Volume 18, Issue 9, September 2011

To achieve ignition, inertial confinement fusion target designs use a sequence of shocks to compress the target before it implodes. To minimize the entropy acquired by the fuel, the strength and timing of these shocks will be precisely set during a series of tuning experiments that adjust the laser pulse to achieve optimal conditions. We report measurements of the velocity and timing of multiple, converging shock wavesinside spherical targets filled with liquid (cryogenic) deuterium. These experiments produced the highest reported shock velocity observed in liquid deuterium (U _{s} = 135 km/s at ∼25 Mb) and observed an increase in shock velocity due to spherical convergence. These directdrive experiments are best simulated when hydrodynamic codes use a nonlocal model for the transport of absorbed laser energy from the coronal plasma to the ablation surface.
 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Resonances of surface and volume plasmons in atomic clusters
View Description Hide DescriptionThe resonance phenomena caused by the excitation of the surface and volume plasmons in the metal and ionized atomic clusters are studied in the framework of hydrodynamic and kinetic approaches with the inclusion of radiative, collisional, and kinetic (collisionless) damping mechanisms. The resonances of dipole moment at the frequencies of the volume plasmons are found to be strongly damped by the collisioninduced losses, while the field amplitude at the central region of the cluster may exhibit large increase at the resonance of both kind of plasmons.

The effects of strong temperature anisotropy on the kinetic structure of collisionless slow shocks and reconnection exhausts. II. Theory
View Description Hide DescriptionSimulations of collisionless oblique propagating slow shocks have revealed the existence of a transition associated with a critical temperature anisotropy ɛ = 1 − μ_{0}(P _{} − P _{⊥})/B ^{2} = 0.25 (Y.H. Liu, J. F. Drake, and M. Swisdak, Phys. Plasmas 18, 062110 (2011)). An explanation for this phenomenon is proposed here based on anisotropic fluid theory, in particular, the anisotropic derivative nonlinearSchrödingerBurgers equation, with an intuitive model of the energy closure for the downstream counterstreaming ions. The anisotropy value of 0.25 is significant because it is closely related to the degeneracy point of the slow and intermediate modes and corresponds to the lower bound of the coplanar to noncoplanar transition that occurs inside a compound slow shock (SS)/rotational discontinuity (RD) wave. This work implies that it is a pair of compound SS/RD waves that bound the outflows in magnetic reconnection, instead of a pair of switchoff slow shocks as in Petschek’s model. This fact might explain the rareness of insitu observations of Petschekreconnectionassociated switchoff slow shocks.

Continuum modes in rotating plasmas: General equations and continuous spectra for large aspect ratio tokamaks
View Description Hide DescriptionA theory for localized lowfrequency ideal magnetohydrodynamical (MHD) modes in axisymmetric toroidal systems is generalized to take into account both toroidal and poloidal equilibrium plasma flows. The general set of equations describing the coupling of shear Alfvén and slow (sound) modes and defining the continuous spectrum of rotating plasmas in axisymmetric toroidal systems is derived. The equations are applied to study the continuous spectra in large aspect ratio tokamaks. The unstable continuous modes in the case of predominantly poloidal plasma rotation with the angular velocity exceeding the sound frequency are found. Their stabilization by the shear Alfvén coupling effect is studied.

Relativistic Bernstein waves in a degenerate plasma
View Description Hide DescriptionBernstein mode for a relativistic degenerate electron plasma is investigated. Using relativistic VlasovMaxwell equations, a general expression for the conductivity tensor is derived and then employing FermiDirac distribution function a generalized dispersion relation for the Bernstein mode is obtained. Two limiting cases, i.e., nonrelativistic and ultrarelativistic are discussed. The dispersion relations obtained are also graphically presented for some specific values of the parameters depicting how the propagation characteristics of Bernstein waves as well as the Upper Hybrid oscillations are modified with the increase in plasma number density.

Stimulated Raman backscattering of a laser in a magnetized plasma channel
View Description Hide DescriptionA Gaussian laser beam, propagating as an eigenmode through a low density plasma channel in the presence of an axial magnetic field, undergoes stimulated Raman back scattering, producing an upper hybrid wave and a radially localized electromagnetic sideband wave. The channel may be self created by the laser due to ponderomotive force or by a prepulse. The radial width of sideband is and Langmuir wave of extent . The nonlocal effect arising, due to self generated magnetic field, modifies the electron response to these Eigen modes, reduces the region of nonlocal interaction and hence the growth rate. The growth rate decreases with the pump wave amplitude and it maximum for back scattering. A nonlocal theory of stimulated Raman backscattering of a laser, propagating through a plasma channel in the presence of an axial magnetic field, is developed. The laser excites a forward propagating upper hybrid mode, that is strongly localized radially, and a backward propagating electromagnetic wavesideband. The growth rate significantly decreases with the magnetic field.

