Volume 19, Issue 8, August 2012

Using resistive compressible magnetohydrodynamics, we investigate the energy release and transfer by magnetic reconnection in finite (closed or periodic) systems. The emphasis is on the magnitude of energy released and transferred to plasma heating in configurations that range from highly compressible to incompressible, based on the magnitude of the background (ratio of plasma pressure over magnetic pressure) and of a guide field in twodimensional reconnection. As expected, the system becomes more incompressible, and the role of compressional heating diminishes, with increasing or increasing guide field. Nevertheless, compressional heating may dominate over Joule heating for values of the guide field of 2 or 3 (in relation to the reconnecting magnetic field component) and of 5–10. This result stems from the strong localization of the dissipation near the reconnection site, which is modeled based on particle simulation results. Imposing uniform resistivity, corresponding to a Lundquist number of to , leads to significantly larger Ohmic heating. Increasing incompressibility greatly reduces the magnetic flux transfer and the amount of energy released, from of the energy associated with the reconnecting field component, for zero guide field and low , to for large values of the guide field or large . The results demonstrate the importance of taking into account plasma compressibility and localization of dissipation in investigations of heating by turbulent reconnection, possibly relevant for solar wind or coronal heating.
 LETTERS


Simulation of currentfilament dynamics and relaxation in the Pegasus Spherical Tokamak
View Description Hide DescriptionNonlinear numerical computation is used to investigate the relaxation of nonaxisymmetric currentchannels from washergun plasma sources into “tokamaklike” plasmas in the Pegasus toroidal experiment [Eidietis et al. J. Fusion Energy 26, 43 (2007)]. Resistive MHD simulations with the NIMROD code [Sovinec et al. Phys. Plasmas10(5), 1727–1732 (2003)] utilize ohmic heating, temperaturedependent resistivity, and anisotropic, temperaturedependent thermal conduction corrected for regions of low magnetization to reproduce critical transport effects. Adjacent passes of the simulated currentchannel attract and generate strong reversed current sheets that suggest magnetic reconnection. With sufficient injected current, adjacent passes merge periodically, releasing axisymmetric current rings from the driven channel. The current rings have not been previously observed in helicity injection for spherical tokamaks, and as such, provide a new phenomenological understanding for filament relaxation in Pegasus. After largescale poloidalfield reversal, a hollow current profile and significant poloidal flux amplification accumulate over many reconnection cycles.

A Vlasov equilibrium for space charge dominated beam in a misaligned solenoidal channel
View Description Hide DescriptionThe effect of displacement and rotational misalignments of solenoid magnets with respect to the ideal beam propagation axis on the dynamics of intense charged particle beams have been studied. The equation of motion of the beam centroid has been obtained and found to be independent of any specific beam distribution. A Vlasov equilibrium distribution for the intense beam propagation through misaligned focussing channel has been obtained. Selfconsistent simulation confirms the analytical result.

Transition from interpulse to afterglow plasmas driven by repetitive shortpulse microwaves in a multicusp magnetic field
View Description Hide DescriptionIn the poweroff phase, plasmas generated by repetitive shortpulse microwaves in a multicusp magnetic field show a transitive nature from interpulse to afterglow as a function of pulse duration t_{w} = 20–200 μs. The ionized medium can be driven from a highly non equilibrium to an equilibrium state inside the pulses, thereby dictating the behavior of the plasma in the poweroff phase. Compared to afterglows, interpulse plasmas observed for t_{w} < 50 μs are characterized by a quasisteadystate in electron density that persists for ∼ 20–40 μs even after the end of the pulse and has a relatively slower decay rate (∼ 4.3 × 10^{4} s^{−1}) of the electron temperature, as corroborated by optical measurements. The associated electron energy probability function indicates depletion in low energy electrons which appear at higher energies just after the end of the pulse. The transition occurs at t_{w} ∼ 50 μs as confirmed by time evolution of integrated electron numbers densities obtained from the distribution function.

