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Sep 2006

Volume 13, Issue 9, Articles (09xxxx)

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Three-dimensional stereoscopy of Yukawa (Coulomb) balls in dusty plasmas

Sebastian Käding and André Melzer

Phys. Plasmas 13, 090701 (2006); http://dx.doi.org/10.1063/1.2354149 (4 pages) | Cited 18 times

Online Publication Date: 11 September 2006

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A stereoscopic approach with standard video cameras for positioning and tracking of micrometer sized polymer particles in a radio-frequency gas discharge is presented. The stereoscopy is applied to simultaneously determine the positions of all particles in a three-dimensional strongly coupled spherical dusty plasma (Yukawa ball). The accuracy of the stereoscopic method is discussed. The shell structure and the occupation number of various Yukawa balls are determined and compared to recent simulations and models.
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52.27.Lw Dusty or complex plasmas; plasma crystals
52.27.Gr Strongly-coupled plasmas
82.70.Dd Colloids
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back to top Basic Plasma Phenomena, Waves, Instabilities

Finite element implementation of Braginskii’s gyroviscous stress with application to the gravitational instability

N. M. Ferraro and S. C. Jardin

Phys. Plasmas 13, 092101 (2006); http://dx.doi.org/10.1063/1.2236277 (12 pages) | Cited 7 times

Online Publication Date: 1 September 2006

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A general coordinate-independent expression for Braginskii’s form of the ion gyroviscosity in the two-dimensional potential field representation is presented, and is implemented in a full two-dimensional, two-fluid extended magnetohydrodynamic (MHD) numerical model. The expression for the gyroviscous force requires no field to be differentiated more than twice, and thus is appropriate for finite elements with first derivatives continuous across element boundaries (C1 finite elements). From the extended MHD model, which includes the full gyroviscous stress, are derived linear dispersion relations of a homogeneous equilibrium and of an inverted-density profile in the presence of gravity. The treatment of the gravitational instability presented here extends previous work on the subject [M. N. Rosenbluth, N. A. Krall, and N. Rostoker, Nucl. Fusion Suppl. 1, 143 (1962); K. V. Roberts and J. B. Taylor, Phys. Rev. Lett. 8, 197 (1962)]. Linear and nonlinear simulations of the gravitational instability are presented. Simulations are shown to agree closely with the derived dispersion relations in the linear regime. The “gyroviscous cancellation” effect is demonstrated, and some limitations of the math* approximation are discussed.
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52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.25.Fi Transport properties
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.65.Kj Magnetohydrodynamic and fluid equation
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

m = 1 ideal internal kink modes in a line-tied screw pinch

Yi-Min Huang, Ellen G. Zweibel, and Carl R. Sovinec

Phys. Plasmas 13, 092102 (2006); http://dx.doi.org/10.1063/1.2336506 (15 pages) | Cited 12 times

Online Publication Date: 1 September 2006

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It is well known that the radial displacement of the m = 1 internal kink mode in a periodic screw pinch has a steep jump at the resonant surface where k∙B = 0 [ Rosenbluth, Dagazian, and Rutherford, Phys. Fluids 16, 1894 (1973) ]. In a line-tied system, relevant to solar and astrophysical plasmas, the resonant surface is no longer a valid concept. It is then of interest to see how line-tying alters the aforementioned result for a periodic system. If the line-tied kink also produces a steep gradient, corresponding to a thin current layer, it may lead to strong resistive effects even with weak dissipation. Numerical solution of the eigenmode equations shows that the fastest growing kink mode in a line-tied system still possesses a jump in the radial displacement at the location coincident with the resonant surface of the fastest growing mode in the periodic counterpart. However, line-tying thickens the inner layer and slows down the growth rate. As the system length L approaches infinity, both the inner layer thickness and the growth rate approach the periodic values. In the limit of small ϵ ∼ Bϕ/Bz, the critical length for instability Lc ∼ ϵ−3. The relative increase in the inner layer thickness due to line-tying scales as ϵ−1(Lc/L)2.5.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Tn Ideal and resistive MHD modes; kinetic modes
52.55.Ez Theta pinch
52.25.Fi Transport properties
02.60.Cb Numerical simulation; solution of equations

Low frequency instabilities during dust particle growth in a radio-frequency plasma

Maxime Mikikian, Marjorie Cavarroc, Lénaïc Couëdel, and Laïfa Boufendi

Phys. Plasmas 13, 092103 (2006); http://dx.doi.org/10.1063/1.2337793 (8 pages) | Cited 15 times

