A large-orbit gyrotron may operate at higher beam currents if one introduces a plasma in its interaction region. The plasma, however, is unstable to an upper-hybrid electrostatic perturbation driven via cyclotron interaction by the rotating relativistic electron beam. The growth rate of the instability is comparable to the growth rate of the cyclotron maser instability when the plasma frequency is of the order of the electron cyclotron frequency.

Reduced, approximate MHD equations are derived for the case where the magnetic field is close to a potential field. The potential field can have an arbitrary three-dimensional structure, as long as it is non-vanishing. Finite current and pressure effects are included.

A study is made of the influence of nonlinearity upon the structure of a steady-state disturbance brought about by low-frequency (ω[Lt ]ωi) monochromatic magnetosound propagating in a transversally inhomogeneous low-pressure plasma (β[Lt ]me/mi), in the vicinity of the Alfvén resonance point for the case when the principal linear mechanism for forming the transverse structure is provided by magnetic field diffusion due to small plasma resistivity. It is shown that the nonlinear properties of the fundamental harmonic of a disturbance are determined by its self-action through a plasma density variation that it produces. The disturbance structure in the region of the Alfvén resonance is described.

We reconsider the problem of particle acceleration by large-amplitude electromagnetic waves. We make use of a fully relativistic Hamiltonian formalism to show that, as opposed to nonelativistic results obtained by Kuo and Lee, acceleration in unmagnetized systems is severely arrested when the phase velocity of the electromagnetic mode approaches the speed of light. For subluminal waves, however, acceleration is shown to be still effective.

The stability condition and growth rate of the ideal, internal m=n=1 kink mode in a toroidal plasma are calculated by means of a direct inverse-aspect-ratio expansion of the magnetohydrodynamic (MHD) equations, rather than by using the energy principle. The analysis is based on the use of computer-aided algebra. The general equation for incompressible MHD oscillations in a low-β circular tokamak is derived to lowest order in the inverse aspect ratio. This derivation generalizes the Pfirsch-Schlüter factor for the kinetic energy in toroidal geometry.

Fast computer codes for evaluating non-thermal velocity distributions are needed in order to carry out routine analysis of neutron signals in plasmas heated by neutral-beam injection (NBI). By neglecting the magnetic field inhomogeneity along a field line, i.e. neglecting trapped-particle effects, calculations of the velocity distribution can be made relatively rapidly. In this paper, we investigate under which circumstances such an approximation is justified. We solve the bounce-averaged Fokker–Planck equation, which includes particle trapping, by expressing the solution in terms of a series of appropriate eigenfunctions of the pitch-angle scattering operator. The eigenfunctions, eigenvalues and time-dependent coefficient functions are calculated numerically. We use the solution for calculating the effect of particle trapping on neutron production for beam-heated deuterium plasmas.

The general theory developed in Part I of the present series is here applied to axisymmetric solutions of the equations governing the magnetohydrodynamics of ideal incompressible fluids. We first show a helpful analogy between axisymmetric MHD flows and flows of a stratified fluid in the Boussinesq approximation. We then construct a general Casimir as an integral of an arbitrary function of two conserved fields, namely the vector potential of the magnetic field and the scalar field associated with the ‘modified vorticity field’, the additional frozen-in field introduced in Part I. Using this Casimir, sufficient conditions for linear stability to axisymmetric perturbations are obtained by standard Arnold techniques. We exploit Arnold's method to obtain sufficient conditions for nonlinear (Lyapunov) stability of the MHD flows considered. The appropriate norm is a sum of the magnetic and kinetic energies and the mean square vector potential of the magnetic field.

It is found that the admixture of weak higher short-wavelength modes (several percent of the coupled power) in the spatial power spectrum of the lower-hybrid waves radiated from the waveguide grill into an inhomogeneous scrape-off-layer plasma in tokamaks has a profound influence on the ponderomotive effects of these waves. Using the barometric formula with the ponderomotive force potential for the electron density, we solve the coupling problem self-consistently for four modes using the shooting and matching method to fulfil surface impedance boundary conditions determined by infinite-grill theory. For the symmetric spectrum, below threshold, the total reflection coefficient is independent of the coupled power. Also, at these power levels, isolated density depressions (cavitons) are formed in the spatial locations where there is constructive superposition of short- and long-wavelength modes. Intense mutual mode conversion of these waves occurs at these sites. For power levels above threshold, the reflection coefficient increases until it saturates at higher powers. Numerical results are given for the 24-waveguide grill mounted on the ASDEX tokamak.

The non-oscillating part of the magnetic moment field (called the inverse Faraday effect (IFE) for this field from a circularly polarized wave in a medium) is calculated for the interaction of an elliptically polarized wave with a weakly ionized magnetized plasma in a kinetic theory model and with unmagnetized Vlasov plasmas. For a weakly ionized magnetized plasma, the induced field increases with both temperature and ambient magnetic field. For an unmagnetized plasma, it increases parabolically with temperature. The induced magnetic field is found to vary parabolically with temperature in the case of an unmagnetized Vlasov plasma.

The linear and nonlinear response tensors describe the response of a plasma to an electromagnetic field disturbance. A novel construction of the linear and quadratic response tensors for an unmagnetized collisionless plasma is presented here using a convenient 4-tensor notation. The construction uses the equations of charge continuity and gauge invariance, together with symmetry properties and dimensional arguments, to constrain the coefficients of an arbitrary linear combination of tensors. A new interpretation of the response tensors follows as expressions uniquely determined by fundamental physical constraints, and not simply as coefficients in a perturbation expansion of induced plasma response.

In earlier work, we have noted on semi-empirical grounds that the electrical conductivity σ in strongly coupled plasmas can be written as a linear form σ=σ0Γ in terms of the usual plasma coupling parameter Γ. Here, this is combined with the Wiedemann–Franz law to yield a zeroth-order treatment of thermal conductivity κ in such strongly coupled plasmas. Some refinement is needed to explain the properties of the heavier liquid alkali metals beginning with Na. This refinement follows from the nearly free-electron theory of electrical resistivity ρ=σ−1. Finally, a relation is forged between ρ, κ and the shear viscosity η at the freezing point of liquid alkali metals.

This work is concerned with the investigation of non-ideal (resistive) MHD effects on the excitation of Alfvén waves by externally launched fast-mode waves, in simulated tokamak plasmas; both continuum range, CR ({ωAlf(r)}min <ω<{ωAlf(r)}max) and discrete range, DR, where global Alfvén eigenmodes, GAEs (ω<{ωAlf(r)}min) exist, are considered. (Here, ωAlf(r)≡ωAlf[n(r), B0(r)] is an eigenfrequency of the shear Alfvén wave.) For this, a cylindrical current carrying plasma surrounded by a helical sheet-current antenna and situated inside a perfectly conducting shell is used. Toroidicity effects are simulated by adopting for the axial equilibrium magnetic field component a suitable radial profile; shear and finite relative poloidal magnetic field are properly accounted for. A dielectric tensor appropriate to the physical conditions considered in this paper is derived and presented. When the resistive wave equation is solved and the current drive by helicity injection, IHICD, is calculated, the following illustrative results are found to hold. For CR, (i) the maximum power absorption as well the maximum helicity injection current drive increase significantly with decreasing resistivity (i.e. with increasing temperature); (ii) unlike the power absorption, which is a maximum at a frequency between the lower and the upper edge of the CR, the total current drive is a maximum at the lower edge, and decreases strongly with increasing frequency; (iii) the behaviour of the efficiency closely follows that of the current drive; (iv) the smaller the resistivity, the smaller is the radial distance from the axis (x=0) of the maximum current-drive density. For DR, (i) the maximum power absorption in the discrete GAE case increases with decreasing resistivity even more strongly than in the CR case; (ii) unlike the CR case, the total helicity-injection current has, for almost all GAEs, a symmetric frequency dependence about the line centre; its maximum value as well as the efficiency increase strongly with decreasing resistivity; (iii) unlike the continuum case, the efficiency is almost constant over the entire width of the discrete-mode range; its value increases strongly with the GAE rank.

The development of anisotropies in an initially isotropic spectrum is studied numerically for compressible magnetohydrodynamic (MHD) turbulence in the presence of the Hall term. Building on a previous study where it was shown that spectral cascades in the Hall MHD system differ from the standard MHD case, particularly at high cross-helicities, we use an isotropic high cross-helicity initial state to study anisotropies of the Hall MHD system for a variety of mean magnetic field strengths and sonic Mach numbers. Strong anisotropies, which maximize at the ion-inertial length scale, appear for several plasma states and are categorized according to their plasma beta β: high-β Hall MHD simulations (β>1) show strong anisotropies relative to the standard MHD case, intermediate-β Hall MHD simulations (β≈1) show smaller anisotropy differences relative to the standard MHD case, and low-β Hall MHD simulations (β<1) again show strong anisotropies relative to the standard model. It is suggested that these anisotropy enhancements are due to nonlinear cascade suppression of propagating Alfvén waves in the field-aligned direction. This is different from the dynamics in the highly oblique directions, where non-propagating density and magnetic-energy anticorrelations appear.

Mathematically exact solutions describing propagating waves are constructed for a cold magnetized plasma bounded by a rigid cylindrical dielectric. Possible particle sources and sinks due to chemical reactions are allowed. It is found that the volume waves can be either amplified or damped because of their density dependence, while the surface waves are unaffected by the sources and sinks.

The description of oscillations in inhomogeneous magnetohydrodynamic plasmas in terms of spatial Fourier modes is extended beyond the previous analyses of the incompressible case to a fully compressible plasma in a rigid box. Attention is focused upon the cusp and Alfvén continua and the discrete fast-mode spectrum. As well as providing a convenient method of numerical solution, the modal approach yields novel insights; in particular, the energy ultimately ‘absorbed’ resonantly is just that initially (and always) residing in the continua, and is readily calculated.

In the analysis of the propagation of electromagnetic waves in the electron cyclotron frequency range, in both isotropic media and magnetoactive plasmas, the role of diffractive effects, which are not accounted for by geometrical optics, may no longer be neglected when highly collimated beams are to be employed. Moreover, when lenses, mirrors, refractive gradients and/or wave cut-offs are placed along the beam trajectory, the very concept of independent optical rays tends to introduce singularities, which do not always correspond to physical features. A quasi-optical approach has previously been shown to present the advantage of allowing a description (at the lowest order of approximation) of the diffractive widening of the beam. The specific aim of this paper is to test, when reflection, refraction or beam focusing indicates the need for particular attention, the solution method employed within such an approach. The results presented here concern the propagation and power deposition profiles, in a number of crucial physical situations, of narrow electron cyclotron beams launched, in Gaussian form, either into isotropic transparent media or through anisotropic toroidal plasmas of fusion interest.

A systematic study of non-inductive current drive via helicity injection by global Alfvén eigenmode (GAE) waves is carried out. For illustration, the first radial mode of the discrete resonant GAE spectrum is considered. The following aspects are given special attention: spectral analysis, radial dependence and efficiency – all of these as functions of the characteristics of the waves launched by an external, concentric antenna (i.e. wave frequency and poloidal and toroidal wavenumbers). The tokamak plasma is simulated by a current-carrying cylindrical plasma column surrounded by a helical sheet current and situated inside a perfectly conducting shell, with incorporation of equilibrium (simulated) toroidal field, magnetic shear and a relatively large poloidal magnetic field component. Within the framework of low-β MHD model equations and for typical tokamak physical parameters, the following basic results are obtained: (1) in the range of poloidal wavenumbers −3[les ]m[les ]3 and toroidal wavenumbers −20[les ]n[les ]20, resonant GAE peaks below the Alfvén continuum are found; (2) the power absorption (P), current drive (I) and corresponding frequency of the GAE modes depend strongly on the sets of (m, n) values considered; (3) the ‘net’ current drive is positive (i.e. flows in the direction of the equilibrium current j0z) for m=−1, −2, −3 and −20[les ]n[les ]−1 as well as for m=+1, +2, +3 and n>10; (4) in the cases m=−1, −2, −3, the efficiency of current drive, I/P, increases with [mid ]m[mid ] and 1/[mid ]n[mid ]; (5) the radial localization of the current drive in each of the cases considered is determined and tabulated.

The stochastic properties of a plasma are taken into account in the consideration of the modulational interactions of waves associated with lower-hybrid (LH) resonance. The limits of applicability of the theory of weak plasma turbulence in the description of the modulational processes are found. It is demonstrated that the development of the modulational instability of waves with frequencies at the LH resonance results in a rapid decrease in stochasticity. This effect is associated with the formation of coherent structures due to the modulational interactions. Eventually a state with local minima of entropy in places where the coherent structures are located is formed. The description of the interaction between waves and particles in the coherent structures is discussed.

The effects of electron-beam density on large-amplitude ion-acoustic waves areinvestigated in an electron-beam–plasma system with trapped electrons, using the pseudopotential method. The region of existence of ion-acoustic waves is examined, and it is shown that the conditions for their existence depend sensitively on parameters such as the electron-beam density, the electrostatic potential and the ion temperature. It turns out that a decrease in trapped electrons, an increase in beam density and a decrease in ion temperature increase the propagation speed of ion-acoustic waves, and the region of their existence spreads as the beam density decreases, the effect of trapped electrons decreases and the Mach numbers increases. New effects of electron-beam density on large-amplitude ion-acoustic waves in a plasma with trapped electrons are predicted.

Recent experiments and 2D laminar plasma–fluid simulations have indicated that plasma detachment from the divertor plate is strongly tied to plasma recombination. With plasma recombination, a neutral gas blanket will form between the divertor plate and the plasma frame front. Because of plasma-neutral coupling, the plasma flow along the field lines will drive neutral gas flow with Mach number [ges ]1 and Reynolds number [ges ]1000. A compressible set of conservation and transport equations are solved with 2D mean toroidal flow and 3D turbulence effects over various toroidal cavity geometries. The radial structure of the temperature profile is determined for both turbulent and laminar flow as the flame front propagates down the toroidal cavity. Quantitative results are obtained for the increased heat transfer to the toroidal walls due to turbulence as well as radial profiles for the transport coefficients. It is found that heat loads to the toroidal walls can be increased by factors of 5–20 over that for laminar flow for the cavity geometries studied here. This increased heat transfer to the toroidal walls will lead to decreased levels of heat flux impinging on the divertor plate.