Spectroscopic observation of simultaneous bidirectional reconnection outflows in a laboratory plasma
View Description Hide DescriptionWe report a precise, direct spectroscopic measurement of simultaneous bidirectional outflows from a reconnection event in a laboratory plasma. Outflow speeds are as Alfvénic and Abel analysis shows that the outflows are generated in the plasma core. A SweetParker like analysis of outflow speed coupled with external measurements of reconnectionelectric field and assumption of Spitzer resistivity predict an aspect ratio of the reconnection layer and reconnection rate that are close to that measured in the experiment and in simulations. However, this analysis underestimates the absolute scale of the layer, indicating other than 2D resistive physics is at play.
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 ARTICLES

 Basic Plasma Phenomena, Waves, Instabilities

Backward mode of the ioncyclotron wave in a semibounded magnetized Lorentzian plasma
View Description Hide DescriptionThe backward modes of the surface ioncyclotron wave are investigated in a semibounded magnetized Lorentzian plasma. The dispersion relation of the backward mode of the surface ioncyclotron wave is obtained using the specular reflection boundary condition with the plasmadielectric function. The result shows that the nonthermal effect suppresses the wave frequency as well as the group velocity of the surface ioncyclotron wave. It is also found that the nonthermal effect on the surface ioncyclotron wave increases with an increase of the wave number. In addition, it is found that the propagation domain of the surface ioncyclotron wave increases with an increase of the ratio of the electron plasma frequency to the electron gyrofrequency. It is also found that the nonthermal effect increases the propagation domain of the surface ioncyclotron wave in a semibounded magnetized Lorentzian plasma.

Laser induced fluorescence measurements of ion velocity and temperature of drift turbulence driven sheared plasma flow in a linear helicon plasma device
View Description Hide DescriptionUsing laser induced fluorescence(LIF), radial profiles of azimuthal ion fluid velocity and ion temperature are measured in the controlled shear decorrelation experiment (CSDX) linear helicon plasma device. Ion velocities and temperatures are derived from the measured Doppler broadened velocity distribution functions of argon ions. The LIF system employs a portable, high power (>300 mW), narrowband (∼1 MHz) tunable diode laserbased system operating at 668.614 nm. Previous studies in CSDX have shown the existence of a radially sheared azimuthal flow as measured with time delay estimation methods and Mach probes. Here, we report the first LIFmeasurements of sheared plasma fluid flow in CSDX. Above a critical magnetic field, the ion fluid flow profile evolves from radially uniform to peaked on axis with a distinct reversed flow region at the boundary, indicating the development of a sheared azimuthal flow. Simultaneously, the ion temperature also evolves from a radially uniform profile to a profile with a gradient. Measurements in turbulent and coherent drift wave mode dominated plasmas are compared.

Kink modes and surface currents associated with vertical displacement events
View Description Hide DescriptionThe fast termination phase of a vertical displacement event (VDE) in a tokamak is modeled as a sequence of shrinking equilibria, where the core current profile remains constant so that the safetyfactor at the axis, , remains fixed and the systematically decreases. At some point, the n = 1 kink mode is destabilized. Kink modes distort the magnetic field lines outside the plasma, and surface currents are required to nullify the normal component of the Bfield at the plasma boundary and maintain equilibrium at finite pressure. If the plasma touches a conductor, the current can be transferred to the conductor, and may be measurable by the halo current monitors. This report describes a practical method to model the plasma as it evolves during a VDE, and determine the surface currents, needed to maintain equilibrium. The main results are that the onset conditions for the disruption are that the growthrate of the n = 1 kink exceeds half the Alfven time and the associated surface current needed to maintain equilibrium exceeds one half of the core plasma current. This occurs when drops below a low integer, usually 2. Application to NSTX provides favorable comparison with nonaxisymmetric halocurrent measurements. The model is also applied to ITER and shows that the 2/1 mode is projected to be the most likely cause of the final disruption.