Online Publication Date: 6 September 2006

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In this paper, instabilities appearing in a dusty plasma are experimentally investigated. These low frequency self-excited instabilities appear during dust particle growth and are characterized by a frequency spectrum evolving during this process. The onset, the time evolution and the main characteristics of these instabilities are investigated thanks to electrical and optical measurements. Both signals show a clear evolution scheme with a well-defined succession of phases. From the beginning to the end of this scheme, regular oscillations and/or chaotic regimes are observed. Finally, instabilities stop when the dust particle size reaches a few hundreds of nanometers and a stable three-dimensional dust cloud is obtained. A dust-free region called void is then usually observed in the plasma center.
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52.27.Lw Dusty or complex plasmas; plasma crystals
52.35.−g
52.25.Vy Impurities in plasmas
52.25.Gj Fluctuation and chaos phenomena
52.35.Ra Plasma turbulence

Electron energy distribution functions in low-pressure inductively coupled bounded plasmas

Albert Meige and Rod W. Boswell

Phys. Plasmas 13, 092104 (2006); http://dx.doi.org/10.1063/1.2339024 (5 pages) | Cited 23 times

Online Publication Date: 7 September 2006

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The electron energy distribution function (EEDF) in a low-pressure inductively coupled plasma confined between two infinite plates separated by 10 cm is investigated using a one-dimensional particle-in-cell simulation including Monte Carlo collisions. At low pressure, where the electron mean free path is of the order of or greater than the system length, the EEDF is close to Maxwellian, except for its tail, depleted at high energy. We give clear evidence that this depletion is mostly due to the high-energy electrons escaping to the walls. As a result of the EEDF nonlocality, the break energy, for which the depletion of the Maxwellian starts, is found to track the plasma potential. At a higher pressure, the electron mean free paths of the various elastic and inelastic collisions become shorter than the system length, resulting in a loss of nonlocality and the break energy of the distribution function moves to energies lower than the plasma potential.
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52.40.Hf Plasma-material interactions; boundary layer effects
52.65.Rr Particle-in-cell method
52.65.Pp Monte Carlo methods
52.25.Dg Plasma kinetic equations
52.20.Fs Electron collisions
52.25.Fi Transport properties

A semi-analytic model for localized variable charge dust acoustic waves

Mouloud Tribeche, Leila Ait Gougam, and Kamal Aoutou

Phys. Plasmas 13, 092105 (2006); http://dx.doi.org/10.1063/1.2338772 (4 pages) | Cited 4 times

Online Publication Date: 8 September 2006

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A semi-analytic model for nonlinear variable charge dust acoustic waves is outlined. It is shown that rarefactive variable charge dust acoustic solitons involving cusped density humps can exist. The effects of dust dynamics as well as equilibrium dust charge on these nonlinear localized structures are briefly discussed.
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52.27.Lw Dusty or complex plasmas; plasma crystals
52.35.Dm Sound waves
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Sb Solitons; BGK modes

Inhomogeneity scale lengths in a magnetized, low-temperature, collisionless, Q-machine plasma column containing perpendicular-velocity shear

E. W. Reynolds, M. E. Koepke, J. J. Carroll, and S. Shinohara

Phys. Plasmas 13, 092106 (2006); http://dx.doi.org/10.1063/1.2338293 (12 pages) | Cited 1 time

Online Publication Date: 11 September 2006

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Radial inhomogeneity scale lengths for radial electric field, ion density, and magnetic-field-aligned (parallel) electron-drift velocity have been measured and interpreted in magnetized, low-temperature, collisionless plasma. The effect of a narrow layer of inhomogeneity in these parameters on the excitation of electrostatic ion-cyclotron waves is investigated. When the ion Larmor radius ρi is on the order of, or larger than, the half-width at half-maximum σr{Er} of the Gaussian-like, radially localized, radial electric-field profile Er(r), the radial profile of the azimuthal ion rotation velocity, measured using laser-induced fluorescence (LIF), has a peak that, because of finite-Larmor-radius effects, is significantly lower than the peak of the combined radial profile of the E×B and diamagnetic drift velocities. Results of an experimentally validated test-particle simulation are presented and applied using experimentally relevant electric-field profiles. Two experimental configurations are explored for which the ions enter into the electric field at different rates. In one configuration, the ions experience an effectively adiabatic increase in electric-field strength. In the other configuration, the increase in electric-field strength is effectively instantaneous. The simulation reproduces both the main features of the radial profile of LIF-measured ion flow and the observed density depletion in regions of relatively high plasma potential for experimental conditions in which no waves were observed. The density depletion is interpreted as resulting from the finite-Larmor-radius ion orbits in the presence of an inhomogeneous electric field with radial scale length σr{Er} ≈ ρi.
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52.20.−j
52.20.Dq Particle orbits
52.25.Xz Magnetized plasmas
52.27.Aj Single-component, electron-positive-ion plasmas
52.30.−q
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.65.Cc Particle orbit and trajectory
52.70.Nc Particle measurements

