Physics of Plasmas

Published by American Institute of Physics
Online ISSN: 1089-7674
Print ISSN: 1070-664X
Color online Contour maps of a radial flow, b azimuthal flow, and c axial flow velocity on a r-z plane. Figures 4b, 4d, and 4f indicate the cross sectional views of the flow velocity.
Color online Radial profile of the plasma potential measured with the emissive probe closed circles. The solid line is obtained by integrating the azimuthal flow velocity with respect to radius r.
(a) Schematic of the HYPER-I device and (b) axial profile of the magnetic field intensity.
The flow structure of ions in a diverging magnetic field has been experimentally studied in an electron cyclotron resonance plasma. The flow velocity field of ions has been measured with directional Langmuir probes calibrated with the laser induced fluorescence spectroscopy. For low ion-temperature plasmas, it is concluded that the ion acceleration due to the axial electric field is important compared with that of gas dynamic effect. It has also been found that the detachment of ion stream line from the magnetic field line takes place when the parameter |f(ci)L(B)∕V(i)| becomes order unity, where f(ci), L(B), and V(i) are the ion cyclotron frequency, the characteristic scale length of magnetic field inhomogeneity, and the ion flow velocity, respectively. In the detachment region, a radial electric field is generated in the plasma and the ions move straight with the E×B rotation driven by the radial electric field.
The material of limiter in HT-7 tokamak was changed from graphite to molybdenum in the last experimental campaign. The pitch angle scattering of runaway electrons due to anomalous Doppler resonance effects was observed. The experimental results agree very well with the stable boundary condition expected from the linear resistive theory but only agree with that from the nonlinear evolutionary of runaway-electron distribution theory in low electric field region. The current carried by runaway electrons is the same under different limiter conditions.
A novel electron beam focusing scheme for medical X-ray sources is described in this paper. Most vacuum based medical X-ray sources today employ a tungsten filament operated in temperature limited regime, with electrostatic focusing tabs for limited range beam optics. This paper presents the electron beam optics designed for the first distributed X-ray source in the world for Computed Tomography (CT) applications. This distributed source includes 32 electron beamlets in a common vacuum chamber, with 32 circular dispenser cathodes operated in space charge limited regime, where the initial circular beam is transformed into an elliptical beam before being collected at the anode. The electron beam optics designed and validated here are at the heart of the first Inverse Geometry CT system, with potential benefits in terms of improved image quality and dramatic X-ray dose reduction for the patient.
Measurements of ion energy distribution are performed in the accelerated plasma of a coaxial electromagnetic plasma gun operating in a gas-puff mode at relatively low discharge energy (900 J) and discharge potential (4 kV). The measurements are made using a Thomson-type mass and energy spectrometer with a gated microchannel plate and phosphor screen as the ion sensor. The parabolic ion trajectories are captured from the sensor screen with an intensified charge-coupled detector camera. The spectrometer was designed and calibrated using the Geant4 toolkit, accounting for the effects on the ion trajectories of spatial non-uniformities in the spectrometer magnetic and electric fields. Results for hydrogen gas puffs indicate the existence of a class of accelerated protons with energies well above the coaxial discharge potential (up to 24 keV). The Thomson analyzer confirms the presence of impurities of copper and iron, also of relatively high energies, which are likely erosion or sputter products from plasma-electrode interactions.
Color online Illustration showing currents induced by electrostatic pickup and how they influence the measured signal voltage, U S , in an unbalanced circuit a and a balanced circuit b.
Circuit diagram of Rogowski coil pair with integrator and differential amplifier circuit.
Measurements are presented of the time-dependent current distribution inside a coaxial electromagnetic plasma gun. The measurements are carried out using an array of six axially distributed dual-Rogowski coils in a balanced circuit configuration. The radial current distributions indicate that operation in the gas-puff mode, i.e., the mode in which the electrode voltage is applied before injection of the gas, results in a stationary ionization front consistent with the presence of a plasma deflagration. The effects of varying the bank capacitance, transmission line inductance, and applied electrode voltage were studied over the range from 14 to 112 μF, 50 to 200 nH, and 1 to 3 kV, respectively.
The propagation of ultra intense laser pulses through matter is connected with the generation of strong moving magnetic fields in the propagation channel as well as the formation of a thin ion filament along the axis of the channel. Upon exiting the plasma the magnetic field displaces the electrons at the back of the target, generating a quasistatic electric field that accelerates and collimates ions from the filament. Two-dimensional Particle-in-Cell simulations show that a 1 PW laser pulse tightly focused on a near-critical density target is able to accelerate protons up to an energy of 1.3 GeV. Scaling laws and optimal conditions for proton acceleration are established considering the energy depletion of the laser pulse.
Ion-to-magnetohydrodynamic scale physics of the transverse velocity shear layer and associated Kelvin-Helmholtz instability (KHI) in a homogeneous, collisionless plasma are investigated by means of full particle simulations. The shear layer is broadened to reach a kinetic equilibrium when its initial thickness is close to the gyrodiameter of ions crossing the layer, namely, of ion-kinetic scale. The broadened thickness is larger in B⋅Ω<0 case than in B⋅Ω>0 case, where Ω is the vorticity at the layer. This is because the convective electric field, which points out of (into) the layer for B⋅Ω<0 (B⋅Ω>0), extends (reduces) the gyrodiameters. Since the kinetic equilibrium is established before the KHI onset, the KHI growth rate depends on the broadened thickness. In the saturation phase of the KHI, the ion vortex flow is strengthened (weakened) for B⋅Ω<0 (B⋅Ω>0), due to ion centrifugal drift along the rotational plasma flow. In ion inertial scale vortices, this drift effect is crucial in altering the ion vortex size. These results indicate that the KHI at Mercury-like ion-scale magnetospheric boundaries could show clear dawn-dusk asymmetries in both its linear and nonlinear growth.
