The effect of Raman instabilities on the production of fast electrons in laser–plasma interaction has been investigated for laser intensities well above the electron trapping threshold. The results of one-dimensional particle-in-cell simulations show that in this regime the presence of Raman backscattering (RBS) hampers fast-electron production, and that its suppression increases the yield of high-energy electrons ($>$15 MeV). Such suppression has been realized either through deletion of all backscattered radiation from the simulations or through direct stimulation of Raman forward scattering (RFS). An increased high-energy electron yield has been observed for both methods. In addition, the influence of various laser and plasma parameters on the production of highly energetic electrons has been investigated. Specifically, the effects of plasma density ramps, skews in the temporal envelopes of the laser pulses, and laser frequency chirp (both pulse-length preserving and bandwidth preserving) have been examined. For each parameter, its influence on the yield of high-energy electrons can be explained from the way it affects the balance between RBS and RFS excitation in laser–plasma interaction.

For a particle moving in a non-uniform static magnetic field under the action of a wave, ponderomotive effects result from radiofrequency-driven oscillations nonlinearly coupled with Larmor rotation. Using the Lagrangian and Hamiltonian formalisms, we show how, despite this coupling, two independent integrals of the particle motion are approximately conserved. These are the magnetic moment of free Larmor rotation and the quasi-energy of the guiding center motion parallel to the d.c. magnetic field. Under the assumption of non-resonant interaction of the particle with the radiofrequency field, these integrals represent adiabatic invariants of the particle motion.

The shielding of a one-dimensional, planar, permeable test charge has been studied theoretically. General expressions are derived and evaluated which show how the screening of a test charge, represented by the floating potential $\psi$, surface charge density q and screening length L, depends on various plasma parameters such as the temperature of electron and ions and particle streaming velocities. Particular attention has been given to analyzing the influence of particle trapping (reflection) in the charging and screening problem. No charging model can adequately describe the screening mechanism unless proper care is taken in choosing suitable distribution functions for both plasma species. In this paper, such a theory has been developed that provides the general idea about the charging of a grid in plasmas under different environments and conditions. As the main outcome we have found that the shielding of a non-propagating test charge is stronger, the larger the trapped ion population and the higher the temperature ratio Te/Ti are. Flux equality in the case of a propagating test charge restricts the solubility of the shielding problem to non-Boltzmann electrons and to a weak $\psi$ and q only. In the cold ion limit a lower bound for the ion streaming velocity is found than that predicted by Bohm's criterion.

The effect on the propagation of ion-acoustic solitons and double layers has been studied in collisionless weakly relativistic plasma consisting of two-electron temperature with isothermal electrons and finite ion temperature. The Korteweg de-Vries (KdV) equation is derived for ion-acoustic solitons propagating in a collisionless plasma. This equation is solved in a stationary frame to obtain the expression for soliton phase velocity, soliton width and peak soliton amplitude. It is observed that these quantities are significantly influenced by the relativistic effect, ion temperature, low-temperature electron density and ratio of cold to hot electron temperatures. Many features expected from hot ion theory and two species electron plasmas automatically emerge. The analysis is further extended to higher order nonlinearity and modified Korteweg de-Vries (mKdV) equation is derived. Even though compressive and rarefactive ion-acoustic solitons are obtained, only rarefactive ion-acoustic double layers are obtained in the present investigation.

Correlation effects play an important role in the description of turbulent transport. The present paper considers the influence of drift flow and time-dependence effects on the passive scalar behavior in the framework of the percolation approach. The renormalization method of a small parameter in continuum percolation models is reviewed. The modification is suggested of the renormalization condition of the small parameter of the percolation model in accordance with the additional external influences superimposed on the system. This approach makes it possible to consider simultaneously both parameters: the characteristic drift velocity $U_{\rm d}$ and the characteristic perturbation frequency $\omega $. The effective diffusion coefficient $D_{\rm eff} \,{\propto}\, \omega ^{1/7}$ satisfactorily describes the low-frequency region $\omega $, where the long-range correlation effects play a significant role. The character of the dependence of $D_{\rm eff}$ on the drift flow amplitude $U_{\rm d}$ in different regimes is analyzed.

