primary feature of this new ionexospheric model is that it can handle an arbitrary (including nonmonotonic) potential energy distribution. This was one of the limiting constraints on the existing models in this class, and these constraints are generalized for an arbitrary potential energy composition. The formulation for relating current density to the fieldaligned potential as well as formulas for density, temperature, and energy flux calculations are presented for several distribution functions, ranging from a biLorentzian with a loss cone to an isotropic Maxwellian. A comparison of these results with previous models shows that the formulation reduces to the earlier models under similar assumptions.

Interacting eigenmodes of a plasma diode with a density gradient
View Description Hide DescriptionThe formation of narrow high frequency electric field spikes in plasma density gradients is investigated using onedimensional particle in cell simulations. It is found that the shape of the plasma density gradient is very important for the spike formation. A coupling to the ion motion, is not necessary for the formation of hf spikes. However, the hf spike influences the ion motion, and ion waves are seen in the simulations. Dispersion relations are calculated using realistic, nonMaxwellian, distribution functions. The spike can be seen as a coupled system of two eigenmodes of a plasma diodefed by a beamplasma interaction. Based on a simplified fluid description of such eigenmodes, explanations for the localization of the spike, spatially and in frequency, are given. The amplitude of the oscillating density is comparable with the dc level close to the cathode. This sets a limit of a wave amplitude in the whole system.

The finite length diocotron mode
View Description Hide DescriptionA simple model is presented of a finite length electron plasma column supporting a small amplitude diocotron wave with mode number The electrons are contained inside conducting cylinders in an axial magnetic field, with negative voltages on end cylinders providing axial containment. The diocotron mode is the drift orbit of an offset electron column around the cylinder axis, due to radial electric fields from image charges on the wall. The model predicts that the mode frequency will be higher than that of an infinitely long column due to θdrifts from the radial containment fields at the plasma ends. The predicted dependencies on plasma length, radius, and temperature agree well with experiments, where frequency increases up to are observed. For very short plasmas, these containment fields predominate over the image charge fields, and the plasma orbit is called the “magnetron” mode. The shift in the magnetron frequency due to image charges is also calculated.

Chaos in relativistic electron plasma and nonlinear dynamics in oblique propagation of electrostatic waves
View Description Hide DescriptionNonlinear interaction between electrostatic waves propagating obliquely to an ambient uniform magnetic field, and electron plasma in relativistic formalism are analyzed in detail. Resonances among the harmonics are delineated and a qualitative expression for the overlapping parameter leading to stochasticisty is analytically derived. A novel feature of this analysis is revealed in the form of threshold wave amplitude especially at the onset of chaos. The interesting profiles concerning the variation of threshold amplitude with harmonics magnetic field lines and wave vector pertaining to ensemble of electrostatic waves are displayed and discussed along with the phasespace topology mappings. These findings may provide important information concerning astrophysical scenarios, which include intergalactic plasmas, cosmic plasma particles, synchrotron radiation, and pulsar plasma analysis.

Nonlinear dynamics of electromagnetic turbulence in a nonuniform magnetized plasma
View Description Hide DescriptionBy using the hydrodynamic electron response with fixed (kinetic) ions along with Poisson’s equation as well as Ampère’s law, a system of nonlinear equations for lowfrequency (in comparison with the electron gyrofrequency) long(short) wavelength electromagnetic waves in a nonuniform resistive magnetoplasma has been derived. The plasma contains equilibrium density gradient and sheared equilibrium plasma flows. In the linear limit, local dispersion relations are obtained and analyzed. It is found that sheared equilibrium flows can cause instability of Alfvénlike electromagnetic waves even in the absence of a density gradient. Furthermore, it is shown that possible stationary solutions of the nonlinear equations without dissipation can be represented in the form of various types of vortices. On the other hand, the temporal behavior of our nonlinear dissipative systems without the equilibrium density inhomogeneity can be described by the generalized Lorenz equations which admit chaotic trajectories. The density inhomogeneity may lead to even qualitative changes in the chaotic dynamics. The results of our investigation should be useful in understanding the linear and nonlinear properties of nonthermal electromagnetic waves in space and laboratory plasmas.

Kelvin–Helmholtz instability of magnetized plasma with polytropic pressure laws
View Description Hide DescriptionThe Kelvin–Helmholtz (KH)instability of two fluids of a plasma, streaming in opposite directions with the same velocity and in the presence of an external magnetic field, is investigated. The external magnetic field in both fluids are in different directions. The usual magnetohydrodynamic(MHD)equations with anisotropic pressures are considered. The generalized pressure relation is used and two equations of state for two pressures are taken up in the problem. The equations are linearized and initially two different flow velocities are taken for the system. The problem is solved and a dispersion relation is obtained. It is found that the instability condition for the static configuration depends on the polytropic index of the pressure relations. The condition of instability is further obtained for MHD and Chew–Goldberger–Low (CGL) systems. For the nonstatic streaming configuration it is also found that growth rate of KH instability depends on various polytropic indices and magnetic field.

