Volume 22, Issue 7, July 2015
Index of content:

The magnetized shock problem is studied in the context where supersonic plasma flows past a solid obstacle. This problem exhibits interesting and important phenomena such as a bow shock, magnetotail formation, reconnection, and plasmoid formation. This study is carried out using a discontinuous Galerkin method to solve an extended magnetohydrodynamic model (XMHD). The main goals of this paper are to present a reasonably complete picture of the properties of this interaction using the MHD model and then to compare the results to the XMHD model. The inflow parameters, such as the magnetosonic Mach number Mf and the ratio of thermal pressure to magnetic pressure β, can significantly affect the physical structures of the flowobstacle interaction. The Hall effect can also significantly influence the results in the regime in which the ion inertial length is numerically resolved. Most of the results presented are for the twodimensional case; however, two threedimensional simulations are presented to make a connection to the important case in which the solar wind interacts with a solid body and to explore the possibility of performing scaled laboratory experiments.
 LETTERS


Coupling of transit time instabilities in electrostatic confinement fusion devices
View Description Hide DescriptionA model of the behavior of transit time instabilities in an electrostatic confinement fusion reactor is presented in this letter. It is demonstrated that different modes are excited within the spherical cathode of a Farnsworth fusor. Each of these modes is dependent on the fusion products as well as the acceleration voltage applied between the two electrodes and they couple to a resulting oscillation showing nonlinear beat phenomena. This type of instability is similar to the transit time instability of electrons between two resonant surfaces but the presence of ions and the occurring fusion reactions alter the physics of this instability considerably. The physics of this plasma instability is examined in detail for typical physical parameter ranges of electrostatic confinement fusion devices.

New regime of low ion collisionality in the neoclassical equilibrium of tokamak plasmas
View Description Hide DescriptionThe neoclassical description of an axisymmetric toroidal plasma equilibrium is formulated for an unconventionally low ordering of the collisionality that suits realistic thermonuclear fusion conditions. This requires a driftkinetic analysis to the second order of the ion Larmor radius, which yields a new contribution to the leading solution for the nonMaxwellian part of the ion distribution function if the equilibrium geometry is not updown symmetric. An explicit geometrical factor weighs this second Larmorradius order, lowcollisionality effect that modifies the neoclassical ion parallel flow, and the ion contribution to the bootstrap current.

 TUTORIAL


Designing a tokamak fusion reactor—How does plasma physics fit in?
View Description Hide DescriptionThis paper attempts to bridge the gap between tokamak reactor design and plasma physics. The analysis demonstrates that the overall design of a tokamak fusion reactor is determined almost entirely by the constraints imposed by nuclear physics and fusion engineering. Virtually, no plasma physics is required to determine the main design parameters of a reactor: . The one exception is the value of the toroidal current , which depends upon a combination of engineering and plasma physics. This exception, however, ultimately has a major impact on the feasibility of an attractive tokamak reactor. The analysis shows that the engineering/nuclear physics design makes demands on the plasma physics that must be satisfied in order to generate power. These demands are substituted into the wellknown operational constraints arising in tokamak physics: the Troyon limit, Greenwald limit, kink stability limit, and bootstrap fraction limit. Unfortunately, a tokamak reactor designed on the basis of standard engineering and nuclear physics constraints does not scale to a reactor. Too much current is required to achieve the necessary confinement time for ignition. The combination of achievable bootstrap current plus current drive is not sufficient to generate the current demanded by the engineering design. Several possible solutions are discussed in detail involving advances in plasma physics or engineering. The main contribution of the present work is to demonstrate that the basic reactor design and its plasma physics consequences can be determined simply and analytically. The analysis thus provides a crisp, compact, logical framework that will hopefully lead to improved physical intuition for connecting plasma physic to tokamak reactor design.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Exchange Coulomb interaction in nanotubes: Dispersion of Langmuir waves
View Description Hide DescriptionThe microscopic derivation of the Coulomb exchange interaction for electrons located on the nanotubes is presented. The derivation is based on the manyparticle quantum hydrodynamic method. We demonstrate the effect of curvature of the nanocylinders on the force of exchange interaction. We calculate corresponding dispersion dependencies for electron oscillations on the nanotubes.

