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The wandering of magnetic field lines is an important topic in theoretical plasma physics and astrophysics. Previous analytical work, as well as computer simulations, is based on magnetostatic models to warrant mathematical and numerical tractability. Recently, we have studied the first time field line random walk in dynamical turbulence by using a field line tracing method. These calculations were performed for a slab model of the turbulence. It is the purpose of the present paper to use the latter method to compute the field line diffusion coefficient for dynamical two-dimensional turbulence. Two models for the dynamical correlation function are used, namely the damping model of dynamical turbulence and the nonlinear anisotropic dynamical turbulence model. It is shown that the largest scales of the turbulence and the choice of the dynamical turbulence model have a strong influence on the diffusivity of the field lines and the absolute value of the diffusion coefficient. [ABSTRACT FROM AUTHOR]

Proton imaging is a powerful tool for probing electromagnetic fields in a plasma, providing a path-integrated map of the field topology. However, in cases where the field structure is highly inhomogeneous, inferring spatial properties of the underlying field from proton images can be difficult. This problem is exemplified by recent experiments, which used proton imaging to probe the filamentary magnetic field structures produced by the Weibel instability in collisionless counterstreaming plasmas. In this paper, we perform analytical and numerical analyses of proton images of systems containing many magnetic filaments. We find that, in general, the features observed on proton images do not directly correspond to the spacing between magnetic filaments (the magnetic wavelength) as has previously been assumed and that they instead correspond to the filament size. We demonstrate this result by Fourier analysis of synthetic proton images for many randomized configurations of magnetic filaments. Our results help guide the interpretation of experimental proton images of filamentary magnetic structures in plasmas. [ABSTRACT FROM AUTHOR]

In this paper, a coaxial gyrotron with a double electron beam is investigated on the ohmic loss, starting current, mode competition, and beam wave interaction. Its beam-wave interaction equation and dependence of the starting current on the static magnetic field and parameter K (the ratio of the current of an electron beam to the total current of a double electron beam) are given. On this basis, a 4 MW 170 GHz coaxial gyrotron with a double electron beam is studied. By the numerical calculation, the influence of K on the starting current is analyzed under a given static magnetic field and at different guiding center radii of the double electron beam. Studies show that the ability of the gyrotron to suppress the mode competition has a relation with the selection of the guiding center radii of the two electron beams. Then, the investigation of a time-dependent multi-mode competition of the gyrotron is performed, which shows that the gyrotron can stably operate in the T E 38 , 18 − mode. The results show that by considering the ohmic loss, the gyrotron can operate at 170.4 GHz with the output power of 4.04 MW and the beam-wave interaction efficiency of 35.47% when B = 6.82 T, U = 88 KV, I = 129 A, and K = 0.4. Each of the two electron beams in the gyrotron has different beam-wave interaction efficiencies. Compared to the coaxial gyrotron with one electron beam, the beam-wave interaction efficiency of each electron beam in the coaxial gyrotron with a double electron beam has a different increase. [ABSTRACT FROM AUTHOR]

Implosions of (quasi-)spherical loads with mass redistribution and displacement modification are investigated numerically. Both methods can theoretically counterbalance the nonuniformity of magnetic pressure along the load surface and realize quasi-spherical Z-pinch implosions. Mass redistribution is feasible for spherical loads with large radius and weight, while the displacement modification is more suitable for light loads, such as those composed of wire arrays. Simulation results suggest that, for mass redistributed spherical loads, wall instabilities induced by polar mass flows will deform the imploding shell. For prolate spherical loads, in which the wall instability cannot develop, the kinetic energy distribution is disturbed at high latitude. These passive behaviors and their possible mitigation methods, such as reshaping the electrode, are investigated numerically in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the formation of ring-shaped and gyro-phase restricted velocity distribution functions (VDFs) at the edges of a cloud of protons injected into non-uniform distributions of the electromagnetic field. The velocity distribution function is reconstructed using the forward test-kinetic method. We consider two profiles of the electric field: (1) a non-uniform E-field obtained by solving the Laplace equation consistent with the conservation of the electric drift and (2) a constant and uniform E-field. In both cases, the magnetic field is similar to the solutions obtained for tangential discontinuities. The initial velocity distribution function is Liouville mapped along numerically integrated trajectories. The numerical results show the formation of an energy-dispersed structure due to the energy-dependent displacement of protons towards the edges of the cloud by the gradient-B drift. Another direct effect of the gradient-B drift is the formation of ring-shaped velocity distribution functions within the velocity-dispersed structure. Higher energy particles populate the edges of the proton beam, while smaller energies are located in the core. Non-gyrotropic velocity distribution functions form on the front-side and trailing edge of the cloud; this effect is due to remote sensing of energetic particles with guiding centers inside the beam. The kinetic features revealed by the test-kinetic solutions have features similar to in-situ velocity distribution functions observed by Cluster satellites in the magnetotail, close to the neutral sheet. [ABSTRACT FROM AUTHOR]

Plasma from the Earth’s magnetosheath has previously been observed inside the magnetosphere. Inhomogeneities in the magnetosheath plasma, here called plasmoids, can impact the magnetopause and doing so set up a polarizing field that allows it to penetrate the magnetopause and enter the magnetosphere. A set of simulations of plasmoids with different dimensions is presented in this paper. For plasmoids that are longer than those previously published, waves propagating upstream from the barrier are found. It is also found that the penetration process causes the part of the plasmoid that is upstream of the barrier to rotate. The role of plasmoid width and cross sectional shape in penetration is studied, and for plasmoids that are less than half an ion gyroradius wide, the plasmoid is compressed to obtain a vertically oriented elliptical cross section, regardless of the initial shape. When the initial plasmoid width exceeds the ion gyroradius, the plasmoid still penetrates through a mechanism involving a potential that propagates upstream from the magnetic barrier. [ABSTRACT FROM AUTHOR]