Parametric decays in relativistic magnetized electronpositron plasmas with relativistic temperatures
View Description Hide DescriptionThe nonlinear evolution of a circularly polarized electromagnetic wave in an electronpositron plasma propagating along a constant background magnetic field is considered, by studying its parametric decays. Relativistic effects, of the particle motion in the wave field and of the plasma temperature, are included to obtain the dispersion relation of the decays. The exact dispersion relation of the pump wave has been previously calculated within the context of a relativistic fluid theory and presents two branches: an electromagnetic and an Alfvén one. We investigate the parametric decays for the pump wave in these two branches, including the anomalous dispersion zone of the Alfvén branch where the group velocity is negative. We solve the nonlinear dispersion relation for different pump wave amplitudes and plasma temperatures, finding various resonant and nonresonant wave couplings. We are able to identify these couplings and study their behavior as we modify the plasma parameters. Some of these couplings are suppressed for larger amplitudes or temperatures. We also find two kinds of modulational instabilities, one involving two sideband daughter waves and another involving a forwardpropagating electroacoustic mode and a sideband daughter wave.

Oscillating plasma bubbles. I. Basic properties and instabilities
View Description Hide DescriptionPlasma bubbles are created in an ambient discharge plasma. A bubble is a plasma volume of typically spherical shape, which is separated from the ambient plasma by a negatively biased grid of high transparency. Ions and electrons from the ambient plasma flow into the bubble volume. In steady state the flow of particles and currents is divergencefree, which is established by the plasma potential inside the bubble. The grid has two sheaths, one facing the ambient plasma, the other the bubble plasma. The inner sheath is observed to become unstable, causing the plasma potential in the bubble to oscillate. The instability arises from an excess of ions and a deficiency of electrons. Its frequency is in the range of the ion plasma frequency but depends on all parameters which influence the charge density in the sheath. When the grid voltage is very negative, electrons cannot enter the outer sheath, and the inner sheath becomes a virtual anode which reflects ions such that the bubble interior is empty. When an electron source is placed into the bubble it can neutralize the ions and the bubble refills. Without plasma sources or sinks the bubble plasma is extremely sensitive to perturbations by probes. Modified currentvoltage characteristics of Langmuir and emissive probes are demonstrated. A sequence of papers first describes the basic steadystate properties, then the time evolution of bubbles, the effects of electron sources in bubbles, and the role of the grid and bubble geometry. The physics of plasma bubbles is important to several fields of basic plasma physics such as sheaths,sheathinstabilities,diagnostic probes, electrostatic confinement, and current and space charge neutralization of beams.

Oscillating plasma bubbles. II. Pulsed experiments
View Description Hide DescriptionTimedependent phenomena have been investigated in plasma bubbles which are created by inserting spherical grids into an ambient plasma and letting electrons and ions form a plasma of different parameters than the ambient one. There are no plasma sources inside the bubble. The grid bias controls the particle flux. There are sheaths on both sides of the grid, each of which passes particle flows in both directions. The inner sheath or plasma potential develops self consistently to establish charge neutrality and divergence free charge and mass flows. When the electron supply is restricted, the inner sheath exhibits oscillations near the ion plasma frequency. When all electrons are excluded, a virtual anode forms on the inside sheath, reflects all ions such that the bubble is empty. By pulsing the ambient plasma, the lifetime of the bubble plasma has been measured. In an afterglow, plasmaelectrons are trapped inside the bubble and the bubble decays as slow as the ambient plasma. Pulsing the grid voltage yields the time scale for filling and emptying the bubble. Probes have been shown to modify the plasma potential. Using pulsed probes, transient ringing on the time scale of ion transit times through the bubble has been observed. The start of sheathoscillations has been investigated. The instability mechanism has been qualitatively explained. The dependence of the oscillation frequency on electrons in the sheath has been clarified.