Computational extended magnetohydrodynamical study of shock structure generated by flows past an obstacle
View Description Hide DescriptionThe magnetized shock problem is studied in the context where supersonic plasma flows past a solid obstacle. This problem exhibits interesting and important phenomena such as a bow shock, magnetotail formation, reconnection, and plasmoid formation. This study is carried out using a discontinuous Galerkin method to solve an extended magnetohydrodynamic model (XMHD). The main goals of this paper are to present a reasonably complete picture of the properties of this interaction using the MHD model and then to compare the results to the XMHD model. The inflow parameters, such as the magnetosonic Mach number Mf and the ratio of thermal pressure to magnetic pressure β, can significantly affect the physical structures of the flowobstacle interaction. The Hall effect can also significantly influence the results in the regime in which the ion inertial length is numerically resolved. Most of the results presented are for the twodimensional case; however, two threedimensional simulations are presented to make a connection to the important case in which the solar wind interacts with a solid body and to explore the possibility of performing scaled laboratory experiments.

Kinetic theory of the filamentation instability in a collisional currentdriven plasma with nonextensive distribution
View Description Hide DescriptionThe evolution of filamentation instability in a weakly ionized currentcarrying plasma with nonextensive distribution was studied in the diffusion frequency region, taking into account the effects of electronneutral collisions. Using the kinetic theory, Lorentz transformation formulas, and BhatnagarGrossKrook collision model, the generalized dielectric permittivity functions of this plasma system were achieved. By obtaining the dispersion relation of lowfrequency waves, the possibility of filamentation instability and its growth rate were investigated. It was shown that collisions can increase the maximum growth rate of instability. The analysis of temporal evolution of filamentation instability revealed that the growth rate of instability increased by increasing the qparameter and electron drift velocity. Finally, the results of Maxwellian and qnonextensive velocity distributions were compared and discussed.

Shocks in unmagnetized plasma with a shear flow: Stability and magnetic field generation
View Description Hide DescriptionA pair of curved shocks in a collisionless plasma is examined with a twodimensional particleincell simulation. The shocks are created by the collision of two electronion clouds at a speed that exceeds everywhere the threshold speed for shock formation. A variation of the collision speed along the initially planar collision boundary, which is comparable to the ion acoustic speed, yields a curvature of the shock that increases with time. The spatially varying Mach number of the shocks results in a variation of the downstream density in the direction along the shock boundary. This variation is eventually equilibrated by the thermal diffusion of ions. The pair of shocks is stable for tens of inverse ion plasma frequencies. The angle between the mean flow velocity vector of the inflowing upstream plasma and the shock's electrostatic field increases steadily during this time. The disalignment of both vectors gives rise to a rotational electron flow, which yields the growth of magnetic field patches that are coherent over tens of electron skin depths.

Nonlinear damping of a finite amplitude whistler wave due to modified two stream instability
View Description Hide DescriptionA twodimensional, fully kinetic, particleincell simulation is used to investigate the nonlinear development of a parallel propagating finite amplitude whistler wave (parent wave) with a wavelength longer than an ion inertial length. The cross field current of the parent wave generates shortscale whistler waves propagating highly oblique directions to the ambient magnetic field through the modified twostream instability (MTSI) which scatters electrons and ions parallel and perpendicular to the magnetic field, respectively. The parent wave is largely damped during a time comparable to the wave period. The MTSIdriven damping process is proposed as a cause of nonlinear dissipation of kinetic turbulence in the solar wind.

