Volume 7, Issue 7, July 2000
 LETTERS


Heating experiment of fieldreversed configuration plasma by lowfrequency magnetic pulse
View Description Hide DescriptionAn effective heating method and experimental verification for a fieldreversed configuration (FRC) plasma by applying the lowfrequency magnetic pulse is presented. The lowfrequency magnetic field is applied by an antenna that consists of two singleturn coils, and the frequency of the magnetic field is lower than the ion cyclotron frequency at the separatrix. An increase of the plasma energy and a fluctuation of the internal magnetic field are simultaneously observed. The comparison of the total temperature and the ion temperature shows that the increase of the plasma energy is mostly due to the ion heating. The fluctuation is directly observed by the internal magnetic probe arrays. The analysis of the phase velocity along the equilibrium magnetic field implies that the Alfvén wave is excited and propagates.

Decay of the daughter electromagnetic wave driven by stimulated Raman scattering into two Langmuir waves
View Description Hide DescriptionMuch attention has been focused on the saturation of stimulated Raman scattering by the decay of its daughter waves. This research has almost exclusively dealt with the decay of the daughter Langmuir wave into secondary Langmuir waves and ion acoustic waves. In this Letter, the decay of the Raman driven electromagnetic wave into two Langmuir waves, twoplasmon decay, is discussed for the first time. It is shown that based on the stimulated Raman scatteringreflectivity levels measured in experiments, this instability should be present in current laser–plasma experiments. In addition, experimental signatures of this process are discussed.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

A new acousticlike mode in an unmagnetized dusty plasma
View Description Hide DescriptionIt is shown that because of the dependence of the plasma potential φ on the dust number density for given background plasma parameters and the dust grain radius, viz. the dusty plasma is endowed with an effective temperature which is proportional to The gradient of the effective pressure provides a restoring force for a new acousticlike mode, which is referred to as the dust electroacoustic (DEA) mode whose phase velocity equals where is the dust mass. The acousticlike nature of the DEA mode is interpreted in terms of an effective screening (due to the dust charge fluctuations), called the “Coulomb screening,” with the screening length where is the dust charge.

The spectrum of the curl operator on spherically symmetric domains
View Description Hide DescriptionThis paper presents a mathematically complete derivation of the minimumenergy divergencefree vector fields of fixed helicity, defined on and tangent to the boundary of solid balls and spherical shells. These fields satisfy the equation where λ is the eigenvalue of curl having smallest nonzero absolute value among such fields. It is shown that on the ball the energy minimizers are the axially symmetric spheromak fields found by Woltjer and Chandrasekhar–Kendall, and on spherical shells they are spheromaklike fields. The geometry and topology of these minimumenergy fields, as well as of some higherenergy eigenfields, are illustrated.

Confinement and manipulation of nonneutral plasmas using rotating wall electric fields
View Description Hide DescriptionA “rotating wall” perturbation technique enables confinement of up to electrons or ions in Penning–Malmberg traps for periods of weeks. These rotating wall electric fields transfer torque to the particles by exciting Trivelpiece–Gould plasma modes with and or 2. Modes that rotate faster than the plasma column provide a positive torque that counteracts the background drags, resulting in radial plasma compression or steadystate confinement in nearthermal equilibrium states. Conversely, modes that rotate slower than the plasma provide a negative torque, and enhanced plasma expansion is observed. The observed Trivelpiece–Gould mode frequencies are well predicted by linear, infinitelength, guidingcenter theory.
 Nonlinear Phenomena, Turbulence, Transport

Collapses of density and vorticity by convection in simple twodimensional flows
View Description Hide DescriptionThe initial value problem of an ideal, compressible medium is studied in twodimensional geometry by the Lagrangian method. It is shown that the nonlinearity of a convectiondriven flow can lead to singularities at finite time in density and vorticity. Conditions for the appearance of such a behavior are presented.

