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Volume 13, Issue 10, October 2006
 LETTERS


Probabilistic analysis of turbulent structures from twodimensional plasma imaging
View Description Hide DescriptionA method is presented to construct objectrelated structure observables, such as size, mass, shape, and trajectories from twodimensional plasma imaging data. The probability distributions of these observables, deduced from measurements of many realizations, provide a robust framework in which the fluctuations, the turbulence, and the related transport are characterized. The results for imaging data recorded in the presence of driftinterchange instabilities and turbulence on the TORPEXtoroidal plasma experiment [A. Fasoli et al., Phys. Plasmas13, 055902 (2006)] are discussed.

Multiple eigenmodes of geodesic acoustic mode in collisionless plasmas
View Description Hide DescriptionWe report a series of eigenmodes of the geodesic acoustic mode (GAM), which includes the standard GAM, a branch of lowfrequency mode, and a series of ion sound wavelike modes. The case of is investigated, and eigenfrequencies of these modes are obtained analytically from a linear gyrokinetic model in collisionless plasmas with a rigid constant electrostatic potential around a magnetic surface.

Gain curves for directdrive fast ignition at densities around
View Description Hide DescriptionThe maximum gain attainable from fastignited directdrive implosions is derived based on realistic target designs and laser pulses, onedimensional simulations of the implosion, and twodimensional simulations of ignition by a collimated electron beam and burn propagation. Since the implosion characteristics are set by the optimized target design, the ratio of the thermonuclear energy to the compression laser energy is a unique function of the driver energy on target. It is shown that, if ignited, the fuel assembled by a UV laser can yield close to of thermonuclear energy.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

On the stability of Alfvén discontinuity
View Description Hide DescriptionThe stability of Alfvén discontinuities for the equations of ideal compressible magnetohydrodynamics (MHD) is studied. The Alfvén discontinuity is a characteristic discontinuity for the hyperbolic system of MHDequations but, as in the case of shock waves, there is a mass flux through its front. The Lopatinskii condition for a planar Alfvén discontinuity is tested numerically, and the domain in the space of parameters of the discontinuity where it is unstable is determined. In fact, in this domain the Alfvén discontinuity is not only unstable, but the initialboundaryvalue problem for corresponding linearized equations is illposed in the sense of Hadamard.

Short wavelength quantum electrodynamical correction to cold plasmawave propagation
View Description Hide DescriptionThe effect of short wavelength quantum electrodynamic (QED) correction on plasmawave propagation is investigated. The effect on plasma oscillations and on electromagnetic waves in an unmagnetized as well as a magnetized plasma is investigated. The effects of the short wavelength QED corrections are most evident for plasma oscillations and for extraordinary modes. In particular, the QED correction allow plasma oscillations to propagate, and the extraordinary mode loses its stop band. The significance of our results is discussed.

Exact linearized Coulomb collision operator in the moment expansion
View Description Hide DescriptionIn the moment expansion, the Rosenbluth potentials, the linearized Coulomb collision operators, and the moments of the collision operators are analytically calculated for any moment. The explicit calculation of Rosenbluth potentials converts the integrodifferential form of the Coulomb collision operator into a differential operator, which enables one to express the collision operator in a simple closed form for any arbitrary mass and temperature ratios. In addition, it is shown that gyrophase averaging the collision operator acting on arbitrary distribution functions is the same as the collision operator acting on the corresponding gyrophase averaged distribution functions. The moments of the collision operator are linear combinations of the fluid moments with collision coefficients parametrized by mass and temperature ratios. Useful forms involving the small massratio approximation are easily found since the collision operators and their moments are expressed in terms of the mass ratio. As an application, the general moment equations are explicitly written and the higher order heat flux equation is derived.

Experimental characterization of driftinterchange instabilities in a simple toroidal plasma
View Description Hide DescriptionLow frequency electrostatic instabilities are investigated on TORPEX[Fasoli, Labit, McGrath, Müller, Podestà, and Poli, Bull. Am. Phys. Soc.48, 119 (2003)], a toroidal device for basic plasma physics experiments with a toroidalmagnetic field and a small vertical magnetic field. A twodimensional (2D) profile of the frequency and amplitude of density and potential fluctuations is reconstructed using electrostatic probes with high space and time resolution. The measured phase velocity, corrected for the Doppler shift induced by the drift, is consistent with the electron diamagnetic drift velocity. The local dispersion relation,measured along and across the magnetic field, is in agreement with the predictions of a linear kinetic slab model for drift waves. Unstable modes are generated in regions of unfavorable curvature, where the pressure gradient is colinear with the magnetic field gradient. It is demonstrated that the curvature of the magnetic field lines is essential for driving the observed instabilities, which are therefore identified as driftinterchange modes.

