Volume 19, Issue 1, January 2012

Astrophysical fluids are generically turbulent and this must be taken into account for most transport processes. We discuss how the preexisting turbulence modifies magnetic reconnection and how magnetic reconnection affects the MHDturbulent cascade. We show the intrinsic interdependence and interrelation of magnetic turbulence and magnetic reconnection, in particular, that strong magnetic turbulence in 3D requires reconnection and 3D magnetic turbulence entails fast reconnection. We follow the approach in Eyink et al. [Astrophys. J. 743, 51 (2011)] to show that the expressions of fast magnetic reconnection in A. Lazarian and E. T. Vishniac [Astrophys. J. 517, 700 (1999)] can be recovered if Richardson diffusion of turbulent flows is used instead of ordinary Ohmic diffusion. This does not revive, however, the concept of magnetic turbulent diffusion which assumes that magnetic fields can be mixed up in a passive way down to a very small dissipation scales. On the contrary, we are dealing the reconnection of dynamically important magnetic field bundles which strongly resist bending and have well defined mean direction weakly perturbed by turbulence. We argue that in the presence of turbulence the very concept of fluxfreezing requires modification. The diffusion that arises from magnetic turbulence can be called reconnectiondiffusion as it based on reconnection of magnetic field lines. The reconnectiondiffusion has important implications for the continuous transport processes in magnetized plasmas and for star formation. In addition, fast magnetic reconnection in turbulent media induces the First order Fermi acceleration of energetic particles, can explain solar flares and gamma ray bursts. However, the most dramatic consequence of these developments is the fact that the standard flux freezing concept must be radically modified in the presence of turbulence.
 LETTERS


Chorus wave amplification: A free electron laser in the Earth’s magnetosphere
View Description Hide DescriptionA new theoretical model for whistlermode chorus amplification in the Earth’s magnetosphere is presented. We derive, based on the freeelectron laser mechanism in a highgain amplifier, a new closed set of selfconsistent relativistic equations that couple the Hamiltonian equations for particles with Maxwell’sequations. We demonstrate that these equations predict, through a cubic equation,whistler amplification levels in good agreement with those observed in the Earth’s magnetosphere.

A Maxwell formulation for the equations of a plasma
View Description Hide DescriptionIn light of the analogy between the structure of electrodynamics and fluid dynamics, the fluid equations of motion may be reformulated as a set of Maxwell equations. This analogy has been explored in the literature for incompressible turbulent flow and compressible flow but has not been widely explored in relation to plasmas. This letter introduces the analogous fluid Maxwell equations and formulates a set of Maxwell equations for a plasma in terms of the species canonical vorticity and its cross product with the species velocity. The form of the source terms is presented and the magnetohydrodynamic(MHD) limit restores the typical variety of MHD waves.

Particle beam selfmodulation instability in tapered and inhomogeneous plasma
View Description Hide DescriptionThe particle beam selfmodulation instability in tapered and inhomogeneous plasmas is analyzed via an evolution equation for the beam radius. For a sufficiently fast taper, the instability is suppressed, and the condition for growth suppression is derived. The form of the taper to phase lock a trailing witness bunch in the plasma wave driven by a selfmodulated beam is determined, which can increase the energy gain by several orders of magnitude. Growth of the instability places stringent constraints on the initial background plasma densityfluctuations.