Nonlinear dynamics of electron flows with density gradient in spherical diodes
View Description Hide DescriptionA variety of Pierce diodes formed by a pair of grounded concentric spheres with electrons streaming radially are investigated with particleincell simulations and analytical models. The electrons flow parallel or antiparallel to a density gradient in convergent or divergent diodes, respectively. The existence and stability (or instability) of laminar steady states with space charge and nonuniform velocity that are possible for a given set of diode parameters, are crucial to determine the outcome of the numerical experiments. The dispersion relation for the stability of the initial constant velocity states and the concomitant energy flow balance are examined in relation to the nonlinear dynamical evolution. Spherical diodes have properties that are common to a dual pair of diodes with reciprocal ratios of collector to emitter radii. Stable oscillatory electrostatic states, associated with Hopf bifurcations, are observed in the simulations. The breakdown of the laminar electron flow has completely different physical characteristics in divergent and convergent diodes.

Linear deltaf simulations of nonlocal electron heat transport
View Description Hide DescriptionNonlocal electron heat transport calculations are carried out by making use of some of the techniques developed previously for extending the method to transport time scale simulations [S. Brunner, E. Valeo, and J. Krommes, Phys. Plasmas 6, 4504 (1999)]. By considering the relaxation of small amplitude temperature perturbations of an homogeneous Maxwellian background, only the linearized Fokker–Planck equation has to be solved, and direct comparisons can be made with the equivalent, nonlocal hydrodynamic approach [V. Yu. Bychenkov et al., Phys. Rev. Lett. 75, 4405 (1995)]. A quasineutralityconserving algorithm is derived for computing the selfconsistent electric fields driving the return currents. In the lowcollisionality regime, results illustrate the importance of taking account of nonlocality in both space and time.

Quantitative comparison of reduceddescription particleincell and quasilinearZakharov models for parametrically excited Langmuir turbulence
View Description Hide DescriptionThe effect of kinetic processes on the saturation of parametric instabilities in an electromagnetically driven plasma is investigated. A reduceddescription particleincell technique is used as a benchmark to test a new quasilinearZakharov model which accounts for electron heating due to Landau damping by coupling the quasilinear diffusion equation to the Zakharov equations. The reduceddescription particleincell method utilizes a twotimescale approximation which significantly reduces the numerical dissipation and ion noise levels. This approach allows accurate modeling of Langmuir and ion acoustic waves in regimes typically studied with Zakharov simulations. The comparison of the two models is performed for the test case of a onedimensional homogeneous plasma driven by a spatially uniform pump in both the Langmuir decay instability cascade and collapse regimes. Good agreement is found in both weakly and strongly driven regimes for the total Langmuir wave energy and evolved electron velocity distributions. Electron heating significantly decreases saturation levels in strongly driven regimes by increasing the Landau damping rate, bringing the quasilinearZakharov simulations in much closer agreement with the reduceddescription particleincell simulations than standard Zakharov simulations, which do not account for the evolution of the electron distribution.

Shocks associated with the Kelvin–Helmholtzresistive instability
View Description Hide DescriptionIn this paper, a new type of shock associated with magnetic reconnection processes has been explored using a compressible magnetohydrodynamics simulation method. The simulations have shown that, when there are strong fieldaligned shear flows at the two sides of a currentsheet, the coupling mode between Kelvin–Helmholtz and resistiveinstabilities will appear; further, reflected shocks and incident shocks can be produced at both sides of the boundary layer. Both the reflected shocks and incident shocks are fast shocks, through which the magnetic field strength, density, and temperature all increase sharply, while the plasma velocity decreases steeply. It is expected that some inhomogeneous structures can be formed at plasma boundary layer regions due to the existence of fast fieldaligned shear flow driven shocks.

Nonmodal energetics of electromagnetic drift waves
View Description Hide DescriptionThe linear properties of an electromagnetic driftwave model are examined. The linear system is nonnormal in that its eigenvectors are not orthogonal with respect to the energy inner product. The nonnormality of the linear evolution operator can lead to enhanced finitetime growth rates compared to modal growth rates. Previous work with an electrostatic driftwave model found that nonmodal behavior is important in the hydrodynamic limit. Here, similar behavior is seen in the hydrodynamic regime even with the addition of magnetic fluctuations. However, unlike the results for the electrostatic driftwave model, nonmodal behavior is also important in the adiabatic regime with moderate to strong magnetic fluctuations.

Motion of extended vortices in an inhomogeneous pure electron plasma
View Description Hide DescriptionThe motion of extended vortices in a pure electron plasma with an inhomogeneous, centrally peaked, density in a Penning–Malmberg trap is studied by means of a twodimensional electrostatic Eulerian code that solves the evolution equation for the electron distribution function in the guiding center approximation, coupled to the Poisson equation for the electrostatic potential. Vortices corresponding to electron density clumps propagate inward, as discussed in a recently proposed model for the case of point vortices, and carry inward both high and low density plasma. New, longlived, structures consisting of a higher and of a lower density vortex pair are formed in the presence of a small amount of vorticity reconnection.

Nonlinear evolution of parametric instability of a largeamplitude nonmonochromatic Alfvén wave
View Description Hide DescriptionThe nonlinear evolution of the parametric instability of a finite amplitude Alfvén wave is studied in a onedimensional geometry. The linear stage of this instability had been examined in a previous paper [Malara and Velli, Phys. Plasmas 3, 4427 (1996)], in which it has been shown that even a nonmonochromatic broadband wave is unstable. In the present paper, the time evolution is followed up to saturation, by numerically integrating the full set of magnetohydrodynamic(MHD)equations. Several configurations of the Alfvénic pump wave, as well as different values of the plasma are examined. The saturation level of the instability does not depend on the spectral width of the pump wave, but it depends on the value of For the final state is characterized by a crosshelicity and a moderate level of density fluctuations: The Alfvénic correlation of the initial wave is completely destroyed, even for a broadband initial spectrum. For the final crosshelicity is closer to that of the initial wave, indicating a lower saturation level. The parametric process appears to be nonlocal in the wavevector space also in the nonmonochromatic case, this feature becoming more relevant with increasing
 Magnetically Confined Plasmas, Heating, Confinement

On neoclassical transport near the magnetic axis
View Description Hide DescriptionThe theory of neoclassical transport near the magnetic axis in a tokamak is discussed. It is shown that the ordinary treatment of transport in the plateau regime holds in most of the region within a trapped orbit width of the magnetic axis, and is not modified by “potato” orbits. It is also demonstrated that transport at low collisionality is not diffusive in nature and cannot be described independently of the sources of particles and heat in the region near the magnetic axis. A variational principle is formulated for the nearaxis transport problem.

Dielectric response function and stopping power of dense magnetized plasma
View Description Hide DescriptionUsing a kinetictheoretic approach to Fokker–Planck equilibrium of thermonuclear α particles in dense and magnetized plasmas, the corresponding longitudinal dielectric function is investigated at length. It is used to evaluate the energy loss of the through the excitation of collective plasma modes. Specific attention was paid to the case of extreme magnetization, as well as to the parallel stopping of α particles in dense and hot plasmas of magnetized target fusion(MTF) interest. Maximum stopping is shown to be strongly dependent on magnetic field intensity.

Positive voltage spikes in runaway tokamak discharges
View Description Hide DescriptionPositive voltage spikes caused by a fast decrease of the plasma current are observed in runaway dominated discharges in the small Brazilian Tokamak TBR1[Kuznetsov et al., Phys. Plasmas 6, 4002 (1999)]. Comparison of the measured voltage spike with the value given by the solution of the onedimensional diffusion equation for the toroidalelectric field permits one to infer the plasma conductivity and initial electric field distribution. An additional runaway generation due to voltage spikes can be important. In this case, both the decay time of the voltage spike and the total toroidalcurrent perturbation can decrease substantially.