Oscillating plasma bubbles. III. Internal electron sources and sinks
View Description Hide DescriptionAn internal electron source has been used to neutralize ions injected from an ambient plasma into a spherical grid. The resultant plasma is termed a plasma “bubble.” When the electron supply from the filament is reduced, the sheath inside the bubble becomes unstable. The plasma potential of the bubble oscillates near but below the ion plasma frequency. Different modes of oscillations have been observed as well as a subharmonic and multiple harmonics. The frequency increases with ion density and decreases with electron density. The peak amplitude occurs for an optimum current and the instability is quenched at large electron densities. The frequency also increases if Langmuir probes inside the bubble draw electrons. Allowing electrons from the ambient plasma to enter, the bubble changes the frequency dependence on grid voltage. It is concluded that the net space charge density in the sheath determines the oscillation frequency. It is suggested that the sheathinstability is caused by ion inertia in an oscillatingsheath electric field which is created by ion bunching.

Oscillating plasma bubbles. IV. Grids, geometry, and gradients
View Description Hide DescriptionPlasma bubbles are created in an ambient plasma. The bubble is formed inside a cavity bounded by a negatively biased grid. Ions are injected through the grid and neutralized by electrons from either the background plasma or an internal electron emitter. The external electron supply is controlled by the grid bias relative to the external plasma potential. When the electron flux is restricted to the ion flux, the sheath of the bubble becomes unstable and causes the plasma potential to oscillate near the ion plasma frequency. The exact frequency depends on the net space charge density in the bubble sheath. The frequency increases with density and grid voltage, provided the grid forms a parallel equipotential surface. The present investigation shows that when the Debye length becomes smaller than the grid openings the electron flux cannot be controlled by the grid voltage. The frequency dependence on grid voltage and density is modified creating frequency and amplitude jumps. Low frequency sheathoscillations modulate the high frequency normal oscillations. Harmonics and subharmonics are excited by electrons in an ionrich sheath. When the plasma parameters vary over the bubble surface, the sheath may oscillate at different frequencies. A cavity with two isolated grids has been used to investigate anisotropies of the energetic electron flux in a discharge plasma. The frequency dependence on grid voltage is entirely different when the grid controls the energetic electrons or the bulk electrons. These observations are important to several fields of basic plasma physics, such as sheaths,sheathinstabilities,diagnostic probes, current, and space charge neutralization of ion beams.

The role of compressibility in energy release by magnetic reconnection
View Description Hide DescriptionUsing resistive compressible magnetohydrodynamics, we investigate the energy release and transfer by magnetic reconnection in finite (closed or periodic) systems. The emphasis is on the magnitude of energy released and transferred to plasma heating in configurations that range from highly compressible to incompressible, based on the magnitude of the background (ratio of plasma pressure over magnetic pressure) and of a guide field in twodimensional reconnection. As expected, the system becomes more incompressible, and the role of compressional heating diminishes, with increasing or increasing guide field. Nevertheless, compressional heating may dominate over Joule heating for values of the guide field of 2 or 3 (in relation to the reconnecting magnetic field component) and of 5–10. This result stems from the strong localization of the dissipation near the reconnection site, which is modeled based on particle simulation results. Imposing uniform resistivity, corresponding to a Lundquist number of to , leads to significantly larger Ohmic heating. Increasing incompressibility greatly reduces the magnetic flux transfer and the amount of energy released, from of the energy associated with the reconnecting field component, for zero guide field and low , to for large values of the guide field or large . The results demonstrate the importance of taking into account plasma compressibility and localization of dissipation in investigations of heating by turbulent reconnection, possibly relevant for solar wind or coronal heating.

Beamwave interaction analysis of a magnetically insulated line oscillator
View Description Hide DescriptionMagnetically insulated line oscillator (MILO) using a metal discloaded coaxial cylindrical waveguide as its RF interaction structure is field analyzed for the beamwave interaction using the linearized Vlasov equation. The beam present dispersion relation of the device is obtained applying the modal matching technique which is further used to estimate the oscillation frequency, temporal growth rate, output energy, and other device parameters. Further, MILO is simulated using commercial pic code “magic,” and the electron momentum and energy plots are found to be in agreement with those obtained through the present analysis within 5%. Furthermore, the device temporal growth rate reported in the literature for the experimental MILO device is also compared with the present analytical theory and found in agreement ∼5%.

