A rotating and magnetized three-dimensional axisymmetric equilibrium for hot plasma confined by a gravitational field is found. The plasma density and current can exhibit strong equatorial plane localization, resulting in disk equilibria with open magnetic field lines. The associated equatorial plane pinching results in magnetic field flaring, implying a strong gravitational squeezing of the plasma carrying ambient magnetic field lines toward the gravitational source. At high plasma pressure, the magnetic field becomes strongly radial outside the disk. The model predicts the rotation frequency bound, the condition for a plasma disk, and the requirement for strong magnetic field flaring.

Plasmas are ubiquitous in nature, surround our local geospace environment, and permeate the universe. Plasma phenomena in space give rise to energetic particles, the aurora, solar flares and coronal mass ejections, as well as many energetic phenomena in interstellar space. Although plasmas can be studied in laboratory settings, it is often difficult, if not impossible, to replicate the conditions (density, temperature, magnetic and electric fields, etc.) of space. Single-point space missions too numerous to list have described many properties of near-Earth and heliospheric plasmas as measured both in situ and remotely (see http://www.nasa.gov/missions/#.U1mcVmeweRY for a list of NASA-related missions). However, a full description of our plasma environment requires three-dimensional spatial measurements. Cluster is the first, and until data begin flowing from the Magnetospheric Multiscale Mission (MMS), the only mission designed to describe the three-dimensional spatial structure of plasma phenomena in geospace. In this paper, we concentrate on some of the many plasma phenomena that have been studied using data from Cluster. To date, there have been more than 2000 refereed papers published using Cluster data but in this paper we will, of necessity, refer to only a small fraction of the published work. We have focused on a few basic plasma phenomena, but, for example, have not dealt with most of the vast body of work describing dynamical phenomena in Earth's magnetosphere, including the dynamics of current sheets in Earth's magnetotail and the morphology of the dayside high latitude cusp. Several review articles and special publications are available that describe aspects of that research in detail and interested readers are referred to them (see for example, Escoubet et al. 2005Multiscale Coupling of Sun-Earth Processes, p. 459, Keith et al. 2005Sur. Geophys.26, 307–339, Paschmann et al. 2005Outer Magnetospheric Boundaries: Cluster Results, Space Sciences Series of ISSI. Berlin: Springer, Goldstein et al. 2006Adv. Space Res.38, 21–36, Taylor et al. 2010The Cluster Mission: Space Plasma in Three Dimensions, Springer, pp. 309–330 and Escoubet et al. 2013Ann. Geophys.31, 1045–1059).

The TORPEX basic plasma physics device at the Center for Plasma Physics Research (CRPP) in Lausanne, Switzerland is described. In TORPEX, simple magnetized toroidal configurations, a paradigm for the tokamak scrape-off layer (SOL), as well as more complex magnetic geometries of direct relevance for fusion are produced. Plasmas of different gases are created and sustained by microwaves in the electron-cyclotron (EC) frequency range. Full diagnostic access allows for a complete characterization of plasma fluctuations and wave fields throughout the entire plasma volume, opening new avenues to validate numerical codes. We detail recent advances in the understanding of basic aspects of plasma turbulence, including its development from linearly unstable electrostatic modes, the formation of filamentary structures, or blobs, and its influence on the transport of energy, plasma bulk and suprathermal ions. We present a methodology for the validation of plasma turbulence codes, which focuses on quantitative assessment of the agreement between numerical simulations and TORPEX experimental data.

A new turbulent plasma source at the Swarthmore Spheromak Experiment (SSX) facility is described. The MHD wind tunnel configuration employs a magnetized plasma gun to inject high-beta plasma into a large, well-instrumented, vacuum drift region. This provides unique laboratory conditions approaching that in the solar wind: there is no applied background magnetic field in the drift region and has no net axial magnetic flux; the plasma flow speed is on the order of the local sound speed (M ~ 1), so flow energy density is comparable to thermal energy density; and the ratio of thermal to magnetic pressure is of order unity (plasma β ~ 1) so thermal energy density is also comparable to magnetic energy density. Results presented here and referenced within demonstrate the new capabilities and show how the new platform is proving useful for fundamental plasma turbulence studies.

A gas-filled cylindrical liner z-pinch configuration has been used to drive convergent radiative shock waves into different gases at velocities of 20–50 km s−1. On application of the 1.4 MA, 240 ns rise-time current pulse produced by the Magpie generator at Imperial College London, a series of cylindrically convergent shock waves are sequentially launched into the gas-fill from the inner wall of the liner. This occurs without any bulk motion of the liner wall itself. The timing and trajectories of the shocks are used as a diagnostic tool for understanding the response of the liner z-pinch wall to a large pulsed current. This analysis provides useful data on the liner resistivity, and a means to test equation of state (EOS) and material strength models within MHD simulation codes. In addition to providing information on liner response, the convergent shocks are interesting to study in their own right. The shocks are strong enough for radiation transport to influence the shock wave structure. In particular, we see evidence for both radiative preheating of material ahead of the shockwaves and radiative cooling instabilities in the shocked gas. Some preliminary results from initial gas-filled liner experiments with an applied axial magnetic field are also discussed.

