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.

The lifetimes, volume densities of energy, electron and ion densities and other parameters of ball lightning cores with the nonrelativistic electrons are estimated. The model according to which the motion of the electrons of the ball lightning core is the superposition of the oscillatory motion and the thermal motion in the directions perpendicular to those of the oscillations is proposed. Some problems related to isolation of the ball lightning core from the atmosphere and the transfer of the atmospheric pressure on it are considered.

Disruptions with runaway electron generation have been deliberately induced by injection of argon using a disruption mitigation valve. A second disruption mitigation valve has been utilised to inject varying amounts of helium after a short time delay. No generation of runaway electrons has been observed when more than a critical amount of helium has been injected no later than 5 ms after the triggering of the first valve. The required amount of helium for suppression of runaway electron generation is up to one order of magnitude lower than the critical density according to Connor & Hastie (1975) and Rosenbluth & Putvinski (1997).

Creation of plasmas by intense laser pulses and consequent laser–plasma interactions involve highly non-linear processes. In particular, a variation of the refractive index induced by the laser action turns into a self-phase modulation (SPM) of the laser field. This effect, already observed with nanosecond laser pulses, achieves striking evidence with ultra-short pulses whose intensity can produce index changes in a time as short as a single optical cycle. In this condition, spectral modifications of the laser pulse produced by SPM may strongly modify the laser–plasma interaction. At the same time, the spectral analysis of the transmitted and scattered laser radiation gives valuable information on a variety of processes occurring in the plasma. In this paper we simply consider a few results, which can be attributed to SPM, with the aim of comparing nanosecond and sub-picosecond laser interaction regimes at moderate laser intensities.

An ultra-relativistic electron beam propagating through a high-Z solid triggers an electromagnetic cascade, whereby a large number of high-energy photons and electron–positron pairs are produced mainly via the bremsstrahlung and Bethe–Heitler processes, respectively. These mechanisms are routinely used to generate positron beams in conventional accelerators such as the electron–positron collider (LEP). Here we show that the application of similar physical mechanisms to a laser-driven electron source allows for the generation of high-quality positron beams in a much more compact and cheaper configuration. We anticipate that the application of these results to the next generation of lasers might open the pathway for the realization of an all-optical high-energy electron–positron collider.

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.

The HYPER-II device has been constructed in Kyushu University to investigate the flow structure formation in an ion-unmagnetized plasma, which is an intermediate state of plasma and consists of unmagnetized ions and magnetized electrons. High density plasmas are produced by electron cyclotron resonance heating, and the flow field structure in an inhomogeneous magnetic field is investigated with a directional Langmuir probe method and a laser-induced fluorescence method. The experimental setup has been completed and the diagnostic systems have been installed to start the experiments. A set of coaxial electrodes will be introduced to control the azimuthal plasma rotation, and the effect of plasma rotation to generation of rectilinear flow structure will be studied. The HYPER-II experiments will clarify the overall flow structure in the inhomogeneous magnetic field and contribute to understanding characteristic feature of the intermediate state of plasma.

The behavior of waves in a one-dimensional (1D) dusty plasma lattice where the dust interacts via Yukawa and electric dipole interactions is discussed theoretically. This study is motivated by recent reports on electrorheological dusty plasmas (e.g. Ivlev et al. 2008Phys. Rev. Lett.100, 095003) where the dipole interaction arises due to an external uniaxial AC electric field that distorts the Debye sphere surrounding each grain. Application to possible dusty plasma experimental parameters is discussed.

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.

In experiments with neutral beam injection at the early stage of a Globus-M discharge, instabilities were observed that were excited by fast ions in the frequency range of 50–200 kHz, which were identified as toroidal Alfvén eigenmodes (TAE) (Petrov et al., Plasma Phys. Rep., vol. 37, 2011, pp. 1001–1005). In contradiction with the NSTX and MAST tokamaks, a regime of TAE generation was realized with strongly developed single modes. Magnetic measurements with fast Mirnov probes have shown that most of the modes have toroidal number $n=1$. The influence of the modes on the fast particle confinement was recorded by means of a tangentially directed neutral particle analyser (NPA) and neutron detector. Hydrogen and deuterium were used as target plasma and injected beam for study of the isotopic effect. At deuterium injection into the deuterium plasma, TAE led to the neutron rate dropping by 25 %, whereas NPA fluxes of high energy dropped by 75 %. At hydrogen injection, the drop in the measured NPA fluxes did not exceed 25 %.

The dynamics of burning plasma is very complicated physics, which is dominated by multi-scale and multi-physics phenomena. To understand such phenomena, numerical simulations are indispensable. Fundamentals of numerical methods used in fusion science numerical modeling are briefly discussed in this paper. In addition, the parallelization technique such as open multi processing (OpenMP) and message passing interface (MPI) parallel programing are introduced and the loop-level parallelization is shown as an example.