The effects of nonthermal electron distributions on iontemperaturegradient driven driftwave instabilities in electronion plasma
View Description Hide DescriptionThe effects of nonthermal electron distributions on electrostaticiontemperaturegradient(ITG) driven driftwave instabilities in the presence of equilibrium density, temperature, and magnetic field gradients are investigated here. By using Braginskii’s transportequations for ions and Cairns as well as Kappa distribution for electrons, the coupled modeequations are derived. The modified ITG driven modes are derived, and it is found both analytically as well as numerically that the nonthermal distribution of electrons significantly modify the real frequencies as well as the growth rate of the ITG driven drift wave instability. The growth rate of iontemperaturegradient driven instability is found to be maximum for Cairns, intermediate for Kappa, and minimum for the Maxwellian distributed electron case. The results of present investigation might be helpful to understand several wave phenomena in space and laboratory plasmas in the presence of nonthermal electrons.

Nonmodal analysis of the diocotron instability: Plane geometry
View Description Hide DescriptionThe comprehensive investigation of the temporal evolution of the diocotron instability of the plane electron strip on the linear stage of its development is performed. By using the method of Kelvin of the shearing modes, the role of the initial perturbations of the electron density is elucidated, which is connected with the problem of the continuous spectrum. The linear nonmodal evolution process detected by the solution of the initial value problem, leads toward convergence to the phaselocking configuration of the mutually growing normal modes.

Extending magnetohydrodynamics to the slow dynamics of collisionless plasmas
View Description Hide DescriptionA fluid approach aimed to provide a consistent description of the slow dynamics of a collisionless plasma, is presented. In this regime, both Landau damping and finite Larmor radius effects cannot be ignored. Two models are discussed; one retains the dynamics at subionic scales, while the other is restricted to scales larger than the ion gyroscale. Special attention is paid to the capability of these approaches to accurately reproduce the properties of linear waves that are known to play an important role, for example, in the smallscale dynamics of solar wind turbulence.

Integral equation for electrostatic waves generated by a point source in a spatially homogeneous magnetized plasma
View Description Hide DescriptionThe electric field generated by a time varying point charge in a threedimensional, unbounded, spatially homogeneous plasma with a uniform background magnetic field and a uniform (static) flow velocity is studied in the electrostatic approximation which is often valid in the near field. For plasmas characterized by Maxwelldistribution functions with isotropic temperatures, the linearized VlasovPoisson equations may be formulated in terms of an equivalent integral equation in the time domain. The kernel of the integral equation has a relatively simple mathematical form consisting of elementary functions such as exponential and trigonometric functions (sines and cosines), and contains no infinite sums of Bessel functions. Consequently, the integral equation is amenable to numerical solutions and may be useful for the study of the impulse response of magnetized plasmas and, more generally, the response to arbitrary waveforms.

Numerical studies of a plasma diode with external forcing
View Description Hide DescriptionWith reference to laboratory Qmachine 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 particleincell 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 exchangecollisions 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.

Classical field isomorphisms in twofluid plasmas
View Description Hide DescriptionPrevious work recognized a new framework for the equations of a multifluid plasma, wherein each species can be described by a set of equations remarkably similar to the Maxwell equations of classical electrodynamics. This paper extends the previous effort to form an exact isomorphism between the multifluid theory and classical electrodynamics. The major benefits of the new formulation are that the explicit coupling between different species is minimized, and theorems and techniques of classical electrodynamics can be immediately applied to the new multifluid formulation. We introduce the exact isomorphism and investigate some of the immediate consequences from classical electrodynamics. To provide a visualization of the isomorphism, previous 1D and 2D numerical simulations are postprocessed and presented to illustrate the generalized fields and source terms.