Lower-hybrid drift and Buneman instabilities operate in current sheets with or without the guide field. The lower-hybrid drift instability is a universal instability in that it operates for all parameters. In contrast, the excitation of Buneman instability requires sufficiently thin current sheet. That is, the relative electron-ion drift speed must exceed the threshold in order for Buneman instability to operate. Traditionally, the two instabilities were treated separately with different mathematical formalisms. In a recent paper, an improved electrostatic dispersion relation was derived that is valid for both unstable modes [P. H. Yoon and A. T. Y. Lui, Phys. Plasmas 15, 072101 (2008)]. However, the actual numerical analysis was restricted to a one-dimensional situation. The present paper generalizes the previous analysis and investigates the two-dimensional nature of both instabilities. It is found that the lower-hybrid drift instability is a flute mode satisfying k·B=0 and k·∇n=0, where k represents the wave number for the most unstable mode, B stands for the total local magnetic field, and ∇n is the density gradient. This finding is not totally unexpected. However, a somewhat surprising finding is that the Buneman instability is a field-aligned mode characterized by k×B=0 and k·∇n=0, rather than being a beam-aligned instability. [ABSTRACT FROM AUTHOR]

In this paper, the generation of high-quality and high-energy micro electron beam in vacuum by a chirped Gaussian laser pulse in the presence of an axial magnetic field is numerically investigated. The features of energy and angular spectra, emittances, and position distribution of electron beam are compared in two cases, i.e., in the presence and absence of an external magnetic field. The electron beam is accelerated with higher energy and qualified in spatial distribution in the presence of the magnetic field. The presence of an axial magnetic field improves electron beam spatial quality as well as its gained energy through keeping the electron motion parallel to the direction of propagation for longer distances. It has been found that a 64 μm electron bunch with about MeV initial energy becomes a 20 μm electron beam with high energy of the order of GeV, after interacting with a laser pulse in the presence of an external magnetic field. [ABSTRACT FROM AUTHOR]

Experimental data compiled over five decades of dense plasma focus research are consistent with the snowplow model of sheath propagation, based on the hypothetical balance between magnetic pressure driving the plasma into neutral gas ahead and "wind pressure" resisting its motion. The resulting sheath velocity, or the numerically proportional "drive parameter," is known to be approximately constant for devices optimized for neutron production over 8 decades of capacitor bank energy. This paper shows that the validity of the snowplow hypothesis, with some correction, as well as the non-dependence of sheath velocity on device parameters, have their roots in local conservation laws for mass, momentum, and energy coupled with the ionization stability condition. Both upper and lower bounds on sheath velocity are shown to be related to material constants of the working gas and independent of the device geometry and capacitor bank impedance. [ABSTRACT FROM AUTHOR]

The plasma scrape-off layer (SOL) in a tokamak is characterized by ion flow down a long narrow flux tube terminating on a solid surface. The ion flow velocity along a magnetic field line can be equal to or greater than sonic at the entrance of a Debye sheath or upstream in the presheath. This paper presents a numerical study of the transition between subsonic and supersonics flows. A quasineutral one-dimensional (1D) fluid code has been used for modeling of plasma transport in the SOL along magnetic field lines, both in steady state and under transient conditions. The model uses coupled equations for continuity, momentum, and energy balance with ionization, radiation, charge exchange, and recombination processes. The recycled neutrals are described in the diffusion approximation. Standard Bohm sheath criterion is used as boundary conditions at the material surface. Three conditions conducive for the generation of supersonic flows in SOL plasmas have been explored. It is found that in steady state high (attached) and low (detached) divertor temperatures cases, the role of particle, momentum, and energy loss is critical. For attached case, the appearance of shock waves in the divertor region if the incoming plasma flow is supersonic and its effect on impurity retention is presented. In the third case, plasma expansion along the magnetic field can yield time-dependent supersonic solutions in the quasineutral rarefaction wave. Such situations can arise in the parallel transport of intermittent structures such as blobs and edge localized mode filaments along field lines. [ABSTRACT FROM AUTHOR]

In this paper we extend the new techniques of W. Tierens and D. D. Zutter, J. Comput. Phys. 231, 5144 (2012) to include finite Larmor radius effects up to second order in the Larmor radius. We limit ourselves to the case of propagation perpendicular to the background magnetic field Bvector 0. We show that our time-domain technique is able to produce the lowest-order Bernstein wave (a wave believed to be useful for heating fusion devices [H. P. Laqua, Plasma Phys. Controlled Fusion 49, R1 (2007)]). The discrete equations retain many of the favourable properties described in W. Tierens and D. D. Zutter, J. Comput. Phys. 231, 5144 (2012), i.e., unconditional stability and a straightforward relation between the second-order accurate continuous dispersion relation and the dispersion relation of the discretized problem. The theory is illustrated by a place-independent and a place-dependent temperature numerical example. [ABSTRACT FROM AUTHOR]

