Volume 20, Issue 9, September 2013

In this paper, we present the response of a 3D thin multiply connected wall to an external kink mode perturbation in axisymmetric tokamak configurations. To calculate the contribution of the plasma perturbed magnetic field in the vacuum region, we have made use of the concept of surface currents [following C. V. Atanasiu, A. H. Boozer, L. E. Zakharov, and A. A. Subbotin, Phys. Plasmas 6, 2781 (1999)]. The wall response is expressed in terms of a stream function of the wall surface currents, which are obtained by solving a diffusion type equation, taking into account the contribution of the wall currents themselves iteratively. The use of stream function makes the approach applicable for both wellstudied earlier Resistive Wall Modes and for Wall Touching Kink Modes, which were discovered recently as a key phenomenon in disruptions [L. E. Zakharov, S. A. Galkin, and S. N. Gerasimov, Phys. Plasmas 19, 055703 (2012)]. New analytical expressions, suitable for numerical calculations of toroidal harmonics of the vacuum magnetic fields from the surface currents on axisymmetric shells, are derived.
 LETTERS


Spectral evolution of twodimensional kinetic plasma turbulence in the wavenumberfrequency domain
View Description Hide DescriptionWe present a method for studying the evolution of plasma turbulence by tracking dispersion relations in the energy spectrum in the wavenumberfrequency domain. We apply hybrid plasma simulations in a simplified twodimensional geometry to demonstrate our method and its applicability to plasma turbulence in the ion kinetic regime. We identify four dispersion relations: ionBernstein waves, oblique whistler waves, oblique Alfvén/ioncyclotron waves, and a zerofrequency mode. The energy partition and frequency broadening are evaluated for these modes. The method allows us to determine the evolution of decaying plasma turbulence in our restricted geometry and shows that it cascades along the dispersion relations during the early phase with an increasing broadening around the dispersion relations.

Magnetic reconnection process in transient coaxial helicity injection
View Description Hide DescriptionThe physics of magnetic reconnection and fast flux closure in transient coaxial helicity injection experiments in NSTX is examined using resistive MHD simulations. These simulations have been performed using the NIMROD code with fixed boundary flux (including NSTX poloidal coil currents) in the NSTX experimental geometry. Simulations show that an X point is formed in the injector region, followed by formation of closed flux surfaces within 0.5 ms after the driven injector voltage and injector current begin to rapidly decrease. As the injector voltage is turned off, the field lines tend to untwist in the toroidal direction and magnetic field compression exerts a radial J × B force and generates a bidirectional radial pinch flow to bring oppositely directed field lines closer together to reconnect. At sufficiently low magnetic diffusivity (high Lundquist number), and with a sufficiently narrow injector flux footprint width, the oppositely directed field lines have sufficient time to reconnect (before dissipating), leading to the formation of closed flux surfaces. The reconnection process is shown to have transient SweetParker characteristics.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

The effect of finite Larmor radius corrections on Jeans instability of quantum plasma
View Description Hide DescriptionThe influence of finite Larmor radius (FLR) effects on the Jeans instability of infinitely conducting homogeneous quantum plasma is investigated. The quantum magnetohydrodynamic (QMHD) model is used to formulate the problem. The contribution of FLR is incorporated to the QMHD set of equations in the present analysis. The general dispersion relation is obtained analytically using the normal mode analysis technique which is modified due to the contribution of FLR corrections. From general dispersion relation, the condition of instability is obtained and it is found that Jeans condition is modified due to quantum effect. The general dispersion relation is reduced for both transverse and longitudinal mode of propagations. The condition of gravitational instability is modified due to the presence of both FLR and quantum corrections in the transverse mode of propagation. In longitudinal case, it is found to be unaffected by the FLR effects but modified due to the quantum corrections. The growth rate of Jeans instability is discussed numerically for various values of quantum and FLR corrections of the medium. It is found that the quantum parameter and FLR effects have stabilizing influence on the growth rate of instability of the system.

Detection of electromagnetic pulses produced by hypervelocity micro particle impact plasmas
View Description Hide DescriptionHypervelocity micro particles (mass < 1 ng), including meteoroids and space debris, routinely impact spacecraft and produce plasmas that are initially dense (∼1028 m−3), but rapidly expand into the surrounding vacuum. We report the detection of radio frequency (RF) emission associated with electromagnetic pulses (EMPs) from hypervelocity impacts of micro particles in groundbased experiments using micro particles that are 15 orders of magnitude less massive than previously observed. The EMP production is a stochastic process that is influenced by plasma turbulence such that the EMP detection rate that is strongly dependent on impact speed and on the electrical charge conditions at the impact surface. In particular, impacts of the fastest micro particles occurring under spacecraft charging conditions representative of high geomagnetic activity are the most likely to produce RF emission. This new phenomenon may provide a source for unexplained RF measurements on spacecraft charged to high potentials.

