Volume 20, Issue 1, January 2013

An analytic model of the electric and magnetic fields surrounding the nonlinear plasma “bubble” formed around the highcurrent electron bunch in a plasma wakefield accelerator is developed. The model, justified by the results of particleincell simulations, accurately captures the thin highdensity plasma sheath and extended return current layer surrounding the bubble. The resulting global fields inside and outside the bubble are used to investigate electron selfinjection in a plasma with a smooth density gradient. It is shown that accurate description of the current/density sheaths is crucial for quantitative description of selfinjection.
 LETTERS


Derivation of stochastic differential equations for scrapeoff layer plasma fluctuations from experimentally measured statistics
View Description Hide DescriptionA stochastic differential equation for intermittent plasma density dynamics in magnetic fusion edge plasma is derived, which is consistent with the experimentally measured gamma distribution and the theoretically expected quadratic nonlinearity. The plasma density is driven by a multiplicative Wiener process and evolves on the turbulence correlation time scale, while the linear growth is quadratically damped by the fluctuation level. The sensitivity of intermittency to the nonlinear dynamics is investigated by analyzing the nonlinear Langevin representation of the beta process, which leads to a rootsquare nonlinearity.

Plasma turbulence in the scrapeoff layer of tokamak devices
View Description Hide DescriptionPlasma turbulence is explored in the scrapeoff layer of tokamak devices using threedimensional global twofluid simulations. Two transport regimes are discussed: one in which the turbulent fluctuations saturate nonlinearly due to the KelvinHelmholtz instability, and another in which the fluctuations saturate due to a local flattening of the plasma gradients and associated removal of the linear instability drive. Focusing on the latter regime, analytical estimates of the crossfield transport and plasma profile gradients are obtained that display Bohmscaling diffusion properties.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

A large volume uniform plasma generator for the experiments of electromagnetic wave propagation in plasma
View Description Hide DescriptionA large volume uniform plasma generator is proposed for the experiments of electromagnetic (EM) wave propagation in plasma, to reproduce a “black out” phenomenon with long duration in an environment of the ordinary laboratory. The plasma generator achieves a controllable approximate uniform plasma in volume of 260 mm× 260 mm× 180 mm without the magnetic confinement. The plasma is produced by the glow discharge, and the special discharge structure is built to bring a steady approximate uniform plasma environment in the electromagnetic wave propagation path without any other barriers. In addition, the electron density and luminosity distributions of plasma under different discharge conditions were diagnosed and experimentally investigated. Both the electron density and the plasma uniformity are directly proportional to the input power and in roughly reverse proportion to the gas pressure in the chamber. Furthermore, the experiments of electromagnetic wave propagation in plasma are conducted in this plasma generator. Blackout phenomena at GPS signal are observed under this system and the measured attenuation curve is of reasonable agreement with the theoretical one, which suggests the effectiveness of the proposed method.

Unique topological characterization of braided magnetic fields
View Description Hide DescriptionWe introduce a topological flux function to quantify the topology of magnetic braids: nonzero, linetied magnetic fields whose field lines all connect between two boundaries. This scalar function is an ideal invariant defined on a crosssection of the magnetic field, and measures the average poloidal magnetic flux around any given field line, or the average pairwise crossing number between a given field line and all others. Moreover, its integral over the crosssection yields the relative magnetic helicity. Using the fact that the flux function is also an action in the Hamiltonian formulation of the field line equations, we prove that it uniquely characterizes the field line mapping and hence the magnetic topology.

Towards a complete parametrization of the ordinarymode electromagnetic instability in counterstreaming plasmas. I. Minimizing ion dynamics
View Description Hide DescriptionThe ordinary mode instability can be driven by drifting biMaxwellian plasma particle distributions with and without temperature anisotropy. Here, the linear instability analysis is generalized for realistic settings, when the plasma streams are magnetized and hot enough. The new parametrization proposed in this study enables a better understanding of the interplay of counterstreaming and temperature anisotropy, providing the derivation of new regimes of the ordinary mode instability. Accurate analytical forms are derived for the instability conditions for general values of the temperature anisotropy, the streaming velocity, and the parallel plasma beta. To keep the analysis straightforward, the role of ions is minimized.