 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Poynting vector, energy densities, and pressure of collective transverse electromagnetic fluctuations in unmagnetized plasmas
View Description Hide DescriptionA systematic calculation of the electromagnetic properties (Poynting vector, electromagnetic energy, and pressure) of the collective transverse fluctuations in unmagnetized plasmas with velocityanisotropic plasmaparticle distributions functions is presented. Timeaveraged electromagnetic properties for monochromatic weakly damped wavelike fluctuations and spaceaveraged electromagnetic properties for monochromatic weakly propagating and aperiodic fluctuations are calculated. For aperiodic fluctuations, the Poynting vector as well as the sum of the spaceaveraged electric and magnetic field energy densities vanish. However, aperiodic fluctuations possess a positive pressure given by its magnetic energy density. This finite pressure density p_{a} of aperiodic fluctuations has important consequences for the dynamics of cosmic unmagnetized plasmas such as the intergalactic medium after reionization. Adopting the standard cosmological evolution model, we show that this additional pressure changes the expansion law of the universe leading to further deceleration. Negative vacuum pressure counterbalances this deceleration to an accelerating universe provided that the negative vacuum pressure is greater than 1.5p_{a} , which we estimate to be of the order 2.1 · 10^{−16 }dyn cm^{−2}.

Adiabatic nonlinear waves with trapped particles. I. General formalism
View Description Hide DescriptionA Lagrangian formalism is developed for a general nondissipative quasiperiodic nonlinear wave with trapped particles in collisionless plasma. The adiabatic timeaveraged Lagrangian density is expressed in terms of the singleparticle oscillationcenter Hamiltonians; once those are found, the complete set of geometricaloptics equations is derived without referring to the MaxwellVlasov system. The number of trapped particles is assumed fixed; in particular, those may reside close to the bottom of the wave trapping potential, so they never become untrapped. Then their contributions to the wave momentum and the energy flux depend mainly on the trappedparticle density, as an independent parameter, and the phase velocity rather than on the wave amplitude a explicitly; hence, acquires aindependent terms. Also, the wave action is generally not conserved, because it can be exchanged with resonant oscillations of the trappedparticle density. The corresponding modification of the wave envelope equation is found explicitly and the new action flow velocity is derived. Applications of these results are left to the other two papers of the series, where specific problems are addressed pertaining to properties and dynamics of waves with trapped particles.

Adiabatic nonlinear waves with trapped particles. II. Wave dispersion
View Description Hide DescriptionA general nonlinear dispersion relation is derived in a nondifferential form for an adiabatic sinusoidal Langmuir wave in collisionless plasma, allowing for an arbitrary distribution of trapped electrons. The linear dielectric function is generalized, and the nonlinear kinetic frequency shift ω_{NL} is found analytically as a function of the wave amplitude a. Smooth distributions yield , as usual. However, beamlike distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation. Such beams are formed whenever the phase velocity changes, because the trapped distribution is in autoresonance and thus evolves differently from the passing distribution. Hence, even adiabatic ω_{NL}(a) is generally nonlocal.

Adiabatic nonlinear waves with trapped particles. III. Wave dynamics
View Description Hide DescriptionThe evolution of adiabatic waves with autoresonant trapped particles is described within the Lagrangianmodel developed in Paper I, under the assumption that the action distribution of these particles is conserved, and, in particular, that their number within each wavelength is a fixed independent parameter of the problem. Onedimensional nonlinear Langmuir waves with deeply trapped electrons are addressed as a paradigmatic example. For a stationary wave, tunneling into overcritical plasma is explained from the standpoint of the action conservation theorem. For a nonstationary wave, qualitatively different regimes are realized depending on the initial parameter S, which is the ratio of the energy flux carried by trapped particles to that carried by passing particles. At S < 1/2, a wave is stable and exhibits group velocity splitting. At S > 1/2, the trappedparticle modulational instability (TPMI) develops, in contrast with the existing theories of the TPMI yet in agreement with the general sideband instability theory. Remarkably, these effects are not captured by the nonlinear Schrödinger equation, which is traditionally considered as a universal model of wave selfaction but misses the trappedparticle oscillationcenter inertia.