The influence of the trapped electrons fraction on the growth-rate of the ion temperature gradient (ITG) modes is studied numerically for JET relevant conditions. As a possible mechanism for increasing the ITG mode growth rate with an increase in the fraction of trapped electrons, a shift in the real frequency is assumed that leads to less Landau damping. Another possible mechanism is the destabilizing contribution of dissipation effects.

We have developed a new set of transport equations for magnetized, fully ionized gases designed to cover the entire regime from collision-dominated to collisionless flow. The equations are based on a skewed bi-Maxwellian velocity distribution function and describe number density, $n$, flow velocity, ${\vek u}$, parallel and perpendicular temperature, $T_{\parallel}$ and $T_{\perp}$, and heat flow, $\mathbf q$. We choose a velocity distribution function $f(\vek v) = f^{\mathrm{bM}}(1+\phi)$ where $f^{\mathrm{bM}}$ is a bi-Maxwellian and the ‘skewness’, $\phi$, is proportional to $c^3$ instead of the more commonly used $\phi\propto c \ (c \equiv |\vek v-\vek u|)$. We find transport coefficients (heat flux and thermal force) in the collision-dominated limit that are in good agreement with results from classical transport theory. The equations also describe, reasonably well, the flow of collisionless, ionized gases, and should therefore be well suited to describe the transition region–corona–solar wind system and other fully ionized, expanding stellar atmospheres.

Electron acceleration by large amplitude electrostatic waves in astrophysical plasmas is studied using particle-in-cell (PIC) simulations. The waves are excited initially at the electron plasma frequency $\omega_{\rm pe}$ by a Buneman instability driven by ion beams: the parameters of the ion beams are appropriate for high Mach number astrophysical shocks, such as those associated with supernova remnants (SNRs). If $\omega_{\rm pe}$ is much higher than the electron cyclotron frequency $\Omega_{\rm e}$, the linear phase of the instability does not depend on the magnitude of the magnetic field. However, the subsequent time evolution of particles and waves depends on both $\omega_{\rm pe}/\Omega_{\rm e}$ and the size of the simulation box $L$. If $L$ is equal to one wavelength, $\lambda_0$, of the Buneman-unstable mode, electrons trapped by the waves undergo acceleration via the surfatron mechanism across the wave front. This occurs most efficiently when $\omega_{\rm pe}/\Omega_{\rm e} \simeq 100$: in this case electrons are accelerated to speeds of up $c/2$ where $c$ is the speed of light. In a simulation with $L=4\lambda_0$ and $\omega_{\rm pe}/\Omega_{\rm e} = 100$, it is found that sideband instabilities give rise to a broad spectrum of wavenumbers, with a power law tail. Some stochastic electron acceleration is observed in this case, but not the surfatron process. Direct integration of the electron equations of motion, using parameters approximating to those of the wave modes observed in the simulations, suggests that the surfatron is compatible with the presence of a broad wave spectrum if $\omega_{\rm pe}/\Omega_{\rm e}> 100$. It is concluded that a combination of stochastic and surfatron acceleration could provide an efficient generator of mildly relativistic electrons at SNR shocks.

The concept of the fast ignitor for laser fusion has led to some modifications in applying petawatt-picosecond (PW-ps) laser-produced high intensity particle beams to ignite deuterium-tritium (DT) fuel. Some very anomalous measurements of ion emission from targets irradiated by picosecond laser pulses led to the development of a skin depth interaction scheme where a defined control of prepulses is necessary. Based on these experimental facts, we have applied a one-dimensional two-fluid hydrodynamic code to understand how the nonlinear ponderomotive force generates two plasma blocks, one moving against the laser light (ablation) and the other moving into the target. This compressed block produces an ion current density of above 10$^{11}$ A cm$^{-2}$ and an ion energy of about 100 keV. This may be a rather promising option to use PW-ps laser pulses for igniting fusion in solid density DT fuel, realizing very high gain controlled fusion reactions.