A novel large-orbit electron gun with a gradual reversal of the magnetic field for the 8 mm third-harmonic peniotron is numerically studied in this paper. In the permanent magnetic condition, an electron beam with axial velocity spread of 4.78%, guiding center deviation of 7.18%, and velocity ratio of 2.2 is generated in the gun, satisfying the special requirements of beam-wave interaction in the third-harmonic peniotron. Compared with the traditional three stage method, it is unnecessary here to generate a thin tubular electron beam before the reversal point and the mutational distribution of reversal magnetic field. In addition, the emission band can be placed in the area of axial magnetic field where its magnitude decreases gradually, which reduces the structure complexity and the difficulties in tube-making process greatly. Finally, the peniotron is predicted to yield an output power of 31.9 kW at 30 GHz, with its microwave conversion efficiency of up to 49.4%, which shows the perfect matching between its high frequency system and its electron-optical system. According to the numerical calculations, the device performance is very sensitive to the relative axial position between the magnetic system and the electrode system. If the magnetic system shifts 0.8 mm to the right, the device efficiency would decrease from 49.4% to 31.7%. This phenomenon provides meaningful information in the device hot-test. [ABSTRACT FROM AUTHOR]

In this paper, the effects of magnetic field gradient (i.e., the magnetic field transition layer effects) on the Rayleigh-Taylor instability (RTI) with continuous magnetic field and density profiles are investigated analytically. The transition layers of magnetic field and density with two different typical profiles are studied and the analytic expressions of the linear growth rate of the RTI are obtained. It is found that the magnetic field effects strongly reduce the linear growth rate of the RTI, especially when the perturbation wavelength is short. The linear growth rate of the RTI increases with the thickness of the magnetic field transition layer, especially for the case of small thickness of the magnetic field transition layer. When the magnetic field transition layer width is long enough, the linear growth rate of the RTI can be saturated. Thus when one increases the width of the magnetic field transition layer, the linear growth rate of the RTI increases only in a certain range, which depends on the magnetic field strength. The numerical results are compared with the analytic linear growth rates and they agree well with each other. [ABSTRACT FROM AUTHOR]

The Rayleigh-Taylor instability arises whenever two fluids with different densities are arranged such that the heavier fluid sits above the lighter fluid, with a sharp interface in between. The magnetic Rayleigh-Taylor instability has the further complication due to the presence of a magnetic field throughout both media. The two fluids in question may also have differing magnetic properties, such as the magnetic permeability. When the fluids in consideration are in fact plasmas comprised of charged particles, induced currents, magnetic fields, and Lorentz forces can all act in ways that will affect the stability of the system. Stable base flows exist for the 2D case, and small sinusoidal disturbances to the base flow will grow in the unstable scenario. The numerical method described in this paper calculates the growth of the interface in the nonlinear regime, since closed form solutions are obtained only in the linear approximation. Through the analysis of both the fluid and magnetic vorticities and streamfunctions, the simulated results can be explained from the principles of magnetohydrodynamics. A range of simulations is presented, looking at cases with different initial conditions, cases with strong and weak magnetic fields, and cases with magnetic fields oriented at different angles relative to the interface of the two fluids. It is shown in particular how different initial conditions give rise to outcomes that are very different in terms of the geometry of the interface between the two fluids, primarily the differences between a single mode disturbance and a multimode disturbance to the interface at time t = 0. [ABSTRACT FROM AUTHOR]

In recent work, a technique was developed to extract high quality beams from single-component plasmas confined in a Penning-Malmberg trap in a 4.8 T magnetic field. In this paper, a procedure is developed to extract these beams from the confining magnetic field and then focus them to create especially tailored electrostatic beams. Electron beams are extracted from the field in two stages: they are first transported to a region of reduced field (1 mT), and then taken to zero field with a nonadiabatic, fast extraction. Once in the field-free region, the beams are focused using an Einzel lens. Experimental results and numerical simulations are presented to illustrate the extraction and focusing process. Theoretical expressions are developed to describe the modifications to the relevant beam energy and spatial distributions. Where possible, analytic expressions are presented for the case relevant here of beams with Gaussian radial profiles. Beam emittance considerations are discussed as well as prospects for further development of these techniques. Application of these techniques to provide high-quality positron beams is also discussed. [ABSTRACT FROM AUTHOR]

Magnetic fields are an essential component of a plasma. In many astrophysical, solar, magnetospheric, and laboratory situations the magnetic field in the plasma can be very dynamic and form highly complex structures. One approach to unraveling these structures is to determine the magnetic skeleton of the field, a set of topological features that divide the magnetic field into topologically distinct domains. In general, the features of the magnetic skeleton are difficult to locate, in particular those given by numerical experiments. In this paper, we propose a new set of tools to find the skeleton of general magnetic fields including null points, spines, separatrix surfaces, and separators. This set of tools is found to be considerably better at finding the skeleton than the currently favored methods used in magnetohydrodynamics. [ABSTRACT FROM AUTHOR]

The paper investigates the role of relative motion between the fluid components of a plasma model, which is simulated by concatenation of two anisotropic magnetohydrodynamic (MHD) fluids, on the propagation of low-frequency waves and instabilities. The gyrotropic pressure of both the MHD components is given by generalized polytropic laws that allow the system to reduce to a variety of states. The linearized analysis is carried out and dispersion relation is derived using the normal mode technique. The dispersion relation, which gives numerous earlier results as special cases, is discussed both analytically as well as numerically for parameters appropriate for the space plasma. It is found that the relative motion between the two components, besides modifying the condition for fire-hose instability, causes the concatenated system to exhibit different kinds of relative ordering of the magnitudes of phase speeds of the various MHD modes in the directions parallel and antiparallel to the magnetic field. The relative motion between the components also influences the phase relationship between density and magnetic field fluctuations for the various compressive modes in the background ambient plasma. [ABSTRACT FROM AUTHOR]

