A microwave coherent backscattering experiment has been carried out on Mirabelle, a weakly ionized plasma device, with the objective of measuring the electron-density fluctuation level. The experiment is a preliminary step in order to prepare the detection system for a microwave stimulated-backscattering experiment. The incident electromagnetic wave is focused in front of a plane grid, which excites ion acoustic or electron Bernstein waves and induces fluctuations in the plasma. The backscattering signal is collected by the launching circuit and detected by homodyne mixing. The typical ratio of the scattered power to the incident power is about 10−12 and the relative density fluctuations is of the order of δne/ne ≈10−3 against a background electron density ne=(1–5)×109 cm−3. The backscattering measurement is also compared with Langmuir-probe measurements, and gives good agreement with the relative density fluctuations. The spectral width of the backscattered signal has also been studied, by taking into account effects due to the incident-wave focusing and plasma-wave damping.

The equilibrium of a resistive axisymmetric plasma with purely toroidal flow surrounded by a conductor is investigated within the framework of nonlinear magnetohydrodynamic theory. It is proved that (a) the poloidal current-density vanishes and (b) apart from an idealized case, the pressure profile should vanish on the plasma boundary. For the cases of isothermal magnetic surfaces, isentropic magnetic surfaces and magnetic surfaces with constant density, the equilibrium states obey an elliptic partial differential equation for the poloidal magnetic flux function, which is identical in form to the corresponding equation governing ideal equilibria. The conductivity, which can be neither uniform nor a surface quantity, results, however, in a restriction of the possible classes of equilibrium solutions; for example for the cases considered, the only possible equilibria with Spitzer conductivity are of cylindrical shape.

The infinite set of moments of the two-particle distribution function is found exactly for the uniform cooling state of a hard-sphere gas with inelastic collisions. Their form shows that velocity correlations cannot be neglected, and consequently the ‘molecular chaos’ hypothesis leading to the inelastic Boltzmann and Enskog kinetic equations must be questioned.

Although most magnetic neutral points occurring in nature seem to form part of a continuum, recent studies of reconnection have centred on static equilibria in the neighbourhood of an isolated three-dimensional null point. The linear stability of this configuration is studied here. It is found that one may choose a flux surface so that transverse oscillations localized around the surface and polarized within it must grow exponentially in time. This means that any static equilibrium containing an isolated three-dimensional null point is linearly unstable.

A brief review of two alternative descriptions of non-equilibrium processes in a fully ionized plasma is presented. The example of ‘Landau damping’ is used to demonstrate that some fundamental problems remain unsolved in the kinetic theory of plasmas. These arise from inconsistent descriptions of the transition from the reversible equations of the mechanics of charged particles and fields to the irreversible equations for a continuous medium in the theory of plasmas. These difficulties can be overcome through consistently defining the structure of the continuous medium and the characteristics of dynamic instability of motion of particles. This leads to generalized irreversible kinetic equations that provide the basis for a unified description of non-equilibrium processes in a plasma on kinetic and hydrodynamic scales.

The process of expansion into a vacuum of a collisionless plasma bunch with relativistic electron temperature is investigated for the one-dimensional case. Self-similar solutions for the evolution of the electron distribution function and ion acceleration are obtained, taking account of cooling of the electron component of plasma for the cases of non-relativistic and ultrarelativistic electron energies.

We present stability results for plane soliton solutions of two versions of the two-dimensional KdV equation, namely the Zakharov–Kuznetsov (ZK) equation and the Kadomtsev–Petviashvili equation for positive dispersion (KP+ equation). To do this we use a linear variation-of-action method (VAM). Others have used this method, but with little success when applied to these two equations. The best results have given the correct instability range, but the predicted growth rates have significant errors. For the ZK equation we show, by paying more attention to the spatially asymptotic form of the trial function, how better estimates of the dispersion relation can be obtained. We go on to obtain the exact dispersion relation for perturbations of the plane soliton solution of the KP+ equation.

