A single-particle theory is developed to investigate particle acceleration along and across a magnetic field and the generation of an electric field transverse to the magnetic field induced by electromagnetic waves in a magnetized plasma. The almost perpendicularly propagating waves accelerate particles via their Landau and cyclotron damping, and the ratio of parallel and perpendicular drift velocities vs∥/vd can be proved to be proportional to k∥/k⊥. Simultaneously, an intense cross-field electric field E0 = B0×vd/c is generated via the dynamo effect owing to perpendicular particle acceleration to satisfy the generalized Ohm’s law. This means that this cross-field particle drift in a collisionless plasma is identical to E×B drift. It is verified that the transport equations obtained are exactly equivalent to those derived from the θ-dependent quasilinear velocity-space diffusion equation obtained from the Vlasov–Maxwell equations.

In this paper, the general theory developed by Vladimirov and Moffatt [J. Fluid Mech.283, 125–139 (1995)] and Vladimirov et al. [J. Fluid Mech.329, 187–205 (1996); J. Plasma Phys.57, 89–120 (1997)] is extended to nonlinear (Lyapunov) stability for axisymmetric (invariant under rotations around fixed axis) solutions of the ideal incompressible magnetohydrodynamic flows for a situation of arbitrary flow and a poloidal field. The appropriate norm is the sum of magnetic and kinetic energies and the mean square vector potential of the magnetic field.

A new one-dimensional analysis of the collective interaction in a free-electron laser with combined helical wiggler and uniform axial magnetic fields is presented. Maxwell's curl relations and the cold-fluid equations are employed, with the appropriate form of solution for right and left circularly polarized electromagnetic waves and space-charge waves. A set of three linear homogeneous algebraic equations for the electric field amplitudes of the three propagating waves is derived. This set may be employed to obtain the general dispersion relation in the form of a tenth-degree polynomial equation. With the left circular wave assumed to be nonresonant, the dispersion relation reduces to a seventh-degree polynomial equation corresponding to four space-charge modes and three right circular modes. The results of a numerical study of the spatial growth rate and radiation frequency are presented.

Abstract. We study numerically the collapse behavior of self-generated magnetic fields described by the nonlinear coupling equations in laser-produced plasmas. The results show that magnetic fields self-generated by transverse pumping plasmons near critical points may collapse, leading to the enhancement of magnetic fields about up to 0.18 MG and 1.8 MG at laser irradiances of 1012 W cm−2 and 1016 W cm−2 respectively, which are similar to the experimental results.

Abstract. The general theory of self-similar magnetohydrodynamic (MHD) expansion waves is presented. Building on the familiar hydrodynamic results, a complete range of possible field–flow and wave-mode orientations are explored. When the magnetic field and flow are parallel, only the fast-mode wave can undergo an expansion to vacuum conditions: the self-similar slow-mode wave has a density that increases monotonically. For fast-mode waves with the field at an arbitrary angle with respect to the flow, the MHD equations have a critical point. There is a unique solution that passes through the critical point that has ½γβ = 1 and Br = 0 there, where γ is the polytropic index, β the local plasma beta and Br the radial component of the magnetic field. The critical point is an umbilical point, where sound and Alfvén speeds are equal, and the transcritical solution undergoes a change from a fast-mode to a slow-mode expansion at the critical point. Slow-mode expansions exist for field-flow orientations where the angle between field and flow lies either between 90° and 180° or between 270° and 360°. There is also an umbilic point in these solutions when the initial plasma beta β0 exceeds a critical value βcrit. When β0 [ges ] βcrit, the solutions require a transition through a critical point. When β0 < βcrit, there is a smooth solution involving an inflection in the density and angular velocity. For other angles between field and flow, all the slow-mode waves are compressive. An analytic solution for the case of a magnetic field everywhere perpendicular to the flow with γ = 2 is presented.

In an ion-beam–inhomogeneous-plasma system, when the drift frequency ω* exceeds a harmonic of the ion cyclotron frequency nωci, ion cyclotron harmonic waves are excited via the plasma inhomogeneity. These waves are strongly enhanced by ion-beam injection parallel to the magnetic field. As the plasma inhomogeneity is increased, the number of unstable modes increases as does their amplitude. Ion cyclotron harmonic waves with frequencies up to 4ωci are observed experimentally; at least five modes become unstable, and these unstable waves have different az-imuthal mode numbers l = 1 or 2. The dispersion relations of observed multiple ion cyclotron harmonic waves agree well with the theoretical ones, taking into account the plasma inhomogeneity and the ion beam.

The resonant transition radiation from an electron charge that moves along the concentration gradient of a cold isotropic plasma is calculated. The possibility of using this radio-emission for inhomogeneous plasma diagnostics is discussed. Measurements of this kind of radiation in a planar-stratified cold isotropic plasma give the possibility of finding out the profile function of the plasma concentration profile (parts of the plasma density profile where the density is increased over its previous maximum value along the direction of the plasma bunch velocity).