Shearflowdriven ion cyclotron instabilities of magnetic fieldaligned flow of inhomogeneous plasma
View Description Hide DescriptionThe effect of magnetic fieldaligned flow with a transverse flow velocity gradient (velocity shear) on the generation of electrostatic ion cyclotron waves is studied analytically by using kinetic formalism. It is shown that flow shear not only modifies the frequency and growth rate of a known currentdriven electrostaticion cyclotron instability (CDEIC), but is the source of the development of specific kinetic and hydrodynamic shearflowdriven ion cyclotron instabilities at the levels of current along the ambient magnetic field, which is subcritical for the development of the CDEIC instability.

Twodimensional electronelectron twostream instability of an inertial electrostatic confinement device
View Description Hide DescriptionTheoretical works by Barnes and Nebel [D. C. Barnes and R. A. Nebel, Phys. Plasmas5, 2498 (1998);R. A. Nebel and D. C. Barnes, Fusion Technol.38, 28 (1998)] have suggested that a tiny oscillating ion cloud (referred to as the periodically oscillating plasma sphere or POPS) may undergo a selfsimilar collapse in a harmonic oscillator potential formed by a uniform electron background. A major uncertainty in this oscillating plasma scheme is the stability of the virtual cathode that forms the harmonic oscillator potential. The electronelectron twostream stability of the virtual cathode has previously been studied with a fluid model, a slab kinetic model, a spherically symmetric kinetic model, and experimentally [R. A. Nebel and J. M. Finn, Phys. Plasmas8, 1505 (2001);R. A. Nebel et al., Phys. Plasmas12, 040501 (2005)]. Here the mode is studied with a twodimensional particleincell code. Results indicate stability limits near those of the previously spherically symmetric case.

Cumulative effect of the filamentation and Weibel instabilities in counterstreaming thermal plasmas
View Description Hide DescriptionIntroducing a thermal particle distribution is important for a realistic investigation of counterstreaming plasmas with finite temperatures. Such counterstreaming thermal plasmas are described by the particle distributions, which include the counterstreams and thermal distribution as well. Two nonrelativistic counterstreams are considered here, with a biMaxwellian thermal anisotropy for each of them. This type of distribution is often expected to be found in both laboratory or cosmic plasmas, and it is able to cumulate the effects of the filamentation and Weibel instability. Comparing with the growth rates of each of these instabilities, the cumulative effect provides larger values, if they are emitted in the same direction. If the thermal anisotropy is negative, which means that Weibel instability develops on a perpendicular direction with respect to the filamentation instability, then their cumulative effect will suppress the instability. In both of these cases, the cumulative effect of the filamentation and Weibel instabilities can modify significantly the effective growth rate of the electromagnetic unstable modes.

On the current sheet model with distribution
View Description Hide DescriptionThe present paper (re)derives current sheet equilibrium solutions on the basis of the socalled distribution functions for the particles. The present work builds upon a recent paper [W.Z. Fu and L.N. Hau, Phys. Plasmas12, 070701 (2005)], where the authors formulated the equilibrium current sheet model with the distribution. According to their work, however, the global temperature profile monotonically increases in the asymptotic regime. In the present paper it is shown that the presence of a finite stationary background population of the particles arrests the unlimited increase of the global temperature profile in the asymptotic limit. The present paper further extends the analysis by considering a current sheet model where the electron current is embedded within a thicker ion current layer, and where there exists a weak electrostatic potential drop across the current sheet.

Photon Landau damping of electron plasma waves with photon recoil
View Description Hide DescriptionPhoton Landau damping of electron plasma waves with relativistic phase velocity is described, using a photon kinetic theory where photon recoil is taken into account. An exact form of the wave kinetic equation is used. Kinetic and fluid regimes of photon beam instabilities are discussed. Diffusion in the photon momentum space is derived and a quasilinear wave kinetic equation is established. In the present approach, photon recoil effects associated with the emission or absorption of plasmons are included. The neglect of recoil, which is equivalent to using the geometric optics approximation, reduces the present results to those already existing in the literature.

The Weibel instability on strongly magnetized microwave produced plasma
View Description Hide DescriptionThe electron distribution function (EDF) of plasma generated due to the interaction between a circularly polarized intense microwave (MW) field with a dilute gas is investigated in the presence of a static magnetic field. Making use of the EDF, the electron dielectric permittivity tensor is obtained. Taking into account the anisotropic structure of EDF, it is evident that the Weibel instability can occur in such plasmas. Therefore, using the adiabatic approximation, the dispersion relation is obtained for small electron perturbations across the MW field. By solving the dispersion relation, it is shown that not only does the magnetic field decrease the growth rate of the Weibel instability, but that a sufficiently strong magnetic field can make the instability completely disappear.

Highfrequency electron drift instability in the crossfield configuration of Hall thrusters
View Description Hide DescriptionA systematic study of a highfrequency electron drift instability is presented. It has very large wave numbers corresponding to wavelengths close to the electron gyroradius. The threedimensional dispersion relation is derived for a model of a crossed electric and magnetic field configuration existing in the Hall thruster. It is shown that the instability develops in packets of oblique unstable modes perpendicular to the magnetic field. The evolution of the instability is also studied for distorted electron distribution functions obtained in particleincell simulations.

