The physics model of electron cyclotron heating (ECH) and current drive (ECCD) is becoming well validated through systematic comparisons of theory and experiment. This work has shown that ECH and ECCD can be highly localized and robustly controlled in toroidal plasma confinement systems, leading to applications including stabilization of magnetohydrodynamic instabilities like neoclassical tearing modes, control and sustainment of desired profiles of current density and plasma pressure, and studies of localized transport in laboratory plasmas. The experimental work was supported by a broad base of theory based on first principles which is now well encapsulated in linear ray tracing codes describing wave propagation, absorption, and current drive and in fully relativistic quasilinear Fokker–Planck codes describing in detail the response of the electrons to the energy transferred from the wave. The subtle balance between wave-induced diffusion and Coulomb relaxation in velocity space provides an understanding of the effects of trapping of current-carrying electrons in the magnetic well. Strong quasilinear effects and radial transport of electrons, which may broaden the driven current profile, have also been observed under some conditions and appear to be consistent with theory, but in large devices these are usually insignificant. The agreement of theory and experiment, the wide range of established applications, and the technical advantages of ECH support the application of ECH in next-step tokamaks and stellarators.

Abstract. Optimal design and use of electron cyclotron heating (ECH) requires that accurate and relatively quick computer codes be available for prediction of wave coupling, propagation, damping, and current drive at realistic levels of EC power. To this end, a number of codes have been developed in laboratories worldwide. A detailed comparison of these codes is desirable since they use a variety of methods for modeling 2 the behavior and effects of the waves. The approach used in this benchmarking study is to apply these codes to a small number of representative cases. Following minor remedial work on some codes, the agreement between codes for off-axis application is excellent.The largest systematic differences are found between codes with weakly relativistic and fully relativistic evaluation of the resonance condition, but even there the differences amount to less than 0.02 in normalized minor radius. For some other cases, for example for central current drive, the code results may differ significantly due to differences in the physics models used.

Green's-function techniques are used to calculate electron cyclotron current drive (ECCD) efficiency in general tokamak geometry in the low-collisionality regime. Fully relativistic electron dynamics is employed in the theoretical formulation. The highvelocity collision model is used to model Coulomb collisions and a simplified quasilinear rf diffusion operator describes wave-particle interactions. The approximate analytic solutions which are benchmarked with a widely used ECCD model, facilitate time-dependent simulations of tokamak operational scenarios using the non-inductive current drive of electron cyclotron waves.

A series of carefully designed experiments on DIII-D have taken advantage of a broad set of turbulence and profile diagnostics to rigorously test gyrokinetic turbulence simulations. In this paper the goals, tools and experiments performed in these validation studies are reviewed and specific examples presented. It is found that predictions of transport and fluctuation levels in the mid-core region (0.4 < ρ < 0.75) are in better agreement with experiment than those in the outer region (ρ � 0.75) where edge coupling effects may become increasingly important and multiscale simulations may also be necessary. Validation studies such as these are crucial in developing confidence in a first-principles based predictive capability for ITER.

Localized currents due to electron cyclotron current drive have been measured for the first time in experiments on the DIII-D tokamak. The location of driven current in the plasma has been varied from near the center of the tokamak out to half of the minor radius. The measured current drive efficiency agrees with quasilinear Fokker-Planck calculations near the center and exceeds the predicted value with increasing minor radius. Reduction of the trapped electron fraction due to finite collisionality is a leading candidate to explain the discrepancy. PACS numbers: 52.55.Fa, 52.25.Fi, 52.35.Hr, 52.50.Gj The experiments reported here represent the first direct measurements of localized, noninductive current generation by electron cyclotron waves in a high-temperature tokamak plasma. The motivations for this research are to supply the toroidal current necessary for plasma confinement in a tokamak by means other than the transformer action, and to allow feedback control of the current profile to extend the fusion performance beyond the stability limits found for inductively driven tokamaks [1]. These conditions can only be realized in steady state at high energy gain if the bulk of the current in the plasma is driven by self-generated currents [2] due to density and temperature gradients (bootstrap current), somewhat analogous to thermoelectric currents in metals. It is unlikely, however, that the bootstrap current will perfectly match the desired profile; therefore, a flexible, localized source of noninductive current will be needed for control. Current driven by absorption of electron cyclotron waves, as reported here, is a leading candidate to fulfill this role because the location of the driven current is easily controlled and these waves can be launched with high power density into the plasma with a remote launching structure. In addition to these practical considerations, these experiments provide a unique test of the electron dynamics where magnetic mirror trapping of electrons with low parallel velocity should be important. (Trapped electrons are those which are confined to the outward side of the tokamak due to conservation of energy and magnetic moment as they move in the spatially varying magnetic field.) The trapping effects have profound implications in many areas of magnetic confinement physics, and a clear local test of the theoretical treatment has not been carried out.Two gyrotron oscillators at 110 GHz are the source of the electron cyclotron waves [3]. In the experiments reported here, approximately 1 MW of power is applied to the plasma for up to 1 s. The waves are launched at an angle with respect to the major radius to generate current parallel to the existing current [4]. Between discharges, the launched beam can be steered in the vertical direction and wave absorption takes place near the intersection of the ray trajectories and the second harmonic of the electron cyclotron frequency.In previous experiments with off-axis electron cyclotron current drive (ECCD), the magnitude of the driven cur...

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This work describes active control algorithms used by DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] to stabilize and maintain suppression of 3/2 or 2/1 neoclassical tearing modes (NTMs) by application of electron cyclotron current drive (ECCD) at the rational q surface. The DIII-D NTM control system can determine the correct q-surface/ECCD alignment and stabilize existing modes within 100–500ms of activation, or prevent mode growth with preemptive application of ECCD, in both cases enabling stable operation at normalized beta values above 3.5. Because NTMs can limit performance or cause plasma-terminating disruptions in tokamaks, their stabilization is essential to the high performance operation of ITER [R. Aymar et al., ITER Joint Central Team, ITER Home Teams, Nucl. