Volume 7, Issue 12, December 2000
 LETTERS


Destabilizing effect of thermal conductivity on the Rayleigh–Taylor instability in a plasma
View Description Hide DescriptionIt is shown that the Rayleigh–Taylor instability in a compressible medium is not necessarily stabilized by thermal conductivity. It is pointed out that one can use the destabilization effect for in situ measurements of thermal conductivity in highenergydensity experiments. The other consequence is generation of smallscale turbulence in supernovae, giving rise to significant turbulentviscosity.

Tokamak, reversed field pinch and intermediate structures as minimumdissipative relaxed states
View Description Hide DescriptionThe principle of minimum energy dissipation rate is utilized to develop a unified model for relaxation in toroidal discharges. The Euler–Lagrange equation for such relaxed states is solved in toroidal coordinates for an axisymmetric torus by expressing the solutions in terms of Chandrasekhar–Kendall (C–K) eigenfunctions analytically continued in the complex domain. The C–K eigenfunctions are hypergeometric functions that are solutions of the scalar Helmholtz equation in toroidal coordinates in the largeaspectratio approximation. Equilibria are constructed by assuming the total current at the edge. This yields the eigenvalues for a given aspectratio. The most novel feature of the present model is that solutions allow for tokamak, low as well as reversed field pinchlike behavior with a change in the eigenvalue characterizing the relaxed state.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

The diocotron spectrum of a toroidal nonneutral plasma
View Description Hide DescriptionThe equilibrium and stability of a toroidalnonneutral plasma of low density has been studied numerically. The equilibrium is computed using the variational moment method, while linear stability is computed using a Fourier representation in the poloidal coordinate and a finite difference approximation in the radial coordinate. The computation has been carried out for various configurations to obtain frequencies of stable modes and the growth rate of instabilities.

Limit of temperature anisotropy relaxation by ion cyclotron waves: A statistical theory
View Description Hide DescriptionThe ion velocity distribution resulting from ion anisotropy reduction by the growth of ion cyclotron waves has been investigated by the use of a Maximum Entropy Principle. The anisotropy is reduced due to waves induced by an electromagnetic instability, but the system saturates before a completely isotropic Maxwellian distribution is realized, and a nonzero level of anisotropy remains in the final state. This is because the scattering process has a restriction; waves do not alter particle energy in the wave rest frame. Taking this restriction into account as an additional constraint, the final state is calculated by maximizing the entropy. The results show that the upper bound of the plasma β and anisotropy are inversely correlated, which is quantitatively in agreement with recent studies on satellite observations, numerical simulations, and laboratory experiments.

Variational principle for nonlinear gyrokinetic Vlasov–Maxwell equations
View Description Hide DescriptionA new variational principle for the nonlinear gyrokinetic Vlasov–Maxwell equations is presented. This Eulerianvariational principle uses constrained variations for the gyrocenter Vlasov distribution in eightdimensional extended phase space and turns out to be simpler than the Lagrangianvariational principle recently presented by H. Sugama [Phys. Plasmas 7, 466 (2000)]. A local energy conservation law is then derived explicitly by the Noether method. In future work, this new variational principle will be used to derive selfconsistent, nonlinear, lowfrequency Vlasov–Maxwell bouncegyrokinetic equations, in which the fast gyromotion and bouncemotion time scales have been eliminated.

Relativistic magnetohydrodynamics revisited
View Description Hide DescriptionMagnetohydrodynamics is discussed within the framework of irreversible thermodynamics. The nonrelativistic version is reviewed by introducing the electromagnetic field as an external force. Results are discussed and emphasis is placed on the fact that the transport equations, being of a parabolic type, violate causality. The relativistic version is next considered using Kaluza’s ideas about unifying fields in terms of the corresponding space–time curvature for a given metric. The outcome of this approach is rewarding. The conservationequations follow in a direct way as well as the entropy balance equation with an entropy production whose form suggests the type of constitutive equations that are consistent with its semipositive character. Further, the resulting transport equations are of a hyperbolic type in agreement with causality. Therefore, relativistic magnetohydrodynamics is placed within a thermodynamic framework consistent with the second law.
 Nonlinear Phenomena, Turbulence, Transport