Two secondary parametric instabilities providing cascade channels for the Langmuir sidebands of the oscillating two-stream instability (OTSI) and parametric decay instability (PDI), which are excited by O-mode high-frequency (HF) heating waves, are studied. The first one decays a Langmuir pump wave into a Langmuir sideband and an ion acoustic decay mode. Both resonant and nonresonant cascade processes are considered. Nonresonant cascade of Langmuir waves proceeds at the same location and is increasingly hampered by the frequency mismatch effect. Resonant cascade takes place in different resonant locations to minimize the frequency mismatch effect, but it has to overcome the severe propagation loss of the mother Langmuir wave in each cascade step. This process produces a narrow spectrum of frequency-downshifted (from the HP wave frequency) plasma waves. The second employs the lower-hybrid wave as the decay mode. Only the nonresonant cascade is of interest, because the propagation loss of the mother Langmuir wave in each resonant cascade step is far too severe. This is a three-dimensional coupling process, because the wavevectors of coupled three waves have to be matched in three-dimensional space, rather than matched in the conventional way on the plane of the pump wavevector and the geomagnetic field. A broad spectrum of frequency-downshifted plasma waves can be produced by this process in a narrow altitude range preferentially located near the matching heights of Langmuir sidebands of the OTSI and PDI.

Abstract. We present an analysis of the compression ratio in MHD shocks. Although the equation describing the compression ratio has been in the literature for decades, we believe that our results are interesting and complementary to the earlier research. We concentrate on the behavior of the compression ratio in a bow shock as a function of the angle between the shock normal and the plasma velocity. For this problem, we find non-unique solutions in certain regimes, which we investigate in detail. We also find regimes where the compression ratio in fast bow shocks achieves a local maximum in more than one location. In the last section, we consider the compression ratio in slow shocks and make some conclusions about the shape of the shock in this flow regime.

A wave coupling formalism for magnetohydrodynamic (MHD) waves in a non-uniform background flow is used to study parametric instabilities of the large-amplitude, circularly polarized, simple plane Alfvén wave in one Cartesian space dimension. The large-amplitude Alfvén wave (the pump wave) is regarded as the background flow, and the seven small-amplitude MHD waves (the backward and forward fast and slow magnetoacoustic waves, the backward and forward Alfvén waves, and the entropy wave) interact with the pump wave via wave coupling coefficients that depend on the gradients and time dependence of the background flow. The dispersion equation for the waves D(k,ω) = 0 obtained from the wave coupling equations reduces to that obtained by previous authors. The general solution of the initial value problem for the waves is obtained by Fourier and Laplace transforms. The dispersion function D(k,ω) is a fifth-order polynomial in both the wavenumber k and the frequency ω. The regions of instability and the neutral stability curves are determined. Instabilities that arise from solving the dispersion equation D(k,ω) = 0, both in the form ω = ω(k), where k is real, and in the form k = k(ω), where ω is real, are investigated. The instabilities depend parametrically on the pump wave amplitude and on the plasma beta. The wave interaction equations are also studied from the perspective of a single master wave equation, with multiple wave modes, and with a source term due to the entropy wave. The wave hierarchies for short- and long-wavelength waves of the master wave equation are used to discuss wave stability. Expanding the dispersion equation for the different long-wavelength eigenmodes about k = 0 yields either the linearized Korteweg–deVries equation or the Schrödinger equation as the generic wave equation at long-wavelengths. The corresponding short-wavelength wave equations are also obtained. Initial value problems for the wave interaction equations are investigated. An inspection of the double-root solutions of the dispersion equation for k, satisfying the equations D(k,ω) = 0 and ∂D(k,ω) = ∂k = 0 and pinch point analysis shows that the solutions of the wave interaction equations for hump or pulse-like initial data develop an absolute instability. Fourier solutions and asymptotic analysis are used to study the absolute instability.

Self-focusing is one of the key issues in laser plasma physics applications. Problems involving a multidimensional beam within an inhomogeneous plasma are diffficult to handle. This paper presents the investigation of two-dimensional self-focusing of a laser beam in a plasma whose density n(r, z) is a function of radial as well as z coordinates. The nonlinear mechanism responsible for modification of the background density and the dielectric function is of ponderomotive type. A variational technique is used here for deriving the equations for the beam width and the longitudinal phase. It is observed numerically that an initially diffracting beam is accompanied by oscillatory self-focusing of the beam with distance of propagation. The effect of inhomogeneity scale lengths is also observed. The increase in Lr (= L∥/L⊥) results in oscillatory self-focusing and defocusing with distance of propagation. Furthermore, critical fields for self-trapping of a laser beam as a function of refraction, diffraction lengths and scale lengths of inhomogeneities are also evaluated. Lastly, whatever parameters are chosen, the phase is always negative.