Dynamic magnetic reconnection in three space dimensions: Fan current solutions
View Description Hide DescriptionThe problem of incompressible, nonlinear magnetic reconnection in threedimensional “open” geometries is considered. An analytic treatment shows that dynamic “fan current” reconnection may be driven by superposing long wavelength, finite amplitude, plane wave disturbances onto threedimensional magnetic points. The nonlinear reconnection of the field is preceded by an advection phase in which magnetic shear waves drive large currents as they localize in the vicinity of the magnetic null. Analytic arguments, reinforced by detailed simulations, show that the ohmic dissipation rate can be independent of the plasma resistivity if the merging is suitably driven.

Resonant excitation and control of high order dispersive nonlinear waves
View Description Hide DescriptionAutoresonant excitation of high order nonlinear waves with space–time varying parameters is investigated. A class of driven, twocomponent nonlinear waves described by the variational principle is studied in detail. The autoresonance in the system proceeds as an external eikonal pump wave excites a nonlinear daughter wave after crossing the linear resonance surface. Beyond the linear resonance, the pump and the daughter waves stay phase locked in an extended region of space–time despite the variation of the system’s parameters. The theory of the autoresonance is developed on the bases of the averaged variational principle and comprises a generalization of the formalism for scalar fields. The relation of the wave autoresonance problem to an associated two degrees of freedom problem in nonlinear dynamics is discussed. The conditions for the stable autoresonant solutions are (a) the adiabaticity of the driven system and (b) a sufficient nonlinearity. The theory is applied to the problem of resonant excitation and control of a Korteweg–de Vries (KdV) wave by means of launching an external pump wave with space–time varying frequency and wave vector. Numerical examples for temporal and spatial autoresonance in this system are presented.

Alfvén waves and waveinduced transport near an X point
View Description Hide DescriptionThe behavior of Alfvén waves and the corresponding variation of the waveinduced transport coefficients along a field line including the divertor Xpoint region are examined. It is shown that several competing effects exist and can be quantified using a quasilinear diffusion model that takes the magnetic geometry of the X point into account. To address the issue of mode behavior and the validity of the eikonal approximation near the X point, an exact analytical solution of an equation describing Alfvén waves in the Xpoint region is obtained. The results suggest that the Xpoint region can only dominate Alfvén waveinduced transport on flux surfaces that are very close to the separatrix.

Notched velocity profiles and the radial electric field in high ion temperature plasmas in the Tokamak Fusion Test Reactor
View Description Hide DescriptionA large “notch,” or nonmonotonic feature, appears in measuredtoroidalvelocity profiles of the carbon impurity in the TokamakFusion Test Reactor (TFTR) [Plasma Phys. Controlled Fusion26, 11 (1984)], centered near the radius of strongest ion temperature gradient. This is explained as a consequence of radial momentum transport dominated by anomalous diffusion together with parallel heat friction on the impurity ions arising from the hydrogenic neoclassical parallel heat flow. The toroidalvelocity profile of the hydrogenic species is predicted to be monotonic, from measurements of the impurity toroidalvelocity, consistent with the anomalous radial diffusion of toroidal momentum. This supports a neoclassical calculation of the radial electric field for nearbalanced beam injection. In supershot plasmas [Phys. Rev. Lett. 58, 1004 (1987)], a well structure in the radial electric field profile is found in the enhanced confinement region. An associated shear layer separates the core, where the local confinement trends are favorable, from the degraded outer region. This provides a mechanism for the nonlinear coupling of the ion temperature gradient, ion thermal confinement, and the radial electric field, which may help explain the favorable core confinement trends of very high temperature supershot plasmas.

Optical probing of fiber pinch plasmas
View Description Hide DescriptionAn experimental study of optical probing of a dense pinch plasma using the MAGPIE (megaampere generator for plasma implosion experiments) generator [I. H. Mitchell et al., Rev. Sci. Instrum. 67, 1533 (1996)] is reported. The generator was operated with a peak current of 1.1 MA rising in 150 ns (10%–90%). The loads were 33 μm diam carbon fibers. Faraday rotation was used to investigate the distribution of the current flowing in the plasma. A measurableFaraday rotation angle was observed only in a time window from 50 to 60 ns after the current start, due to the fact that this effect depends on a combination of the magneticfield strength and electron number density. A new type of selfreferencing cyclic radial shear interferometer was used to evaluate the plasma density profiles which are necessary for the reconstruction of the current distribution. It was calculated that was flowing in the plasma at 52 ns after the current start. Shadowgraphy was used to study the dynamics of the plasma and to investigate the formation of instabilities.Plasma instabilities were observed at very early times These instabilities appeared to be not entirely axisymmetric implying the existence of and maybe higher modes as well as The perturbations increased with time and evolved into density islands (isolated plasma fragments) distributed along the axis at late times