Hole equilibria in Vlasov–Poisson systems: A challenge to wave theories of ideal plasmas
View Description Hide DescriptionA unified description of weak hole equilibria in collisionless plasmas is given. Two approaches, relying on the potential method rather than on the Bernstein, Greene, Kruskal method and associated with electron and ion holes, respectively, are shown to be equivalent. A traveling wavesolution is thereby uniquely characterized by the nonlinear dispersion relation and the “classical” potential which determine the phase velocity and the spectral decomposition of the wave structure, respectively. A new energy expression for a hole carrying plasma is found. It is dominated by a trapped particle contribution occurring one order earlier in the expansion scheme than the leading term in conventional schemes based on a truncation of Vlasov’s equation. Linear wave theory— reconsidered by taking the infinitesimal amplitude limit—is found to be deficient, as well. Neither Landau nor van Kampen modes and their general superpositions can adequately describe these trapped particle modes due to an incorrect treatment of resonant particles for phase velocities in the thermal range. It is therefore concluded that wavetheories in their present form, dictated by linearity, are not yet properly shaped to describe the dynamics of ideal plasmas (and fluids) correctly.

Kinetic modeling of a onedimensional, bounded plasma in the ambipolar regime
View Description Hide DescriptionIn this paper we present a selfconsistent kinetic simulation of a diffusion dominated bulk plasma region. Collisions have been modeled by a velocitydependent Krook collision operator. The technique is capable of handling large systems—the results presented here are for systems in extent—yet retains the details of the edge physics present. The distribution functions for the trapped and the transiting orbits and their moments are obtained. The density and potential profiles inside the bulk shows overall agreement with ambipolar predictions. The kinetic equivalent of is obtained and compared to the fluid prediction. The validity of the code and the observed deviations from fluid treatments are discussed.

Finger instability in radiatively driven dusty plasmas
View Description Hide DescriptionIn this work the dynamics of a threefluid plasma consisting of electrons, ions and charged dust particles are considered. The plasma is illuminated by a radiation field, which, through absorbtion, accelerates the dust particles. By direct and Coulomb collisions the gained momentum is partially transmitted to electrons and ions. A steady state can be achieved by an external gravitational field acting against the radiation. After presenting the steadystate flow, linear perturbations of dynamical variables with the wave vector perpendicular to the radiation flux are considered. A linear analysis is performed by reducing the full threefluid description to a suitable onefluid system of equations, assuming the plasma to be quasineutral and omitting plasma species separation. It is demonstrated that when the drag force between ions and dust particles is a decreasing function of their relative velocity, the steady state is unstable against the formation of parallel layered streams with high and low relative flow velocities, i.e., multiple current sheets. The temporal evolution of this instability is then investigated by means of numerical simulations in the framework of a complete threefluid model.

Generalized weak turbulence theory
View Description Hide DescriptionIn this article we present the derivation of a generalized weak turbulence kinetic equation for unmagnetized collisionless plasmas in a uniform medium. For the sake of simplicity the present formulation assumes longitudinal electrostaticinteraction only, and the effects of spontaneous thermal fluctuations are ignored. In spite of these simplifications, the present formalism represents a generalization of the existing weak turbulencetheory in that a nonlinear eigenmode excited in a turbulent plasma with frequency close to twice the plasma frequency is incorporated into the discussion. Traditional weak turbulencetheory emphasizes various linear and nonlinear interactions among wave modes in quiescent plasmas (i.e., Langmuir and ionsound waves). In contrast, the present formalism describes linear and nonlinear interactions among Langmuir, ionsound, and the new nonlinear eigenmode.Nonlinear wave kinetic equations for these modes are systematically derived, and the particle kinetic equation which generalizes the well known quasilinear diffusion equation, is also derived.

