Table of contents

It is shown that the neglect of plasma birefringence in Faraday rotation measurements on tokamak experiments leads to an apparent shift of the magnetic axis and to an apparent decrease of the central safety factor, q₀. The dependence of these effects on plasma parameters and on the radiation wavelength is found.

Energy and particle confinement in tokamaks is usually anomalous, greatly exceeding neoclassical predictions. It is desirable to develop an understanding of the underlying processes to increase the confidence in extrapolation of tokamak behaviour towards reactor regimes. The literature abounds with theoretical expressions for anomalous transport coefficients based on turbulent diffusion due to various micro-instabilities. These often purport to provide explanations of tokamak confinement at the level of global scaling laws. However, comparison with experimental data from local transport analyses offers a far more stringent test of these theories. This review presents the available theories for turbulent transport coefficients, particularly ion and electron thermal diffusivities, in a way that will facilitate a programme of testing models against data. It provides a brief description of the basis for each theory to place it in context and then presents the resulting turbulent diffusivity. Particular emphasis is placed on the validity conditions under which the expressions may be used; this is important when subjecting them to meaningful tests against data. The present review emphasizes the more recent developments, building on earlier ones by Liewer and Ross et al. The results of this work have already been of value in carrying out a programme of testing theories against high quality JET data (Conner et al. (1993) and Tibone et al. (1994)).

The ponderomotive stabilization of plasma in an axisymmetric mirror device is considered. It is assumed that (i) the RF field is excited by a full-turn-loop antenna and (ii) its frequency is below the eigenfrequency spectrum of the plasma column. It is shown that the dissipation of the RF power drives an instability that originates from a resonant-particle interaction. This instability is weak except for the case when the minority ion scheme of ICRF heating is used. However, even in the latter case, the resonant-particle instability can be suppressed by quasilinear diffusion of the minority ions in the velocity space at a sufficiently high level of RF power. With the instability suppressed, a simple criterion for the ponderomotive force to stabilize flute perturbations in mirror plasmas is obtained.

Parametric instabilities of electrostatic electron waves in relatively weak magnetic fields were investigated in a unified manner. As the propagation angle is shifted from the angle parallel to the ambient magnetic field to the perpendicular one, the electrostatic electron normal modes in such a system change from Langmuir to upper-hybrid waves through oblique Langmuir waves. These waves are unstable to various parametric instabilities, such as the modulational and decay instabilities. The present analysis extends the previous work (Akimoto K 1989 Phys. Fluids B1 1998) on parametric instabilities of Langmuir waves to those of electrostatic electron waves that are not field-aligned, and carries out a comparative study of parametric instabilities of the electron waves by numerically solving a dispersion equation. The author finds that as the propagation angle shifts from the field-aligned direction, the maximum growth rate of the dominant instability frequently increases, yet remains of the same order of magnitude; on the other hand, the topological structure of the growth rate contours may change dramatically, even if the propagation angle is only slightly shifted. In addition, the growth rate contours for an upper-hybrid wave show a variety of interesting patterns as the parameters, such as the wavenumber of the pump waves are varied. The overall results indicate that upper-hybrid and oblique Langmuir turbulence isotropizes faster than Langmuir turbulence, and may often be dissipated without the formation of the condensate at any point in the process.

The conservation of magnetic helicity, K= integral A.B d³x, determines whether tearing activity increases or decreases the net plasma current I in a tokamak. A centrally peaked distribution of current is shown to lose current during a relaxation and a hollow distribution to gain current, the change can be approximately=20% of the total current. Tearing activity relaxes the current distribution j/sub ////B towards a spatial constant k_T=((V_b integral d psi )+( integral eta _ck_ad psi ))/( integral eta _cd psi ) with V_b the applied loop voltage, k_a( psi ) the distribution of the bootstrap and driven currents, eta _c the resistivity coefficient and psi the toroidal flux. It is the resistivity weighting of k_T that accounts for the change in the net plasma current I.