High power laser coupling to carbon nanotubes and ion Coulomb explosion
View Description Hide DescriptionLinear and non linear interaction of laser with an array of carbon nanotubes is investigated. The ac conductivity of nanotubes, due to uneven response of free electrons in them to axial and transverse fields, is a tensor. The propagation constant for ppolarization shows resonance at a specific frequency that varies with the direction of laser propagation. It also shows surface plasmon resonance at , where is the plasma frequency of free electrons inside a nanotube, assumed to be uniform plasma cylinder. The attenuation constant is also resonantly enhanced around these frequencies. At large laser amplitude, the nanotubes behave as thin plasma rods. As the electrons get heated, the nanotubes undergo hydrodynamic expansion. At an instant when plasma frequency reaches , the electron temperature rises rapidly and then saturates. For a Gaussian laser beam, the heating rate is maximum on the laser axis and falls off with the distance r from the axis. When the excursion of the electrons Δ is comparable or larger than the radius of the nanotube rc , the nanotubes undergo ion Coulomb explosion. The distribution function of ions turns out to be a monotonically decreasing function of energy.

Hamiltonian magnetohydrodynamics: Lagrangian, Eulerian, and dynamically accessible stability—Theory
View Description Hide DescriptionStability conditions of magnetized plasma flows are obtained by exploiting the Hamiltonian structure of the magnetohydrodynamics (MHD) equations and, in particular, by using three kinds of energy principles. First, the Lagrangian variable energy principle is described and sufficient stability conditions are presented. Next, plasma flows are described in terms of Eulerian variables and the noncanonical Hamiltonian formulation of MHD is exploited. For symmetric equilibria, the energyCasimir principle is expanded to second order and sufficient conditions for stability to symmetric perturbation are obtained. Then, dynamically accessible variations, i.e., variations that explicitly preserve invariants of the system, are introduced and the respective energy principle is considered. General criteria for stability are obtained, along with comparisons between the three different approaches.

Investigation of anisotropic photonic band gaps in threedimensional magnetized plasma photonic crystals containing the uniaxial material
View Description Hide DescriptionIn this paper, the dispersive properties of threedimensional (3D) magnetized plasma photonic crystals (MPPCs) composed of anisotropic dielectric (the uniaxial material) spheres immersed in homogeneous magnetized plasma background with facecenteredcubic (fcc) lattices are theoretically investigated by the plane wave expansion method, as the Voigt effects of magnetized plasma are considered. The equations for calculating the anisotropic photonic band gaps (PBGs) in the first irreducible Brillouin zone are theoretically deduced. The anisotropic PBGs and two flatbands regions can be obtained. The effects of the ordinaryrefractive index, extraordinaryrefractive index, filling factor, plasma frequency, and external magnetic field on the dispersive properties of the 3D MPPCs are investigated in detail, respectively, and some corresponding physical explanations are also given. The numerical results show that the anisotropy can open partial band gaps in 3D MPPCs with fcc lattices and the complete PBGs can be found compared to the conventional 3D MPPCs doped by the isotropic material. The bandwidths of PBGs can be tuned by introducing the magnetized plasma into 3D PCs containing the uniaxial material. It is also shown that the anisotropic PBGs can be manipulated by the ordinaryrefractive index, extraordinaryrefractive index, filling factor, plasma frequency, and external magnetic field, respectively. The locations of flatbands regions cannot be manipulated by any parameters except for the plasma frequency and external magnetic field. Introducing the uniaxial material can obtain the complete PBGs as the 3D MPPCs with high symmetry and also provides a way to design the tunable devices.

Effects of alpha beam on the parametric decay of a parallel propagating circularly polarized Alfven wave: Hybrid simulations
View Description Hide DescriptionAlfven waves with a finite amplitude are found to be unstable to a parametric decay in low beta plasmas. In this paper, the parametric decay of a circularly polarized Alfven wave in a protonelectronalpha plasma system is investigated with onedimensional (1D) hybrid simulations. In cases without alpha particles, with the increase of the wave number of the pump Alfven wave, the growth rate of the decay instability increases and the saturation amplitude of the density fluctuations slightly decrease. However, when alpha particles with a sufficiently large bulk velocity along the ambient magnetic field are included, at a definite range of the wave numbers of the pump wave, both the growth rate and the saturation amplitude of the parametric decay become much smaller and the parametric decay is heavily suppressed. At these wave numbers, the resonant condition between the alpha particles and the daughter Alfven waves is satisfied, therefore, their resonant interactions might play an important role in the suppression of the parametric decay instability.

