Ultra-cold plasmas obtained by ionization of atomic Rydberg states are qualified as classical and strongly coupled electron fluids. They are shown to share several common trends with ultra-cold electron flows used for ion-beam cooling. They exhibit specific stopping behaviour to charged particle beams, which may be used for diagnostic purposes. Ultra-cold plasmas are easily strongly magnetized. Then, one expects a strongly anisotropic behaviour of low ion velocity slowing down when the target electron cyclotron radius becomes smaller than the corresponding Debye length.

A unified energy principle approach is presented for analysing the magnetohydrodynamic (MHD) stability of plasmas consisting of multiple ideal and relaxed regions. The gauge a = ξ × B for the vector potential, a, of linearized perturbations is used, with the equilibrium magnetic field B obeying a Beltrami equation, ∇ × B = αB, in relaxed regions. In a region with such a force-free equilibrium Beltrami field we show that ξ obeys the same Euler–Lagrange equation whether ideal or relaxed MHD is used for perturbations, except in the neighbourhood of the magnetic surfaces where B · ∇ is singular. The difference at singular surfaces is analysed in cylindrical geometry: in ideal MHD only Newcomb's small solutions are allowed, whereas in relaxed MHD only the odd-parity large solution and even-parity small solution are allowed. A procedure for constructing global multi-region solutions in cylindrical geometry is presented. Focusing on the limit where the two interfaces approach each other arbitrarily closely, it is shown that the singular-limit problem encountered previously by Hole et al. in multi-region relaxed MHD is stabilized if the relaxed-MHD region between the coalescing interfaces is replaced by an ideal-MHD region. We then present a stable (k, pressure) phase-space plot, which allows us to determine the form a stable pressure and field profile must take in the region between the interfaces. From this knowledge, we conclude that there exists a class of single-interface plasmas that were found to be stable by Kaiser and Uecker, but are shown to be unstable when the interface is resolved.

The dynamics of nonlinear two-dimensional plasma waves under non-equilibrium conditions is studied in the framework of the two-fluid hydrodynamic approach. The field of initial velocities for a twirling cylindrical plasma is considered as the initial non-equilibrium state. The influence of initial conditions on the formation and existence of nonlinear electron waves is discussed.

Runaway electron ream instabilities have been observed in Ohmic plasmas in the HT-7 tokamak. The instability regime is characterized by relaxations in the electron cyclotron emission due to the relativistic anomalous Doppler resonance effect which transfers energy from parallel to perpendicular motion. Two types of instabilities in the slide-away regime have been observed in the HT-7 tokamak. The scaling of the threshold value for the instabilities to occur has been derived. It is found that the threshold value is linearly dependent on the plasma current and independent of the toroidal magnetic field strength.

The dynamic behaviour of a positive column oxygen plasma is investigated both experimentally and theoretically. In the experiment the response of the discharge current to small external perturbations of the electrical field is measured. Using these data the electrical impedance of the plasma is obtained dependent on the frequency of the external perturbation. A drift approximation model is presented, which covers the experimental findings over a wide range of the perturbation frequency. It appears that the influence of the fluctuations of the neutral species is negligible and the dynamic behaviour of the plasma is mostly governed by the charged particles. This provides a simple expression for the plasma impedance which allows the reaction rate and transport coefficients, as well as discharge parameters, to be validated.

Counterstreaming plasma systems with intrinsic temperature anisotropies are unstable against the excitation of Weibel-type instabilities, namely, filamentation and Weibel instabilities, and their cumulative effect. Here, the analysis is extended to counterstreaming plasmas with weakly relativistic bulk velocities, while the thermal velocities are still considered to be non-relativistic. Such plasma systems are relevant for fusion plasma experiments and the more violent astrophysical phenomena, such as jets in gamma-ray burst sources. Simple analytical forms of the dispersion relations are derived in the limit of a small transverse temperature or a large temperature anisotropy of the beams. The aperiodic growing solutions are plotted systematically for the representative cases chosen in Paper I (Lazar et al. 2009 J. Plasma Phys. 75, in press). In the limit of slow non-relativistic plasma flows, the numerical solutions fit well with those obtained in Paper I, but for weakly relativistic streams an important deviation is found.