Schematic of the high efficiency thermionic magnicon amplifier.
Design for the 500 kV, 210A magnicon electron gun, showing electrode geometry, selected electron trajectories and equipotentials.
Cross-section of the magnicon circuit, showing the axial magnetic field.
Steady-state simulation of the thermionic magnicon design for a 1.5-mm-diam. beam.
The magnicon is a scanning-beam microwave amplifier that is being developed as a high power, highly efficient microwave source for use in powering the next generation of high gradient electron linear accelerators. In this paper, we present a progress report on a new thermionic magnicon experiment designed to produce more than 50 MW at 11.4 GHz, using a 210 A, 500 kV beam from an ultrahigh convergence thermionic electron gun driven by a rep-rated modulator. This new design has a predicted efficiency in excess of 60%
Components of the wave magnetic field in a helicon discharge have been measured with a single-turn, coaxial magnetic probe. Left- and right-handed helical antennas, as well as plane-polarized antennas, were used; and the results were compared with the field patterns computed for a nonuniform plasma. The results show that the right-hand circularly polarized mode is preferentially excited with all antennas, even those designed to excite the left-hand mode. For right-hand excitation, the radial amplitude profiles are in excellent agreement with computations.
Field emitter arrays (FEA) are promising electron sources for vacuum microelectronic microwave amplifiers and oscillators. In this paper, microelectronic analogs of "classic" microwave devices are considered. Traveling wave klystrons, klystrodes and cross-field amplifiers with FEA are described. Basic output parameters (gain, efficiency, etc.) of these devices are calculated. A model of a self-excited vacuum microtriode oscillator is developed. The oscillator is studied numerically, as well as by experimental investigation of the circuit analog model. Chaotic generation in the oscillator under external harmonic driving is analyzed. The rf interaction with the electron beam modulated by the field emission in a twystrode is investigated using a particle-in-cell code and a one-dimensional nonlinear code. (C) 2002 American Institute of Physics.
In order to estimate the radiated power that can be expected from the next-generation z-pinch driver such as ZR at 28 MA, current-scaling experiments have been conducted on the 18-MA driver Z. We report on the current scaling of single 40-mm diameter tungsten 240-wire arrays with a fixed 110-ns implosion time. The wire diameter is decreased in proportion to the load current. The load current is reduced by reducing the charge voltage on the Marx banks. On one shot firing only 3 of the 4 levels of the Z machine further reduced the load current. The radiated energy scales as the current squared as expected but the radiated power scales as the current to the 3.5 power due to increased pinch instability at lower current. As the current is reduced the rise-time of the x-ray pulse increases and at the lowest current value of 10.4 MA a shoulder appears on the leading edge of the x-ray pulse. We will report on experiments in February 2002 which will attempt to image the pinch along the axis to determine the nature of the reduced stability at lower currents.
Test particle motion is analyzed analytically and numerically in the field configuration consisting of the equilibrium self-electric and self-magnetic fields of a well-matched, thin, continuous, intense charged-particle beam and an applied periodic focusing solenoidal magnetic field. The self fields are determined self-consistently, assuming the beam to have a uniform-density, rigid-rotor Vlasov equilibrium distribution. Using the Hamilton-Jacobi method, the betatron oscillations of test particles in the average self fields and applied focusing field are analyzed, and the nonlinear resonances induced by periodic modulations in the self fields and applied field are determined. The Poincare surface-of-section method is used to analyze numerically the phase-space structure for test particle motion outside the outermost envelope of the beam over a wide range of system parameters. For vacuum phase advance sigma(v)=80 degrees, it is found that the phase-space structure is almost entirely regular at low beam intensity (phase advance sigma greater than or similar to 70 degrees, say), whereas at moderate beam intensity (30 degrees less than or similar to sigma less than or similar to 70 degrees), nonlinear resonances appear, the most pronounced of which is the third-order primary nonlinear resonance. As the beam intensity is further increased (sigma less than or similar to 30 degrees), the widths of the higher-order nonlinear resonances increase, and the chaotic region of phase space increases in size. Furthermore, the many chaotic layers associated with the separatrices of the primary and secondary nonlinear resonances are still divided by the remaining invariant Kolmogorov-Arnold-Moser surfaces, even at very high beam intensities. The implications of the rich nonlinear resonance structure and chaotic particle motion found in the present test-particle studies are discussed in the context of halo formation. (C) 1999 American Institute of Physics. [S1070-664X(99)03409-6].
Universal voltage‐current characteristics are presented for a planar diode, showing the general transition from the Fowler–Nordheim relation to the Child–Langmuir law. These curves are normalized to the intrinsic scales that are constructed from the Fowler–Nordheim coefficients A, B. They provide an immediate assessment of the importance of the space charge effects, once the gap voltage, gap spacing, and the Fowler–Nordheim coefficients are specified. An example in the parameter regime of vacuum microelectronics is presented.