Phase mixing and nonlinearity in geodesic acoustic modes
View Description Hide DescriptionPhase mixing and nonlinear resonance detuning of geodesic acoustic modes in a tokamak plasma are examined. Geodesic acoustic modes (GAMs) are tokamak normal modes with oscillations in poloidal flow constrained to lie within flux surfaces. The mode frequency is sonic, dependent on the local flux surface temperature. Consequently, mode oscillations between flux surfaces get rapidly out of phase, resulting in enhanced damping from the phase mixing. Damping rates are shown to scale as the negative 1/3 power of the large viscous Reynolds number. The effect of convective nonlinearities on the normal modes is also studied. The system of nonlinear GAM equations is shown to resemble the Duffing oscillator, which predicts resonance detuning of the oscillator. Resonant amplification is shown to be suppressed nonlinearly. All analyses are verified by numerical simulation. The findings are applied to a recently proposed GAM excitation experiment on the DIIID tokamak.

Third harmonic stimulated Raman backscattering of laser in a magnetized plasma
View Description Hide DescriptionThis article studies the nonlinear Raman shifted third harmonic backscattering of an intense extraordinary laser wave through a homogenous transversely magnetized cold plasma. Due to the relativistic nonlinearity, the plasma dynamic is modified in the presence of transversely magnetic field, and this can generate the third harmonic scattered wave and an electrostatic upper hybrid wave via the Raman scattering process. Using the nonlinear wave equation, the mechanism of nonlinear third harmonic Raman scattering is discussed in detail to obtain the maximum growth rate of instability in the mildly relativistic regime. The growth rate decreases as the static magnetic field increases. It also increases with the pump wave amplitude.

Resistive magnetohydrodynamic reconnection: Resolving longterm, chaotic dynamics
View Description Hide DescriptionIn this paper, we address the longterm evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (gridadaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shockcapturing, conservative, gridadaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shockcapturing, high order finite differences, and particle in celllike methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.

One and twophoton ionization of hydrogen atom embedded in Debye plasmas
View Description Hide DescriptionWe present a detailed analysis of the plasmainduced resonancelike atomic structures near the ionization threshold in one and twophoton ionization of hydrogen atom. Such resonancelike structures result from the migration of the upper bound excited states of boundbound atomic transitions into the continuum due to the less attractive screened Coulomb potential which simulates the external environmental effect for an atom embedded in Debye plasma. The change from the resonancelike narrow structures into broad continuous spectra as the plasma effect increases could be accounted for by the overlap between the respective wavefunctions of the atomic electron in the initial state and its corresponding outgoing ionized state in the continuum.

Eulerian simulations of collisional effects on electrostatic plasma waves
View Description Hide DescriptionThe problem of collisions in a plasma is a wide subject with a huge historical literature. In fact, the description of realistic plasmas is a tough problem to attack, both from the theoretical and the numerical point of view. In this paper, a Eulerian timesplitting algorithm for the study of the propagation of electrostatic waves in collisional plasmas is presented. Collisions are modeled through onedimensional operators of the FokkerPlanck type, both in linear and nonlinear forms. The accuracy of the numerical code is discussed by comparing the numerical results to the analytical predictions obtained in some limit cases when trying to evaluate the effects of collisions in the phenomenon of wave plasma echo and collisional dissipation of BernsteinGreeneKruskal waves. Particular attention is devoted to the study of the nonlinear Dougherty collisional operator, recently used to describe the collisional dissipation of electron plasma waves in a pure electron plasma column [M. W. Anderson and T. M. O'Neil, Phys. Plasmas 14, 112110 (2007)]. Finally, for the study of collisional plasmas, a recipe to set the simulation parameters in order to prevent the filamentation problem can be provided, by exploiting the property of velocity diffusion operators to smooth out small velocity scales.

Study on longitudinal dispersion relation in onedimensional relativistic plasma: Linear theory and Vlasov simulation
View Description Hide DescriptionThe dispersion relation of onedimensional longitudinal plasma waves in relativistic homogeneous plasmas is investigated with both linear theory and Vlasov simulation in this paper. From the VlasovPoisson equations, the linear dispersion relation is derived for the proper onedimensional Jüttner distribution. Numerically obtained linear dispersion relation as well as an approximate formula for plasma wave frequency in the long wavelength limit is given. The dispersion of longitudinal wave is also simulated with a relativistic Vlasov code. The real and imaginary parts of dispersion relation are well studied by varying wave number and plasma temperature. Simulation results are in agreement with established linear theory.

Influence of ionization on reflection of solitary waves in a magnetized plasma
View Description Hide DescriptionThe reflection of nonlinear solitary waves is studied in a nonuniform, magnetized plasma diffusing from an ionization source along the magnetic field lines. Contribution of the ionization term is included in the continuity equation. The behavior of solitary waves is governed by modified form of Korteweg–de Vries equation (called mKdV equation). In order to investigate the reflection of solitary waves, the mKdV equations for the right and left going waves are derived, and solved by finding new transformations coupled at the point of reflection, for obtaining the expression of reflection coefficient. Contrary to the case of usual inhomogeneous plasma, the present analysis shows that a combination of usual sech 2 structure and tanh structure (called the tail of soliton) arises due to the influence of ionization term. Interestingly, this tailing structure disappears after the reflection of the soliton and hence, the soliton is downshifted prominently.

