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The relativistic dispersion relation including temperature anisotropy and a parallel drift has been derived for electron cyclotron waves of frequency up to third harmonics, and solved for a perpendicularly stratified plasma around the fundamental and second harmonic resonances. For quasiperpendicular propagation, damping of fundamental modes is much more sensitively affected by T∥ than by T⊥. This is also true for the ordinary mode of oblique propagation. The theory has been extended to a bulk thermal distribution with a two‐temperature or three‐temperature tail distribution by a simple summation of each contribution to the dispersion tensor. The effect of a tail distribution is relatively small if the tail is localized in the resonant layer for the bulk electrons. For a nonlocal tail distribution, the existence of a tail becomes important.

Fluid equations with transport effects have been derived from summing up discrete particle effects in the configuration space. The diffusion coefficient takes a form different from, but equivalent to, the Kubo formula. By taking into account the decoherence along the field lines, the diffusive damping in the perpendicular direction, and the finite Larmor radius effect in the cyclotron resonance, it is shown that the diffusion of magnetized 3d plasma has a regime of B−3/2 scaling which lies between the Bohm diffusion of B−1 and the classical diffusion of B−2.

An electromagnetic (EM) wave at the mode conversion layer transfers its energy to the electrostatic (ES) wave whose amplitude can be greatly enhanced due to its slow group velocity near the cut off layer. The large amplitude ES wave produces the density compression, indispensable for the nonlinear coupling in the EM wave, leading to the localized vortex flow. A dc magnetic field, tantamount to the vorticity, is generated as a result of the conservation of canonical momentum.

The equations governing the mode conversion between an electromagnetic wave and the plasma wave are derived from the relativistic Vlasov equation. They are further reduced to a two dimensional matrix equation involving only two electric field components. It is shown that the mode conversion efficiency diminishes to zero at both 0° and 90° of incidence angles, becomes insignificant beyond 45° and tends to improve with higher plasma temperature.

The molecular dynamics simulation with the use of the empirical Tersoff potential is applied to study the thermal characteristics of carbon nanotubes (CNTs). A thermal reservoir is devised to control the temperature and to exact the heat flux input. The quantum effect defining the precise temperature from the absolute zero Kelvin and up is included by applying phonon (boson) statistics to the specific heat. At low temperature, the CNT thermal conductivity increases with increasing temperature. After reaching its peak, which is limited by the length of the CNT, it decreases with temperature due to phonon-phonon interactions. The scaling law of thermal conductivity as a function of temperature and length is inferred from the simulation results, allowing prediction for CNTs of much longer length beyond what MD could simulate.

A theory is presented for the rate of thermal relaxation of a two-dimensional plasma in a strong uniform d.c. magnetic field. The Vahala—Montgomery kinetic description is completed by providing a cut-off time for the time of interaction of two particles which contribute to the collision term. The kinetic equation preclicts that thermal relaxation occurs as a function of the dimensionless time (ωpt) (ωp/Ω) (n0λ2D)−½, where ωp, is the plasma frequency, Ω is the gyrofrequency, and n0 λ2D is the number of particles per Debye square. By contrast, in the absence of an external magnetic field, a two-dimensional plasma relaxes as a function of (ωpt) (n0λ2D)−1.

The thermal relaxation process for a spatially uniform two-dimensional plasma in a uniform d.c. magnetic field is simulated numerically. Thermal relaxation times are defined in terms of the time necessary for the numerically computed Boltzmann H function to decrease through a given part of the distance to its minimum value. Dependence of relaxation time on two parameters is studied: number of particles per Debye square n0 λ2D and ratio of gyrofrequency to plasma frequency Ω/ωp. When Ω2/ω2p becomes ≫[ln (L/2πλD)]−½, where L is the linear dimension of the system, it is found that the relaxation time varies to a good approximation as (n0 λ2D)½ and Ω/ωp.

Given that the wave numbers of X and O modes merge as they approach the plasma boundary, a pure mode reflected from the plasma by a cut off may excite both modes due to polarization change when it is reflected off the vacuum vessel wall since the tangential components of the electric field change sign. This may explain the good central heating in DIII‐D ECH experiments in which the fundamental X‐mode is launched from the low field side.

A large‐amplitude rf electric field can heat particles at their gyrofrequency and its harmonics despite a significant mismatch between the wave frequency and the gyrofrequency through physical processes analogous to the trapping of particles in large‐amplitude waves. For eE0k0/mΩ2 near unity, the fundamental and the second harmonic resonances may overlap and give rise to stochasticity. The implications for cyclotron heating are discussed.