Analysis of the tokamak rippleblocked ion distribution with abrupt changes of a radial electric field
View Description Hide DescriptionConvective transport of nonthermal, rippleblocked ions in the presence of a rapidly varying radial electric field is investigated by numerically solving a relevant kinetic equation in tokamak geometry. Near the plasma periphery, at small poloidal angles, a strong suppression in the deeply rippleblocked ion distribution is observed in the absence of a radial electric field for particle energies exceeding a collisional threshold. The deficit of the rippleblocked ions is found to be rapidly filled by the onset of an inward radial electric field of a sufficient magnitude. The time scale for this filling can be explained by the different blockedion drift orbit topologies generated by the radial electric field, and it is determined by the convective drift time of rippleblocked ions from the inner, wellfilled ripple region to the depleted region along these orbits. Consequently, the time scale can be much faster than the collisional time scale, and the blocked ion distribution function should faithfully follow the changes in the radial electric field. Thus the present mechanism gives a physical basis for the earlier interpretation of experimental results [W. Herrmann and ASDEX Upgrade Team, Phys. Rev. Lett. 75, 4401 (1995)] that the measured changes in the neutral fluxes from charge exchange processes with rippleblocked ions are caused by changes in the radial electric field. The dependence of the neutral flux changes on collisionality as well as on the width and magnitude of a radial electric field with a Gaussian potential profile are studied.

Longitudinal permittivity of a tokamak plasma with elliptic and circular magnetic surfaces
View Description Hide DescriptionThe contributions of untrapped and three groups of trapped particles to the longitudinal permittivity of a tokamak plasma with elliptic magnetic surfaces are derived for radio frequency waves in a wide range of frequencies, mode number, and plasma parameters. The analytical expressions of the longitudinal permittivity elements are obtained by using the kinetic theory of dielectrictensor elements, where the drift kinetic equation is solved as a boundaryvalue problem. Considered is a collisionless plasma model of an axisymmetric tokamak with small ellipticity and a large aspect ratio. The limit to the known results for toroidal plasmas with the circular crosssection of the magnetic surfaces is shown.

Observations of fast anisotropic ion heating, ion cooling, and ion recycling in largeamplitude drift waves
View Description Hide DescriptionLargeamplitude drift wavefluctuations are observed to cause severe ion temperatureoscillations in plasmas of the Caltech Encore tokamak [J. M. McChesney, P. M. Bellan, and R. A. Stern, Phys. Fluids B 3, 3370 (1991)]. Experimental investigations of the complete ion dynamical behavior in these waves are presented. The wave electric field excites stochastic ion orbits in the plane normal to , resulting in rapid heating. Ion–ion collisions impart energy along relaxing the temperatureanisotropy. Hot ions with large orbit radii escape confinement, reaching the chamber wall and cooling the distribution. Cold ions from the plasma edge convect back into the plasma (i.e., recycle), causing further cooling and significantly replenishing the density depleted by orbit losses. The ion–ion collision period fluctuates strongly with the drift wave phase, due to intense 50%) fluctuations in and . Evidence for particle recycling is given by observations of bimodal ion velocity distributions near the plasma edge, indicating the presence of cold ions (0.4 eV) superposed atop the hot (4–8 eV) plasma background. These appear periodically, synchronous with the drift wave phase at which ion fluid flow from the wall toward the plasma center peaks. Evidence is presented that such a periodic heat/loss/recycle/cool process is expected in plasmas with strong stochastic heating.

Superbanana orbits and redistribution of marginally trapped fast ions during sawtooth crashes
View Description Hide DescriptionThe work represents the first step in studying the effect of sawtooth crashes on the “resonant” fast ions, i.e., the ions that are trapped or marginally untrapped with respect to the helical perturbation associated with the sawtooth crash. The simplest case is considered, when the particles in the absence of perturbations are marginally trapped in the tokamakmagnetic field and characterized by narrow orbits. It is shown that in the presence of perturbation the guiding centers of the banana orbits oscillate in the toroidal and radial directions, forming “superbanana” orbits. The radial width of such “superbananas” constitutes a significant part of the sawtooth mixing radius, which implies that sawteeth can strongly redistribute these particles.

Twodimensional calculation of eddy currents on external conducting walls induced by low external modes
View Description Hide DescriptionThe results of twodimensional calculations of eddy currents induced on external conducting walls surrounding a tokamak are reported. The computed eddy currents are generated by low external idealmagnetohydrodynamic (MHD)instabilities. For a given toroidal mode number the eddy current patterns are found to be very similar in a variety of plasma configurations, e.g., different edge safety factors and different plasma–wall separation distances, in high beta plasmas. This result is promising for the design of active feedback coils for the stabilization of the resistive wall mode. Also, the effects of having a partial wall that has a poloidal gap on the outboard side are considered. Using the expected gap size in the proposed Korea SuperconductingTokamak Advanced Research (KSTAR) [“The KSTAR tokmak,” in Proceedings of the 17th Symposium on Fusion Engineering, San Diego, 1997 (Institute of Electrical and Electronics Engineers, New York, in press), Paper No. O3.1], the calculation shows that active coils mounted behind the partial walls (the KSTAR passive plates) cover an adequate portion of the eddy current dominant region, enabling feedback stabilization.