A general theory for gaugefree lifting
View Description Hide DescriptionA theory for lifting equations of motion for charged particle dynamics, subject to given electromagnetic like forces, up to a gaugefree system of coupled Hamiltonian VlasovMaxwell like equations is given. The theory provides very general expressions for the polarization and magnetization vector fields in terms of the particle dynamics description of matter. Thus, as is common in plasma physics, the particle dynamics replaces conventional constitutive relations for matter. Several examples are considered including the usual VlasovMaxwell theory, a guiding center kinetic theory, VlasovMaxwell theory with the inclusion of spin, and a VlasovMaxwell theory with the inclusion of Dirac's magnetic monopoles. All are shown to be Hamiltonian field theories and the Jacobi identity is proven directly.

The interaction of two nonplanar solitary waves in electronpositronion plasmas: An application in active galactic nuclei
View Description Hide DescriptionIn the present research paper, the effect of bounded nonplanar (cylindrical and spherical) geometry on the interaction between two nonplanar electrostatic solitary waves (NESWs) in electron–positron–ion plasmas has been studied. The extended Poincaré–Lighthill–Kuo method is used to obtain nonplanar phase shifts after the interaction of the two NESWs. This study is a first attempt to investigate nonplanar phase shifts and trajectories for NESWs in a twofluid plasma (a pairplasma) consisting of electrons and positrons, as well as immobile background positive ions in nonplanar geometry. The change of phase shifts and trajectories for NESWs due to the effect of cylindrical geometry, spherical geometry, the physical processes (either isothermal or adiabatic), and the positions of two NESWs are discussed. The present investigation may be beneficial to understand the interaction between two NESWs that may occur in active galactic nuclei.

Spontaneous threedimensional magnetic reconnection in merging toroidal plasma experiment
View Description Hide DescriptionWe investigated a new phenomenon of threedimensional (3D) magnetic reconnection in TS4 torus plasma merging experiments by directly measuring the 3D structures of the current sheet. Removal of all toroidal asymmetry of the device reveals that a strong external drive of reconnection inflow increases the toroidal asymmetry of the current sheet only during the reconnection. This spontaneous 3D deformation of the current sheet increases the reconnection outflow as well as the reconnection electric field, probably because local compression of the current sheet to a thickness less than the ion gyroradius triggers its strong dissipation of the current sheet, responsible for the onset of 3D reconnection. These mechanisms indicate that the 3D reconnection is a newly observed spontaneous process of fast reconnection.

A simple class of singular, two species Vlasov equilibria sustaining nonmonotonic potential distributions
View Description Hide DescriptionWe present new elementary, exact weak singular solutions of the steady state, two species, electrostatic, one dimensional VlasovPoisson equations. The distribution of the hot, finite mass, mobile ions is assumed to be log singular at the position of the electric potential's minimum. We show that the electron energy distributions on opposite sides of this minimum are not equal. This leads to a jump discontinuity of the electron distribution across its separatrix. A simple relation exists between the difference of these two electron distributions and that of the ions. The velocity Fourier transform of the electron singular distribution is smooth and appears as a simple Neumann series. Elementary, finite amplitude profiles of the electric potential result from Poisson equation, which are smoothly, but nonmonotonically and asymmetrically distributed in space. Two such profiles are given explicitly as appropriate for a nonmonotonic double layer and for a plasma bounded by a surface. The distributions of both electrons and ions supporting such potential meet smooth and kinetically stable boundary conditions at one plasma boundary. For sufficiently small potential to electron temperature ratios, the nonthermal, discontinuous electron distribution resulting at the other plasma boundary is also stable against Landau damped perturbations of the electron distribution.

Dynamics of exploding plasmas in a large magnetized plasma
View Description Hide DescriptionThe dynamics of an exploding laserproduced plasma in a large ambient magnetoplasma was investigated with magnetic flux probes and Langmuir probes. Debrisions expanding at superAlfvénic velocity (up to ) expel the ambient magnetic field, creating a large ( ) diamagnetic cavity. We observe a field compression of up to as well as localized electron heating at the edge of the bubble. Twodimensional hybrid simulations reproduce these measurements well and show that the majority of the ambient ions are energized by the magnetic piston and swept outside the bubble volume. Nonlinear shearAlfvén waves ( ) are radiated from the cavity with a coupling efficiency of 70% from magnetic energy in the bubble to the wave.

