Volume 23, Issue 6, June 2016

The expansion of a magnetized highpressure plasma into a lowpressure ambient medium is examined with particleincell simulations. The magnetic field points perpendicular to the plasma's expansion direction and binary collisions between particles are absent. The expanding plasma steepens into a quasielectrostatic shock that is sustained by the lowerhybrid (LH) wave. The ambipolar electric field points in the expansion direction and it induces together with the background magnetic field a fast E cross B drift of electrons. The drifting electrons modify the background magnetic field, resulting in its pileup by the LH shock. The magnetic pressure gradient force accelerates the ambient ions ahead of the LH shock, reducing the relative velocity between the ambient plasma and the LH shock to about the phase speed of the shocked LH wave, transforming the LH shock into a nonlinear LH wave. The oscillations of the electrostatic potential have a larger amplitude and wavelength in the magnetized plasma than in an unmagnetized one with otherwise identical conditions. The energy loss to the drifting electrons leads to a noticeable slowdown of the LH shock compared to that in an unmagnetized plasma.
 LETTERS


Structural and phase transformations in zinc and brass wires under heating with highdensity current pulse
View Description Hide DescriptionThe work is focused on revealing the mechanism of structure and phase transformations in the metal wires under heating with a highdensity current pulse (the electric explosion of wires, EEWs). It has been demonstrated on the example of brass and zinc wires that the transition of a current pulse with the density of j ≈ 3.3 × 10^{7} A/cm^{2} results in homogeneous heating of the crystalline structure of the metal/alloy. It has been determined that under heating with a pulse of highdensity current pulse, the electric resistance of the liquid phases of zinc and brass decreases as the temperature increases. The results obtained allow for a conclusion that the presence of the particles of the condensed phase in the expanding products of EEW is the result of overheating instabilities in the liquid metal.

Experimental observation of turbulence transition and a critical gradient threshold for trapped electron mode in tokamak plasmas
View Description Hide DescriptionIn HL2A and JTEXT ohmic confinement regimes, an electrostatic turbulence with quasicoherent characteristics in spectra of density fluctuations was observed by multichannel microwave reflectometers. These quasicoherent modes (QCMs) were detectable in a large plasma region (). The characteristic frequencies of QCMs were in the range of 30–140 kHz. The mode is rotated in the electron diamagnetic direction. In the plasmas with QCMs, trapped electron mode (TEM) was predicted to be unstable by gyrokinetic simulations. The combined experimental results show that the TEM is survived in the linear ohmic confinement regime of plasmas. The quasicoherent TEM was replaced by broadband fluctuations when the plasma transits from linear to saturated ohmic confinement regime. The observation was strongly related to the turbulence transition from TEM to ion temperature gradient mode. A critical gradient threshold for TEM excitation in electron temperature gradient was directly found. The effect of TEM on density profile peaking was presented.

Transport and deceleration of fusion products in microturbulence
View Description Hide DescriptionThe velocityspace distribution of alpha particles born in fusion devices is subject to modification at moderate energies due to turbulent transport. Therefore, one must calculate the evolution of an equilibrium distribution whose functional form is not known a priori. Using a novel technique, applicable to any trace impurity, we have made this calculation for fully nonlinear gyrokinetic simulations not only possible but also particularly efficient. We demonstrate a microturbulenceinduced departure from the local slowingdown distribution, an inversion of the energy distribution, and associated modifications to the alpha heating and pressure profiles in an ITERlike scenario.
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 MINITUTORIAL


Stringent limitations on reductive perturbation studies of nonplanar acoustic solitons in plasmas
View Description Hide DescriptionMore than fifty years ago, the Kortewegde Vries equation was shown to describe not only solitary surface waves on shallow water, but also nonlinear ionacoustic waves. Because of the algorithmic ease of using reductive perturbation theory, intensive research followed on a wide range of wave types. Soon, the formalism was extended to nonplanar modes by introducing a stretching designed to accommodate spherically and cylindrically symmetric ionacoustic waves. Over the last two decades many authors followed this approach, but almost all have ignored the severe restrictions in parameter space imposed by the Ansatz. In addition, for other steps in the formalism, the justification is often not spelled out, leading to effects that are physically undesirable or ambiguous. Hence, there is a need to critically assess this approach to nonplanar modes and to use it with the utmost care, respecting the restrictions on its validity. Only inward propagation may be meaningfully studied and respect for weak nonlinearities of at most 1/10 implies that one cannot get closer to the axis or centre of symmetry than about 30 Debye lengths. Thus, one is in a regime where the modes are quasiplanar and not particularly interesting. Most papers disregard these constraints and hence reach questionable conclusions.
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 TUTORIAL