On the singularity of the VlasovPoisson system
View Description Hide DescriptionThe VlasovPoisson system can be viewed as the collisionless limit of the corresponding FokkerPlanckPoisson system. It is reasonable to expect that the result of Landau damping can also be obtained from the FokkerPlanckPoisson system when the collision frequency ν approaches zero. However, we show that the collisionless VlasovPoisson system is a singular limit of the collisional FokkerPlanckPoisson system, and Landau's result can be recovered only as the ν approaches zero from the positive side.

Thomson scattering measurement of a shock in laserproduced counterstreaming plasmas
View Description Hide DescriptionWe report the first direct measurement of temporally and spatially resolved plasma temperatures at a shock as well as its spatial structure and propagation in laserproduced counterstreaming plasmas. Two shocks are formed in counterstreaming collisionless plasmas early in time, and they propagate opposite directions. This indicates the existence of counterstreaming collisionless flows to keep exciting the shocks, even though the collisional effects increase later in time. The shock images are observed with optical diagnostics, and the upstream and downstream plasma parameters of one of the shocks are measured using Thomson scattering technique.

Magnetic ramp scale at supercritical perpendicular collisionless shocks: Full particle electromagnetic simulations
View Description Hide DescriptionSupercritical perpendicular collisionless shocks are known to exhibit foot, ramp, and overshoot structures. The shock ramp structure is in a smaller scale in contrast to other microstructures (foot and overshoot) within the shock front. Onedimensional full particle simulations of strictly perpendicular shocks over wide ranges of ion beta , Alfvén Mach number MA , and iontoelectron mass ratio mi /me are presented to investigate the impact of plasma parameters on the shock ramp scale. Main results are (1) the ramp scale can be as small as several electron inertial length. (2) The simulations suggest that in a regime below the critical ion beta value, the shock front undergoes a periodic selfreformation and the shock ramp scale is timevarying. At higher ion beta values, the shock front selfreformation is smeared. At still higher ion beta value, the motion of reflected ions is quite diffuse so that they can lead to a quasisteady shock ramp. Throughout the above three conditions, the shock ramp thickness increases with . (3) The increase (decrease) in Mach number and the decrease (increase) in the beta value have almost equivalent impact on the state (i.e., stationary or nonstationary) of the shock ramp. Both of front and ramp thicknesses are increased with MA .

Axisymmetric curvaturedriven instability in a model divertor geometry
View Description Hide DescriptionA model problem is presented which qualitatively describes a pressuredriven instability which can occur near the nullpoint in the divertor region of a tokamak where the poloidal field becomes small. The model problem is described by a horizontal slot with a vertical magnetic field which plays the role of the poloidal field. Linetying boundary conditions are applied at the planes defining the slot. A toroidal field lying parallel to the planes is assumed to be very strong, thereby constraining the possible structure of the perturbations. Axisymmetric perturbations which leave the toroidal field unperturbed are analyzed. Ideal magnetohydrodynamics is used, and the instability threshold is determined by the energy principle. Because of the boundary conditions, the Euler equation is, in general, nonseparable except at marginal stability. This problem may be useful in understanding the source of heat transport into the private flux region in a snowflake divertor which possesses a large region of small poloidal field, and for code benchmarking as it yields simple analytic results in an interesting geometry.

Gyroinduced acceleration of magnetic reconnection
View Description Hide DescriptionThe linear and nonlinear evolution of magnetic reconnection in collisionless hightemperature plasmas with a strong guide field is analyzed on the basis of a twodimensional gyrofluid model. The linear growth rate of the reconnecting instability is compared to analytical calculations over the whole spectrum of linearly unstable wave numbers. In the strongly unstable regime (large ), the nonlinear evolution of the reconnecting instability is found to undergo two distinctive acceleration phases separated by a stall phase in which the instantaneous growth rate decreases. The first acceleration phase is caused by the formation of strong electric fields close to the Xpoint due to ion gyration, while the second acceleration phase is driven by the development of an open Petscheklike configuration due to both ion and electron temperature effects. Furthermore, the maximum instantaneous growth rate is found to increase dramatically over its linear value for decreasing diffusion layers. This is a consequence of the fact that the peak instantaneous growth rate becomes weakly dependent on the microscopic plasma parameters if the diffusion region thickness is sufficiently smaller than the equilibrium magnetic field scale length. When this condition is satisfied, the peak reconnection rate asymptotes to a constant value.