Magneto-flow instability in symmetric field profiles

T. Tatsuno and W. Dorland

Phys. Plasmas 13, 092107 (2006); http://dx.doi.org/10.1063/1.2338819 (14 pages) | Cited 6 times

Online Publication Date: 12 September 2006

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Since Rayleigh’s early work on shear-flow driven instabilities in fluids, it has been known that sheared flows are usually unstable only in the presence of an inflection point in the velocity profile. However, in magnetohydrodynamics, there are important instabilities for which no inflection point is required. In tokamak experiments, strongly sheared flows are associated with transport barriers. Instabilities that may limit the height and extent of transport barriers are of central importance. Here, we present linear and nonlinear simulations of an ideal magnetohydrodynamic instability that is driven by sheared flows without inflection points—instead, the instability mechanism requires reversed magnetic shear. Several symmetric field profiles are studied. In general, the instability leads to current profile modifications that push the local minimum value of the safety factor (qmin) upward. The possibility of causing disruption in a relatively slow time scale is pointed out when qmin crosses a rational (especially integral) value. The time scale of the instability is governed by the transit time of the shear flow, which is typically smaller than that of the Alfvén velocity. Characteristics of this instability are compared with recent experimental observations.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.55.Tn Ideal and resistive MHD modes; kinetic modes
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.55.Fa Tokamaks, spherical tokamaks
52.25.Fi Transport properties
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)

Non-neutral plasma equilibria with weak axisymmetric magnetic perturbations

I. A. Kotelnikov, M. Romé, and A. Kabantsev

Phys. Plasmas 13, 092108 (2006); http://dx.doi.org/10.1063/1.2344930 (12 pages) | Cited 4 times

Online Publication Date: 12 September 2006

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The effect of weak axisymmetric magnetic and/or electrostatic perturbations on the equilibrium of a non-neutral plasma in a Malmberg-Penning trap is analyzed. Analytical and semianalytical solutions for the potential variations inside the trap are found in a paraxial limit of the perturbations for various radial density profiles of the plasma, including the case of global thermal equilibrium. It is shown that a magnetic perturbation produces a potential variation with a sign which is changing along the plasma radius. The fraction of magnetically and electrostatically trapped particles thus created is calculated explicitly for the case of a Maxwellian distribution function, and it is shown to be independent from the sign of the magnetic field perturbation. The analysis of the potential perturbation is extended to the case of an anisotropic distribution function, with an arbitrary ratio between the parallel and the perpendicular plasma temperature. Two-dimensional thermal equilibrium simulations for parameters relevant to the CamV device [ A. A. Kabantsev, J. H. Yu, R. B. Lynch, and C. F. Driscoll, Phys. Plasmas 10, 1628 (2003) ] confirm the predictions of the analytical theory for smooth and weak perturbations of the magnetic field.
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52.27.Jt Nonneutral plasmas
52.55.Lf Field-reversed configurations, rotamaks, astrons, ion rings, magnetized target fusion, and cusps
52.25.Tx Emission, absorption, and scattering of particles
52.25.Kn Thermodynamics of plasmas
52.25.Fi Transport properties

A comparison of ultrarelativistic electron- and positron-bunch propagation in plasmas

C. T. Zhou, X. T. He, and M. Y. Yu

Phys. Plasmas 13, 092109 (2006); http://dx.doi.org/10.1063/1.2345580 (5 pages) | Cited 12 times

Online Publication Date: 12 September 2006

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Beam-driven acceleration of electrons and positrons by the electric field of the plasma wakefield is considered in detail using a self-consistent relativistic cylindrical particle-in-cell code with implicit electromagnetic solver. The plasma characteristics, such as the particle motion, the density, the temperatures, the wake fields, and the energies and their transfer, are investigated. Strong local energization and heating of the plasma electrons are observed. Small groups of ions in the wake can also attain temperatures higher than the secondary ionization potential of lithium vapor. It is verified that an electron bunch indeed excites a wakefield of higher energy than a positron bunch, which, in fact, behaves like a negative charge plasma bunch because of the suck-in of background plasma electrons.
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52.65.Rr Particle-in-cell method
52.40.Mj Particle beam interactions in plasmas
41.75.Ht Relativistic electron and positron beams
41.75.Lx Other advanced accelerator concepts