Two-dimensional electromagnetic (EM) particle-in-cell simulations were performed to study the effect of the displacement current and the self-magnetic field on the space-charge limited current density or the Child-Langmuir law of a short-pulse electron flow with a propagation distance of ζ and an emitting width of W from the classical regime to the relativistic regime. Numerical scaling of the two-dimensional electromagnetic Child-Langmuir (CL) law was constructed, and it scales with (ζ / W) and (ζ / W)<sup>2</sup> at the classical and relativistic regimes, respectively. Our findings reveal that the displacement current can considerably enhance the space-charge limited (SCL) current density as compared to the well-known two-dimensional electrostatic (ES) Child-Langmuir law even at the classical regime.
A theory describing the influence of reflections on operation of gyrotrons with radial output is presented. The theory is used for evaluating the effect of reflections on the operation of the 170 GHz ITER coaxial cavity gyrotron, which is under development in cooperation between EUROATOM Associations (CRPP Lausanne, FZK Karlsruhe, and HUT Helsinki) together with European tube industry (Thales Electron Devices, Velizy, France). It is shown that for optimally chosen external magnetic field value and electron beam radius, possible reflections do not change the final steady-state operation, which corresponds to generation of a 2.2 MW millimeter-wave power. The effect of deviation of the magnetic field and the beam radius from optimal values on the device operation is also studied.
Summary form only given. A general theory of multipactor between parallel capacitor plates with orthogonal electric and magnetic fields is given. Expressions are derived for the resonant phases at which the rf-driven cascades occur; these reduce to previously derived expressions in the limit of vanishing magnetic field. This work also obtains the conditions governing the stability of the motion about those phases, as well as a dynamic constraint from imposing the restriction that each impact on a plate is the first impact that is allowed by the equations of motion. Chaotic effects from the random ejection velocities of the secondaries are addressed for the first time
A novel crossed-field secondary-emission (CFSE) electron source that is capable of producing high current tubular electron beams is described. This new electron source is based on the mechanism of secondary emission multiplication of electron current in a magnetron-like device having smooth cylindrical electrodes. The input electron current may be as low as a few mA. The multiplication process starts at the negative slope of an applied voltage pulse. After initiation, the current is extracted from the diode region with no regard to the voltage pulse shape and as a consequence, the CFSE electron source can operate in a long pulse mode. At the diode voltage of ~40 kV for a diode gap of ~6 mm, the output current reaches a value of more than 100A. A further increase of current up to 1 kA is feasible
Summary form only given. The current densities of ions and electrons to the wall of a hot-filament discharge device are examined both experimentally and theoretically. The ion current to the wall as a function of neutral gas pressure is found theoretically from a model of the sheath and presheath that includes charge-exchange collisions of the ions with neutrals. The electron current is found from a model based upon the energy distributions of secondary-electrons from ionization of the neutral gas and of secondary electrons from the wall. In a hot-filament discharge device with argon plasma (density 0.2-4.5times10<sup>9</sup> cm<sup>-3</sup>, electron temperature 0.14-0.21 eV, pressure 0.3-12 mtorr), a gridded energy analyzer is placed behind a slit in the wall and the current collected is recorded as a function of the retarding potential. The dependence of the collector current on the grid bias potential identifies the electrons in the 10-65 eV range as being mostly secondaries from ionization and those in the 0-10 eV range as being mostly secondaries from the wall. Ions are collected at the most negative grid bias voltages. The measured ion currents are within about 40% of values calculated from a model with charge exchange collisions of ions, and at the highest pressure differ by about a factor of three from the collisionless value, indicating that the Bohm ion current should be corrected for collisions when the charge exchange mean free path is less than about 0.2 of the plasma radius.
It is demonstrated that new modes of particle oscillations, associated with magnetic properties, can exist in a one-dimensional chain of charged magnetized particles in a plasma. The stability of equilibria, transitions between the different equilibria, and a critical dependence on the external fields and plasma parameters are investigated.
Summary form only given, as follows. In low voltage gyrodevices operating at high cyclotron harmonics the electrons are weakly coupled to the synchronous harmonic of an electromagnetic field. To realize efficient operation of a device it is necessary to compensate for this weak coupling by increasing the resonator Q-factor. When the required Q-factor is on the order of the ohmic Q-factor, the optimization of gyrotron parameters should be modified by taking into account ohmic losses of the microwave power. In the present paper this modification has been done and the optimization of two- and three-cavity gyrodevices operating at cyclotron harmonics has been considered
More recently, N. Roy et al. [Phys. Plasmas \textbf{19}, 033705 (2012)] have investigated the occurrence of nonlinear solitary and double-layers in an ultrarelativistic dusty electron-positron-ion degenerate plasma using a Sagdeev potential method. They have considered a full parametric examination on Mach-number criteria for existence of such nonlinear excitations using the specific degeneracy limits of Chandrasekhar equation of state (EoS) for Fermi-Dirac plasmas. In this comment we point-out a misleading extension of polytropic EoS to study the Fermi-Dirac relativistically degenerate plasmas.
Recently, Yan-Xia Xu, et al. in the article Ref. [Phys. Plasmas \textbf{18}, 052301 (2011)] have studied the effects of various plasma parameters on interaction of two ion-acoustic solitary waves in an unmagnetized three-dimensional electron-positron-ion quantum plasma. They have used the extended reductive perturbation technique, the so-called, extended Poincare'-Lighthill-Kuo (PLK) technique, to deduce from the model governing the quantum hydrodynamics (QHD) differential equations leading to the soliton dynamical properties, namely, Korteweg-de Vries evolution equations (one for each wave) and coupled differential equations describing the phase-shift in trajectories of solitons due to the two dimensional collision. The variation of the calculated collision phase-shifts are then numerically inspected in terms of numerous plasma fractional parameters. In this comment we give some notes specific to the validity of the results of above-mentioned article and refer to important misconceptions about the use of the Fermi-temperature in quantum plasmas, appearing in this article and many other recently published ones.