Relation of astrophysical turbulence and magnetic reconnection^{a)}
View Description Hide DescriptionAstrophysical fluids are generically turbulent and this must be taken into account for most transport processes. We discuss how the preexisting turbulence modifies magnetic reconnection and how magnetic reconnection affects the MHDturbulent cascade. We show the intrinsic interdependence and interrelation of magnetic turbulence and magnetic reconnection, in particular, that strong magnetic turbulence in 3D requires reconnection and 3D magnetic turbulence entails fast reconnection. We follow the approach in Eyink et al. [Astrophys. J. 743, 51 (2011)] to show that the expressions of fast magnetic reconnection in A. Lazarian and E. T. Vishniac [Astrophys. J. 517, 700 (1999)] can be recovered if Richardson diffusion of turbulent flows is used instead of ordinary Ohmic diffusion. This does not revive, however, the concept of magnetic turbulent diffusion which assumes that magnetic fields can be mixed up in a passive way down to a very small dissipation scales. On the contrary, we are dealing the reconnection of dynamically important magnetic field bundles which strongly resist bending and have well defined mean direction weakly perturbed by turbulence. We argue that in the presence of turbulence the very concept of fluxfreezing requires modification. The diffusion that arises from magnetic turbulence can be called reconnectiondiffusion as it based on reconnection of magnetic field lines. The reconnectiondiffusion has important implications for the continuous transport processes in magnetized plasmas and for star formation. In addition, fast magnetic reconnection in turbulent media induces the First order Fermi acceleration of energetic particles, can explain solar flares and gamma ray bursts. However, the most dramatic consequence of these developments is the fact that the standard flux freezing concept must be radically modified in the presence of turbulence.

Ion acoustic solitons in a plasma with twotemperature kappadistributed electrons
View Description Hide DescriptionExistence domains and characteristics of ion acoustic solitons are studied in a twotemperature electron plasma with both electron components being kappadistributed, as found in Saturn’smagnetosphere. As is the case for doubleBoltzmann electrons, solitons of both polarities can exist over restricted ranges of fractional hot electron density ratio for this plasma model. Low κ values, which indicate increased suprathermal particles in the tail of the distribution, yield a smaller domain in the parameter space of hot density fraction and normalized solitonvelocity (f, M), over which both soliton polarities are supported for a given plasma composition (the coexistence region). For some density ratios that support coexistence, solitons occur even at the lowest (critical) Mach number (i.e., at the acoustic speed), as found recently for a number of other plasma models. Like Maxwellians, lowκ distributions also support positive potential double layers over a narrow range of low fractional cool electron density (<10%).

Effect of ionization distribution on the low frequency oscillations mode in Hall thrusters
View Description Hide DescriptionIt is found that the discharge parameters have notable effects on the mode of discharge current low frequency oscillation in Hall thrusters, but different discharge parameters might form the similar low frequency oscillation mode. In order to study the mechanism of oscillation mode formation, the ionization distribution in the discharge channel was measured experimentally, and onedimensional quasineutrality hydrodynamic model was used to study the relationship between ionization distribution and the oscillation mode. Researches show that the low frequency oscillation with a narrow and condensed ionization distribution has the mode of lower amplitude and scattered frequency. The low frequency oscillation amplitude would become high and have dominative frequency component with the relative wide ionization distribution. Therefore, it can be concluded that the difference of ionization distribution characteristics is the main reason of the oscillation mode variation, and discharge parameters are only the external control parameters of ionization distribution characteristics.

A comprehensive study of different gases in inductively coupled plasma torch operating at one atmosphere
View Description Hide DescriptionA numerical study is done to understand the possible operating regimes of RFICP torch (3 MHz, 50 kW) using different gases for plasma formation at atmospheric pressure. A two dimensional numerical simulation of RFICP torch using argon, nitrogen, oxygen, and air as plasma gas has been investigated using computational fluid dynamic (CFD) software fluent^{©}. The operating parameters varied here are central gas flow,sheath gas flow, RFpower dissipated in plasma, and plasma gas. The temperature contours, flow field, axial, and radial velocity profiles were investigated under different operating conditions. The plasmaresistance,inductance of the torch, and the heat distribution for various plasma gases have also been investigated. The plasma impedance of ICP torch varies with different operating parameters and plays an important role for RF oscillator design and power coupling. These studies will be useful to decide the design criteria for ICP torches required for different material processing applications.