New approach for the study of linear Vlasov stability of inhomogeneous systems

Enrico Camporeale, Gian Luca Delzanno, Giovanni Lapenta, and William Daughton

Phys. Plasmas 13, 092110 (2006); http://dx.doi.org/10.1063/1.2345358 (23 pages) | Cited 3 times

Online Publication Date: 14 September 2006

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This paper presents an alternative technique for solving the linearized Vlasov-Maxwell set of equations, in which the velocity dependence of the perturbed distribution function is described by means of an infinite series of orthogonal functions, chosen as Hermite polynomials. The orthogonality properties of such functions allow us to decompose the Vlasov equation into a set of infinite coupled linear equations. With a suitable truncation relation, the problem is transformed in an eigenvalue problem. This technique is based on solid but easy concepts, not attempting to evaluate the integration over the unperturbed trajectories and can be applied to any equilibrium. Although the solutions are approximate, because they neglect contributions of higher order coefficients of the series, the physical meaning of the low-order coefficients is clear. Furthermore the accuracy of the solution, which depends on the number of terms taken into account in the Hermite series, appears to be merely a problem of computational power. The method has been tested for a 1D Harris equilibrium, known to give rise to several instabilities like tearing, drift kink, and lower hybrid. The results are shown in agreement with those obtained by Daughton with a traditional technique based on the integration over unperturbed orbits.
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52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)
52.25.Dg Plasma kinetic equations
52.25.Fi Transport properties
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.20.Dq Particle orbits
02.60.Jh Numerical differentiation and integration

Electron plasmas: Confinement and mode structure in a small aspect ratio toroidal experiment

S. Pahari, H. S. Ramachandran, and P. I. John

Phys. Plasmas 13, 092111 (2006); http://dx.doi.org/10.1063/1.2345584 (12 pages) | Cited 8 times

Online Publication Date: 15 September 2006

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Toroidal electron plasmas have remained less explored due to their poor confinement properties. Their equilibrium, stability, and confinement properties are therefore not entirely understood and continue to remain a topic of intense ongoing research. Large aspect-ratio theory suggests poor confinement in toroidal devices can be overcome by the application of a radial electric field; this has been verified successfully in some of the recent experiments. In the present paper, we report the longest confinement time without these external forces. Increasing the toroidicity has helped us to generate these forces intrinsically. To this end, a trap to confine electron plasmas has been created in a small aspect-ratio ( ≈ 1.6) torus. Electrons after being injected from a thermionic source are seen to remain confined with a purely toroidal magnetic field. The confinement time is far more than known single particle drift time scales. Importantly, it is in the absence of any external electric field, additional rotational transform, and/or magnetic fields, which, although not required, in principle, may appear essential particularly due to their role in improving confinement in some of the recent large aspect-ratio traps. The successful confinement in the small aspect-ratio limit has also led to several interesting observations: the evolution of the confined plasma is marked by an interesting nonlinear (large amplitude), electrostatic wave activity. Coherent, periodic, double peak oscillations result from a low-frequency E×B motion of a toroidal vortex in a plasma that closely leans against the inner wall. As many as 16 highly phase-coherent harmonics with dominant power in m = 2 suggest that the mode is not merely a center-of-charge motion. Rather, a strong coupling of modes leads to a novel nonlinear state. The predominant energy is present in the shaping of the electron cloud (m = 2) and not in the displacement of the center of charge (m = 1) seen in large aspect-ratio traps. The absence of any power-law tail suggests absence of any turbulence, at least on time scales longer than the wall-probe resolution (40 ns). The frequency, (around 100 kHz at 200 G) shows an unusual shear in time: it reduces as the mode evolves, but later increases as the mode dies.
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52.55.Lf Field-reversed configurations, rotamaks, astrons, ion rings, magnetized target fusion, and cusps
52.55.Dy General theory and basic studies of plasma lifetime, particle and heat loss, energy balance, field structure, etc.
52.25.Fi Transport properties
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.35.We Plasma vorticity

Generation of suprathermal electrons and Alfvén waves by a high power pulse at the electron plasma frequency