Previous work on asymmetry-induced transport in a modified Malmberg–Penning trap showed that the radial particle flux was empirically constrained to be of the form Γ(ε)=-(B0/B)1.33D(ε)[∇n0+f(ε)], where ε=ω-lωR, ωR(r)=vθ/r is the column rotation frequency, ω and l are the asymmetry frequency and azimuthal mode number, ∇n0 is the radial density gradient, B is the magnetic field, B0 is an empirical constant, and D(ε) and f(ε) are unknown functions. In this paper, it is shown that further constraints can be placed upon D(ε) and f(ε) by comparing data near the ε=0 points to a first order expansion of Γ(ε). It is shown that dD/dε(0)≠0, in contradiction to resonant particle theory, and that f(ε) can only be a fraction of the size predicted by that theory. Finally, it is shown that dD/dε(0) exhibits a power-law scaling with radius, magnetic field, and the bias of the center conductor of the trap. [ABSTRACT FROM AUTHOR]

In this paper, memory and nonlocal effects on fluctuating mass diffusion are addressed in the context of fusion plasmas. Nonlocal effects are included by considering a diffusivity coefficient depending on the size of the container in the transverse direction to the applied magnetic field. It is obtained by resorting to the general formulation of the extended version of irreversible thermodynamics in terms of the higher order dissipative fluxes. The developed model describes two different types of the particle density time correlation function. Both have been observed in tokamak and nontokamak devices. These two kinds of time correlation function characterize the wave and the diffusive transport mechanisms of particle density perturbations. A transition between them is found, which is controlled by the size of the container. A phase diagram in the {L,2π/k} space describes the relation between the dynamics of particle density fluctuations and the size L of the system together with the oscillating mode k of the correlation function. [ABSTRACT FROM AUTHOR]

Drift wave turbulence is known to self-organize to form axisymmetric macroscopic flows. The basic mechanism for macroscopic flow generation is called inverse energy cascade. Essentially, it is an energy transfer from the short wavelengths to the long wavelengths in the turbulent spectrum due to nonlinear interactions. A class of macroscopic flows, the poloidally symmetric zonal flows, is widely recognized as a key constituent in nearly all cases and regimes of microturbulence, also because of the realization that zonal flows are a critical agent of self-regulation for turbulent transport. In tokamaks and other toroidal magnetic confinement systems, axisymmetric flows exist in two branches, a zero frequency branch and a finite frequency branch, named Geodesic Acoustic Modes (GAMs). The finite frequency is due to the geodesic curvature of the magnetic field. There is a growing body of evidence that suggests strong GAM activity in most devices. Theoretical investigation of the GAMs is still an open field of research. Part of the difficulty of modelling the GAMs stems from the requirement of running global codes. Another issue is that one cannot determine a simple one to one relation between turbulence stabilization and GAM activity. This paper focuses on the study of ion temperature gradient turbulence in realistic tokamak magnetohydrodynamic equilibria. Analytical and numerical analyses are applied to the study of geometrical effects on zonal flows oscillations. Results are shown on the effects of the plasma elongation on the GAM amplitude and frequency and on the zonal flow residual amplitude. [ABSTRACT FROM AUTHOR]

The moment equation approach to neoclassical transport is used to calculate neoclassical particle and heat fluxes, impurity transport, the ambipolar electric field, and momentum damping rates. These equations are often written in Hamada coordinates which makes it easier to obtain analytic solutions. However, previous simplifying assumptions used to evaluate the basis vectors analytically are often invalid for advanced stellarator configurations. In this paper, a numerical method is presented by which the Hamada basis set can be determined for an arbitrary three dimensional toroidal confinement device by integrating along a magnetic field line. The method is applied to the magnetic configuration in the Helically Symmetric Experiment [F. S. B. Anderson, A. F. Almagri, D. T. Anderson, P. G. Matthews, J. N. Talmadge, and J. L. Shohet, Fusion Technol. 27, 273 (1995)] and compared to the large-aspect-ratio tokamak approximation to the basis set. The results indicate that the numerical technique is a more accurate method to specify the basis vectors, especially in a device with negligible toroidal curvature. [ABSTRACT FROM AUTHOR]

Using a separated spin evolution quantum hydrodynamic model, we have derived generalized formula for drift effects of electrons in the inhomogeneous and nonuniform magnetized spin quantum plasma. We report, for the first time, the appearance of new spin dependent drift along with grad-B drift and diamagnetic drift. These results can be used to study the drift effects on various waves and instabilities. To check the applicability of our results, we have derived the dispersion relation of ordinary-mode (O-mode) incorporating electron spin, gradient in density, and magnetic field. We have studied various new features due to electron spin, perpendicular spin drifts, and grad B on the propagation of O-mode. Numerical analysis is presented for the choice of laboratory plasma parameters. [ABSTRACT FROM AUTHOR]

The effect of ion temperature, magnitude of magnetic field and its orientation on a magnetized plasma sheath consisting of electrons and two species of positive ions are investigated. Using three-fluid hydrodynamic model and some dimensionless variables, the dimensionless equations are obtained and solved numerically. It is found that with the increase of the ion temperature and magnetic field strength there is a significant change in ion densities and energies in the sheath. It is also noticed that increase of magnetic field angle enhances the ion density near the sheath edge for a constant ion temperature. With increase in ion temperature and magnetic field angle, the lighter ion density near the sheath edge enhances and reverses for the heavier ion species. [ABSTRACT FROM AUTHOR]