Electromagnetic vortices in streaming pair plasmas
View Description Hide DescriptionTwo coupled nonlinear equations for a perturbed electromagnetic field in an electron–positron streaming plasma which is placed in a nonuniform magnetic field are derived and solved analytically, yielding stationary solutions in the form of vortices consisting of monopolar and quadrupolar parts. It is shown that vortices are created in and carried by a specific given linear shear flow profile and a given nonuniformity of the magnetic shear.

Theory of Langmuir wave generation in the presence of Alfvén wave turbulence in an electronpositron plasma: Case III
View Description Hide DescriptionThe plasmamaserinteraction of a test Langmuir wave in the presence of Alfvén waveturbulence is studied theoretically in a magnetized electronpositron (ep) plasma, where the turbulence is produced by both electron and positron temperature anisotropies. Langmuir waves are generated without the necessity of an electron or positron beam component. The growth takes place in the direction of propagation of the Alfvén waves.

Simulation studies of heavy ion heating by currentdriven instabilities
View Description Hide DescriptionNonlinear evolution of currentdriven instabilities and associated energy transport among different particle species are studied by means of a twodimensional, electrostatic, particle simulation code with full ion and electron dynamics. The plasma is assumed to consist of hydrogen (H) and helium (He) ions and electrons with the electron temperature larger than the ion temperatures; the electrons drift along a uniform magnetic field with an initial speed equal to the thermal speed. Then, simulations show that after the development of ion acoustic waves and fundamental H cyclotron waves, second harmonicwaves are destabilized due to the change in the electron velocity distribution function parallel to the magnetic field, Even though the linear theory based on the initial conditions predicts that the second harmonics are only marginally unstable, they eventually grow to the largest amplitudes and heat He ions more significantly than H ions. The instabilities of these three kinds of modes with different phase velocities give rise to flattening of over a region larger than the thermal speed.

Scaling properties of threedimensional isotropic magnetohydrodynamic turbulence
View Description Hide DescriptionA comprehensive picture of threedimensional (3D) isotropic magnetohydrodynamic(MHD)turbulence is presented based on the first mode numerical simulations performed. Both temporal and spatial scaling properties are studied. For finite magnetic helicity H the energy decay is governed by the constancy of H and the decrease of the ratio of kinetic and magnetic energy A simple model consistent with a series of simulation runs predicts the asymptotic decay laws For nonhelical MHDturbulence, the energy decays faster, The energy spectrum follows a law, clearly steeper than previously found in 2D MHDturbulence. The scaling exponents of the structure functions are consistent with a modified She–Leveque model which corresponds to a basic Kolmogorov scaling and sheetlike dissipative structures. The difference between the 3D and the 2D behavior can be related to the eddy dynamics in 3D and 2D hydrodynamicturbulence.

Role of collective effects in dominance of scattering off thermal ions over Langmuir wave decay: Analysis, simulations, and space applications
View Description Hide DescriptionLangmuir waves driven to high levels by beam instabilities are subject to nonlinear processes, including the closely related processes of scattering off thermal ions (STI) and a decay process in which the ion response is organized into a product ion acoustic wave. Calculations of the nonlinear growth rates predict that the decay process should always dominate STI, creating two paradoxes. The first is that three independent computer simulation studies show STI proceeding, with no evidence for the decay at all. The second is that observations in space of type III solar radio bursts and Earth’s foreshock, which the simulations were intended to model, show evidence for the decay proceeding but no evidence for STI. Resolutions to these paradoxes follow from the realization that a nonlinear process cannot proceed when its growth rate exceeds the minimum frequency of the participating waves, since the required collective response cannot be maintained and the waves cannot respond appropriately, and that a significant number of efoldings and wave periods must be contained in the time available. It is shown that application of these “collective” and “time scale” constraints to the simulations explains why the decay does not proceed in them, as well as why STI proceeds in specific simulations. This appears to be the first demonstration that collective constraints are important in understanding nonlinear phenomena. Furthermore, applying these constraints to space observations, it is predicted that the decay should proceed (and dominate STI) in type III sources and the high beam speed regions of Earth’s foreshock for a specific range of wave levels, with a possible role for STI alone at slightly higher wave levels. Deeper in the foreshock, for slower beams and weaker wave levels, the decay and STI are predicted to become ineffective. Suggestions are given for future testing of the collective constraint and an explanation for why waves in space are usually much weaker than in the simulations.