Radial particle distribution for N = 190 particles given in cylindrical coordinates. Left: experiment, right two figures: simulation results with Coulomb ( κ = 0), and Yukawa ( κ = 1) potential. The length unit in the right two figures is r oc , given by Eq. (4), from Ref. [24]. 
Number of particles N s on the shells of Yukawa balls with different N and κ. Table contains experimental (last line) and theoretical shell configurations for N = 190. N 1. .. N 4 denote the particle numbers on the i-th shell beginning in the center. Figure shows the shell populations for 40 experimentally observed Yukawa balls (symbols) and molecular dynamics simulation results for several κ values [24]. κ is given in units of r −1 0 defined by mω 2 r 2 0 = e 2 /r 0 , temperature is in
(Color) 19-electron quantum Wigner "crystal" (left), radially ordered crystal (center) and mesoscopic fermionic liquid (right). From left to right quantum melting at constant temperature occurs. Dots correspond to the probability density ρ of the electrons in the 2D plane which varies
(Color) Snapshots of a Coulomb crystal of heavy particles (red clouds) embedded into a Fermi gas of electrons (yellow) in a macroscopic two-component (neutral) plasma (spin averaged results) for mass ratio M = 12 (top left), M = 50 (top right), M = 100 (bottom left), M = 400 (bottom right). The density corresponds to r se = 0.64, the temperature is T e = T h = 0.06E R. First-principle two-component PIMC simulations.
(Color) Left: mean-square relative heavy particle distance fluctuations versus mass ratio M for T e = 0.096 and r se = 0.63. Symbols are simulation results, the line is the best fit [55]. Right: Qualitative phase diagram of a Coulomb crystal of heavy particles ("holes") in a macroscopic two-component (neutral) plasma. T e = 3 2 k B T /E R. Taken from Refs. [53, 55].
Strong correlation effects in classical and quantum plasmas are discussed. In particular, Coulomb (Wigner) crystallization phenomena are reviewed focusing on one-component non-neutral plasmas in traps and on macroscopic two-component neutral plasmas. The conditions for crystal formation in terms of critical values of the coupling parameters and the distance fluctuations and the phase diagram of Coulomb crystals are discussed. Comment: 19 pages, 6 figures
For each value of r b and γ p , a value of 1 is displayed 
Numerically integrated electron trajectory for γ p = 
For each value of r b and γ p , a value of 1 is displayed 
Thomas has recently derived scaling laws for X-ray radiation from electrons accelerated in plasma bubbles, as well as a threshold for the self-injection of background electrons into the bubble [A. G. R. Thomas, Phys. Plasmas 17, 056708 (2010)]. To obtain this threshold, the equations of motion for a test electron are studied within the frame of the bubble model, where the bubble is described by prescribed electromagnetic fields and has a perfectly spherical shape. The author affirms that any elliptical trajectory of the form x'^2/{\gamma}_p^2 + y'^2 = R^2 is solution of the equations of motion (in the bubble frame), within the approximation p'_y^2/p'_x^2 \ll 1. In addition, he highlights that his result is different from the work of Kostyukov et al. [Phys. Rev. Lett. 103, 175003 (2009)], and explains the error committed by Kostyukov-Nerush-Pukhov-Seredov (KNPS). In this comment, we show that numerically integrated trajectories, based on the same equations than the analytical work of Thomas, lead to a completely different result for the self-injection threshold, the result published by KNPS [Phys. Rev. Lett. 103, 175003 (2009)]. We explain why the analytical analysis of Thomas fails and we provide a discussion based on numerical simulations which show exactly where the difference arises. We also show that the arguments of Thomas concerning the error of KNPS do not hold, and that their analysis is mathematically correct. Finally, we emphasize that if the KNPS threshold is found not to be verified in PIC (Particle In Cell) simulations or experiments, it is due to a deficiency of the model itself, and not to an error in the mathematical derivation.
Zaghloul [Phys. Plasmas 17, 062701 (2010); arXiv:1010.1161v1] reconsiders the occupation probability formalism in plasma thermodynamics and claims inconsistencies in previous models. I show that the origin of this incorrect claim is an omission of the configurational factor from the partition function. This arXiv version is supplemented with two appendices, where I add remarks and comments on two more recent publications of the same author on the same subject: on his response to this Comment [Phys. Plasmas 17, 124705 (2010)] and on his criticism towards the Hummer and Mihalas's (1988) formalism [Phys. Plasmas 17, 122903 (2010); arXiv:1010.1102v1].