A reversed shear Alfvén eigenmodes (RSAEs) theory has been developed for reversed magnetic field shear plasmas when the safety factor minimum, qmin , is at or above a rational value. The modes we study are known sometimes as either the bottom of the frequency sweep or the down sweeping RSAEs. We show that, strictly speaking, the ideal MHD theory is not compatible with the eigenmode solution in the reversed shear plasma with qmin above integer values. Corrected by a special analytic finite Larmor radius (FLR) condition, MHD dispersion of these modes nevertheless can be developed. Numerically, MHD structure can serve as a good approximation for the RSAEs.The large radial scale part of the analytic RSAE solution can be obtained from ideal MHD and expressed in terms of the Legendre functions. The kinetic equation with FLR effects for the eigenmode is solved numerically and agrees with the analytic solutions. Properties of RSAEs and their potential implications for plasma diagnostics are discussed. [ABSTRACT FROM AUTHOR]

The dynamics of ablated plasmas of wire-array Z-pinches are studied numerically in (r,θ) geometry by using the magnetohydrodynamic (MHD) simulation model in which the mass injection boundary conditions are presented, and two-dimensional spatio-temporal distributions of magnetic field and precursor current during the ablation phase are obtained. The ablated-plasma dynamics contains four processes: drifting toward the axis, arriving at the axis and forming the precursor column, and contraction and expansion of the precursor column. The relationship among the maximum inward velocity of ablated plasma streams and the initial wire array parameters is analyzed and it is found that this velocity is relatively sensitive to the change of inter-wire separation but weakly depends on the original array radius. The results are in reasonable agreement with the experiments on MAGPIE facility. The origin of the current flow in the precursor plasmas is analyzed from the point of view of the B-field convection in (r,θ) plane. The dynamics of ablation streams determine the distribution of magnetic field and the current density Jz inside the wire array. The precursor current can be approximately calculated by the integral of Jz inside the region of a radius near to the column. In this model, the fraction of precursor current is less than 10% of the total current, which is close to the experimental results. When the current waveform is fixed, the increase of the inter-wire gap or decrease of the initial radius will lead to the increase of the precursor current. [ABSTRACT FROM AUTHOR]

In order to study the effect of magnetic field strength on low frequency oscillation in Hall thrusters, experiments were carried out with different operating parameters. Experimental results show that the effect of magnetic field strength on the low frequency oscillation changes with operating parameters. In the decline zone of magnetoampere characteristic curve, low frequency oscillation increases with the increase of magnetic field strength at low mass flow rate, while decreases with the increase of magnetic field strength at high mass flow rate. With further experiments and numerical simulations, it is found that the change of electron current at low mass flow rate and the change of ion current at high mass flow rate account for the variations of low frequency oscillation. Finally, the physical analysis is performed. [ABSTRACT FROM AUTHOR]

Two-dimensional stationary nontearing inertial scale electron magnetohydrodynamic (EMHD) instability is described. The physical mechanism of the instability is illustrated. Analytical asymptotic estimate of the growth rate is provided and verified with a numerical calculation of the instability, also describing the characteristic structure of the eigenmode. Natural occurrence of the instability is demonstrated in a nonlinear EMHD simulation of a system undergoing magnetic reconnection, where the instability manifests itself on the outflow side of the magnetic field separatrix and may affect the self-determined length of the layer. [ABSTRACT FROM AUTHOR]

The interactions of a relativistic free electron with a pulsed electromagnetic (EM) plane wave in the presence of constant magnetic fields are studied using the well-known constants of motion. The goal is to determine the energy gained by the electron after the wave has passed. For a constant magnetic field along the axis of the wave, a general solution for the energy gain as a function of the vector potential describing the EM plane wave is obtained. Solutions for magnetic fields transverse to the axis of the wave are sought in the limit where the cyclotron frequency is much less than the wave frequency and are examined using several different profiles for the wave amplitude. For this case, an adiabatic invariant is found that shows that there is no energy gain when an EM plane wave comes and goes with a profile that is slowly varying in time with respect to the cyclotron motion. [ABSTRACT FROM AUTHOR]

A novel method to derive stationary solutions of the Vlasov–Maxwell system is established. This method is based on the assumption that the deviation of the velocity distribution from the Maxwell–Boltzmann distribution can be expanded by the Hermite polynomials. By applying our method, a new two-dimensional equilibrium is derived, which may provide an initial setup for investigations of three-dimensional collisionless reconnection of magnetic fields. [ABSTRACT FROM AUTHOR]

The relativistic motion of a charged particle in a uniform magnetic field and a circularly polarized electromagnetic wave propagating along the direction of magnetic field is studied. By manipulating the integrals of motion, some typical quantities of particle motion have been presented analytically in terms of explicit functions of three free parameters. The results may be of great importance for high-power microwave generation or particle acceleration. [ABSTRACT FROM AUTHOR]

Based on the numerical simulation of Kolmogorov entropy, the dynamic behavior is investigated for the relativistic electrons injected into the wiggler in a self-amplified spontaneous emission free-electron laser system. Results show an interesting phenomenon that the self-fields of the electron beam have an effect of stabilizing the electron's dynamic behavior. It is found that the adiabatic magnetic field of one-dimensional wiggler has trivial influence to the dynamic stability, although it is helpful to the electrons to enter the cavity smoothly. Moreover, the laser field deteriorates the stability of the electron's dynamic behavior as it grows exponentially and becomes very strong in the rear range. [ABSTRACT FROM AUTHOR]