Validation metrics for turbulent plasma transport
View Description Hide DescriptionDeveloping accurate models of plasma dynamics is essential for confident predictive modeling of current and future fusion devices. In modern computer science and engineering, formal verification and validation processes are used to assess model accuracy and establish confidence in the predictive capabilities of a given model. This paper provides an overview of the key guiding principles and best practices for the development of validation metrics, illustrated using examples from investigations of turbulent transport in magnetically confined plasmas. Particular emphasis is given to the importance of uncertainty quantification and its inclusion within the metrics, and the need for utilizing synthetic diagnostics to enable quantitatively meaningful comparisons between simulation and experiment. As a starting point, the structure of commonly used global transport model metrics and their limitations is reviewed. An alternate approach is then presented, which focuses upon comparisons of predicted local fluxes, fluctuations, and equilibrium gradients against observation. The utility of metrics based upon these comparisons is demonstrated by applying them to gyrokinetic predictions of turbulent transport in a variety of discharges performed on the DIIID tokamak [J. L. Luxon, Nucl. Fusion 42, 614 (2002)], as part of a multiyear transport model validation activity.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Derivation of the Hall and extended magnetohydrodynamics brackets
View Description Hide DescriptionThere are several plasma models intermediate in complexity between ideal magnetohydrodynamics (MHD) and twofluid theory, with Hall and Extended MHD being two important examples. In this paper, we investigate several aspects of these theories, with the ultimate goal of deriving the noncanonical Poisson brackets used in their Hamiltonian formulations. We present fully Lagrangian actions for each, as opposed to the fully Eulerian, or mixed EulerianLagrangian, actions that have appeared previously. As an important step in this process, we exhibit each theory's two advected fluxes (in analogy to ideal MHD's advected magnetic flux), discovering also that with the correct choice of gauge they have corresponding Liedragged potentials resembling the electromagnetic vector potential, and associated conserved helicities. Finally, using the EulerLagrange map, we show how to derive the noncanonical Eulerian brackets from canonical Lagrangian ones.

Numerical analysis of electrostatic ion cyclotron instability in an electronpositronion plasma
View Description Hide DescriptionThis paper presents a theoretical study of the effects of positron density on the electrostatic ion cyclotron instability in an electronpositronion plasma using the kinetic theory approach. It is supposed that positrons and electrons can drift parallel to the magnetic field either in the same or the opposite directions. The dispersion relation for the electrostatic ion cyclotron waves in an electronpositronion plasma is derived, and the numerical results are investigated. It is found that an increase in positron concentration increases the critical drift velocity for excitation of the instability in both configurations. It is also found that as the positron concentration increases the growth rate of instability decreases. In addition, it is shown that at low velocities the maximum instability growth rate for the unidirectional case is higher than the counterstreaming case; however, after a certain velocity, the maximum growth rate in the counterstreaming case dominates that of the unidirectional case.

Spinelectron acoustic waves: The Landau damping and ion contribution in the spectrum
View Description Hide DescriptionSeparated spinup and spindown quantum kinetics is derived for more detailed research of the spinelectron acoustic waves (SEAWs). This kinetic theory allows us to obtain the spectrum of the SEAWs including the effects of occupation of quantum states more accurately than the quantum hydrodynamic theory. We derive and apply the quantum kinetic theory to calculate the Landau damping of the SEAWs. We consider the contribution of ions dynamics into the SEAW spectrum. We obtain the contribution of ions in the Landau damping in the temperature regime of classic ions. Kinetic analysis for the ionacoustic, zero sound, and Langmuir waves at the separated spinup and spindown electron dynamics is presented as well.

Weakly relativistic electromagnetic solitons in warm plasmas
View Description Hide DescriptionFor slowly propagating electromagnetic solitons, validity of the cold plasma model is addressed using a more realistic model involving effects arising due to temperature as well as ion dynamics. Small amplitude single peak structures which are quasineutral are studied, and different regions of existence of bright and dark classes of solitons are delineated. Influence of temperature on spectral characteristics of the solitary structures is presented.

Kinetic calculation of the resistive wall mode and fishbonelike mode instability in tokamak
View Description Hide DescriptionKinetic effects of both trapped thermal and energetic particles on the resistive wall mode (RWM) and on the fishbonelike mode (FLM) are investigated in theory. Here, the trapped thermal particles include both ions and electrons. The FLM is driven by trapped energetic particles. The results demonstrate that thermal particle collisions can either stabilize or destabilize the RWM, depending on the energetic particle pressure . Furthermore, the critical value of for triggering the FLM is increased when the thermal particle contribution is taken into account. The critical value sensitively depends on the plasma collision frequency. In addition, the plasma inertia is found to have a negligible influence on the FLM.

