The propagation of long, nonlinear, non-axisymmetric surface waves in a magnetic cylinder is considered. It is supposed that the electrical conductivity is infinite, the fluid is incompressible and there is no magnetic field outside the cylinder. The nonlinear integro-differential equation governing the wave propagation is derived using the reductive perturbation method. The interesting and important point is that this equation governs the evolution of all nonaxisymmetric modes simultaneously. This is because the phase velocities of all non-axisymmetric modes are equal to the kink speed in the linear, infinitely long-wavelength approximation, and as a result all non-axisymmetric modes interact strongly in the nonlinear case. Solutions of the governing equation in the form of periodic helical waves of permanent form are obtained numerically.

We construct a continuity equation for electrons in microwave-afterglow plasmas. The self-similar solution of the equation is obtained for a plasma with plane, cylindrical or spherical geometry.

It is shown that the phase of the electromagnetic wave emitted through stimulated emission is intrinsically random. The insensitivity of the phase of the laser field to any disturbance in the laser cavity parameter derives from the fact that stimulated and spontaneous emissions take place concurrently at the same wave vector, the phases of spontaneous emission are mildly bunched, and the central limit theorem can be applied to the phase of the laser field. The two spectral lines observed in the Smith-Purcell free-electron laser experiment show that both classical and quantum-mechanical free-electron lasings, in which the wigglers behave as classical waves and wiggler quanta respectively, take place concurrently at different laser wavelengths in the case of the electric wiggler. It is shown that the coherence of the classical free-electron laser is achieved through modulation of the relativistic electron mass by the electric wiggler. The classical free-electron lasing is calculated using the quantum-augmented classical theory. In this, the probability of stimulated emission is first evaluated by interpreting the classically derived energy exchange between an electron and the laser field from a quantum-mechanical viewpoint. Then the laser gain is obtained from this probability by using a relationship between the two quantities derived by quantum kinetics. The wavelength of the fundamental line of classical free-electron lasing is twice the wavelength of the fundamental line of the free-electron two-quantum Stark emission, which is the quantum free-electron lasing in the electric wiggler. The gain of the classical free-electron lasing appears to scale as λ3w/γ3, where γ is the Lorentz factor of the electron beam and λw is the wavelength of the wiggler.

It is shown using the photon concept that free-electron lasing (or net stimulated bremsstrahlung) is unrelated to the electron phase with respect to the laser wave, while the net acceleration (or net two-photon absorption) in an RF acceleration cavity depends on the electron phase with respect to the RF wave. The gain formula for the free-electron laser using a magnetic wiggler (MFEL) derived using the recently developed quantum-augmented classical theory in which the electron phase is ignored is in excellent agreement with that obtained quantum-mechanically. It is found by means of this theory that if an electric wiggler is added to a MFEL, the synchronization between the transverse velocity and the laser wave, which is required for coherence of the laser light, is not affected, while the laser gain is enhanced owing to the increase in the amplitude of the energy modulation by the electric wiggler. As a configuration of this turbo-MFEL, a two-beam elliptical wake-field cavity is proposed. An electron beam injected in the antiparallel direction along the lasing-beam path in this cavity lases through transverse wiggling by the transverse wake field and energy modulation by the longitudinal wake produced by relativistic drivingbeam bunches. This laser (WFEL) becomes of greater advantage compared with the MFEL as the laser wavelength is made shorter. It is also shown that the amplification of the WFEL is much greater than that of the present MFEL if we can produce a wake field whose longitudinal component has field strength greater than 1 MV m–1.

The propagation of a Langmuir wave with a small group of trapped particles in a weakly non-uniform plasma along a density gradient is considered. The dynamics of trapped electrons accelerated by the wave is investigated in the adiabatic approximation, including the relativistic case. The set of equations describing the self-consistent spatial evolution of the wave—trapped-particles system is obtained and analysed. It is shown that the possibility exists of wave transmission through a classically forbidden barrier as a consequence of the reversibility of the wave—particle interaction. The conditions of validity of the theory developed are also discussed.

We have investigated a mode-coupling mechanism between kinetic Alfvén waves and a collisional drift wave in an inhomogeneous cylindrical plasma. Drift waves satisfying the condition k⊥D > 1/r0 (where r0 is the radius of the plasma cylinder) are stabilized by the low-frequency ponderomotive force generated by the kinetic Alfvén waves. For typical plasma parameters and a moderate level of Alfven-wave intensity the stabilization factor is comparable to the destabilization mechanism due to collisions.

The poloidal electric field generated by electron-cyclotron resonance heating is investigated for a tokamak plasma in the collisionless regime. This poloidal electric field is calculated by solving an adjoint equation to the linearized Fokker-Planck equation with a quasi-linear diffusion term. It is found from this calculation that the magnitude and the sign of the poloidal electric field depend strongly on the values of the inverse aspect ratio, the poloidal angle of the absorption point, the parallel velocity of resonant electrons normalized by the thermal velocity, and the strength of the relativistic correction to the resonance condition.

A one-dimensional model explaining the mechanism of excitation of electrostatic fields by linearly polarized radio-frequency waves in a plasma layer is presented. It is shown that the ponderomotive and driving forces influence this process strongly; however, these forces act at different times when a wave front passes through the plasma. We consider a semi-infinite plasma, and a plasma layer with and without current. It is observed that near to the plasma boundaries, where the electric field is large, there arise amplitude field oscillations, which are slowly exponentially damped in space. It is shown that the physical processes arising near the boundary x = L are similar to those at the boundary x = 0. It is seen that the current in the plasma block excitation at the boundary x = L.

The theory of linear interaction between internal kink modes and fusionproduced high-energy alpha particles in a toroidal plasma is extended by including finite-banana-width corrections to the alpha dynamics. An important implication of the theory for the stability properties of kink modes is that the finite-banana-width effects increase the value of the poloidal alpha beta required to attain the stable domain of operation as well as that required to excite the high-frequency fishbone instability. Furthermore, these effects lead to a reduction in the instability growth rate in both the low- and high-frequency unstable regimes.

We study linear wave propagation in the case of equal-mass plasmas. We show that the special symmetry of such plasmas simplifies the problem and causes the disappearance of well-known phenomena such as Faraday rotation and whistler wave modes. We exploit the Symmetry of the problem to derive analytical expressions for wave propagation for various fluid models of the plasma. We also find which distribution functions will retain the symmetry properties of the fluid models.

The resonant characteristics of an incompressible ideal MHD fluid are highly structured. To help expose this structure, an equivalent electrical analogue of the MHD system is developed. The model, in the form of a transmission line, makes it possible to identify a number of new and important concepts, one of which is the effective impedance. This in turn enables entire regions of MHD fluid to be replaced with equivalent impedances. When fully exploited, the model also provides a more consistent interpretation of the spectrum of ideal MHD. The discrete Alfvén modes are found to be highly degenerate, while the transition to a discontinuous profile is accompanied by a redistribution of an uncountably infinite number of ‘poles’ from the continuous spectrum and onto the Alfvén modes. In addition, the electrical analogue shows that within a continuously structured fluid the characteristic behaviour is not necessarily dominated by the ‘surface mode’ alone. This view is also supported by the results of a numerical simulation of the linear MHD equations. Depending on the initial conditions, the collective behaviour can have any frequency within the range spanned by the transition zone. The energy itself is monitored using a new pair of energy and flux expressions derived from a variational (Lagrangian) description of the MHD system. Again the electrical model is used to provide a physical interpretation of the individual terms within these expressions. In particular, it allows a partition of the total energy into separate kinetic- and potential-energy terms.