The calculation of temperature in a plasma system that is not in thermal equilibrium remains a topic of debate. In our article [Dong and Paty, Phys. Plasmas 18, 030702 (2011)] we use the average kinetic energy to calculate the 'kinetic temperature' in a non-equilibrium system to quantify the heating of ions by low-frequency Alfvén waves in a partially ionized plasma (i.e., where collisions with neutrals can not be ignored). We implement a method previously used by Wang, Wu and Yoon [Wang, Wu and Yoon, Phys. Rev. Lett. 96, 125001 (2006)] and several others studying the effects of low frequency Alfvén waves in collisionless plasmas. This method is appropriate for several reasons discussed in this response. Most notably, we implement it to investigate heating of the plasma population since the bulk velocity of the particle ensemble perpendicular to the ambient magnetic field remains zero during the numerical experiment. [ABSTRACT FROM AUTHOR]

In a magnetized plasma with a temperature anisotropy T||>T⊥ (where || and ⊥ denote directions with respect to the uniform magnetic field B0), the nonresonant Weibel instability can develop and destabilize purely growing, ordinary plasma modes (k=k⊥). This paper presents a rigorous extended analysis of this instability on the basis of a new threshold b0(k), which enables to determine the instability conditions as well as the upper limits of the growth rates. Accurate analytical forms of the threshold conditions are provided here for the first time and for the full physical range of the temperature anisotropy and the parallel plasma beta. The marginal and threshold conditions for the plasma parameters, which directly lead to an instability of the ordinary mode, are explicitly derived numerically and analytically. The new analytical tools developed here provide premises for a comprehensive investigation of the interplay of this instability with the firehose instability, as they both can develop in the same conditions. [ABSTRACT FROM AUTHOR]

This paper investigates the filamentation instability of a non-relativistic electron beam passing through a periodic longitudinal magnetic field and an infinite uniform magnetized plasma. The linearized fluid-Maxwell equations are used to derive an equation for the dispersion relation of quantum magnetized plasma. The resulting dispersion equation is analyzed numerically over a wide range of system parameters. It is found that the growth rate of the filamentation instabilities is strongly affected by the strength of the periodic magnetic field. [ABSTRACT FROM AUTHOR]

The dynamics of self-generated magnetic B-fields produced following the interaction of a high contrast, high intensity (I>1019W cm-2) laser beam with thin (3 μm thick) solid (Al or Au) targets is investigated experimentally and numerically. Two main sources drive the growth of B-fields on the target surfaces. B-fields are first driven by laser-generated hot electron currents that relax over ~10-20 ps. Over longer timescales, the hydrodynamic expansion of the bulk of the target into vacuum also generates B-field induced by non-collinear gradients of density and temperature. The laser irradiation of the target front side strongly localizes the energy deposition at the target front, in contrast to the target rear side, which is heated by fast electrons over a much larger area. This induces an asymmetry in the hydrodynamic expansion between the front and rear target surfaces, and consequently the associated B-fields are found strongly asymmetric. The sole long-lasting (>30 ps) B-fields are the ones growing on the target front surface, where they remain of extremely high strength (~8-10 MG). These B-fields have been recently put by us in practical use for focusing laser-accelerated protons [B. Albertazzi et al., Rev. Sci. Instrum. 86, 043502 (2015)]; here we analyze in detail their dynamics and structure. [ABSTRACT FROM AUTHOR]

Electron transport across a magnetic field in a magnetic-layer-type Hall thruster was numerically investigated for the future predictive modeling of Hall thrusters. The discharge of a 1-kW-class magnetic-layer-type Hall thruster designed for high-specific-impulse operation was modeled using an r-z two-dimensional fully kinetic particle code with and without artificial electron-diffusion models. The thruster performance results showed that both electron transport models captured the experimental result within discrepancies less than 20% in thrust and discharge current for all the simulated operation conditions. The electron cross-field transport mechanism of the so-called anomalous diffusion was self-consistently observed in the simulation without artificial diffusion models; the effective electron mobility was two orders of magnitude higher than the value obtained using the classical diffusion theory. To account for the self-consistently observed anomalous transport, the oscillation of plasma properties was speculated. It was suggested that the enhanced random-walk diffusion due to the velocity oscillation of low-frequency electron flow could explain the observed anomalous diffusion within an order of magnitude. The dominant oscillation mode of the electron flow velocity was found to be 20 kHz, which was coupled to electrostatic oscillation excited by global ionization instability. [ABSTRACT FROM AUTHOR]

The properties of solitary kinetic Alfvén waves (SKAWs) in a finite β plasma with three dimensional non-extensive electrons are investigated. Numerical results show that there only exists sub-Alfvénic hump type SKAW. The down limit of the Alfvén Mach number Mz for the existence of SKAW increases with the increase of β. Whereas, it varies non-monotonously with respect to electron nonextensive parameter q for a given β. In the range of Mz where SKAWs exist for different values of q, a bigger q results in a denser soliton structure, making the magnitude of the static electric field along the background magnetic field enhanced. However, the dependence of the amplitudes of the perpendicular magnetic and electric field on q is non-monotonous. [ABSTRACT FROM AUTHOR]