The neoclassical calculation of the helicon wave theory contains a fundamental flaw. Use is made of a proportional relationship between the magnetic field and its curl to derive the Helmholtz equation describing helicon wave propagation; however, by the fundamental theorem of Stokes, the curl of the magnetic field must be perpendicular to that portion of the field contributing to the local curl. Reexamination of the equations of motion indicates that only electromagnetic waves propagate through a stationary region of constant pressure in a fully ionized, neutral medium. Comment: 7 pages, 1 figure, to be published in Phys. Plasmas,
The geometric analysis of the gyromotion for charged particles in a time-dependent magnetic field by Liu and Qin [Phys. Plasmas 18, 072505 (2011)] is reformulated in terms of the spatial angles that represent the instantaneous orientation of the magnetic field. This new formulation, which includes the equation of motion for the pitch angle, clarifies the decomposition of the gyroangle-averaged equation of motion for the gyrophase into its dynamic and geometric contributions. (C) 2012 American Institute of Physics. []
It is pointed out that electron thermal fluctuations can couple with the ion acoustic mode in an inhomogeneous plasma to generate a low frequency ion time scale electromagnetic wave. This electromagnetic wave can become unstable if the temperature and density gradients are parallel to each other which can be the case in laser-plasmas similar to stellar cores. The comparisons of the present theoretical model with the previous investigations are also presented. The final result is applied to a classical laser induced plasma for illustration.
Parallel electric field in time for three different target densities illuminated with a 2 × 1023 W/cm2 circularly polarized laser both when the ions are infinitely massive and for aluminium ions. The location of the front of the laser is shown as the black line on the coloured contours. The solid colours are for aluminium and the thick white contour line are for immobile ions. (a) is for a target of relativistically corrected critical density, (b) is for a target of 1% critical density, and (c) for 10% of critical. It is clear that as the target density decreases the influence of the ions on the propagation of the laser into the target decreases. (d) shows the increase in laser intensity reflectivity for higher target densities. This increase is monotonic and does not show any sudden jump at the point where a pure electron plasma no longer shows a propagating front.
At laser intensities above 1023W/cm2 the interaction of a laser with a plasma is qualitatively different to the interactions at lower intensities. In this intensity regime solid targets start to become relativistically underdense, gamma-ray production by synchrotron emission starts to become an important feature of the dynamics and, at even higher intensities, electron-positron pair production by the non-linear Breit-Wheeler process starts to occur. Previous work in this intensity regime has considered ion acceleration1,2, identified different mechanisms for the underlying plasma physics of laser generation of gamma-rays3,4,5 considered the effect of target parameters on gamma-ray generation6 and considered the creation of solid density positronium plasma3. However a complete linked understanding of the important new physics of this regime is still lacking. In this paper, an analysis is presented of the effects of target density, laser intensity, target preplasma properties and other parameters on the conversion efficiency, spectrum and angular distribution of gamma-rays by synchrotron emission. An analysis of the importance of Breit-Wheeler pair production is also presented.
We have studied the propagation of fast electrons through laser irradiated Ti foils by monitoring the emission of hard X-rays and K-{\alpha} radiation from bare foils and foils backed by a thick epoxy layer. Key observations include strong refluxing of electrons and divergence of the electron beam in the foil with evidence of magnetic field collimation. Our diagnostics have allowed us to estimate the fast electron temperature and fraction of laser energy converted to fast electrons. We have observed clear differences between the fast electron temperatures observed with bare and epoxy backed targets which may be due to the effects of refluxing.
A minimal model for magnetic reconnection and, generally, low-frequency dynamics in low-beta plasmas is proposed. The model combines analytical and computational simplicity with physical realizability: it is a rigorous limit of gyrokinetics for plasma beta of order the electron-ion mass ratio. The model contains collisions and can be used both in the collisional and collisionless reconnection regimes. It includes gyrokinetic ions (not assumed cold) and allows for the topological rearrangement of the magnetic field lines by either resistivity or electron inertia, whichever predominates. The two-fluid dynamics are coupled to electron kinetics --- electrons are not assumed isothermal and are described by a reduced drift-kinetic equation. The model therefore allows for irreversibility and conversion of magnetic energy into electron heat via parallel phase mixing in velocity space. An analysis of the exchanges between various forms of free energy and its conversion into electron heat is provided. It is shown how all relevant linear waves and regimes of the tearing instability (collisionless, semicollisional and fully resistive) are recovered in various limits of our model. An efficient way to simulate our equations numerically is proposed, via the Hermite representation of the velocity space. It is shown that small scales in velocity space will form, giving rise to a shallow Hermite-space spectrum, whence it is inferred that, for steady-state or sufficiently slow dynamics, the electron heating rate will remain finite in the limit of vanishing collisionality.
It was recently proposed that the electron-frame dissipation measure, the energy transfer from the electromagnetic field to plasmas in the electron's rest frame, identifies the dissipation region of collisionless magnetic reconnection [Zenitani et al. Phys. Rev. Lett. 106, 195003 (2011)]. The measure is further applied to the electron-scale structures of antiparallel reconnection, by using two-dimensional particle-in-cell (PIC) simulations. The size of the central dissipation region is controlled by the electron-ion mass ratio, suggesting that electron physics is essential. A narrow electron jet extends along the outflow direction until it reaches an electron shock. The jet region appears to be anti-dissipative. At the shock, electron heating is relevant to a magnetic cavity signature. The results are summarized to a unified picture of the single dissipation region in a Hall magnetic geometry.