The authors study the full system of Braginskii one-fluid transport equations with a self-consistent account of transport and dissipative phenomena in the screw-pinch geometry and derive exact self-similar solutions. The local and global plasma parameters-magnetic field, temperature and density profiles, magnetic Reynolds number, beta and pinch radius-are determined by a minimal set of external parameters, namely properly scaled magnitude of the applied axial field and an index related to the current time-evolution, and are computed as eigenfunctions and eigenvalues of the corresponding boundary value problem. The paramagnetic and diamagnetic properties of the axial field profiles are discussed in detail. Calculation of the m=1 growth rates demonstrates a relatively weak decrease of the maximum growth rate as the axial field amplitude increases although the range of unstable wavenumbers becomes substantially narrower. The solutions obtained describe plasma dynamics and profile structure in 'stabilized' pinch systems: Z-pinches with externally applied axial field and in ULQ pinches provided self-relaxation processes are suppressed.

The interaction between a lower hybrid wave and a fusion alpha particle displaces the alpha particle simultaneously in space and energy. This results in coupled diffusion. Diffusion of alphas down the density gradient could lead to their transferring energy to the wave. This could, in turn, put energy into current drive. An initial analytic study was done by Fisch and Rax (1992). Here the authors calculate numerical solutions for the alpha energy transfer and study a range of conditions that are favourable for wave amplification from alpha energy. They find that it is possible for fusion alpha particles to transfer a large fraction of their energy to the lower hybrid wave. The numerical calculation shows that the net energy transfer is not sensitive to the value of the diffusion coefficient over a wide range of practical values. An extension of this idea, the use of a lossy boundary to enhance the energy transfer, is investigated. This technique is shown to offer a large potential benefit.

A magnetized plasma is considered. It is shown that the MHD model provides an adequate description of plasma instabilities in the ion-kinetic regime, where the characteristic scales of the plasma motion fall below the ion Larmor radius. This conclusion is the consequence of the fact that the well known relation between the perturbed plasma density and the perturbed electric potential, which follows from the linearized Vlasov equation (the so-called ion-kinetic response), can be derived with a good accuracy from the MHD model when the Hall effect is taken into account Moreover, the MHD ion response coincides with a Pade approximation for the ion-kinetic response.

Several techniques were used to excite toroidal Alfven eigenmodes (TAE) in the Tokamak Fusion Test Reactor (TFTR) (Proc. 13th Int. Conf. on Plasma Physics and Controlled Nuclear Fusion Research Vol 1 (Vienna: IAEA, 1990) 9) at magnetic fields above 10 kG. These involved pellet injection to raise the plasma density, variation of the plasma current to change the energetic ion orbit and the q-profile, and ICRF heating to produce energetic hydrogen ions at velocities comparable with 3.5 MeV alpha particles created in deuterium-tritium (d-t) fusion reactions. The amplitude of the TAE modes observed in ICRF-heated plasmas behaves differently from those driven by neutral beams. This can be explained by the difference in the energetic ion orbits. These experimental results are presented and relevance to fusion reactors are discussed.

The structure and the dynamics of the fast electron tail generated in Tore Supra during lower hybrid current drive experiments are investigated by means of a microwave transmission diagnostic at frequencies close to the electron cyclotron frequency, installed on a vertical chord. Measurements have been performed both in steady state and during the relaxation phase following the end of the lower hybrid power pulse. The measured transmission spectra are compared with simulations performed by means of a 3D Fokker-Planck code and are found to be in excellent agreement with them, both in the general structure and in the level, as well as in the dynamical behaviour. It is shown that this diagnostic yields the extension of the lower hybrid wave spectrum actually sustaining the non-inductive current, as well as substantial indications on its radial location. These results support the use of vertical transmission measurements as the most specific diagnostic method for lower hybrid current drive experiments.

The interaction of alpha -particles in JET tritium discharges with global Alfven waves via inverse Landau damping is analysed. It is found that alpha -particle driven eigenmodes were stable in the PTE1 and should also be stable in a future 50:50 deuterium-tritium mix discharge aiming at Q_DT identical to 1 provided the same ion density as in the discharges with the best deuterium-deuterium performance is maintained.

The influence of the toroidal field ripple on global H-mode performance in JT-60U has been investigated. The ripple size was varied by changing the plasma volume. The ripple losses have been measured by monitoring the local heat load to the first wall and have been simulated by the Orbit Following Monte Carlo code. The global H factors are found to be not very sensitive to the ripple size when the net input power is corrected for the ripple-trapped and banana-drift losses. These results are confirmed by theoretical analysis of the ripple-induced transport coefficients at rho =0.9.