The propagation of intense, short, sinusoidal laser pulses in a magnetized plasma channel has been studied. The wave equation governing the evolution of the radiation field is set up and a variational technique is used to obtain the equations describing the evolution of the laser spot size, pulse length and chirp parameter. Numerical methods are used to analyze the simultaneous evolution of these parameters. The effect of the external magnetic field on initially chirped as well as unchirped laser pulses on the spot size, pulse length and chirping has been analyzed. [ABSTRACT FROM AUTHOR]

Advanced divertors are magnetic geometries where a second X-point is added in the divertor region to address the serious challenges of burning plasma power exhaust. Invoking physical arguments, numerical work, and detailed model magnetic field analysis, we investigate the magnetic field structure of advanced divertors in the physically relevant region for power exhaust-the scrape-off layer. A primary result of our analysis is the emergence of a physical 'metric,' the Divertor Index DI, which quantifies the flux expansion increase as one goes from the main X-point to the strike point. It clearly separates three geometries with distinct consequences for divertor physics-the Standard Divertor (DI = 1), and two advanced geometries-the X-Divertor (XD, DI > 1) and the Snowflake (DI < 1). The XD, therefore, cannot be classified as one variant of the Snowflake. By this measure, recent National Spherical Torus Experiment and DIIID experiments are X-Divertors, not Snowflakes. [ABSTRACT FROM AUTHOR]

The hypothesis that stochastic magnetic fields disrupt zonal flows associated with ion temperature gradient turbulence saturation is investigated analytically with a residual flow calculation in the presence of magnetic flutter. The calculation starts from the time-asymptotic zero-beta residual flow of Rosenbluth and Hinton [Phys. Rev. Lett. 80, 724 (1998)] with the sudden application of an externally imposed, fixed magnetic field perturbation. The short-time electron response from radial charge loss due to magnetic flutter is calculated from the appropriate gyrokinetic equation. The potential evolution has quadratic behavior, with a zero crossing at finite time. The crossing time and its parametric dependencies are compared with numerical results from a gyrokinetic simulation of residual flow in the presence of magnetic flutter. The numerical and analytical results are in good agreement and support the hypothesis that the high-beta runaway of numerical simulations is a result of the disabling of zonal flows by finite-beta charge losses associated with magnetic flutter. [ABSTRACT FROM AUTHOR]

With reference to laboratory Q-machine studies we analyze the dynamics of a plasma diode under external forcing. Assuming a strong axial magnetic field, the problem is analyzed in one spatial dimension by a particle-in-cell code. The cathode is assumed to be operated in electron rich conditions, supplying an abundance of electrons. We compare different forcing schemes with the results obtained by solving the van der Pol equation. In one method of forcing we apply an oscillation in addition to the DC end plate bias and consider both amplitude and frequency variations. An alternative method of perturbation consists of modelling an absorbing grid at some internal position. Also in this case we can have a constant frequency with varying amplitude or alternatively an oscillation with chirped frequency but constant amplitude. We find that the overall features of the forced van der Pol equation are recovered, but the details in the plasma response need more attention to the harmonic responses, requiring extensions of the model equation. The analysis is extended by introducing collisional effects, where we emphasize charge exchange collisions of ions, since these processes usually have the largest cross sections and give significant modifications of the diode performance. In particular we find a reduction in oscillator frequency, although a linear scaling of the oscillation time with the system length remains also in this case. [ABSTRACT FROM AUTHOR]

A theoretical and numerical study of fast electron transport in solid and compressed fast ignition relevant targets is presented. The principal aim of the study is to assess how localized increases in the target density (e.g., by engineering of the density profile) can enhance magnetic field generation and thus pinching of the fast electron beam through reducing the rate of temperature rise. The extent to which this might benefit fast ignition is discussed. [ABSTRACT FROM AUTHOR]

The study of transport in magnetized plasmas is a problem of fundamental interest in controlled fusion, space plasmas, and astrophysics research. Three issues make this problem particularly challenging: (i) The extreme anisotropy between the parallel (i.e., along the magnetic field), χ|, and the perpendicular, χ⊥, conductivities (χ|/χ⊥ may exceed 1010 in fusion plasmas); (ii) Nonlocal parallel transport in the limit of small collisionality; and (iii) Magnetic field lines chaos which in general complicates (and may preclude) the construction of magnetic field line coordinates. Motivated by these issues, we present a Lagrangian Green's function method to solve the local and non-local parallel transport equation applicable to integrable and chaotic magnetic fields in arbitrary geometry. The method avoids by construction the numerical pollution issues of grid-based algorithms. The potential of the approach is demonstrated with nontrivial applications to integrable (magnetic island), weakly chaotic (Devil's staircase), and fully chaotic magnetic field configurations. For the latter, numerical solutions of the parallel heat transport equation show that the effective radial transport, with local and non-local parallel closures, is non-diffusive, thus casting doubts on the applicability of quasilinear diffusion descriptions. General conditions for the existence of non-diffusive, multivalued flux-gradient relations in the temperature evolution are derived. [ABSTRACT FROM AUTHOR]

A possibility of relaxation of an electronegative dusty plasma composed of two flowing ion species with stationary dust particles is explored. It is shown that magnetic field in such a system has the potential to self-organize giving rise to multiple Beltrami fields. When all the inertial and noninertial forces are taken into account, the relaxed state comes out to be a triple curl Beltrami field. On ignoring the inertia of lighter ions relative to heavy ones, double curl Beltrami field appears as a relaxed state which is equivalent to the superposition of two Beltrami fields. It shows the importance of inertia of plasma components in the formation of relaxed magnetic field structures. It is also shown numerically that scale separation allows the simultaneous existence of magnetic field and velocities varying at vastly different length scales. This gives rise to a dynamo mechanism at relaxed equilibrium. The study bears a strong relevance to the formation of multi scale structures in electronegative dusty plasmas, found in space and laboratory. [ABSTRACT FROM AUTHOR]