New solutions are presented to the equilibrium Vlasov-fluid equations in Z-pinch geometry that include the effect of sheared axial ion flow. These are different to previous Vlasov-fluid equilibria in that the ion distribution function shows an axial temperature anisotropy. Examples of three new classes of equilibria are calculated, these being the anisotropic-parabolic (constant current density) and Bennett (constant relative speed) profiles and a set of profiles resulting from assuming that the ion fluid velocity is given by (b1+rp) for b1=−0.5 and p>1.

Based on a database, a number of conclusions are derived concerning the power flow into the divertor region of the ASDEX tokamak. The non-transition to detachment in ASDEX is investigated with respect to the sputtering of the copper divertor plates. Following the definition of the low- and high-recycling regions, the best fittings of the power widths in front of the divertor plates are extracted for Ohmic (OH) or neutral-beam-injection heating in low-confinement mode (NBI, L-mode) shots. On the basis of these fittings, it is concluded that the safety factor q and the electron temperature in the divertor can be considered as the main robust parameters. In contrast, the peak of the power inserted into the divertor does not behave as a robust parameter, thus introducing the problem of colinearities.

Abstract. A code has been developed to study self-organization in spheromaks using the Galerkin method in which the magnetic and velocity fields appearing in the incompressible dissipative MHD equations are expanded in a spectrum of Chandrasekhar–Kendall eigenstates of the curl. The ultimate goal is to apply the Galerkin method in actual spheromak geometry to calculate turbulence levels and associated transport. The present work employs the straight-cylinder approximation, known to give a good representation of internal ideal MHD modes in spheromaks and applied here to resistive tearing modes. Our main result to date is a demonstration that the Galerkin method can exhibit tearing island formation with only a few states in the spectrum. Example quasilinear calculations are presented for a decaying spheromak and for a spheromak created by gun injection.

The self-magnetisation of circumstellar disks is considered within an appropriate multifluid description. These disks are composed of ionised and neutral gas as well as of a charged dust component. The most important equation in this context is the general Ohm’s law that includes a magnetic field generation term due to relative dust–neutral fluid velocities. We show that circumstellar disks can carry their own significant magnetic fields. As long as the stellar gravitation sustains the accretion flow, the self-magnetisation of the disk does not saturate until the field strength reaches its local equipartition value. The magnetic field generation process is illustrated by idealised multifluid simulations that are not restricted to a kinematic description, but model the process in a self-consistent way.

This paper examines the possibility of propagating surface waves in cylindrical plasma–plasma structures enclosed by metal walls and submitted or not to a static magnetic field. We consider the situation in which the inner plasma layer is overdense while the other is underdense. It is shown that outside the electron cyclotron resonance (ECR) conditions, the outer plasma layer plays a role similar to that of an ordinary dielectric layer, just modifying the wavenumber without drastically changing the general characteristics of the wave. At ECR, a major change in the wavenumber and attenuation coefficient is observed, a cutoff occurring on the left side of ECR and a resonance on the right side, provided the outer plasma density is large enough. It is further found that in conditions where the outer plasma layer thickness is very small, wave propagation still occurs, whatever the density value in this region. This suggests that surface wave propagation is possible in plasma–sheath–metal structures.

General similarity solutions of temporal decay of a power spectrum of Alfvén waves in a magnetized plasma are classified in terms of Lie group parameters. One class of these solutions can be mapped to a solution of the Abel equation. A second class is transformed to a solitary-wave solution where the spectrum at short wavelengths is more rapidly damped than at long wavelengths.

The Zakharov–Kuznetsov equation describes the propagation of weak ion acoustic waves in a strongly magnetized plasma. Their dynamics have been studied in a series of papers, one of which gives growth rates of instabilities found numerically, as well as pictures of soliton collisions [J. Plasma Phys.64, 397 (2000) – Part I]. In the present paper, we find good approximate formulas for growth rates of the dominant instability, vastly improving those of Part I. This is done by proceeding to higher order in the expansion, combined with an incorporation of exact values for the boundaries of the unstable region in the formulas. The result is better than we had any right to expect. We next depart from linear stability analysis and look at nonlinear dynamics to obtain a pulse in time. The maximum amplitude of this pulse is seen to be proportional to the linear growth rate, a result that was so far suspected from numerics but not derived theoretically. (This paper can be read independently of Part I.)

A theory of enhanced plasma and ion lines near the reflection height of a pump wave is presented. It is argued that the high-frequency pressure of the pump wave and the averaged pressure of plasma waves localized in small-scale cavitons contribute to the rapid creation of a cavity in the main Airy maximum. Langmuir waves excited later by parametric decay instability are trapped in such a nonstationary cavity. Analytical expressions for adiabatic eigenmodes of Langmuir waves in a nonstationary cavity are presented. Collisionless attenuation of the eigenmodes of Langmuir waves trapped in the cavity is investigated. It is shown that parametric decay instability in a cavity may account for the excitation of plasma and ion-acoustic waves measured by EISCAT UHF radar.