Instability of surface electron cyclotron TMmodes influenced by nonmonochromatic alternating electric field
View Description Hide DescriptionThe influence of nonmonochromaticity of an external alternating electric field on excitation of TM eigenmodes at harmonics of the electron cyclotron frequency is considered here. These TMmodes propagate along the plasma interface in a metal waveguide. An external static constant magnetic field is oriented perpendicularly to the plasma interface. The problem is solved theoretically using the kinetic VlasovBoltzmann equation for description of plasma particles motion and the Maxwell equations for description of the electromagnetic mode fields. The external alternating electric field is supposed to be a superposition of two waves, whose amplitudes are different and their frequencies correlate as 2:1. An infinite set of equations for electric field harmonics of these modes is derived with the aid of nonlinear boundary conditions. This set is solved using the wave packet approach consisting of the main harmonic frequency and two nearest satellite temporal harmonics. Analytical studies of the obtained set of equations allow one to find two different regimes of parametric instability, namely, enhancement and suppression of the instability. Numerical analysis of the instability is carried out for the three first electron cyclotron harmonics.

Variational formulations of guidingcenter VlasovMaxwell theory
View Description Hide DescriptionThe variational formulations of guidingcenter VlasovMaxwell theory based on Lagrange, Euler, and EulerPoincaré variational principles are presented. Each variational principle yields a different approach to deriving guidingcenter polarization and magnetization effects into the guidingcenter Maxwell equations. The conservation laws of energy, momentum, and angular momentum are also derived by Noether method, where the guidingcenter stress tensor is now shown to be explicitly symmetric.

The general dielectric tensor for bikappa magnetized plasmas
View Description Hide DescriptionIn this paper, we derive the dielectric tensor for a plasma containing particles described by an anisotropic superthermal (bikappa) velocity distribution function. The tensor components are written in terms of the twovariables kappa plasma special functions, recently defined by Gaelzer and Ziebell [Phys. Plasmas 23, 022110 (2016)]. We also obtain various new mathematical properties for these functions, which are useful for the analytical treatment, numerical implementation, and evaluation of the functions and, consequently, of the dielectric tensor. The formalism developed here and in the previous paper provides a mathematical framework for the study of electromagnetic waves propagating at arbitrary angles and polarizations in a superthermal plasma.

Confinement time of electron plasma approaching magnetic pumping transport limit in small aspect ratio Cshaped torus
View Description Hide DescriptionA long confinement time of electron plasma, approaching magnetic pumping transport limit, has been observed in SMARTEXC (a small aspect ratio partial torus with ). Investigations of the growth rate reveal that they are governed by instabilities like resistive wall destabilization, ion driven instabilities, and electronneutral collisions. Successful confinement of electron plasmas exceeding poloidal rotations lasting for nearly is achieved by suppressing these instabilities. The confinement time has been estimated in two ways: (a) from the frequency scaling of the linear diocotron mode launched from sections of the wall that are also used as capacitive probes and (b) by dumping the plasma onto a charge collector at different hold times.

The effect of exchangecorrelation coefficient in quantum semiconductor plasma in presence of electronphonon collision frequency
View Description Hide DescriptionThe influence of exchangecorrelation potential, quantum Bohm term, and degenerate pressure on the nature of solitary waves in a quantum semiconductor plasma is investigated. It is found that an amplitude and a width of the solitary waves change with variation of different parameters for different semiconductors. A deformed Kortewegde Vries equation is obtained for propagation of nonlinear waves in a quantum semiconductor plasma, and the effects of different plasma parameters on the solution of the equation are also presented.

Particleincell simulation study of a lowerhybrid shock
View Description Hide DescriptionThe expansion of a magnetized highpressure plasma into a lowpressure ambient medium is examined with particleincell simulations. The magnetic field points perpendicular to the plasma's expansion direction and binary collisions between particles are absent. The expanding plasma steepens into a quasielectrostatic shock that is sustained by the lowerhybrid (LH) wave. The ambipolar electric field points in the expansion direction and it induces together with the background magnetic field a fast E cross B drift of electrons. The drifting electrons modify the background magnetic field, resulting in its pileup by the LH shock. The magnetic pressure gradient force accelerates the ambient ions ahead of the LH shock, reducing the relative velocity between the ambient plasma and the LH shock to about the phase speed of the shocked LH wave, transforming the LH shock into a nonlinear LH wave. The oscillations of the electrostatic potential have a larger amplitude and wavelength in the magnetized plasma than in an unmagnetized one with otherwise identical conditions. The energy loss to the drifting electrons leads to a noticeable slowdown of the LH shock compared to that in an unmagnetized plasma.