An experiment is conducted to confirm the theoretical prediction that a rapidly generated lossy plasma can cause spectral breaking and frequency shift of a high-power microwave pulse. Spectral breaking is the transformation or breaking of a single dominant spectral peak associated with an incident pulse into two spectral peaks. The experiment is conducted by comparing the frequency spectrum of an incident pulse with the spectrum of the pulse transmitted through a self-induced air-breakdown environment. It is shown that as the ionization rate becomes too high, the spectrum of the transmitted pulse breaks up into two peaks: one has an upshifted centre frequency, and the other has a downshifted centre frequency. The results show that the amount of frequency upshift is correlated with the ionization rate, whereas the amount of frequency downshift is correlated with the energy losses from the pulse in the self-generated plasma. These experimental results agree with the theoretical prediction and a numerical simulation, which are also presented.

A stability analysis is performed for solitary ion-acoustic waves in a magnetized plasma in which the electrons are non-isothermal. Including the effect of ion drift velocity and magnetic perturbation, a three-dimensional mKdV equation is derived for ion-acoustic waves. The solitary-wave solution of this equation is found to have a sech4 profile. A stability analysis of this solitary wave is performed using the small-k perturbation expansion method of Rowlands and Infeld. A condition for the onset of instability is obtained. The growth rate of the instability is found to attain a maximum for perturbations in the plane perpendicular to the direction of propagation of the solitary wave.

Taking into account the first non-Markovian correction to the Balescu–Lenard equation, we derive an expression for the pair correlation function and a nonlinear kinetic equation valid for a weakly non-ideal polarized classical plasma. This equation allows for the description of the correlational energy evolution and exhibits global conservation of energy with dynamical polarization.

The nonrelativistic motion of a charged particle in the electromagnetic field of a plane wave is studied. New analytic solutions of the equation of motion are found that manifest the dependence of the period of the particle motion on the wave amplitude.

On account of nonlinear refraction, arising through the relativistic mass effect, a short intense laser pulse tends to accumulate its energy around the intensity maximum, leading to pulse compression over a length Zc≈ τ0c2ω2/ ω2pv, where τ0 and ω are the pulse duration and frequency of the laser, v is the oscillatory electron velocity and ωp is the plasma frequency. When the transverse extent of the laser is finite, nonlinear self-focusing interferes strongly with this process. The self-focusing occurs in a periodic manner on a shorter scale length. However, over long lengths of pulse propagation, pulse compression could be significant.

Linear and nonlinear dust-acoustic wave propagation in a non-ideal classical dusty plasma consisting of electrons, ions and dust grains is investigated by incorporating the van der Waals equation of state for the dust component. For linear waves, it is found from the normal mode dispersion relation that the volume reduction coefficient enhances the phase speed of the dust-acoustic waves, while the molecular cohesive forces lead to a decrease in the phase speed. The relative magnitudes of the two contributions depend on the specific parameter regimes characterizing the non-ideal nature of the dust component. In the high-temperature limit, there is a net increase in the dust-acoustic phase speed, while near the critical point the phase speed is reduced when compared with that for the ideal-gas case. For large amplitudes, we discuss the existence of dust-acoustic solitons by deriving the exact Sagdeev potential. While supersonic solitons are found to be admissible in both the sub- and supercritical parameter regimes, subsonic propagation near the dust-acoustic speed is possible only for the supercritical case. For small but finite amplitudes, explicit analytical solutions have been obtained. A limiting case of these solutions is also discussed.

For low-dimensional Hamiltonian systems with chaotic dynamics, we discuss the differences in the kinetic description, and the necessity of windowing of the time and parameter space, which is imposed by the differences in the phase-space topology and by the stickiness of trajectories at island boundaries.