Gyrokinetic simulations of reverse shear Alfvén eigenmodes in DIIID plasmas
View Description Hide DescriptionA gyrokinetic ion/massless fluid electron hybrid model as implemented in the GEM code [Y. Chen and S. E. Parker, J. Comput. Phys. 220, 837 (2007)] is used to study the reverse shear Alfvén eigenmodes (RSAE) observed in DIIID, discharge #142111. This is a well diagnosed case with measurement of the corelocalized RSAE mode structures and the mode frequency, which can be used to compare with simulations. Simulations reproduce many features of the observation, including the mode frequency upsweeping in time and the sweeping range. A new algorithmic feature is added to the GEM code for this study. Instead of the gyrokinetic Poisson equation itself, its time derivative, or the vorticity equation, is solved to obtain the electric potential. This permits a numerical scheme that ensures the E × B convection of the equilibrium density profiles of each species cancel each other in the absence of any finiteLarmorradius effects. These nonlinear simulations generally result in an electron temperature fluctuation level that is comparable to measurements, and a mode frequency spectrum broader than the experimental spectrum. The spectral width from simulations can be reduced if less steep beam density profiles are used, but then the experimental fluctuation level can be reproduced only if a collision rate above the classical level is assumed.

Nonlinear Raman forward scattering of a short laser pulse in a collisional transversely magnetized plasma
View Description Hide DescriptionNonlinear Raman forward scattering (NRFS) of an intense short laser pulse with a duration shorter than the plasma period through a homogenous collisional transversely magnetized plasma is investigated theoretically when ponderomotive, relativistic and collioninal nonlinearities are taken into account. The plasma is embedded in a uniform magnetic field perpendicular to both, the direction of propagation and electric vector of the radiation field. Nonlinear wave equation is set up and Fourier transformation method is used to solve the coupled equations describing NRFS instability. Finally, the growth rate of this instability is obtained. Thermal effects of plasma electrons and effect of the electronion collisions are examined. It is found that the growth rate of Raman forward scattering first decreases on increasing electron thermal velocity, minimizes at an optimum value, and then increases. Our results also show that the growth rate increases by increasing the electronion collisions.

Investigation of an ionion hybrid Alfvén wave resonator
View Description Hide DescriptionA theoretical and experimental investigation is made of a wave resonator based on the concept of wave reflection along the confinement magnetic field at a spatial location where the wave frequency matches the local value of the ionion hybrid frequency. Such a situation can be realized by shear Alfvén waves in a magnetized plasma with two ion species because this mode has zero parallel group velocity and experiences a cutoff at the ionion hybrid frequency. Since the ionion hybrid frequency is proportional to the magnetic field, it is expected that a magnetic well configuration in a twoion plasma can result in an Alfvén wave resonator. Such a concept has been proposed in various space plasma studies and could have relevance to mirror and tokamak fusion devices. This study demonstrates such a resonator in a controlled laboratory experiment using a H^{+}He^{+} mixture. The resonator response is investigated by launching monochromatic waves and impulses from a magnetic loop antenna. The observed frequency spectra are found to agree with predictions of a theoretical model of trapped eigenmodes.

Linear analysis of time dependent properties of ChildLangmuir flow
View Description Hide DescriptionWe continue our analysis of the time dependent behavior of the electron flow in the ChildLangmuir system, removing an approximation used earlier. We find a modified set of oscillatory decaying modes with frequencies of the same order as the inverse of the electron transient time. This range (typically MHz) allows simple experimental detection and maybe exploitation. We then study the time evolution of the current in response to a slow change of the anode voltage where the same modes of oscillations appear too. The cathode current in this case is systematically advanced or retarded depending on the direction of the voltage change.