Stimulated Raman scattering coupled to decay instability in a plasma channel
View Description Hide DescriptionA non local theory of Stimulated Raman scattering (SRS) coupled to decay instability in a plasma channel is developed. The primary Langmuir wave, produced in the Raman backscattering process, decays into a secondary Langmuir wave of longer wavelength and an ion acoustic wave. This diversion of energy, along with linear Landau damping of the primary Langmuir wave, slows down the Raman process. The nonlocal effects cause further reduction in the growth rate.

Effect of guide field on lowerhybrid drift instabilities in current sheet containing energetic particles
View Description Hide DescriptionThe effect of a guide field on the linear lowerhybrid drift instability (LHDI) in a thin current sheet containing energetic particles is investigated using kinetic theory. It is found that the symmetry properties of the LHD modes are destroyed by the guide field. The LHDI growth rate decreases with the strength of the latter, and the perturbed magnetic field is much higher than that of the guidefield free case.

Minimum energy states of the cylindrical plasma pinch in singlefluid and Hall magnetohydrodynamics
View Description Hide DescriptionRelaxed states of a plasma column are found analytically in singlefluid and Hall magnetohydrodynamics(MHD). We perform complete minimization of the energy with constraints imposed by invariants inherent in the corresponding models. It is shown that the relaxed state in Hall MHD is a forcefree magnetic field with uniform axial flow and/or rigid azimuthal rotation. In contrast, the relaxed states in singlefluid MHD are more complex due to the coupling between velocity and magnetic field. Cylindrically and helically symmetric relaxed states are considered for both models. Helical states may be time dependent and analogous to helical waves, propagating on a cylindrically symmetric background. Application of our results to reversedfield pinches(RFP) is discussed. The radial profile of the parallel momentum predicted by the singlefluid MHD relaxation theory is shown to be in reasonable agreement with experimental observation from the Madison symmetric torus RFP experiment.

Landau damping of a driven plasma wave from laser pulses
View Description Hide DescriptionThe interaction between a laser pulse and a driven plasma wave with a phase velocity approaching the speed of light is studied, and our investigation is focused on the Gaussian laser pulse. It is demonstrated that when the resonance condition between the plasma wave and the laser pulse is satisfied, the Landau damping phenomenon of the plasma wave originated from the laser pulse will emerge. The dispersion relations for the plasma waves in resonance and nonresonance regions are obtained. It is proved that the Landau damping rate for a driven plasma wave is in the resonance region, so the laser pulse can produce an inverse damping effect, namely Landau growth effect, which leads an instability for the plasma wave. The Landau growth means that the energy is transmitted from the laser pulse to the plasma wave, which could be an effective process for enhancing the plasma wave.

The effect of qdistributed electrons on the headon collision of ion acoustic solitary waves
View Description Hide DescriptionThe headon collision of ion acoustic solitary waves (IASWs) in two component plasma comprising nonextensive distributed electrons is investigated. Two opposite directional Kortewgdevries (KdV) equations are derived and the phase shift due to collision is obtained using the extended version of PoincaréLighthillKuo method. Different ranges of nonextensive parameter q are considered and their effects on phase shifts are observed. It is found that the presence of nonextensive distributed electrons plays a significant role on the nature of collision of ion acoustic solitary waves.