B. Van Compernolle, W. Gekelman, and P. Pribyl

Phys. Plasmas 13, 092112 (2006); http://dx.doi.org/10.1063/1.2261850 (12 pages) | Cited 8 times

Online Publication Date: 15 September 2006

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The interaction of a short high power pulse at the electron plasma frequency (f = 9 GHz, pulse length τ = 0.5 μs or 2.5 μs, input power P<80 kW) and a magnetized plasma (n0 ⩽ 2×1012 cm−3, B0 = 1–2.5 kG, helium) capable of supporting Alfvén waves has been studied. The interaction leads to the generation of field aligned suprathermal electrons and shear Alfvén waves. The experiment was performed both in ordinary mode (O mode) and extraordinary mode (X mode), for different background magnetic fields B0 and different power levels of the incoming microwaves.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.25.Tx Emission, absorption, and scattering of particles
52.25.Xz Magnetized plasmas
52.70.Gw Radio-frequency and microwave measurements

Evanescent wave interference and the total transparency of a warm high-density plasma slab

E. Fourkal, I. Velchev, C-M. Ma, and A. Smolyakov

Phys. Plasmas 13, 092113 (2006); http://dx.doi.org/10.1063/1.2354574 (9 pages) | Cited 10 times

Online Publication Date: 19 September 2006

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It is shown that an overcritical density plasma slab can be totally transparent to a p-polarized obliquely incident electromagnetic wave. High transparency is achieved due to the interference of the evanescent waves in the subcritical region. The transmission coefficient has the resonant character due to the excitation of a plasma surface mode (plasmon-polariton). In a warm plasma case, the excitation of the propagating longitudinal (electrostatic) modes becomes possible. It is demonstrated that these longitudinal excitations facilitate the total transparency of an opaque plasma slab creating additional resonances in the transmission property of the system.
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52.40.Db Electromagnetic (nonlaser) radiation interactions with plasma
52.25.Os Emission, absorption, and scattering of electromagnetic radiation
52.35.Hr Electromagnetic waves (e.g., electron-cyclotron, Whistler, Bernstein, upper hybrid, lower hybrid)
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)

Simulation study of spheroidal dust gains charging: Applicable to dust grain alignment

H. Zahed, S. Sobhanian, J. Mahmoodi, and S. Khorram

Phys. Plasmas 13, 092114 (2006); http://dx.doi.org/10.1063/1.2338568 (9 pages) | Cited 1 time

Online Publication Date: 19 September 2006

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The charging process of nonspherical dust grains in an unmagnetized plasma as well as in the presence of a magnetic field is studied. It is shown that unlike the spherical dust grain, due to nonhomogeneity of charge distribution on the spheroidal dust surface, the resultant electric forces on electrons and ions are different. This process produces some surface charge density gradient on the nonspherical grain surface. Effects of a magnetic field and other plasma parameters on the properties of the dust particulate are studied. It has been shown that the alignment direction could be changed or even reversed with the magnetic field and plasma parameters. Finally, the charge distribution on the spheroidal grain surface is studied for different ambient parameters including plasma temperature, neutral collision frequency, and the magnitude of the magnetic field.
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52.27.Lw Dusty or complex plasmas; plasma crystals
52.65.Cc Particle orbit and trajectory
52.25.Fi Transport properties
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.20.Hv Atomic, molecular, ion, and heavy-particle collisions
52.20.Fs Electron collisions

Relativistic Landau damping of longitudinal waves in isotropic pair plasmas

E. W. Laing and D. A. Diver

Phys. Plasmas 13, 092115 (2006); http://dx.doi.org/10.1063/1.2353901 (11 pages) | Cited 3 times

Online Publication Date: 21 September 2006

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Landau damping is described in relativistic electron-positron plasmas. Relativistic electron-positron plasma theory contains important new effects when compared with classical plasmas. For example, there are undamped superluminal wave modes arising from both a continuous and discrete mode structure, the former even in the classical limit. We present here a comprehensive analytical treatment of the general case resulting in a compact and useful form for the dispersion relation. The classical pair-plasma case is addressed, for completeness, in an appendix.
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52.25.Dg Plasma kinetic equations
52.27.Ep Electron-positron plasmas
52.27.Ny Relativistic plasmas
52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
97.60.Gb Pulsars

Rankine-Hugoniot relations of an axial shock in cylindrical non-neutral plasma

Yong He, Xiwei Hu, Yemin Hu, Zhonghe Jiang, and Jianhong Lü

Phys. Plasmas 13, 092116 (2006); http://dx.doi.org/10.1063/1.2355661 (5 pages) | Cited 5 times