Small amplitude nonlinear electron acoustic solitary waves in weakly magnetized plasma
View Description Hide DescriptionNonlinear propagation of electron acoustic waves in homogeneous, dispersive plasma medium with two temperature electron species is studied in presence of externally applied magnetic field. The linear dispersion relation is found to be modified by the externally applied magnetic field. Lagrangian transformation technique is applied to carry out nonlinear analysis. For small amplitude limit, a modified KdV equation is obtained, the modification arising due to presence of magnetic field. For weakly magnetized plasma, the modified KdV equation possesses stable solitary solutions with speed and amplitude increasing temporally. The solutions are valid upto some finite time period beyond which the nonlinear wave tends to wave breaking.

Linear and nonlinear wave propagation in weakly relativistic quantum plasmas
View Description Hide DescriptionWe consider a recently derived kinetic model for weakly relativistic quantum plasmas. We find that that the effects of spinorbit interaction and Thomas precession may alter the linear dispersion relation for a magnetized plasma in case of high plasma densities and/or strong magnetic fields. Furthermore, the ponderomotive force induced by an electromagnetic pulse is studied for an unmagnetized plasma. It turns out that for this case the spinorbit interaction always gives a significant contribution to the quantum part of the ponderomotive force.

Modulational instability of a Langmuir wave in plasmas with energetic tails of superthermal electrons
View Description Hide DescriptionThe impact of superthermal electrons on dispersion properties of isotropic plasmas and on the modulational instability of a monochromatic Langmuir wave is studied for the case when the powerlaw tail of the electron distribution function extends to relativistic velocities and contains most of the plasma kinetic energy. Such an energetic tail of electrons is shown to increase the thermal correction to the Langmuir wave frequency, which is equivalent to the increase of the effective electron temperature in the fluid approach, and has almost no impact on the dispersion of ionacoustic waves, in which the role of temperature is played by the thermal spread of lowenergy core electrons. It is also found that the spectrum of modulational instability in the nonmaxwellian plasma narrows significantly, as compared to the equilibrium case, without change of the maximum growth rate and the corresponding wavenumber.

Timedomain simulation of nonlinear radiofrequency phenomena
View Description Hide DescriptionNonlinear effects associated with the physics of radiofrequency wave propagation through a plasma are investigated numerically in the time domain, using both fluid and particleincell (PIC) methods. We find favorable comparisons between parametric decay instability scenarios observed on the Alcator CMOD experiment [J. C. Rost, M. Porkolab, and R. L. Boivin, Phys. Plasmas 9, 1262 (2002)] and PIC models. The capability of fluid models to capture important nonlinear effects characteristic of waveplasma interaction (frequency doubling, cyclotron resonant absorption) is also demonstrated.

Electromagnetic waves destabilized by runaway electrons in nearcritical electric fields
View Description Hide DescriptionRunaway electron distributions are strongly anisotropic in velocity space. This anisotropy is a source of free energy that may destabilize electromagnetic waves through a resonant interaction between the waves and the energetic electrons. In this work, we investigate the highfrequency electromagnetic waves that are destabilized by runaway electron beams when the electric field is close to the critical field for runaway acceleration. Using a runaway electron distribution appropriate for the nearcritical case, we calculate the linear instability growth rate of these waves and conclude that the obliquely propagating whistler waves are most unstable. We show that the frequencies, wave numbers, and propagation angles of the most unstable waves depend strongly on the magnetic field. Taking into account collisional and convective damping of the waves, we determine the number density of runaways that is required to destabilize the waves and show its parametric dependences.

The incomplete plasma dispersion function: Properties and application to waves in bounded plasmas
View Description Hide DescriptionThe incomplete plasma dispersion function is a generalization of the plasma dispersion function in which the defining integral spans a semiinfinite, rather than infinite, domain. It is useful for describing the linear dielectric response and wave dispersion in nonMaxwellian plasmas when the distribution functions can be approximated as Maxwellian over finite, or semiinfinite, intervals in velocity phasespace. A ubiquitous example is the depleted Maxwellian electron distribution found near boundary sheaths or double layers, where the passing interval can be modeled as Maxwellian with a lower temperature than the trapped interval. The depleted Maxwellian is used as an example to demonstrate the utility of using the incomplete plasma dispersion function for calculating modifications to wave dispersion relations.