Ioncyclotron instability in currentcarrying Lorentzian (kappa) and Maxwellian plasmas with anisotropic temperatures: A comparative study
View Description Hide DescriptionCurrentdriven electrostaticioncyclotron instability has so far been studied for Maxwellianplasma with isotropic and anisotropictemperatures. Since satellitemeasured particle velocity distributions in space are often better modeled by the generalized Lorentzian (kappa) distributions and since temperatureanisotropy is quite common in space plasmas, theoretical analysis of the currentdriven, electrostaticioncyclotron instability is carried out in this paper for electronproton plasma with anisotropictemperatures, where the particle parallel velocity distributions are modeled by kappa distributions and the perpendicular velocity distributions are modeled by Maxwellian distributions. Stability properties of the excited ion cyclotron modes and, in particular, their dependence on electron to ion temperature ratio and ion temperatureanisotropy are presented in more detail. For comparison, the corresponding results for biMaxwellian plasma are also presented. Although the stability properties of the ion cyclotron modes in the two types of plasmas are qualitatively similar, significant quantitative differences can arise depending on the values of and . The comparative study is based on the numerical solutions of the respective linear dispersion relations. Quasilinear estimates of the resonant ion heating rates due to ioncyclotron turbulence in the two types of plasma are also presented for comparison.

Evolution of polarization of an electromagnetic wave propagating in magnetized plasma: Comparison between two alternative formalisms
View Description Hide DescriptionTwo alternative formalisms for the analysis of the evolution of electromagnetic wavepolarization in a magnetized plasma are considered: the coupled wave formalism and the Stokes vector formalism. The first formalism is developed and extended to more general magnetic field configurations than considered hitherto, thus obtaining a new polarization evolution equation. The two formalisms are compared and their relative merits and limitations are described. In particular, it is shown that the equations for polarization evolution are valid for arbitrarily strong anisotropy induced by the magnetic field and that these equations treat implicitly the effect of coupling between the characteristicwaves.

Hall magnetohydrodynamic reconnection in the plasmoid unstable regime
View Description Hide DescriptionA set of reduced Hall magnetohydrodynamic(MHD)equations are used to evaluate the stability of large aspect ratio current sheets to the formation of plasmoids (secondary islands).Reconnection is driven by resistivity in this analysis, which occurs at the resistiveskin depth , where S _{ L } is the Lundquist number, L, the length of the current sheet, ν_{ A,} the Alfvén speed, and γ, the growth rate. Modifications to a recent resistiveMHD analysis [N. F. Loureiro et al., Phys. Plasmas 14, 100703 (2007)] arise when collisions are sufficiently weak that d _{ η } is shorter than the ion skin depth d _{ i } ≡ c/ω _{ pi }. Secondary islands grow faster in this Hall MHD regime: the maximum growth rate scales as and the number of plasmoids as , compared to and S ^{3/8}, respectively, in resistiveMHD.

The two modes extension to the BerkBreizman equation: Delayed differential equations and asymptotic solutions
View Description Hide DescriptionThe integrodifferential BerkBreizman (BB) equation, describing the evolution of particledriven wave mode is transformed into a simple delayed differential equation form ν∂a(τ)/∂τ=a(τ) – a ^{2}(τ – 1) a(τ – 2). This transformation is also applied to the two modes extension of the BB theory. The obtained solutions are presented together with the derived asymptotic analytical solutions and the numerical results.