Chirpdriven giant phase space vortices
View Description Hide DescriptionIn a collisionless, unbounded, onedimensional plasma, modelled using periodic boundary conditions, formation of steady state phase space coherent structures or phase space vortices (PSV) is investigated. Using a high resolution onedimensional VlasovPoisson solver based on piecewiseparabolic advection scheme, the formation of giant PSV is addressed numerically. For an infinitesimal external drive amplitude and wavenumber k, we demonstrate the existence of a window of chirped external drive frequency that leads to the formation of giant PSV. The linear, small amplitude, external drive, when chirped, is shown to couple effectively to the plasma and increase both streaming of “untrapped” and “trapped” particle fraction. The steady state attained after the external drive is turned off and is shown to lead to a giant PSV with multiple extrema and phase velocities, with excess density fraction, defined as the deviation from the Maxwellian background, . It is shown that the process depends on the chirp time duration Δt. The excess density fraction Δn/n 0, which contains both trapped and untrapped particle contribution, is also seen to scale with Δt, only inhibited by the gradient of the distribution in velocity space. Both single step drive and multistep chirp processes are shown to lead to steady state giant PSV, with multiple extrema due to embedded holes and clumps, long after the external drive is turned off.

Excitation of THz hybrid modes in an elliptical dielectric rod waveguide with a cold collisionless unmagnetized plasma column by an annular electron beam
View Description Hide DescriptionThe dispersion relation of electromagnetic waves propagating in an elliptical plasma waveguide with a cold collisionless unmagnetized plasma column and a dielectric rod is studied analytically. The frequency spectrum of the hybrid waves and the growth rate for excitation of the waves by a thin annular relativistic elliptical electron beam (TAREEB) is obtained. The effects of relative permittivity constant of dielectric rod, geometrical dimensions, plasma frequency, accelerating voltage, and current density of TAREEB on the growth rate and frequency spectra of the waveguide will be investigated.

The spectrum of the Sedov–Taylor point explosion linear stability
View Description Hide DescriptionThe linear stability of the spherical selfsimilar Sedov–Taylor blast wave (BW) with a front expanding in a uniform ideal gas with adiabatic index , according to , is studied. The Sedov–Taylor BW (STBW) is crucial to understand the complex structures of late supernova remnants as the STBW has been shown to give rise to the Vishniac instability (VI) [E. T. Vishniac, Astrophys. J. 274, 152 (1983)] and to the Ryu–Vishniac instability (RVI) [D. Ryu and E. T. Vishniac, Astrophys. J. 313, 820 (1987)]. However, these approaches are questionable for several reasons, and especially because they do not provide the same result, in opposition to what could be expected from a physical viewpoint, in the limit . We have revisited the RVI and the VI in great detail by taking great care of the behavior close to the center of symmetry of the configuration where the perturbation of the STBW might diverge. Our method allows one to find new spectra for the growth rate of the instability in terms of the mode number . Two spectrum types are derived: (i) a continuous spectrum for which no dispersion relation can be found, and (ii) a discrete spectrum for which a dispersion relation can be derived. The case (i) is new and could provide the explanation why a set of various numerical simulations (or experiments) of the same STBW problem will not most likely give the same result. The second aspect (ii) is also new for at least two reasons aside the strange structure of the discrete spectrum. First, any dispersion curve contains two types of portions: some portions correspond to growth rates with no singularity at all for the perturbed solution at the origin, while for the other portions of the dispersion curve, divergences of the perturbed STBW might exist except for the pressure. Second, it is shown that for any given value of , no growth rate can exist above an upper limit for the mode number . Finally, our model reconciles the VI and the RVI, and it is demonstrated that both analyses lead to a common analytical dispersion relation for .

Nonmodal theory of the kinetic ion temperature gradient driven instability of plasma shear flows across the magnetic field
View Description Hide DescriptionThe temporal evolution of the kinetic ion temperature gradient driven instability and of the related anomalous transport of the ion thermal energy of plasma shear flow across the magnetic field is investigated analytically. This instability develops in a steady plasma due to the inverse ion Landau damping and has the growth rate of the order of the frequency when the ion temperature is equal to or above the electron temperature. The investigation is performed employing the nonmodal methodology of the shearing modes which are the waves that have a static spatial structure in the frame of the background flow. The solution of the governing linear integral equation for the perturbed potential displays that the instability experiences the nonmodal temporal evolution in the shearing flow during which the unstable perturbation becomes very different from a canonical modal form. It transforms into the nonmodal structure with vanishing frequency and growth rate with time. The obtained solution of the nonlinear integral equation, which accounts for the random scattering of the angle of the ion gyromotion due to the interaction of ions with ensemble of shearing waves, reveals similar but accelerated process of the transformations of the perturbations into the zero frequency structures. It was obtained that in the shear flow the anomalous ion thermal conductivity decays with time. It is a strictly nonmodal effect, which originates from the temporal evolution of the shearing modes turbulence.