It is shown that the energy of protons accelerated in laser–matter interaction experiments may be significantly increased through the process of splitting the incoming laser pulse into multiple interaction stages of equal intensity. From a thermodynamic point of view, the splitting procedure can be viewed as an effective way of increasing the efficiency of energy transfer from the laser light to protons, which peaks for processes having the least amount of entropy gain. It is predicted that it should be possible to achieve at least a 100% increase in the energy efficiency in a six-stage laser proton accelerator compared with a single laser–target interaction scheme.

A dusty plasma consisting of cold and hot electrons, cold ions, and charge fluctuating isolated cold dust has been considered. It has been shown by a normal mode analysis that in such a dusty plasma there exists a new type of electrostatic perturbation mode due to the charge fluctuation of the isolated dust. The basic features of this new electrostatic perturbation mode, which are different from those of the electron-acoustic waves, have also been analytically identified. The implications of these results in both the space and laboratory dusty plasma conditions are briefly discussed.

The toroidal magnetic field of tokamaks is generated by a finite number of coils, which slightly modulates the magnetic field and runaway electrons experience this modulation. The resonant interaction between runaway electrons and the magnetic field ripple has been observed in the HT-7 tokamak. The maximum energy of runaways in the edge region could be blocked by the resonance of gyromotion with the nth harmonic of the magnetic field ripple. This resonant interaction is favorable for the control of runaway energy.

We present an investigation for the generation of intense magnetic fields in dense plasmas with an anisotropic electron Fermi–Dirac distribution. For this purpose, we use a new linear dispersion relation for transverse waves in the Wigner–Maxwell dense quantum plasma system. Numerical analysis of the dispersion relation reveals the scaling of the growth rate as a function of the Fermi energy and the temperature anisotropy. The nonlinear saturation level of the magnetic fields is found through fully kinetic simulations, which indicates that the final amplitudes of the magnetic fields are proportional to the linear growth rate of the instability. The present results are important for understanding the origin of intense magnetic fields in dense Fermionic plasmas, such as those in the next-generation intense laser–solid density plasma experiments.

This work presents a fully analytic way of determining relevant equilibrium quantities of a high-intensity charged particle beam submitted to magnetic focusing while inside a linear channel. Through the current approach, some intermediate steps of our original hybrid model which had to be solved numerically can now be eliminated, leading to the obtainment of a fully analytic expression. This expression relates the initial beam parameters with those at equilibrium, allowing beam macroscopic quantities such as envelope and emittance to be naturally and analytically determined. For validation, full self-consistent N-particle beam numerical simulations have been carried out and the results compared with the predictions supplied by the full analytical model. The agreement is shown to be good with the simulations and also with the original hybrid numerical-analytical version of the model.

In this paper we present a theoretical investigation of the growth/propagation of a ring ripple, superposed on a Gaussian electromagnetic beam propagating along the direction of magnetic field in a magnetoplasma. The nature of propagation of the ripple is analysed in a paraxial-like approximation by radial expansion of the dielectric function, corresponding to the composite (Gaussian and ripple) electric field profile of the beam around the position of the maximum of the ripple. The two cases of collisional plasmas (with negligible thermal conduction) and collisionless plasmas (dominant ponderomotive nonlinearity) are considered. The effect of the magnetic field on the critical curves and focusing/defocusing of the ripple are studied and discussed.

A simple analytic expression of the two-dimensional Child–Langmuir law is derived for non-zero injection velocities and Lau's result is obtained in our model by setting the injection velocity equal to zero. The calculation results show that the modify term in our model is larger than Lau's with a non-zero electronic initial energy, and it is twice as large as Lau's when the electronic initial energy is much greater than the potential energy of the gap.