Predictive transport simulations of internal transport barriers using the MultiMode model
View Description Hide DescriptionThe formation of internal transport barriers observed in both Joint European Torus (JET) [P. H. Rebut, R. J. Bickerton, and B. E. Keen, Nucl. Fusion 25, 1011 (1985)] and Doublet IIID Tokamak (DIIID) [J. L. Luxon and L. G. Davis, Fusion Technol. 8, 441 (1985)] are reproduced in predictive transport simulations. These simulations are carried out for two JEToptimized shear discharges and two DIIID negative central shear discharges using the MultiMode model in the timedependent 11/2D BALDUR transport code [C. E. Singer et al., Comput. Phys. Commun. 49, 275 (1988)]. The Weiland model is used for drift modes in the MultiMode model in combination with either Hahm–Burrell or Hamaguchi–Horton flow shear stabilization mechanisms, where the radial electric field is inferred from the measured toroidal velocity profile and the poloidal velocity profile computed using neoclassical theory. The transport barriers are apparent in both the ion temperature and thermal diffusivity profiles of the simulations. The timing and location of the internal transport barriers in the simulations and experimental data for the DIIID cases are in good agreement, though some differences remain for the JET discharges. The formations of internal transport barriers are interpreted as resulting from a combination of flow shear and weak magnetic shear mechanisms.

Central electron temperature enhancements due to sawtooth stabilization during counter electron cyclotron current drive in Tokamak à Configuration Variable
View Description Hide DescriptionIn the Tokamak à Configuration Variable (TCV), the central electron temperature obtained in discharges with counter (CNTR) electron cyclotron current drive (ECCD) is larger than with COECCD or electron cyclotron resonance heating (ECRH) alone. Comparison of experimental results with calculations by the transport code PRETOR [IAEA Technical Conference on Advances in Simulation and Models of Thermonuclear Plasmas. Montreal 142 (International Atomic Energy Agency, Vienna 1992)] indicates that sawtooth stabilization is responsible for the increased confinement time and the attendant twofold enhancement of the central temperature. Sawtooth stabilization is caused in turn by the central safety factor rising above 1 for CNTRECCD; by contrast, the simulation results show that in the sawtoothing COECCD and ECRH cases.

Magnetohydrodynamic treatment of collisional transport in toroidal configurations: Application to elliptic cross sections
View Description Hide DescriptionTransport in the collisional regime is analyzed here for tokamaks and compact toroid of any shape. Toroidal axisymmetry is assumed. The treatment is performed with an improved system of coordinates, here described. Pfirsch–Schlüter current is determined in a general case. The average velocity around a magnetic surface is found as a function of closed geometrical integrals and separated factors that include the electric and magnetic fields. The contribution of the induced electric field is analyzed and the similarities with the Ware pinch are shown. The general equations have been applied to families of nested curves with elliptic shapes.

The possibility of high amplitude driven contained modes during ion Bernstein wave experiments in the tokamak fusion test reactor
View Description Hide DescriptionExtremely high quasilinear diffusion rates for energetic beam ions can be deduced from mode conversion experiments in the TokamakFusion Test Reactor (TFTR) [K. M. McGuire, H. Adler, P. Alling et al., Phys. Plasmas 2(6), 2176 (1995)]. A comparison of the experimental loss rates with the theoretical prediction for the interaction of energetic ions with mode converted ion Bernstein waves showed the theory to underpredict the diffusion coefficient by a factor of 30–70. An anomalously high diffusion coefficient might enhance the advantageous channeling of energetic alpha particle energy in a tokamak reactor. Resolving this discrepancy is thus of importance from the standpoint of practical interest in an improved tokamak reactor as well as from the standpoint of academic interest in basic wave–particle theory. A mechanism is proposed for this accelerated diffusion involving the excitation of a contained mode, possibly similar to that used in explaining the ICE (ion cyclotron emission) phenomenon, near the edge of a tokamak.