Stimulated scatterings of large-amplitude electromagnetic waves by Langmuir, dust–ion-acoustic and dust-acoustic waves in unmagnetized dusty plasmas are investigated by employing the standard methods of nonlinear three-wave interactions and by incorporating the effects of grain-charge fluctuations, collisions of electrons and ions with dust grains, the plasma drag on a dust grain (for the case of the dust-acoustic wave) and the dependence of the average dust charge on the dusty plasma parameters. Distinction is made between the charging collisions, when electrons and ions are accumulated onto the grain surface; and Coulomb collisions, when electrons and ions are simply deflected from the grain surface. We investigate the regimes for which Coulomb collisions can be treated under the small-angle-deflection approximation. If the intergrain average spacing is equal to or smaller than the Debye length, the collision frequencies of plasma species with dust grains can be much larger than any collision frequency of the plasma species amongst themselves. In the case of Brillouin stimulated scattering, other important contributions to damping come from Landau and dust-charge fluctuation damping. In the case of dust–Brillouin stimulated scattering, the most important contribution to damping comes from dust-charge fluctuation (if the intergrain average spacing is equal to or smaller than the Debye length) and plasma drag on the dust particles (if the intergrain average spacing is larger than the Debye length). We derive the instability thresholds as a function of the density of the dust grains. Because of the inclusion of the new effects, in both Raman and Brillouin scatterings it is found that the instability threshold powers are drastically increased relative to the dust-free case. In the case of dust–Brillouin scattering, a minimum for the threshold power is found in the transition region between ‘dusty’ and ‘dust-in’ plasma. Growth rates near thresholds are also discussed.

An intense short laser pulse incident on a metallic target produces an overdense plasma and excites a plasma surface wave via stimulated Compton scattering. The pump and the surface wave exert a beat-frequency ponderomotive force on the electrons in the skin layer, driving a heavily damped quasimode. The density perturbations due to the quasimode couple with the oscillatory velocity due to the pump to drive the surface wave. The growth period for the process turns out to be about 0.5 ps at a Nd[ratio ]glass laser intensity of 1016W cm−2 and a plasma density of 1.5 times the critical value.

A theoretical investigation has been made of the nonlinear propagation of dust-acoustic waves in a magnetized three-component dusty plasma consisting of a negatively charged dust fluid, free electrons and vortex-like distributed ions. It is found that, owing to the departure from the Boltzmann ion distribution to a vortex-like one, the dynamics of small- but finite-amplitude dust-acoustic waves in a magnetized dusty plasma is governed by the modified Korteweg–de Vries equation. The latter admits a stationary dust-acoustic solitary-wave solution that has larger amplitude, smaller width and higher propagation velocity than that involving adiabatic ions. The effects of external magnetic field, trapped ions and free electrons on the properties of these dust-acoustic solitary waves are briefly discussed.

The nonlinear dynamics and structure of plasmas with tightly twisted magnetic field lines have been studied using a toroidal plasma device. Stepwise magnetohydrodynamic (MHD) relaxation occurs, resulting in a discontinuous change in the pitch of magnetic field lines. This discrete nature of the pitch stems from the instability of kink (torsional) modes. The MHD relaxation stabilizes kink modes by selecting (self-organizing) appropriate pitches. The self-organized state displays the characteristic of a ‘dissipative structure’ in that it is accompanied by enhanced energy dissipation; the global resistance of the plasma current is substantially enhanced. The magnetic energy, which is generated by the internal plasma current, first changes into fluctuation energy through the kink instability, and then it goes mainly to ion thermal energy through viscous dissipation of the fluctuating flow. The viscosity dissipates the fluctuation energy with conservation of helicity. The self-organization of the stabilized magnetic field is characterized by the preferential conservation of the helicity.

Stochastic modelling of turbulence is considered. Exact and approximate solution procedures based on projection techniques are briefly reviewed. Procedures leading to equations that are local in time are discussed. Two different approximations of this type are presented, whose performances are tested and compared on a simple model case.

This paper and a forthcoming one develop the spectral theory of ballooning transformations relevant to tokamak physics from first principles in a rigorous and yet intuitively clear manner. The power of the ballooning representation to throw light on the spectral characteristics of the plasma problems to which it is applicable is emphasized, and examples are given to illustrate the general notions. The ballooning representation is shown to be essentially a method to separate variables and reduce two-dimensional partial differential equations with periodic coefficients to infinite sets of soluble ordinary differential equations. This paper is concerned with an elementary approach to the techniques in the context of nearly exactly soluble problems involving the anisotropic diffusion operator in toroidal geometry. Two different perturbation methods are discussed. Applications to plasma instability problems and the subtleties involving the continuous spectra of ballooning operators will be taken up in Part 2.