Kinetic description of linear wave propagation in inhomogeneous, nonstationary, anisotropic, weakly magnetized, and collisional plasma
View Description Hide DescriptionThis paper addresses the linear propagation of an electron wave in a plasma whose distribution function, at zero order in the wave amplitude, may be chosen arbitrarily, provided that it is not strongly peaked at the wave phase velocity, and that it varies very little over one wave period and one wavelength. Then, from first principles is derived an equation for the wave action density that allows for Landau damping, whose rate is calculated at first order in the variations of the wave number and frequency. Moreover, the effect of collisions is accounted for in a way that adapts to any choice for the collision operator in Boltzmann equation. The wave may also be externally driven, so that the results presented here apply to stimulated Raman scattering.

Influence of wall plasma on microwave frequency and power in relativistic backward wave oscillator
View Description Hide DescriptionThe RF breakdown of the slow wave structure (SWS), which will lead to the generation of the wall plasma, is an important cause for pulse shortening in relativistic backward wave oscillators. Although many researchers have performed profitable studies about this issue, the influence mechanism of this factor on the microwave generation still remains notsoclear. This paper simplifies the wall plasma with an “effective” permittivity and researches its influence on the microwave frequency and power. The dispersion relation of the SWS demonstrates that the introduction of the wall plasma will move the dispersion curves upward to some extent, which is confirmed by particleincell (PIC) simulations and experiments. The plasma density and volume mainly affect the dispersion relation at the upper and lower frequency limits of each mode, respectively. Meanwhile, PIC simulations show that even though no direct power absorption exists since the wall plasma is assumed to be static, the introduction of the wall plasma may also lead to the decrease in microwave power by changing the electrodynamic property of the SWS.

Electromagnetic fluctuations in magnetized plasmas. I. The rigorous relativistic kinetic theory
View Description Hide DescriptionUsing the system of the Klimontovich and Maxwell equations, the general linear fluctuation theory for magnetized plasmas is developed. General expressions for the electromagnetic fluctuation spectra (electric and magnetic fields) from uncorrelated plasma particles in plasmas with a uniform magnetic field are derived, which are covariantly correct within the theory of special relativity. The general fluctuation spectra hold for plasmas of arbitrary composition, arbitrary momentum dependences of the plasma particle distribution functions, and arbitrary orientations of the wave vector with respect to the uniform magnetic field. Moreover, no restrictions on the values of the real and the imaginary parts of the frequency are made. The derived fluctuation spectra apply to both noncollective fluctuations and collective plasma eigenmodes in magnetized plasmas. In the latter case, kinetic equations for the components of fluctuating electric and magnetic fields in magnetized plasmas are derived that include the effect of spontaneous emission and absorption. In the limiting case of an unmagnetized plasmas, the general fluctuation spectra correctly reduce to the unmagnetized fluctuation spectra derived before.

Magnetic antenna excitation of whistler modes. III. Group and phase velocities of wave packets
View Description Hide DescriptionThe properties of whistler modes excited by single and multiple magnetic loop antennas have been investigated in a large laboratory plasma. A single loop excites a wavepacket, but an array of loops across the ambient magnetic field excites approximate plane whistler modes. The single loop data are measured. The array patterns are obtained by linear superposition of experimental data shifted in space and time, which is valid in a uniform plasma and magnetic field for small amplitude waves. Phasing the array changes the angle of wave propagation. The antennas are excited by an rf tone burst whose propagating envelope and oscillations yield group and phase velocities. A single loop antenna with dipole moment across excites wave packets whose topology resembles m = 1 helicon modes, but without radial boundaries. The phase surfaces are conical with propagation characteristics of Gendrin modes. The cones form near the antenna with comparable parallel and perpendicular phase velocities. A physical model for the wave excitation is given. When a wave burst is applied to a phased antenna array, the wave front propagates both along the array and into the plasma forming a “whistler wing” at the front. These laboratory observations may be relevant for excitation and detection of whistler modes in space plasmas.