The interaction of magnetohydrodynamic (MHD) waves in a non-uniform, time-dependent background plasma flow is investigated using Lagrangian field theory methods. The analysis uses Lagrangian maps, in which the position of the fluid element ${\bf x}^*$ is expressed as a vector sum of the position vector x of the background plasma fluid element plus a Lagrangian displacement $\xi({\bf x},t)$ due to the waves. Linear, non-Wentzel–Kramer–Brillouin (WKB) wave interaction equations are obtained by expansion of the Lagrangian out to second order in $\xi$ and $\Delta$S, where $\Delta$S is the Lagrangian entropy perturbation. The characteristic manifolds of the waves are determined by consideration of the Cauchy problem for the wave interaction equations. The manifolds correspond to the usual MHD waves modes, namely the Alfvén waves, the fast and slow magnetoacoustic waves and the entropy wave. The relationships between the characteristic manifolds, and the ray equations of geometrical MHD optics are developed using the theory of Cauchy characteristics for first-order partial differential equations. The first-order differential equations describing the singular manifolds are the dispersion equations for the MHD eigenmodes, where the wave vector ${\bf k}=\nabla\phi$ and frequency $\omega=-\phi_t$ correspond to the characteristic manifolds $\phi({\bf x},t)=$ constant. The form of the characteristic manifolds for both time-dependent and steady MHD flows are developed. The bi-characteristics for steady MHD waves in a steady background flow are related to the group velocity surface and Mach cone for the waves, and determine when the flow is elliptic, hyperbolic, or of mixed hyperbolic-elliptic type. The wave interaction equations are decomposed into coupled equations for the compressible and incompressible perturbations.

We analytically and numerically discuss the plasma distribution and electron temperature enhancement in striations for a given heating source. It is shown that, in stationary conditions, the reduced plasma concentration and the temperature enhancement should be of the same order of magnitude. We deduce that the electron temperature inside striations cannot greatly exceed that in the heated volume. The elongation of striations is calculated for different transverse scales and heating powers. We show that medium sized irregularities are associated with striations and develop after the formation of striations. The peculiarities of the relaxation process for small-scale and medium sized artificial irregularities are investigated and it is found that the relaxation of small-scale irregularities exhibits two time scales, in qualitative agreement with experimental observations.

The magnetic entropy concept is an interpretative and predictive tool based on probability and information, defined in a suitably coarse-grained possibility space of all current density distributions under testable constraints. This paper develops the concept starting from its statistical foundations and then proceeds illustrating its potentiality in the description of the global behavior of macroscopic plasma configurations with practical interest. Finally, the paper discusses the relations of the concept to the dynamics of the underlying system of particles.

The particle diffusion in a stochastic magnetic field is investigated by using the functional integral method. With the ensemble average of a functional representation to a kinetic equation over the fluctuating magnetic field and the random variables modeling the Coulomb collisions, a closed set of equations for an ensemble-averaged distribution function and a response function to an infinitesimal external perturbation is derived within the framework of the direct-interaction (DIA). By using the Markovian approximation to the equation for the response function, the cross-field diffusion coefficients are found to be obtained from nonlinear ordinary differential equations. Explicitly calculated diffusion coefficients for various parameters are also shown in the shearless and sheared configurations.

Waves launched into a magnetized plasma when it is rapidly compressed were studied in the late 1950s by Adlam and Allen. In this paper we show that the equations describing large amplitude magnetized plasma waves, or Adlam–Allen waves, can be reduced to a single nonlinear equation, namely the Korteweg–de Vries equation and that the solutions of this equation are in agreement with the results obtained previously by Adlam and Allen. The solutions of both the Adlam–Allen equations and the Korteweg–de Vries equation take the form of solitary waves and periodic wave trains.