The von-Kármán plasma experiment is a novel versatile experimental device designed to explore the dynamics of basic magnetic induction processes and the dynamics of flows driven in weakly magnetized plasmas. A high-density plasma column (1016–1019 particles. m−3) is created by two radio-frequency plasma sources located at each end of a 1 m long linear device. Flows are driven through J × B azimuthal torques created from independently controlled emissive cathodes. The device has been designed such that magnetic induction processes and turbulent plasma dynamics can be studied from a variety of time-averaged axisymmetric flows in a cylinder. MHD simulations implementing volume-penalization support the experimental development to design the most efficient flow-driving schemes and understand the flow dynamics. Preliminary experimental results show that a rotating motion of up to nearly 1 km/s is controlled by the J × B azimuthal torque.

We analyse, both analytically and numerically, a two-dimensional six-field fluid model for collisionless magnetic reconnection, accounting for temperature and heat flux fluctuations along the direction of the magnetic guide field. We show that the model possesses a Hamiltonian structure with a non-canonical Poisson bracket. This bracket is characterized by the presence of six infinite families of Casimirs, associated with Lagrangian invariants. This reveals that the model can be reformulated as a system of advection equations, thus generalizing previous results obtained for Hamiltonian isothermal fluid models for reconnection. Numerical simulations indicate that the presence of heat flux and temperature fluctuations yields slightly larger growth rates and similar saturated island amplitudes, with respect to the isothermal models. For values of the sonic Larmor radius much smaller than the electron skin depth, heat flux fluctuations tend to be suppressed and temperature fluctuations follow density fluctuations. Increasing the sonic Larmor radius results in an increasing fraction of magnetic energy converted into heat flux, at the expense of temperature fluctuations. In particular, heat flux fluctuations tend to become relevant along the magnetic island separatrices. The qualitative structures associated with the electron field variables are also reinterpreted in terms of the rotation of the Lagrangian invariants of the system.

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.

The West Virginia University Hot hELIcon eXperiment (HELIX) provides variable density and ion temperature plasmas, with controllable levels of thermal anisotropy, for space relevant laboratory experiments in the Large Experiment on Instabilities and Anisotropy (LEIA) as well as fundamental studies of helicon source physics in HELIX. Through auxiliary ion heating, the ion temperature anisotropy (T⊥/T∥) is variable from 1 to 20 for parallel plasma beta (β = 8πnkTi∥/B2) values that span the range of 0.0001 to 0.01 in LEIA. The ion velocity distribution function is measured throughout the discharge volume in steady-state and pulsed plasmas with laser induced fluorescence (LIF). The wavelengths of very short wavelength electrostatic fluctuations are measured with a coherent microwave scattering system. Operating at low neutral pressures triggers spontaneous formation of a current-free electric double layer. Ion acceleration through the double layer is detected through LIF. LIF-based velocity space tomography of the accelerated beam provides a two-dimensional mapping of the bulk and beam ion distribution functions. The driving frequency for the m = 1 helical antenna is continuously variable from 8.5 to 16 MHz and frequency dependent variations of the RF coupling to the plasma allow the spontaneously appearing double layers to be turned on and off without modifying the plasma collisionality or magnetic field geometry. Single and multi-species plasmas are created with argon, helium, nitrogen, krypton, and xenon. The noble gas plasmas have steep neutral density gradients, with ionization levels reaching 100% in the core of the plasma source. The large plasma density in the source enables the study of Aflvén waves in the HELIX device.

A formalism for consideration of island formation is presented using a model of a cylindrical resistively unstable plasma. Both current and pressure driven island formation at resonant surfaces are considered. The proposed formalism of perturbed equilibria avoids problems typical for linear analysis of resistive magneto-hydrodynamic instabilities related to extraction of the so-called small solution near the resonant surfaces. The matching technique of this paper is not sensitive to configuration parameters near the resonant surfaces. The comparison of the perturbed equilibrium method with the frequently used quasilinear mode analysis based on a perturbed averaged current density profile shows that the latter is limited in its applicability and underestimates the stability. Presented here for a cylindrical case, the perturbed equilibrium technique can be used in toroidal perturbed equilibrium codes with minor modifications.