Biskamp and Schwarz [Phys. Plasmas, 8, 3282 (2001)] have reported that the energy spectrum of two-dimensional magnetohydrodynamic turbulence is proportional to $k^{-3/2}$, which is a prediction of Iroshnikov-Kraichnan phenomenology. In this comment we report some earlier results which conclusively show that for two-dimensional magnetohydrodynamic turbulence, Kolmogorov-like phenomenology (spectral index 5/3) is better model than Iroshnikov-Kraichnan phenomenology; these results are based on energy flux analysis. Comment: 2 pages, Revtex, 1 figure (Phys. Plasmas, v9, p1484, 2002)
The tangential layers are characterized by a bulk plasma velocity and a magnetic field that are perpendicular to the gradient direction. They have been extensively described in the frame of the Magneto-Hydro-Dynamic (MHD) theory. But the MHD theory does not look inside the transition region if the transition has a size of a few ion gyroradii. A series of kinetic tangential equilibria, valid for a collisionless plasma is presented. These equilibria are exact analytical solutions of the Maxwell-Vlasov equations. The particle distribution functions are sums of an infinite number of elementary functions parametrized by a vector potential. Examples of equilibria relevant to space plasmas are shown. A model for the deep and sharp density depletions observed in the auroral zone of the Earth is proposed. Tangential equilibria are also relevant for the study of planetary environments and of remote astrophysical plasmas.
Thermally excited phonon spectra of 2D Yukawa solids and liquids in the presence of an external magnetic field are studied using computer simulations. Special attention is paid to the variation of wave spectra in terms of several key parameters, such as the strength of coupling, the screening parameter, and the intensity of the magnetic field. In addition, comparisons are made with several analytical theories, including random-phase approximation, quasi-localized charge approximation, and harmonic approximation, and the validity of those theories is discussed in the present context. Comment: 21 pages 11 figures
The height gmax of the first peak of the PDF as a function of Γ in the vicinity of the liquid-solid transition for a Coulomb system and a Yukawa system with κ = 1. The vertical lines mark the crystallization points, Γc = 137 and Γc = 187, respectively.
We derive an effective coupling parameter for two-dimensional Yukawa systems based on the height of the first maximum of the pair distribution function. Two variants -- one valid in the high-coupling range, the other for arbitrary couplings of the liquid -- are derived. Comparison to previous approaches to Yukawa coupling parameters shows that the present concept is more general and more accurate. Using, in addition, dynamical information contained in the velocity autocorrelation function, we outline a reference data method that can be employed as a non-invasive measurement scheme of the plasma parameters -- the coupling strength and the screening length. This approach requires only input from a time-series of configuration snapshots and particle velocities with no recourse to additional information about the system. Our results should be directly applicable as a simple, yet reliable diagnostic method for a variety of experiments, including dusty plasmas, colloidal suspensions and ions in traps, and can be employed to facilitate comparisons between experiments, theory and simulations.
Scaling relation φ k /f k for three different collision frequencies: ν = 10 −6 , 10 −5 , and 10 −4 (black squares, blue triangles, and red diamonds, respectively). The dashed line corresponds to the scaling k −1 ⊥ 
Normalized free energy flux Π f (k ⊥)/D tot for ν = 10−6, 10−5, and 10−4 (black squares, blue triangles, and red circles, respectively). The green dashed line corresponds to unity, while the other colored dashed lines corresponds to the maximum of the respective flux.
Nonlinear gyrokinetics provides a suitable framework to describe short-wavelength turbulence in magnetized laboratory and astrophysical plasmas. In the electrostatic limit, this system is known to exhibit a free energy cascade towards small scales in (perpendicular) real and/or velocity space. The dissipation of free energy is always due to collisions (no matter how weak the collisionality), but may be spread out across a wide range of scales. Here, we focus on freely-decaying 2D electrostatic turbulence on sub-ion-gyroradius scales. An existing scaling theory for the turbulent cascade in the weakly collisional limit is generalized to the moderately collisional regime. In this context, non-universal power law scalings due to multiscale dissipation are predicted, and this prediction is confirmed by means of direct numerical simulations.
A possible solution to the unexplained high intensity hard x-ray (HXR) emission observable during solar flares was investigated via 3D fully relativistic, electromagnetic particle-in-cell (PIC) simulations with realistic ion to electron mass ratio. A beam of accelerated electrons was injected into a magnetised, Maxwellian, homogeneous and inhomogeneous background plasma. The electron distribution function was unstable to the beam-plasma instability and was shown to generate Langmuir waves, while relaxing to plateau formation. In order to estimate the role of the background density gradient on an unbound (infinite spatial extent) beam, three different scenarios were investigated: a) a uniform density background; b) a weak density gradient, n_R/n_L=3; c) a strong gradient case, n_R/n_L=10, where n_R and n_L denote background electron densities on the left and right edges of the simulation box respectively. The strong gradient case produced the largest fraction of electrons beyond 15 v_th. Further, two cases (uniform and strong gradient background) with spatially localized beam injections were performed aiming to show drifts of the generated Langmuir wave wavenumbers, as suggested in previous studies. For the strong gradient case, the Langmuir wave power is shown to drift to smaller wavenumbers, as found in previous quasi-linear simulations.
This paper presents simulations of isolated 3D filaments in a slab geometry obtained using a newly developed 3D reduced fluid code, written using the BOUT++ framework. First, systematic scans were performed to investigate how the dynamics of a filament are affected by its amplitude, perpendicular size, and parallel extent. The perpendicular size of the filament was found to have a strong influence on its motions, as it determined the relative importance of parallel currents to polarization and viscous currents, whilst drift-wave instabilities were observed if the initial amplitude of the blob was increased sufficiently. Next, the 3D simulations were compared to 2D simulations using different parallel closures; namely, the sheath dissipation closure, which neglects parallel gradients, and the vorticity advection closure, which neglects the influence of parallel currents. The vorticity advection closure was found to not replicate the 3D perpendicular dynamics and overestimated the initial radial acceleration of all the filaments studied. In contrast, a more satisfactory comparison with the sheath dissipation closure was obtained, even in the presence of significant parallel gradients, where the closure is no longer valid. Specifically, it captured the contrasting dynamics of filaments with different perpendicular sizes that were observed in the 3D simulations which the vorticity advection closure failed to replicate. However, neither closure successfully replicated the Boltzmann spinning effects nor the associated poloidal drift of the blob that was observed in the 3D simulations. Although the sheath dissipation closure was concluded to be more successful in replicating the 3D dynamics, it is emphasized that the vorticity advection closure may still be relevant for situations where the parallel current is inhibited from closing through the sheath due to effects such as strong magnetic shear around X points or increased resistivity near the targets.