Theories for the formation of plasma and dust voids (large-amplitude ion and dust holes) in a complex plasma with static and mobile negatively charged dust are presented. It is shown that a plasma (dust) void in a complex plasma with negatively charged static (mobile) dust can be formed due to the presence of negative (positive) plasma potential, which is built up owing to a non-isothermal ion (dust) distribution arising from ion (dust) trapping. The plasma voids shrink when the dust grains are added into the plasma, and they tend to disappear if the dust number density is sufficiently high. On the other hand, the dust voids shrink with an increase in the dust charge density, but enlarges with an increase in the dust temperature.

The interaction of magnetohydrodynamic (MHD) waves in a non-uniform, time-dependent background plasma flow is investigated using Lagrangian field theory methods. The analysis uses Lagrangian maps, in which the exact position of the fluid element ${\bf x}^*$ is expressed as a vector sum of the position vector ${\bf x}$ of the background plasma fluid element plus a Lagrangian displacement $\xib({\bf x},t)$ due to the waves. An exact theory for the wave and background stress energy tensors is developed based on the exact Lagrangian and the exact Lagrangian map. Noether's theorems are used in conjunction with the exact action and Lagrangian maps to determine the general form of conservation laws for the total system of waves and background plasma, corresponding to divergence symmetries of the action. The energy and momentum conservation laws of the system are derived from Noether's first theorem corresponding to the time and space translation symmetries of the action, respectively. As examples of the use of Noether's first theorem, we derive the conservation laws associated with the 10-parameter Galilean group admitted by the MHD equations. This includes the space and time translation symmetries, the space rotations, and the Galilean boosts. A class of solutions of the Lie determining equations for the infinite-dimensional MHD fluid relabeling symmetries are used to discuss the corresponding conservation laws. Ertel's theorem for the conservation of potential vorticity for the system of waves and background gas in ideal gas dynamics is derived from an infinite-dimensional fluid relabeling symmetry of the action.

The radial profiles of current and flow permitted by the relaxed states of a two-fluid cylindrical plasma system using double Beltrami formulation are presented. The relaxed states are then compared with those of the internal conductor plasma configuration. The results show that for appropriate boundary conditions and scale parameters, field-aligned currents and flows could be minimized to a greater extent in an internal conductor plasma system as compared with a simple cylindrical plasma configuration. Consequently, high beta relaxed states with minimum values of parallel components of current and flow could be created using internal conductor plasma configurations.

Strong plasma rotation is an important feature in many high-performance fusion plasmas, especially in plasmas with internal transport barriers (ITBs). An analysis of the impact of plasma rotation, or more specifically of a radial electric field, on the ripple-induced stochastic diffusion of energetic ions is presented. In particular, the influence of a radial electric field on the threshold for stochastic motion and on the diffusion path in real space is investigated.

We have solved the shear flow stability problem of compressible electrically conducting fluid (plasma) in a magnetic field. A comparative analysis is made of the influence of different boundary conditions on shear flow stability. We consider the problems for flows in an unbounded medium and a flow between fixed walls, as well as in the presence of a fixed wall on one side of the shear flow only. Shear flow velocity profiles are treated both in the form of a tangential discontinuity and as being described by a hyperbolic tangent function. For the case of an unbounded flow with a velocity vortex sheet, analytical solutions are found; for all other cases, the solutions are found numerically. Problems are solved for two different positions of the tangential wave vector of oscillations and magnetic field ${\bf k}_t\,{\perp}\, {\bf B}_0$ and ${\bf k}_t\,{\parallel}\, {\bf B}_0$. For shear flows bounded by a fixed wall we found an unstable mode of oscillations produced by the wave, reflected from the wall and transmitted through the shear layer.

A novel integral representation suitable for the study of asymptotic ($L/L_{0}\,{\gg}\,1$, $L$ being the plasma length and $L_{0}$ the basic gain length) stability of the inhomogeneous three-wave interaction is formulated and applied to the special case of uniform gain and ramp wavenumber mismatch. The absolute instability condition is $\kappa L_{0} \,{<}\, \pi /8$ ($\kappa$ being the mismatch gradient), with the wave conversion performed in a zone of width $4/\kappa L_{0}$ located at the boundary of wave incidence.