Recent results of three astrophysically relevant experiments at Caltech are summarized. In the first experiment magnetohydrodynamically driven plasma jets simulate astrophysical jets that undergo a kink instability. Lateral acceleration of the kinking jet spawns a Rayleigh–Taylor instability, which in turn spawns a magnetic reconnection. Particle heating and a burst of waves are observed in association with the reconnection. The second experiment uses a slightly different setup to produce an expanding arched plasma loop which is similar to a solar corona loop. It is shown that the plasma in this loop results from jets originating from the electrodes. The possibility of a transition from slow to fast expansion as a result of the expanding loop breaking free of an externally imposed strapping magnetic field is investigated. The third and completely different experiment creates a weakly ionized plasma with liquid nitrogen cooled electrodes. Water vapour injected into this plasma forms water ice grains that in general are ellipsoidal and not spheroidal. The water ice grains can become quite long (up to several hundred microns) and self-organize so that they are evenly spaced and vertically aligned.

Understanding the key processes occurring in the tokamak scrape-off layer (SOL) is becoming of the outmost importance while we enter the ITER era and we move towards the conception of future fusion reactors. By controlling the heat exhaust, by playing an important role in determining the overall plasma confinement, and by regulating the impurity level in tokamak core, the dynamics of the fusion fuel in the SOL is, in fact, related to some of the most crucial issues that the fusion program is facing today. Because of the limited diagnostic access and in view of predicting the SOL dynamics in future devices, simulations are becoming crucial to address the physics of this region. The present paper, which summarizes the lecture on SOL simulations that was given during the 7th ITER international school (August 25–29, 2014, Aix-en-Provence, France), provides a brief overview of the simulation approaches to the SOL dynamics. First, disentangling the complexity of the system, the key physics processes occurring in the SOL are described. Then, the different simulation approaches to the SOL dynamics are presented, from first-principles kinetic and fluid models, to the phenomenological analysis.

Gyrokinetic simulations of electromagnetic turbulence in magnetically confined torus plasmas including tokamak and heliotron/stellarator are reviewed. Numerical simulation of turbulence in finite beta plasmas is an important task for predicting the performance of fusion reactors and a great challenge in computational science due to multiple spatio-temporal scales related to electromagnetic ion and electron dynamics. The simulation becomes further challenging in non-axisymmetric plasmas. In finite beta plasmas, magnetic perturbation appears and influences some key mechanisms of turbulent transport, which include linear instability and zonal flow production. Linear analysis shows that the ion-temperature gradient (ITG) instability, which is essentially an electrostatic instability, is unstable at low beta and its growth rate is reduced by magnetic field line bending at finite beta. On the other hand, the kinetic ballooning mode (KBM), which is an electromagnetic instability, is destabilized at high beta. In addition, trapped electron modes (TEMs), electron temperature gradient (ETG) modes, and micro-tearing modes (MTMs) can be destabilized. These instabilities are classified into two categories: ballooning parity and tearing parity modes. These parities are mixed by nonlinear interactions, so that, for instance, the ITG mode excites tearing parity modes. In the nonlinear evolution, the zonal flow shear acts to regulate the ITG driven turbulence at low beta. On the other hand, at finite beta, interplay between the turbulence and zonal flows becomes complicated because the production of zonal flow is influenced by the finite beta effects. When the zonal flows are too weak, turbulence continues to grow beyond a physically relevant level of saturation in finite-beta tokamaks. Nonlinear mode coupling to stable modes can play a role in the saturation of finite beta ITG mode and KBM. Since there is a quadratic conserved quantity, evaluating nonlinear transfer of the conserved quantity from unstable modes to stable modes is useful for understanding the saturation mechanism of turbulence.

In the Earth's magnetosphere, the boundary layer regions are the sources for inhomogeneous plasmas and are natural laboratories to study wave phenomena. In these regions, particles distributions also differ from Maxwellian and are found to be non-thermal. Therefore, amplitude of the waves propagating through these regions can vary differently compared to the homogeneous plasmas. In this study, propagation of ion–acoustic waves (IAWs) in an inhomogeneous, warm electron-ion plasma is examined. The electrons are considered to be having non-thermal Cairn's type distribution and ions follow the fluid dynamical equations. Further, inhomogeneity is assumed in equilibrium density of the electrons and ions. The evolution of the nonlinear IAWs is governed by the Korteweg–de Vries (KdV) equation with variable coefficients. Analytical solution of the KdV equation shows that for a cold ion plasma and non-thermal electrons, the amplitude and the width of the nonlinear IAWs decreases and increases, respectively with the inclusion of the non-thermal distribution of electrons. It is interesting to note that nonlinear IAWs in this model can not propagate for whole range of non-thermal parameter, α. The novel result of this study is that for nonlinear IAWs to propagate in the inhomogeneous two component plasma with ions and non-thermal electrons, the non-thermal parameter, α ⩽ 0.155. Results from our study may have impact on the propagation of the IAWs in the boundary layer regions of the Earth's magnetosphere where density inhomogeneities are appreciable.