A 2D simulation study of Langmuir, whistler, and cyclotron maser instabilities induced by an electron ringbeam distribution
View Description Hide DescriptionWe carried out a series of 2D simulations to study the beam instability and cyclotron maserinstability (CMI) with the initial condition that a population of tenuous energetic electrons with a ringbeam distribution is present in a magnetized background plasma. In this paper, weakly relativistic cases are discussed with the ringbeam kinetic energy ranging from 25 to 100 keV. The beam component leads to the twostream or beam instability at an earlier stage, and the beam mode is coupled with Langmuir or whistler mode, leading to excitation of beamLangmuir or beamwhistler waves. When the beam velocity is large with a strong beam instability, the initial ringbeam distribution is diffused in the parallel direction rapidly. The diffused distribution may still support CMI to amplify the X1 mode (the fundamental X mode). On the contrary, when the beam velocity is small and the beam instability is weak, CMI can amplify the Z1 (the fundamental Z mode) effectively while the O1 (the fundamental O mode) and X2 (the second harmonic X mode) modes are very weak and the X1 mode is not excited. In this report, different cases with various parameters are presented and discussed for a comprehensive understanding of ringbeam instabilities.

Interesting features of nonlinear shock equations in dissipative pairionelectron plasmas
View Description Hide DescriptionTwo dimensional nonlinear electrostatic waves are studied in unmagnetized, dissipative pairionelectron plasmas in the presence of weak transverse perturbation. The dissipation in the system is taken into account by incorporating the kinematicviscosity of both positive and negative ions. In the linear case, a biquadratic dispersion relation is obtained, which yields the fast and slow modes in a pairionelectron plasma. It is shown that the limiting cases of electronion and pairion can be retrieved from the general biquadratic dispersion relation, and the differences in the characters of the waves propagating in both the cases are also highlighted. Using the small amplitude approximation method, the nonlinear Kadomtsev Petviashvili Burgers as well as BurgersKadomtsev Petviashvili equations are derived and their applicability for pairionelectron plasma is explained in detail. The present study may have relevance to understand the formation of two dimensional electrostatic shocks in laboratory produced pairionelectron plasmas.

Influences of subAlfvénic shear flows on nonlinear evolution of magnetic reconnection in compressible plasmas
View Description Hide DescriptionInfluences of subAlfvénic shear flows on the nonlinear evolution of the magnetic reconnection are studied in the framework of compressible resistive MHD and compressible Hall MHD. It is found for the first time that the subAlfvénic shear flow can either stabilize or destabilize magnetic reconnection, which is mainly determined by the plasma beta and the half thickness of the shear flow (). The shear flow exhibits a suppressing effect on magnetic reconnection and the boosting effect nearly disappears for the beta plasma , which is associated with the presence of a pair of discontinuities in the upper and lower inflow region. The shear flow has the boosting effect on magnetic reconnection when the half thickness of the shear flow exceeds a critical value in the high beta plasma which is in a good agreement with the results from incompressible simulation. With the inclusion of the Hall effect,shear flow can still either stabilize or destabilize magnetic reconnection, but the boosting effect becomes weaker as the ion inertial length increases.

Analytical and computational study of the ideal full twofluid plasma model and asymptotic approximations for Hallmagnetohydrodynamics
View Description Hide DescriptionThe 5moment twofluid plasma model uses Euler equations to describe the ion and electron fluids and Maxwell’sequations to describe the electric and magnetic fields. Twofluid physics becomes significant when the characteristic spatial scales are on the order of the ion skin depth and characteristic time scales are on the order of the ion cyclotron period. The full twofluid plasma model has disparate characteristic speeds ranging from the ion and electron speeds of sound to the speed of light. Two asymptotic approximations are applied to the full twofluid plasma to arrive at the HallMHD model, namely negligible electron inertia and infinite speed of light. The full twofluid plasma model and the HallMHD model are studied for applications to an electromagneticplasma shock, geospace environmental modeling (GEM challenge) magnetic reconnection, an axisymmetric Zpinch, and an axisymmetric field reversed configuration (FRC).

Shear waves in an inhomogeneous strongly coupled dusty plasma
View Description Hide DescriptionThe properties of electrostatic transverse shear waves propagating in a strongly coupled dusty plasma with an equilibrium density gradient are examined using the generalized hydrodynamic (GH) equation. In the usual kinetic limit, the resulting equation has similarity to zero energy Schrodinger’s equation. This has helped in obtaining some exact eigenmode solutions in both Cartesian and cylindrical geometries for certain nontrivial density profiles. The corresponding velocity profiles and the discrete eigenfrequencies are obtained for several interesting situations and their physics discussed.