In a suitable experimental device, laboratory plasma is produced with conditions and parameters analogous to magnetospheric plasma; we light a rare plasma in a semi-machine using rf-frequency discharge. Three ranges of low-frequency instabilities appear, one of which is identified as drift, caused by electron–neutral collisions. A full theoretical elaboration adapted to production conditions and geometrical symmetry is carried out; one solution of the dispersion relation is sufficient justification for the existence of the instability. The mathematical analysis also has the ambition to give interpretation for other low-frequency waves. Here we make a sound identification of the instability type as drift resistive due to electron–neutral collisions by an investigation of the growth rate. An agreement between experimental results and the theoretical model is obtained. As in the magnetosphere, an external magnetic field restrains the plasma.

The recent analysis of large-amplitude solitary potentials in a charge varying dusty plasma with trapped dust particles (Tribeche, M. 2005 Phys. Plasmas12, 072304) is extended to include the electron trapping self-consistently. The non-isothermal trapped electron charging is investigated based on the orbit motion limited approach. It is found that the nonlinear localized potential structure enlarges when the electrons deviate from isothermality. The effect of this deviation is more significant under certain conditions. The dust particles are locally expelled and pushed out of the region of soliton localization as the electrons evolve far away from their thermodynamic equilibrium.

The gyrocenter phase-space transformation used to describe nonlinear gyrokinetic theory is rediscovered by a recursive solution of the Hamiltonian dynamics associated with the perturbed guiding-center Vlasov operator. The present work clarifies the relation between the derivation of the gyrocenter phase-space coordinates by the guiding-center recursive Vlasov method and the method of Lie-transform phase-space transformations.

In the study of the interaction of ultra-intense laser pulses with thin plasma targets there appears self-generated magnetic fields in the plasma target. The strong magnetic fields were directly measured in the plasma target, and were attributed to a mechanism of non-parallel electron temperature and density gradients. These magnetic fields can become strong enough to significantly affect the plasma transport. The underlying mechanism of the self-generated magnetic fields in the ultra-intense laser–plasma interactions is presented by using a two-dimensional particle-in-cell simulation.

A system of equations for modulational interaction of the electromagnetic branch of drift waves with magnetic cells is constructed. The solution of these equations describes formation of a set of magnetic cells with oppositely directed magnetic fields at their boundaries.

This paper presents an analysis of the spatial growth of a transverse instability, corresponding to the propagation of an electromagnetic beam, with uniform irradiance along the wavefront in a collisional plasma, along the direction of a static magnetic field; expressions have been derived for the rate of growth, the maximum value of the rate of growth and the corresponding value of the wave number of the instability. The instability arises on account of the ejection of electrons from regions where the irradiance of the perturbation is large. The energy balance of the electrons taking into account ohmic heating and the power loss of electrons on account of (i) collisions with ions and neutral species and (ii) thermal conduction has been taken into account for the evaluation of the perturbation in electron temperature, which determines the subsequent growth of the instability. Further, the relationship between the electron density and temperature, as obtained from the kinetic theory, has been used. The filamentation instability becomes enhanced with the increase of the static magnetic field for the extraordinary mode while the reverse is true for the ordinary mode. Dependence of growth rate on irradiance of the main beam, magnetic field and a parameter proportional to the ratio of power loss of electrons by conduction to that by collisions has been numerically studied and illustrated by figures. The dependence of the maximum growth rate and the corresponding optimum value of the wave number of the instability on the irradiance of the main beam has also been studied. The paper concludes with a discussion of the numerical results, so obtained.

Previous results on nonlinear acoustic–gravity waves are reconsidered. It turns out that the mathematical techniques used are somewhat similar to those already adopted by the plasma physics community. Consequently, a future interaction between physicists in different fields, e.g. in meteorology and plasma physics, can be very fruitful.