Magnetic antenna excitation of whistler modes. IV. Receiving antennas and reciprocity
View Description Hide DescriptionAntenna radiation patterns are an important property of antennas. Reciprocity holds in free space and the radiation patterns for exciting and receiving antennas are the same. In anisotropic plasmas, radiation patterns are complicated by the fact that group and phase velocities differ and certain wave properties like helicity depend on the direction of wave propagation with respect to the background magnetic field B 0. Interference and wave focusing effects are different than in free space. Reciprocity does not necessarily hold in a magnetized plasma. The present work considers the properties of various magnetic antennas used for receiving whistler modes. It is based on experimental data from exciting low frequency whistler modes in a large uniform laboratory plasma. By superposition of linear waves from different antennas, the radiation patterns of antenna arrays are derived. Plane waves are generated and used to determine receiving radiation patterns of different receiving antennas. Antenna arrays have radiation patterns with narrow lobes, whose angular position can be varied by physical rotation or electronic phase shifting. Reciprocity applies to broadside antenna arrays but not to end fire arrays which can have asymmetric lobes with respect to B 0. The effect of a relative motion between an antenna and the plasma has been modeled by the propagation of a short wave packet moving along a linear antenna array. An antenna moving across B 0 has a radiation pattern characterized by an oscillatory “whistler wing.” A receiving antenna in motion can detect any plane wave within the group velocity resonance cone. The radiation pattern also depends on loop size relative to the wavelength. Motional effects prevent reciprocity. The concept of the radiation pattern loses its significance for wave packets since the received signal does not only depend on the antenna but also on the properties of the wave packet. The present results are of fundamental interest and of relevance to loop antennas in space.

Remarkable connections between extended magnetohydrodynamics models
View Description Hide DescriptionThrough the use of suitable variable transformations, the commonality of all extended magnetohydrodynamics (MHD) models is established. Remarkable correspondences between the Poisson brackets of inertialess Hall MHD and inertial MHD (which has electron inertia, but not the Hall drift) and extended MHD (which has both effects) are established. The helicities (two in all) for each of these models are obtained through these correspondences. The commonality of all the extended MHD models is traced to the existence of two Liedragged 2forms, which are closely associated with the canonical momenta of the two underlying species. The Liedragging of these 2forms by suitable velocities also leads to the correct equations of motion. The Hall MHD Poisson bracket is analyzed in detail, the Jacobi identity is verified through a detailed proof, and this proof ensures the Jacobi identity for the Poisson brackets of all the models.

Linear and nonlinear evolution of the ion resonance instability in cylindrical traps: A numerical study
View Description Hide DescriptionNumerical experiments have been performed to investigate the linear and nonlinear dynamics, and energetics of the ion resonance instability in cylindrically confined nonneutral plasma. The instability is excited on a set of parametrically different unstable equilibria of a cylindrical nonneutral cloud, composed of electrons partially neutralized by a much heavier ion species of single ionization. A particleincell code has been developed and employed to carry out these simulations. The results obtained from the initial exponential growth phase of the instability in these numerical experiments are in agreement with the linearised analytical model of the ion resonance instability. As the simulations delve much further in time beyond the exponential growth phase, very interesting nonlinear phenomena of the ion resonance instability are revealed, such as a process of simultaneous wave breaking of the excited poloidal mode on the ion cloud and pinching of the poloidal perturbations on the electron cloud. This simultaneous nonlinear dynamics of the two components is associated with an energy transfer process from the electrons to the ions. At later stages there is heating induced crossfield transport of the heavier ions and tearing across the pinches on the electron cloud followed by an inverse cascade of the torn sections.

Electromagnetic drift waves dispersion for arbitrarily collisional plasmas
View Description Hide DescriptionThe impacts of the electromagnetic effects on resistive and collisionless drift waves are studied. A local linear analysis on an electromagnetic driftkinetic equation with BhatnagarGrossKrooklike collision operator demonstrates that the model is valid for describing linear growth rates of drift wave instabilities in a wide range of plasma parameters showing convergence to reference models for limiting cases. The waveparticle interactions drive collisionless driftAlfvén wave instability in low collisionality and high beta plasma regime. The Landau resonance effects not only excite collisionless drift wave modes but also suppress high frequency electron inertia modes observed from an electromagnetic fluid model in collisionless and low beta regime. Considering ion temperature effects, it is found that the impact of finite Larmor radius effects significantly reduces the growth rate of the driftAlfvén wave instability with synergistic effects of high beta stabilization and Landau resonance.