This paper explains how to obtain the distribution function of minority ions in tokamak plasmas using the Monte Carlo method. Since the emphasis is on energetic ions, the guiding-center transformation is outlined, including also the transformation of the collision operator. Even within the guiding-center formalism, the fast particle simulations can still be very CPU intensive and, therefore, we introduce the reader also to the world of high-performance computing. The paper is concluded with a few examples where the presented method has been applied.

We present a comprehensive survey of various computational methods in CEDRES++ (Couplage Equilibre Diffusion Résistive pour l'Etude des Scénarios) for finding equilibria of toroidal plasma. Our focus is on free-boundary plasma equilibria, where either poloidal field coil currents or the temporal evolution of voltages in poloidal field circuit systems are given data. Centered around a piecewise linear finite element representation of the poloidal flux map, our approach allows in large parts the use of established numerical schemes. The coupling of a finite element method and a boundary element method gives consistent numerical solutions for equilibrium problems in unbounded domains. We formulate a new Newton method for the discretized nonlinear problem to tackle the various nonlinearities, including the free plasma boundary. The Newton method guarantees fast convergence and is the main building block for the inverse equilibrium problems that we can handle in CEDRES++ as well. The inverse problems aim at finding either poloidal field coil currents that ensure a desired shape and position of the plasma or at finding the evolution of the voltages in the poloidal field circuit systems that ensure a prescribed evolution of the plasma shape and position. We provide equilibrium simulations for the tokamaks ITER and WEST to illustrate the performance of CEDRES++ and its application areas.

In this study, a theory of free-electron laser (FEL) with a Langmuir wave wiggler in the presence of an axial magnetic field has been presented. The small wavelength of the plasma wave (in the sub-mm range) allows obtaining higher frequency than conventional wiggler FELs. Electron trajectories have been obtained by solving the equations of motion for a single electron. In addition, a fourth-order Runge–Kutta method has been used to simulate the electron trajectories. Employing a perturbation analysis, the dispersion relation for an electromagnetic and space-charge waves has been derived by solving the momentum transfer, continuity, and wave equations. Numerical calculations show that the growth rate increases with increasing the e-beam energy and e-beam density, while it decreases with increasing the strength of the axial guide magnetic field.

The plasma immersion ion implantation process is investigated in the presence of q–nonextensive electrons by using a one-dimensional fluid model. The effect of the nonextensivity parameter, q, on the plasma parameters and sheath dynamics during the implantation process is studied. The results show that the implantation dose can be enhanced in the presence of energetic electrons at the tail of the distribution function. Different parameters of plasma such as sheath thickness, ion velocity and ion density show more change at the larger values of the q–parameter. Furthermore, the results of simulation tend to what is predicted by the Maxwellian electron distribution function (q = 1).

Stability of the plane tangential discontinuity (TD) interface in a multi-component dusty plasma (ions, electrons, neutral particles and charged dust) is considered in hydrodynamical approximation. The criterion of stability does not depend on the presence of dust only on one side of the discontinuity but is changed if the dust penetrates through the discontinuity. Therefore, if the instability criterion is marginal, even weak penetration of the dust through the interface may induce Kelvin–Helmholtz instability. This conclusion also refers to cylindrical TD in the presence of dust, so that generation of helical waves in astrophysical jets, type I comet tails, etc. due to the shear driven Kelvin–Helmholtz instability may be hampered in dusty objects of such a geometry.

Simulation of free electron laser (FEL) with modified wiggler consisting of a conventional planar wiggler with third harmonic field component is presented. A set of self consistent nonlinear differential equations is derived and solved numerically by Runge–Kutta method. The optimum amplitudes of fundamental and third harmonic wiggler filed are obtained to increase the third harmonic radiation in comparison with conventional wiggler and also to have lower electron beam energy compared to conventional wiggler with the same wavelength. For the thermal effect the axial energy spread of electron beam, without any spread in the transverse velocity, is assumed. A peculiar region is found in which there is a sharp increase of the radiation amplitude. Thermal effect of the electron beam was found to be irregular in this peculiar region.

To rigorously model fast ions in fusion plasmas, a non-Maxwellian equilibrium distribution must be used. In this work, the response of high-energy alpha particles to electrostatic turbulence has been analyzed for several different tokamak parameters. Our results are consistent with known scalings and experimental evidence that alpha particles are generally well confined: on the order of several seconds. It is also confirmed that the effect of alphas on the turbulence is negligible at realistically low concentrations, consistent with linear theory. It is demonstrated that the usual practice of using a high-temperature Maxwellian, while previously shown to give an adequate order-of-magnitude estimate of the diffusion coefficient, gives incorrect estimates for the radial alpha particle flux, and a method of correcting it in general is provided. Furthermore, we see that the timescales associated with collisions and transport compete at moderate energies, calling into question the assumption that alpha particles remain confined to a flux surface that is used in the derivation of the slowing-down distribution.