Potential distributions around a moving test charge in quantum plasmas
View Description Hide DescriptionBy using the dielectric response function of quantum electron plasmas, potential distributions around a moving test charge are calculated. The nearfield potential follows the modified DebyeHückel potential, while the farfield potential turns out to be oscillatory. Both the DebyeHückel and wake potentials strongly depend on the Fermi energy and the electron quantum correlation strength. The relevance of the present investigation to semiconductor plasmas is discussed.
 Nonlinear Phenomena, Turbulence, Transport

Gyrokinetic turbulent heating
View Description Hide DescriptionExpressions for particle and energy fluxes and heating rates due to turbulence are derived. These fluxes and heating rates are identified from moments of an extended driftkinetic equation for the equilibrium distribution function. These include neoclassical as well as turbulent diffusion and heating. Phasespace conservation is demonstrated, allowing the driftkinetic equation to be expressed in conservative form. This facilitates taking moments with few approximations, mainly those consistent with drift kinetics for the equilibrium distribution function and the relative smallness of the fluctuations. The turbulent heating is uniquely defined by choosing the standard gyrokinetic definition for the energy flux. With this definition, most of the heating can be expressed in the form of ohmic heating from turbulent parallel and perpendicular current density perturbations. The latter current is identified with gradB and curvature drifts, plus terms involving magnetic perturbations (which are smaller for low beta). A small contribution to the heating comes from the divergence of an energy flux that is dependent on the finite gyroradius of the ions. The fluxes and heating rates are expressed in a form that can be easily evaluated from gyrokineticturbulence simulations.

Nonlinear response of a relativistic plasma to intense fields: Generation of strong quasistatic magnetic fields
View Description Hide DescriptionThe generation of quasistatic magnetic fields by nonlinear interactions of two highfrequency waves are studied on the basis of a correct relativistic kinetic theory for a thermal plasma. The plasma response in the presence of nonlinear excitations is a nonlinear current, which is calculated here within the framework of the relativistic theory. Quasistationary magnetic fields are generated due to the magnetization current. The latter is derived solving the kinetic integrals in the long wavelength limit and it holds for arbitrary plasma temperatures. It also allows for deducing the magnetization currents at nonrelativistic or ultrarelativistic temperatures. The magnitude of quasistationary magnetic fields is estimated for fully relativistic plasmatemperatures, where the relativistic contribution dominates. For typical laboratory or numerical experiments the magnetic field strength can reach values higher than 10 MG.

Energy conversion during magnetic reconnection for magnetotaillike equilibria
View Description Hide DescriptionThe principle of magnetic fieldtoparticle energy conversion for magnetic reconnection, originally developed by the authors for HarrisFadeev equilibria, is extended to include a finite northsouth (normal) component of the magnetic field, which is typical of the Earth’s magnetotail environment. On the basis of the exact conservation laws derived from the nonlinear Vlasov equation, it is demonstrated that a small portion of the energy stored in the magnetic field is released and converted to particle thermal energy as a result of the magnetic field topological transformation, i.e., reconnection. It is also found that the normal field component has a minimal impact on the efficacy of the energy exchange.

Mean sheared flow and parallel ion motion effects on zonal flow generation in iontemperaturegradient mode turbulence
View Description Hide DescriptionThe present work investigates the direct interaction of sheared mean flow with zonal flows (ZFs) and the effect of parallel ion motion on ZF generation in iontemperaturegradient(ITG) background turbulence. An analytical model for the direct interaction of sheared mean flows with zonal flows is constructed. The model used for the toroidal ITG driven mode is based on the equations for ion continuity, ion temperature and parallel ion motion, whereas the ZF evolution is described by the vorticity equation. The behavior of the ZF growth rate and real frequency is examined for typical tokamak parameters. It is shown that in general the zonal flow growth rate is suppressed by the presence of a sheared mean flow. In addition, with parallel ion motion effects the ZFs become more oscillatory for increasing value.

Truncated Painlevé expansion: Tanhtraveling wave solutions and reduction of sinePoisson equation to a quadrature for stationary and nonstationary threedimensional collisionless cold plasma
View Description Hide DescriptionThe relativistic nonlinear selfconsistent equations for a collisionless cold plasma with stationary ions [R. S. Ibrahim, IMA J. Appl. Math.68, 523 (2003)] are extended to 3 and dimensions. The resulting system of equations is reduced to the sinePoisson equation. The truncated Painlevé expansion and reduction of the partial differential equation to a quadrature problem (RQ method) are described and applied to obtain the traveling wave solutions of the sinePoisson equation for stationary and nonstationary equations in 3 and dimensions describing the chargedensity equilibrium configuration model.