The manner in which the rate of magnetic reconnection scales with the Lundquist number in realistic three-dimensional (3D) geometries is still an unsolved problem. It has been demonstrated that in 2D rapid non-linear tearing allows the reconnection rate to become almost independent of the Lundquist number (the `plasmoid instability'). Here we present the first study of an analogous instability in a fully 3D geometry, defined by a magnetic null point. The 3D null current layer is found to be susceptible to an analogous instability, but is marginally more stable than an equivalent 2D Sweet-Parker-like layer. Tearing of the sheet creates a thin boundary layer around the separatrix surface, contained within a flux envelope with a hyperbolic structure that mimics a spine-fan topology. Efficient mixing of flux between the two topological domains occurs as the flux rope structures created during the tearing process evolve within this envelope. This leads to a substantial increase in the rate of reconnection between the two domains.
We present large scale 3D particle-in-cell (PIC) simulations to examine particle energization in magnetic reconnection of relativistic electron-positron (pair) plasmas. The initial configuration is set up as a relativistic Harris equilibrium without a guide field. These simulations are large enough to accommodate a sufficient number of tearing and kink modes. Contrary to the non-relativistic limit, the linear tearing instability is faster than the linear kink instability, at least in our specific parameters. We find that the magnetic energy dissipation is first facilitated by the tearing instability and followed by the secondary kink instability. Particles are mostly energized inside the magnetic islands during the tearing stage due to the spatially varying electric fields produced by the outflows from reconnection. Secondary kink instability leads to additional particle acceleration. Accelerated particles are, however, observed to be thermalized quickly. The large amplitude of the vertical magnetic field resulting from the tearing modes by the secondary kink modes further help thermalizing the non-thermal particles generated from the secondary kink instability. Implications of these results for astrophysics are briefly discussed.
We report the results of a 3D particle-in-cell (PIC) simulation carried out to study the early-stage evolution of the shock formed when an unmagnetized relativistic jet interacts with an ambient electron-ion plasma. Full-shock structures associated with the interaction are observed in the ambient frame. When open boundaries are employed in the direction of the jet; the forward shock is seen as a hybrid structure consisting of an electrostatic shock combined with a double layer, while the reverse shock is seen as a double layer. The ambient ions show two distinct features across the forward shock: a population penetrating into the shocked region from the precursor region and an accelerated population escaping from the shocked region into the precursor region. This behavior is a signature of a combination of an electrostatic shock and a double layer. Jet electrons are seen to be electrostatically trapped between the forward and reverse shock structures showing a ring-like distribution in a phase-space plot, while ambient electrons are thermalized and become essentially isotropic in the shocked region. The magnetic energy density grows to a few percent of the jet kinetic energy density at both the forward and the reverse shock transition layers in a rather short time scale. We see little disturbance of the jet ions over this time scale.
Previous studies [Malara et al ApJ, 533, 523 (2000)] considered small-amplitude Alfven wave (AW) packets in Arnold-Beltrami-Childress (ABC) magnetic field using WKB approximation. In this work linearly polarised Alfven wave dynamics in ABC magnetic field via direct 3D MHD numerical simulation is studied for the first time. Gaussian AW pulse with length-scale much shorter than ABC domain length and harmonic AW with wavelength equal to ABC domain length are studied for four different resistivities. While it is found that AWs dissipate quickly in the ABC field, surprisingly, AW perturbation energy increases in time. In the case of the harmonic AW perturbation energy growth is transient in time, attaining peaks in both velocity and magnetic perturbation energies within timescales much smaller than resistive time. In the case of the Gaussian AW pulse velocity perturbation energy growth is still transient in time, attaining a peak within few resistive times, while magnetic perturbation energy continues to grow. It is also shown that the total magnetic energy decreases in time and this is governed by the resistive evolution of the background ABC magnetic field rather than AW damping. On contrary, when background magnetic field is uniform, the total magnetic energy decrease is prescribed by AW damping, because there is no resistive evolution of the background. By considering runs with different amplitudes and by analysing perturbation spectra, possible dynamo action by AW perturbation-induced peristaltic flow and inverse cascade of magnetic energy have been excluded. Therefore, the perturbation energy growth is attributed to a new instability. The growth rate appears to be dependent on the value of the resistivity and spatial scale of the AW disturbance. Thus, when going beyond WKB approximation, AW damping, described by full MHD equations, does not guarantee decrease of perturbation energy.
The electromagnetic energy equation is analyzed term by term in a 3D simulation of kinetic reconnection previously reported by \citet{vapirev2013formation}. The evolution presents the usual 2D-like topological structures caused by an initial perturbation independent of the third dimension. However, downstream of the reconnection site, where the jetting plasma encounters the yet unperturbed pre-existing plasma, a downstream front (DF) is formed and made unstable by the strong density gradient and the unfavorable local acceleration field. The energy exchange between plasma and fields is most intense at the instability, reaching several $pW/m^3$, alternating between load (energy going from fields to particles) and generator (energy going from particles to fields) regions. Energy exchange is instead purely that of a load at the reconnection site itself in a region focused around the x-line and elongated along the separatrix surfaces. Poynting fluxes are generated at all energy exchange regions and travel away from the reconnection site transporting an energy signal of the order of about $\mathbf S \approx 10^{-3} W/m^2$.