Landau damping of ion acoustic wave in Lorentzian multiion plasmas
View Description Hide DescriptionThe Landau damping rates of ion acoustic wave are studied by using VlasovPoisson model for unmagnetized Lorentzian or kappa distributed plasma containing electrons, positively and negatively charged ions. It is found that the damping rate of ion acoustic wave is increased with the decrease of kappa (i.e., the spectral index of Lorentzian distribution) value. The damping rates of the electrostatic wave in multiion component plasmas are discussed in detail which depends on electron to ion temperature ratio and ions masses and density ratios. The numerical results are also shown by choosing some typical experimental parameters of multiion plasmas.

Timefractional KdV equation for plasma of two different temperature electrons and stationary ion
View Description Hide DescriptionUsing the timefractional KdV equation, the nonlinear properties of small but finite amplitude electronacoustic solitary waves are studied in a homogeneous system of unmagnetized collisionless plasma. This plasma consists of cold electrons fluid, nonthermal hot electrons, and stationary ions. Employing the reductive perturbation technique and the EulerLagrange equation, the timefractional KdV equation is derived and it is solved using variational method. It is found that the timefractional parameter significantly changes the soliton amplitude of the electronacoustic solitary waves. The results are compared with the structures of the broadband electrostatic noise observed in the dayside auroral zone.

Magnetorotational instability in a collisionless plasma with heat flux vector and an isotropic plasma with selfgravitational effect
View Description Hide DescriptionThe linear stability of a differential rotating magnetized plasma is analyzed in the collisionless approximation along with heat flux vector. The dispersion relation is derived and simplified cases are discussed with instability criteria presented. Anisotropicpressures are shown to not only alter the classical instability criterion but also induce new unstable regions. The shear rotating instability in a collisional magnetized plasma with a scalar kinetic pressure in the presence of selfgravitational effect is then considered. Three cases are discussed specifically according to the general dispersion relation. The effects of Jeans term and compressibility on the local shear instability induced by differential rotation are examined and the analytic instability criteria are presented.

Equilibrium velocity distributions in parallel propagating lowfrequency Alfvénic turbulence
View Description Hide DescriptionThe equilibrium velocity distributions in parallel propagating, circularly polarized lowfrequency Alfvénic turbulence are presented. The equilibrium solutions of the monochromatic Alfvén waves are extended to those of incompressible Alfvénic turbulence with the broadband spectrum in low beta plasmas. It is shown that the “apparent temperature” due to the nonresonant ion heating is explained on the basis of the equilibrium velocity distribution. The anisotropic equilibrium velocity distribution corresponding to Alfvénic turbulence in the ChewGoldbergerLow system is also demonstrated. It is suggested that the distribution can be the back ground structure in the asymmetric velocity distributions observed in the solar wind.
 Nonlinear Phenomena, Turbulence, Transport

Magnetohydrodynamically stable axisymmetric mirrors^{a)}
View Description Hide DescriptionMaking axisymmetric mirrors magnetohydrodynamically (MHD) stable opens up exciting opportunities for using mirrordevices as neutron sources, fusionfission hybrids, and purefusion reactors. This is also of interest from a general physics standpoint (as it seemingly contradicts wellestablished criteria of curvaturedriven instabilities). The axial symmetry allows for much simpler and more reliable designs of mirrorbased fusion facilities than the wellknown quadrupole mirror configurations. In this tutorial, after a summary of classical results, several techniques for achieving MHD stabilization of the axisymmetric mirrors are considered, in particular: (1) employing the favorable fieldline curvature in the end tanks; (2) using the linetying effect; (3) controlling the radial potential distribution; (4) imposing a divertor configuration on the solenoidal magnetic field; and (5) affecting the plasma dynamics by the ponderomotive force. Some illuminative theoretical approaches for understanding axisymmetric mirror stability are described. The applicability of the various stabilization techniques to axisymmetric mirrors as neutron sources, hybrids, and purefusion reactors are discussed; and the constraints on the plasma parameters are formulated.

Effect of driving frequency on excitation of turbulence in a kinetic plasma
View Description Hide DescriptionThe effect of driving frequency on the efficiency of turbulence generation through magnetic forcing is studied using kinetic hybrid simulations with fully kinetic ions and fluid electrons. The efficiency of driving is quantified by examining the energy input into magnetic field as well as the thermal energy for various driving frequencies. The driving is efficient in exciting turbulence and heating the plasma when the time period of the driving is larger than the nonlinear time of the system. For driving at faster time scales, the energy input is weak and the steady state energy is much lower. The heating of the plasma is correlated with intermittent properties of the magnetic field, which are manifested as nonGaussian statistics. Implications for turbulence in solar corona are discussed.