We analytically and numerically study the analogue of the Parker (magnetic buoyancy) instability in a uniformly rotating plasma screw pinch confined in a cylinder. Uniform plasma rotation is imposed to create a centrifugal acceleration, which mimics the gravity required for the classical Parker instability. The goal of this study is to determine how the Parker instability could be unambiguously identified in a weakly magnetized, rapidly rotating screw pinch, in which the rotation provides an effective gravity and a radially varying azimuthal field is controlled to give conditions for which the plasma is magnetically buoyant to inward motion. We show that an axial magnetic field is also required to circumvent conventional current driven magnetohydrodynamic (MHD) instabilities such as the sausage and kink modes that would obscure the Parker instability. These conditions can be realized in the Madison plasma Couette experiment (MPCX). Simulations are performed using the extended MHD code NIMROD for an isothermal compressible plasma model. Both linear and nonlinear regimes of the instability are studied, and the results obtained for the linear regime are compared with analytical results from a slab geometry. Based on this comparison, it is found that in a cylindrical pinch, the magnetic buoyancy mechanism dominates at relatively large Mach numbers (M > 5), while at low Mach numbers (M < 1), the instability is due to the curvature of magnetic field lines. At intermediate values of Mach number (1 < M < 5), the Coriolis force has a strong stabilizing effect on the plasma. A possible scenario for experimental demonstration of the Parker instability in MPCX is discussed. [ABSTRACT FROM AUTHOR]

A theory of wiggler pumped ion-channel free-electron laser (WPIC-FEL) and an axial magnetic field is presented. The motion of a relativistic electron is analyzed in the field configuration consisting of a helical wiggler magnetic field, a uniform axial magnetic field, and an electrostatic electric field produced by an ion-channel. An equation for the function [uppercase_phi_synonym], which determines the rate of change of axial velocity with energy, is derived. Numerical calculations are made to illustrate the effects of two electron beam guiding devices on the trajectories. By means of linear fluid theory, the sixth-degree polynomial dispersion equation for electromagnetic and space-charge waves is derived. The dependence of growth rate-frequency curves on the ion-channel frequency and axial magnetic field is studied numerically. [ABSTRACT FROM AUTHOR]

The theory of two-stream free electron lasers (FELs) consisting of a relativistic two stream electron beam transported along the axis of a planar wiggler in the presence of an ion-channel guiding was proposed and investigated. The electron trajectories and the small signal gain are derived. The characteristics of the linear gain and the normalized maximum gain are studied numerically. The comparison of the normalized gains by employing the axial magnetic field and ion-channel guiding in FEL has been studied numerically. The result shows that the maximum gain of the two-stream FEL is more than ten times stronger than conventional gain. Numerical results shown that in two-stream FEL with ion-channel guiding, the maximum value of maximum gain occurs at special range of two electron beam energy difference (Δγ = γ2 - γ1) and energy ratio (γ1/γ2). The results show that the normalized maximum gain in FEL with axial magnetic field is more than 20 times larger than that for using ion-channel guiding. [ABSTRACT FROM AUTHOR]

The effects of quantum statistic and quantum diffraction on the weakly two-dimensional fast quantum dusty magnetosonic wave propagating perpendicular to the external magnetic field are investigated by considering the inertialess electron, inertialess ion, and inertial cold dust in the low frequency limit. A Kadomstev-Petviashvili equation is derived for the magnetosonic solitary wave by using reductive perturbation method. The results show that the amplitude of soliton increases with the increasing of quantum diffraction effects of both electrons and ions, while the amplitude of the soliton decreases with the increasing of the quantum statistic effects. By using the numerical investigations, the interaction law of the nontrivial line-solitons with rich web structure in the interaction area among the line-solitons is studied by the Wronskian determinant method, which shows that there is no exchange of the energy, the momentum, and the angular momentum in the interaction. [ABSTRACT FROM AUTHOR]

In a tokamak disruption, a substantial fraction of the plasma current can be converted into runaway electrons. Although these are usually highly relativistic, their total energy is initially much smaller than that of the pre-disruption plasma. However, following a suggestion by Putvinski et al. [Plasma Phys. Controlled Fusion 39, B157 (1997)], it is shown that as the post-disruption plasma drifts toward the first wall, a non-negligible part of the energy contained in the poloidal magnetic field can be converted into kinetic energy of the runaway electrons. This process is simulated numerically, and it is found that in an ITER-like tokamak runaway electrons can gain kinetic energies up to about 70 MJ by this mechanism. [ABSTRACT FROM AUTHOR]

A scheme employing an external axial magnetic field is proposed to diagnose the intrinsic divergence of laser-generated fast electron beams, and this is studied numerically with hybrid simulations. The maximum beam radius of fast electrons increases with the initial divergence and decreases with the amplitude of the axial magnetic field. It is indicated that the intrinsic divergence of fast electrons can be inferred from measurements of the beam radius at different depth under the axial field. The proposed scheme here may be useful for future fast ignition experiments and in other applications of laser-generated fast electron beams. [ABSTRACT FROM AUTHOR]