Effect of dust charging and trapped electrons on nonlinear solitary structures in an inhomogeneous magnetized plasma
View Description Hide DescriptionMain concerns of the present article are to investigate the effects of dust charging and trapped electrons on the solitary structures evolved in an inhomogeneous magnetized plasma. Such a plasma is found to support two types of waves, namely, fast wave and slow wave. Slow wave propagates in the plasma only when the wave propagation angle θ satisfies the condition , where is the z (x) component of ion drift velocity, σ = T_{i} /T_{eff} , n_{dlh} = n_{d} _{0}/(n_{el} _{0} + n_{eh} _{0}), and together with T_{i} as ion temperature,n_{el} _{0}(n_{eh} _{0}) as the density of trapped (isothermal) electrons, as the dust grain (density n_{d} _{0}) surface potential relative to zero plasma potential, and , where T_{el} (T_{eh} ) is the temperature of trapped (isothermal) electrons. Both the waves evolve in the form of density hill type structures in the plasma, confirming that these solitary structures are compressive in nature. These structures are found to attain higher amplitude when the charge on the dust grains is fluctuated (in comparison with the case of fixed charge) and also when the dust grains and trapped electrons are more in number; the same is the case with higher temperature of ions and electrons. Slow solitary structures show weak dependence on the dust concentration. Both types of structures are found to become narrower under the application of stronger magnetic field. With regard to the charging of dust grains, it is observed that the charge gets reduced for the higher trapped electron density and temperature of ions and electrons, and dust charging shows weak dependence on the ion temperature.

Collisionless distribution function for the relativistic forcefree Harris sheet
View Description Hide DescriptionA selfconsistent collisionless distribution function for the relativistic analogue of the forcefree Harris sheet is presented. This distribution function is the relativistic generalization of the distribution function for the nonrelativistic collisionless forcefree Harris sheet recently found by Harrison and Neukirch [Phys. Rev. Lett. 102, 135003 (2009)], as it has the same dependence on the particle energy and canonical momenta. We present a detailed calculation which shows that the proposed distribution function generates the required current density profile (and thus magnetic field profile) in a frame of reference in which the electric potential vanishes identically. The connection between the parameters of the distribution function and the macroscopic parameters such as the current sheet thickness is discussed.

Shearedflow induced confinement transition in a linear magnetized plasma
View Description Hide DescriptionA magnetized plasma cylinder (12 cm in diameter) is induced by an annular shape obstacle at the Large Plasma Device [W. Gekelman, H. Pfister, Z. Lucky, J. Bamber, D. Leneman, and J. Maggs, Rev. Sci. Instrum. 62, 2875 (1991)]. Sheared azimuthal flow is driven at the edge of the plasma cylinder through edge biasing. Strong fluctuations of density and potential () are observed at the plasma edge, accompanied by a large density gradient () and shearing rate (). Edge turbulence and crossfield transport are modified by changing the bias voltage () on the obstacle and the axial magnetic field () strength. In cases with low and large , improved plasma confinement is observed, along with steeper edge density gradients. The radially sheared flow induced by drift dramatically changes the crossphase between density and potential fluctuations, which causes the waveinduced particle flux to reverse its direction across the shear layer. In cases with higher bias voltage or smaller , large radial transport and rapid depletion of the central plasma density are observed. Twodimensional crosscorrelation measurement shows that a mode with azimuthal mode number and large radial correlation length dominates the outward transport in these cases. Linear analysis based on a twofluid Braginskii model suggests that the fluctuations are driven by both density gradient (drift wave like) and flow shear (KelvinHelmholtz like) at the plasma edge.

Propagation of nonlinear coherent structures in a collisional magnetoplasma with nonthermal electrons and finite ion temperature
View Description Hide DescriptionNonlinear electrostatic waves in dissipative magnetized electronion (ei) plasmas are investigated employing the two fluid model. In this regard, Zakharov Kuznetsov Burgers (ZKB) equation is derived using the small amplitude perturbation expansion method. It is observed that the nonthermal electron population, obliqueness, ion thermal effects, and kinematicviscosity significantly alter the structure of obliquely propagating nonlinear ion acoustic shock waves in dissipative ei magnetoplasmas. It is observed that the system can admit both compressive and rarefactive shocks. The condition for the formation of both types of shocks is also given. The present study may be useful to understand the nonlinear propagation characteristics of electrostatic shock structures in space environments where the nonthermal electrons have been observed by various satellite missions such as Voyager and Freja.