Investigating the effect of integration constants and various plasma parameters on the dynamics of the soliton in different physical plasmas
View Description Hide DescriptionThe nonlinear dynamics and propagation of ion acoustic waves in a relativistic and ideal plasmas, which have the pressure variation of electrons and ions and degenerate electrons, are investigated using the analytic solution of KdV type equations performed applying expansion and expansion methods. The effects of various parameters, such as phase velocity of the ion acoustic wave, the ratio of ion temperature to electron temperature, normalized speed of light, electron and ion streaming velocities, arbitrary and integration constants, on the soliton dynamics are studied. We have found that dim and hump solitons and their amplitudes, widths and dynamics strongly depend on these plasma parameters and integration constants. The source term μ plays also a vital role in the formation of the solitons. Moreover, it is also found that the observed solitary wave solution can be excited from hump soliton to dip soliton. This dramatic change of the solitons can occur due to the various values of the integration constants and ion streaming velocities. Finally, it is important to note that the analytic solutions of the nonlinear equation, reported in this study, could be used to explain the structures of solitons in the astrophysical space and in laboratory plasmas.

Runaway electron generation as possible trigger for enhancement of magnetohydrodynamic plasma activity and fast changes in runaway beam behavior
View Description Hide DescriptionPeculiar phenomena were observed during experiments with runaway electrons: rapid changes in the synchrotron spot and its intensity that coincided with stepwise increases in the electron cyclotron emission (ECE) signal (cyclotron radiation of suprathermal electrons). These phenomena were initially observed in TEXTOR (Tokamak Experiment for Technology Oriented Research), where these events only occurred in the current decay phase or in discharges with thin stable runaway beams at a q = 1 drift surface. These rapid changes in the synchrotron spot were interpreted by the TEXTOR team as a fast pitch angle scattering event. Recently, similar rapid changes in the synchrotron spot and its intensity that coincided with stepwise increases in the nonthermal ECE signal were observed in the EAST (Experimental Advanced Superconducting Tokamak) runaway discharge. Runaway electrons were located around the q = 2 rational magnetic surface (ringlike runaway electron beam). During the EAST runaway discharge, stepwise ECE signal increases coincided with enhanced magnetohydrodynamic (MHD) activity. This behavior was peculiar to this shot. In this paper, we show that these nonthermal ECE steplike jumps were related to the abrupt growth of suprathermal electrons induced by bursting electric fields at reconnection events during this MHD plasma activity. Enhancement of the secondary runaway electron generation also occurred simultaneously. Local changes in the currentdensity gradient appeared because of local enhancement of the runaway electron generation process. These currentdensity gradient changes are considered to be a possible trigger for enhancement of the MHD plasma activity and the rapid changes in runaway beam behavior.

Particles trajectories in magnetic filaments
View Description Hide DescriptionThe motion of a particle in a spatially harmonic magnetic field is a basic problem involved, for example, in the mechanism of formation of a collisionless shock. In such settings, it is generally reasoned that particles entering a Weibel generated turbulence are trapped inside it, provided their Larmor radius in the peak field is smaller than the field coherence length. The goal of this work is to put this heuristic conclusion on firm ground by studying, both analytically and numerically, such motion. A toy model is analyzed, consisting of a relativistic particle entering a region of space occupied by a spatially harmonic field. The particle penetrates the magnetic structure in a direction aligned with the magnetic filaments. Although the conclusions are not trivial, the main result is confirmed.
 Nonlinear Phenomena, Turbulence, Transport

Collisionless relaxation of downstream ion distributions in lowMach number shocks
View Description Hide DescriptionCollisionlessly formed downstream distributions of ions in lowMach number shocks are studied. General expressions for the asymptotic value of the ion density and pressure are derived for the directly transmitted ions. An analytical approximation for the overshoot strength is suggested for the lowβ case. Spatial damping scale of the downstream magnetic oscillations is estimated.