Electroacoustic damping effects on the parametric decays of electromagnetic waves in electron–positron plasmas
View Description Hide DescriptionParametric decays of a linearly polarized electromagnetic wave in an electron–positron plasma, including weakly relativistic effects and damping on the electroacoustic pseudomodes, are studied. The effect of nondissipative Landau damping is simulated through a phenomenological collisionallike term in the fluid equations. It is shown that in general, there are a number of instabilities due to the coupling between electroacoustic and electromagnetic pseudomodes, and between electromagnetic modes. On the other hand, damping effects reduce the growth rate of these instabilities and increase the instability range. It is also shown that there are no threshold effects on any of the decay modes.

Strong narrowband electron cyclotron emission from a mirror plasma heated by electron cyclotron waves
View Description Hide DescriptionStrong electromagnetic radiation is observed in a narrow band slightly above the frequency of a heatingwave that is absorbed by electrons near the electron cyclotron resonance layer in a magnetic beach. The frequency spectrum consists of a sharp component and a broad background, which is enhanced by more than 30 dB and 10 dB, respectively, above the radiation of thermal electrons. This observation is explained in terms of cyclotron radiation emitted by electrons, localized in a magnetic mirror, that are resonantly heated and bunched by a strong monochromatic wave.
 Magnetically Confined Plasmas, Heating, Confinement

The role of thermal instabilities in limiting the density in DIIID
View Description Hide DescriptionThe mechanisms which apparently govern the maximum achievable density in several DIIID [Luxon, Anderson, Batty et al., Plasma Physics on Controlled Nuclear Fusion Research 1986 (IAEA, Vienna, 1987), Vol. 1, p. 159] shots in which different operating procedures were used in building up the density were investigated and compared with the predictions of thermal instability theory. Core MARFEs (multifaceted asymmetric radiation from the edge) followed by a (hightolow confinement mode) transition limit the density well below the Greenwald limit in continuous gas puffed lower singlenull discharges with low triangularity. Similar continuous gas puff fueled discharges with higher triangularity or with pumping in the lower divertor achieve densities at or above the Greenwald value, apparently limited by confinement degradation, without the formation of core MARFEs. Pellet fueled discharges achieve densities up to twice the Greenwald value, limited by global radiative collapse. Thermal instability theory predictions of the limiting core MARFEs, confinement degradation or global radiative collapse are in good agreement with the experimental observations for the shots examined. Evidence for an important role of neutral particles in the plasma edge in core MARFE onset and in confinement degradation was identified.

Drift mode calculations for the Large Helical Device
View Description Hide DescriptionA fully kinetic assessment of the stability properties of toroidal drift modes has been obtained for a case for the Large Helical Device [A. Iiyoshi et al., Nucl. Fusion 39, 1245 (1999)]. This calculation retains the important effects in the linearized gyrokineticequation, using the lowestorder “ballooning representation” for high toroidal mode number instabilities in the electrostatic limit. Results for toroidal drift waves destabilized by trapped particle dynamics and ion temperature gradients are presented, using threedimensional magnetohydrodynamic equilibria reconstructed from experimental measurements. The effects of helically trapped particles and helical curvature are investigated.

Effect of poloidal electric field on electron cyclotron current drive in a tokamak geometry
View Description Hide DescriptionEffect of a poloidal electric field on the electron cyclotron current drive is studied in a tokamak geometry. A general discussion of its influence on the electron phasespace dynamics and current drive efficiency is presented. It is shown that the modification to the current drive efficiency increases as the heating location is moved out in the major radius. It is concluded that the modification is only moderate to insignificant for low magnetic field side heating and for high field side heating) for a poloidal electrostatic potential variation of order inverse aspect ratio under an efficient current drive.