(Color online) System setup and axis.
(Color online) Growth-rate in ω pp units, as a function of ( Z x , Z y ) for 3 field obliquities and 
(Color online) Growth-rate in ω pp units, as a function of ( Z x , Z y ) for 3 field obliquities, 
(Color online) Growth-rate at Z = ∞ for the diluted case, exact value vs. ansatz (13). Parameters are α = 10 −3 and γ b0 = 5. The last row displays the value of | P (0 + iδ d Z∞ ) | times a large amplification factor, where δ d Z∞ is the ansatz (13), and P (x) = 0 the dispersion equation.
The filamentation (Weibel) instability plays a key role in the formation of collisionless shocks which are thought to produce Gamma-Ray-Bursts and High-Energy-Cosmic-Rays in astrophysical environments. While it has been known for long that a flow-aligned magnetic field can completely quench the instability, it was recently proved in 2D that in the cold regime, such cancelation is possible if and only if the field is perfectly aligned. Here, this result is finally extended to a 3D geometry. Calculations are conducted for symmetric and asymmetric counter-streaming relativistic plasma shells. 2D results are retrieved in 3D: the instability can never be completely canceled for an oblique magnetic field. In addition, the maximum growth-rate is always larger for wave vectors lying in the plan defined by the flow and the oblique field. On the one hand, this bears consequences on the orientation of the generated filaments. On the other hand, it certifies 2D simulations of the problem can be performed without missing the most unstable filamentation modes.
We report here, for the first time, an observed instability of a Kelvin-Helmholtz (KH) nature occurring in a fully three-dimensional (3D) current-vortex sheet at the fan plane of a 3D magnetic null point. The current-vortex layer forms self-consistently in response to foot point driving around the spine lines of the null. The layer first becomes unstable at an intermediate distance from the null point, with the instability being characterized by a rippling of the fan surface and a filamentation of the current density and vorticity in the shear layer. Owing to the 3D geometry of the shear layer, a branching of the current filaments and vortices is observed. The instability results in a mixing of plasma between the two topologically distinct regions of magnetic flux on either side of the fan separatrix surface, as flux is reconnected across this surface. We make a preliminary investigation of the scaling of the system with the dissipation parameters. Our results indicate that the fan plane separatrix surface is an ideal candidate for the formation of current-vortex sheets in complex magnetic fields and, therefore, the enhanced heating and connectivity change associated with the instabilities of such layers.
In this work the dynamic magnetic field within a tearing-unstable three-dimensional (3D) current sheet about a magnetic null point is described in detail. We focus on the evolution of the magnetic null points and flux ropes that are formed during the tearing process. Generally, we find that both magnetic structures are created prolifically within the layer and are non-trivially related. We examine how nulls are created and annihilated during bifurcation processes, and describe how they evolve within the current layer. The type of null bifurcation first observed is associated with the formation of pairs of flux ropes within the current layer. We also find that new nulls form within these flux ropes, both following internal reconnection and as adjacent flux ropes interact. The flux ropes exhibit a complex evolution, driven by a combination of ideal kinking and their interaction with the outflow jets from the main layer. The finite size of the unstable layer also allows us to consider the wider effects of flux rope generation. We find that the unstable current layer acts as a source of torsional MHD waves and dynamic braiding of magnetic fields. The implications of these results to several areas of heliophysics are discussed.
Asymmetric current sheets are likely to be prevalent in both astrophysical and laboratory plasmas with complex three dimensional (3D) magnetic topologies. This work presents kinematic analytical models for spine and fan reconnection at a symmetric 3D null with asymmetric current sheets. Asymmetric fan reconnection is characterized by an asymmetric reconnection of flux past each spine line and a bulk flow of plasma across the null point. In contrast, asymmetric spine reconnection is inherently equal and opposite in how flux is reconnected across the fan plane. The higher modes of spine reconnection also include localized wedges of vortical flux transport in each half of the fan. In this situation, two definitions for reconnection rate become appropriate: a local reconnection rate quantifying how much flux is genuinely reconnected across the fan plane and a global rate associated with the net flux driven across each semi-plane. Through a scaling analysis it is shown that when the ohmic dissipation in the layer is assumed to be constant, the increase in the local rate bleeds from the global rate as the sheet deformation is increased. Both models suggest that asymmetry in the current sheet dimensions will have a profound effect on the reconnection rate and manner of flux transport in reconnection involving 3D nulls.
The objective of this article is to report the parallel implementation of the 3D molecular dynamic simulation code for laser cluster interaction. The benchmarking of the code has been done by comparing the simulation results with some of the experiments performed across the globe. Scaling laws for the computational time is being established by varying the number of processor cores and number of macroparticles used. The capabilities of the code are highlighted by implementing various diagnostic tools.
Top-cited authors
Nobuhiko Izumi
  • Lawrence Livermore National Laboratory
George Tynan
  • University of California, San Diego
Abbas Nikroo
  • Lawrence Livermore National Laboratory
S. W. Haan
  • Lawrence Livermore National Laboratory
Harry Robey
  • Lawrence Livermore National Laboratory