In this paper, we report the results of an experimental study of microwave (MW) discharge in the supersonic flow initiated by the laser spark and numerical simulation of multiple laser spark shockwave structures in airflow. The MW discharge initiation has been produced by single and double laser sparks. By using different spatial and temporal configuration of laser sparks in supersonic flow, we demonstrate the feasibility of an MW breakdown threshold decrease and control over shape and location of MW plasma. Calculation of laser spark shock wave structures shows good agreement with experimental shadow photographs both in the front shock wave diameter and its internal structure.

Nonlinear amplitude modulation of ion-acoustic waves (IAWs) in a fully relativistic unmagnetized two-fluid plasma has been theoretically studied by using complete set of fully relativistic dynamic equations. To describe the nonlinear evolution of the wave envelope a nonlinear Schrödinger (NLS) equation is derived by using standard multiple scale perturbation technique. Using this equation it is shown that the wave becomes modulationally unstable as the wavenumber exceeds certain critical value. This critical wavenumber is found to decrease with increase in relativistic effect. The instability growth rate has also been calculated numerically for different values of plasma drift velocity. The growth rate is shown to decrease with increase in the relativistic effect.

Stationary magnetohydrodynamics flows in nozzle-type channels in the presence of a longitudinal magnetic field are divided into three significantly different classes: super-Alfven flows in which the longitudinal plasma velocity is higher than the Alfven velocity calculated by a longitudinal magnetic field, sub-Alfven flows – with the opposite inequality, and Alfven flows in which the longitudinal plasma velocity coincides with the Alfven velocity over the entire length of the channel and the plasma density has a constant value. In the present work, stationary Alfven and close to Alfven magnetohydrodynamic flows obtained by using a numerical modeling of their relaxation processes in coaxial channels in the presence of a longitudinal magnetic field are considered.

The dynamics of the weakly nonlinear and weakly dispersive low frequency longitudinal dust acoustic waves (LDAWs) in a strongly coupled complex (dusty) plasma are investigated using generalized hydrodynamic (GH) model. In presence of strong correlation, the nonlinear wave is shown to be governed by a Korteweg–de Vries (KdV) equation with a nonlocal nonlinear forcing and a linear damping terms. This novel equation is solved numerically to show the competition between nonlinear forcing and dissipative damping in the formation of the localized structures.

The method of perturbation has been applied to derive a general dispersion relation for a free-electron laser (FEL) with background plasma and helical wiggler in the presence of an axial magnetic field. This dispersion relation is solved numerically to find unstable interactions among all of the wave modes. Numerical calculations show that new coupling between the left wave and positive-energy space-charge of electron beam are found when wiggler induced velocity is large. This coupling does not change with increasing the plasma density. The growth rate of FEL is changed with increasing the plasma density and the normalized axial magnetic field.

We studied the positive column of the dc discharge through analytical modeling. We considered the ambipolar regime when the balance of charged particles is determined only by direct ionization of molecules by electrons and ambipolar escape of them to the discharge chamber walls. The approximation chosen permitted us to solve the balance equation and to obtain simple formulas for the reduced electric field. Our calculation data for the positive column in hydrogen agree well with experimental and theoretical data of other authors.

For understanding the effect of resonant helical magnetic field (RHF) and bias on the edge plasma turbulent transport, the radial and poloidal electric field (Er, EP), poloidal and toroidal magnetic field (BP, Br) were detected by the Langmuir probe, magnetic probe and diamagnetic loop. The poloidal, toroidal and radial velocity (VP, Vr, Vt) can be determined from the electric and magnetic field. In the present work, we have investigated the effect of the magnitude of bias (Vbias = 200v, Vbias = 320v) on Er, EP, BP, Bt, VP, Vr, Vt. Moreover, we applied RHF with L = 2, L = 3 and L = 2 and 3 and investigate the effect of the helical windings radius on above parameters. Also, the experiment was repeated by applying the positive biasing potentials and RHF's simultaneously. The results show that by applying bias to the plasma at t = 15 msec at r/a = 0.9, Er, BP and Bt increase while EP decreases. The best modification occurs at Vbias = 200v. By applying RHF to the plasma, both the electric and magnetic field vary. Er reaches the highest in the presence of RHF with L = 3. The same results are obtained for BP, Bt, VP and Vt. While the inverse results are obtained for EP and Vr. Finally, RHF and bias are applied simultaneously to the plasma. With applied bias with Vbias = 200v and RHF with L = 2 and 3, we reach to the ideal circumstance. The same results obtain in the situation with Vbias = 320v and RHF with L = 2 and 3.

There are still open issues within the fluctuation theory of plasmas, in view of the difficulty of formulating adequate theoretical approaches and solving the related equations in particular regimes. A promising alternative approach is direct microphysical modeling based on first principles, as successfully applied to neutral rarefied fluids. Within this approach, the equations of motion of a large ensemble of charged particles are solved numerically while correlations are obtained from statistical analysis of the ensemble at different times. As a first step, in this work we validate the data analysis technique adopted in this numerical scheme for the case of an electron ensemble neglecting Coulomb interactions. The simulation results are compared with the analytical theory of ‘natural’ fluctuations for both un-magnetized and magnetized plasmas. For the latter, the derivations for arbitrary average distribution functions are presented.