Online Publication Date: 21 September 2006

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The Rankine-Hugoniot relations of an axial shock in cylindrical non-neutral plasma with current, electric and magnetic field are presented. These relations are all dependent on the radius of cylindrical plasma, and markedly different from the one-dimensional (i.e., nonradially dependent) case. These two-dimensional Rankine-Hugoniot relations cause at least two important new results. First, the radial profiles of the shock downstream parameters are always different from the upstream profiles due to the magnetic effects. Second, the critical Mach number for the shock existence will depend on the shock carried current (i.e., magnetic field). As an example, a set of shock downstream profiles is provided numerically when the upstream profiles are taken as a kind of typical equilibrium profiles of a Z-pinch-Bennett profiles. By comparing the downstream profiles to the corresponding upstream profiles, the dependents of both the amplitudes and profiles of the downstream parameters on the shock carried current are shown.
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52.35.Tc Shock waves and discontinuities
52.27.Jt Nonneutral plasmas
52.25.Kn Thermodynamics of plasmas
52.25.Fi Transport properties
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.58.Lq Z-pinches, plasma focus, and other pinch devices

Entropy conservation in simulations of magnetic reconnection

J. Birn, M. Hesse, and K. Schindler

Phys. Plasmas 13, 092117 (2006); http://dx.doi.org/10.1063/1.2349440 (6 pages) | Cited 13 times

Online Publication Date: 27 September 2006

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Entropy and mass conservation are investigated for the dynamic field evolution associated with fast magnetic reconnection, based on the “Newton Challenge” problem [ Birn et al., Geophys. Res. Lett. 32, L06105 (2005) ]. In this problem, the formation of a thin current sheet and magnetic reconnection are initiated in a plane Harris-type current sheet by temporally limited, spatially varying, inflow of magnetic flux. Using resistive magnetohydrodynamic (MHD) and particle-in-cell (PIC) simulations, specifically the entropy and mass integrated along the magnetic flux tubes are compared between the simulations. In the MHD simulation these should be exactly conserved quantities, when slippage and Ohmic dissipation are negligible. It is shown that there is very good agreement between the conservation of these quantities in the two simulation approaches, despite the effects of dissipation, provided that the resistivity in the MHD simulation is strongly localized. This demonstrates that dissipation is highly localized in the PIC simulation also, and that heat flux across magnetic flux tubes has negligible effect as well, so that the entropy increase on a full flux tube remains small even during reconnection. The mass conservation also implies that the frozen-in flux condition of ideal MHD is a good integral approximation outside the reconnection site. This result lends support for using the entropy-conserving MHD approach not only before and after reconnection but even as a constraint connecting the two phases.
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52.35.Vd Magnetic reconnection
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.25.Kn Thermodynamics of plasmas
52.65.Rr Particle-in-cell method
52.65.Kj Magnetohydrodynamic and fluid equation
52.25.Fi Transport properties
back to top Nonlinear Phenomena, Turbulence, Transport

Clebsch-type coordinates for nonlinear gyrokinetics in generic toroidal configurations

P. Xanthopoulos and F. Jenko

Phys. Plasmas 13, 092301 (2006); http://dx.doi.org/10.1063/1.2338818 (10 pages) | Cited 17 times

Online Publication Date: 7 September 2006

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The nonlinear gyrokinetic equations are frequently used as a basis for simulations of small-scale turbulence in magnetized toroidal plasmas. In this context, field-aligned coordinates are usually employed in order to minimize the number of necessary grid points. The present work proposes a system of Clebsch-type coordinates which does not depend on the existence of flux surfaces. The construction and use of these coordinates is explained, and the corresponding formulation of the nonlinear gyrokinetic equations is accomplished. This setup paves the way toward the investigation of nonaxisymmetric toroidal geometries, also in the region of magnetic islands as well as inside the ergodic layer where flux surfaces cease to exist. For testing purposes, in the axisymmetric, large aspect ratio case, the well-known math-α expressions are recovered for closed flux surfaces. Moreover, geometric data for a specific stellarator configuration are computed and discussed.
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52.35.Ra Plasma turbulence
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Bj Magnetohydrodynamic waves (e.g., Alfven waves)
52.25.Dg Plasma kinetic equations
52.25.Xz Magnetized plasmas
52.55.Jd Magnetic mirrors, gas dynamic traps

Stability and evolution of one-dimensional relativistic solitons on the ion time scale

G. Lehmann, E. W. Laedke, and K. H. Spatschek

Phys. Plasmas 13, 092302 (2006); http://dx.doi.org/10.1063/1.2338820 (9 pages) | Cited 17 times

Online Publication Date: 11 September 2006

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The one-dimensional dynamics of trapped relativistic electromagnetic radiation, which appears during laser plasma interaction, is investigated within a relativistic fluid-Maxwell model. The modifications of plasma density due to trapped laser fields are considered for linear as well as circular polarizations. It is shown that standing (V = 0) solitons are stable on the electron time scale. However, the stability region does not agree with the prediction from the Vakhitov-Kolokolov criterion. Ions always drive the standing solitons unstable, irrespective of the polarization. The stability of moving (0<V<c) solitons, which have been obtained in the literature as stationary solutions of the fluid-Maxwell equations including ion dynamics, is demonstrated. The problem of soliton generation is addressed. The time evolution of the so called post-solitons, which are generated behind a broad laser pulse propagating in underdense plasma, is analyzed. The effect of finite electron and ion temperatures is briefly discussed.
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52.35.Sb Solitons; BGK modes
52.38.Hb Self-focussing, channeling, and filamentation in plasmas
52.65.Kj Magnetohydrodynamic and fluid equation
42.65.Tg Optical solitons; nonlinear guided waves

Equilibrium structures in partially ionized rotating plasmas within Hall magnetohydrodynamics

V. Krishan and Z. Yoshida

Phys. Plasmas 13, 092303 (2006); http://dx.doi.org/10.1063/1.2345176 (5 pages) | Cited 5 times

Online Publication Date: 11 September 2006

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The formation of equilibrium structures in partially ionized rotating plasmas, consisting of electrons, ions, and neutral molecules, including the Hall effect, is studied in order to diagnose the possible velocity and the magnetic field configurations in a self-consistent manner. A few simple examples show that the linear and the nonlinear force-free magnetic configurations along with essentially nonlinear Beltrami flow field seem to be the general features of plasmas in the special case of the Keplerian rotation relevant for astrophysical plasmas. Thus rotation along with axial bipolar flows emerges as a natural pattern in gravitationally controlled magnetohydrodynamic systems. However, the equilibrium conditions permit more general flow and the magnetic field profiles that can perhaps be fully explored numerically. A special class of equilibria with unit magnetic Prandtl number and equal values of the fractional ion mass density α = ρi/ρn and the Hall parameter ϵ = λi/L exists where ρ’s are the uniform mass densities, λi is the ion inertial scale, and L is the scale of the equilibrium structure. An approximate scaling law between the ionization fraction and the scale of the structure is found. Further by expressing the not so well known ionization fraction in terms of the temperature of the system, assuming thermal equilibrium, relationships among the extensive parameters such as the scale, the neutral particle density, the flow velocity, the temperature, and the magnetic field of the equilibrium structure can be determined. There seems to be a good overlap between the Hall and the thermal equilibria. The validity of the neglect of the ion dynamics is discussed.
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52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.25.Ya Neutrals in plasmas
52.25.Fi Transport properties
52.25.Kn Thermodynamics of plasmas
52.25.Jm Ionization of plasmas

Vlasov simulation of amplitude-modulated Langmuir waves

Takayuki Umeda

Phys. Plasmas 13, 092304 (2006); http://dx.doi.org/10.1063/1.2348088 (5 pages) | Cited 6 times

Online Publication Date: 11 September 2006

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Mechanisms for the generation of Langmuir wave packets are studied by performing a one-dimensional electrostatic Vlasov simulation. The present simulation of a weak-electron-beam instability without ion dynamics suggests two new processes for the amplitude modulation of Langmuir waves. The beam instability excites Langmuir modes over a wide wave number range, but the saturation of the most unstable Langmuir mode “filters” the growth of sideband modes. Specific upper and lower sideband modes linearly grow to a high saturation level. Then the primary Langmuir mode is amplified and strongly modulated through interaction with the sideband modes.
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52.35.Fp Electrostatic waves and oscillations (e.g., ion-acoustic waves)
52.65.Ff Fokker-Planck and Vlasov equation
52.25.Dg Plasma kinetic equations
52.25.Fi Transport properties
52.40.Mj Particle beam interactions in plasmas
52.35.Py Macroinstabilities (hydromagnetic, e.g., kink, fire-hose, mirror, ballooning, tearing, trapped-particle, flute, Rayleigh-Taylor, etc.)

Shear-driven magnetic reconnection in viscous resistive incompressible plasmas

Yuri E. Litvinenko

Phys. Plasmas 13, 092305 (2006); http://dx.doi.org/10.1063/1.2345178 (4 pages) | Cited 4 times

Online Publication Date: 12 September 2006

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Planar magnetic reconnection, driven by shear flows in viscous resistive incompressible plasmas, is analyzed. Time-dependent profiles of the flow velocity and the reconnecting magnetic field are computed by solving the magnetohydrodynamic equations for disturbances of a magnetostatic configuration. The resulting asymptotic profiles for large times are characterized by boundary layers, formed at the boundaries of the region, rather than by a localized reconnecting current sheet within the region. Analysis of steady viscoresistive solutions confirms that a smooth solution, reached by a dynamically evolving system, must be nonlocalized. The results imply that at least two-dimensional shear flows are required for driving magnetic reconnection in viscous resistive plasmas.
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52.35.Vd Magnetic reconnection
52.30.Cv Magnetohydrodynamics (including electron magnetohydrodynamics)
52.25.Fi Transport properties
52.65.Kj Magnetohydrodynamic and fluid equation
52.40.Hf Plasma-material interactions; boundary layer effects

A radially resolved kinetic model for nonlocal electron ripple diffusion losses in tokamaks

Scott Robertson

Phys. Plasmas 13, 092306 (2006); http://dx.doi.org/10.1063/1.2356023 (10 pages)

Online Publication Date: 22 September 2006

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A relatively simple radially resolved kinetic model is applied to the ripple diffusion problem for electrons in tokamaks. The distribution function f(r,v) is defined on a two-dimensional grid, where r is the radial coordinate and v is the velocity coordinate. Particle transport in the radial direction is from ripple and banana diffusion and transport in the velocity direction is described by the Fokker-Planck equation. Particles and energy are replaced by source functions that are adjusted to maintain a constant central density and temperature. The relaxed profiles of f(r,v) show that the electron distribution function at the wall contains suprathermal electrons that have diffused from the interior that enhance ripple transport. The transport at the periphery is therefore nonlocal. The energy replacement times from the computational model are near to the experimental replacement times for tokamak discharges in the compilation by Pfeiffer and Waltz [Nucl. Fusion 19, 51 (1979)] .
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52.25.Dg Plasma kinetic equations
52.25.Fi Transport properties

Interplay between transport barriers and density gradient

Y. Sarazin, V. Grandgirard, G. Dif-Pradalier, X. Garbet, and Ph. Ghendrih

Phys. Plasmas 13, 092307 (2006); http://dx.doi.org/10.1063/1.2345177 (9 pages) | Cited 4 times

Online Publication Date: 22 September 2006

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The present paper addresses two critical issues of zonal flows: the evidence of control parameters of their driving term, namely the Reynolds stress, and how they back-react on turbulence and transport. Kinetic nonlinear simulations are performed with the GYSELA code [ V. Grandgirard et al., J. Comput. Phys. (to be published) ], which models the slab branch of the ion temperature gradient driven instability in the four-dimensional drift-kinetic regime. First, the numerical results show that the gradient of the guiding center density, related to the general potential vorticity, is stabilizing both linearly, by increasing the instability threshold, and nonlinearly, by activating zonal flows. Accordingly, the Reynolds stress is found to scale like LΩ−2 in the quasilinear regime, LΩ being the gradient length of the guiding center density. Second, the local temperature gradient appears to increase linearly with the curvature of the zonal flows, regardless of its sign. Such behavior agrees qualitatively with a perturbative theory. Indeed, while linear eigenmodes are localized at the maximum of the temperature gradient in the absence of zonal flows, they tend to be expelled if both exhibit a maximum at the same location. In this case, the reduction mechanism of the turbulent transport results from the ability of large zonal flow curvatures to render strong temperature gradients stable with respect to perturbations.
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52.25.Fi Transport properties
52.35.Ra Plasma turbulence
52.25.Dg Plasma kinetic equations
52.35.Mw Nonlinear phenomena: waves, wave propagation, and other interactions (including parametric effects, mode coupling, ponderomotive effects, etc.)
52.35.Qz Microinstabilities (ion-acoustic, two-stream, loss-cone, beam-plasma, drift, ion- or electron-cyclotron, etc.)
52.35.We Plasma vorticity
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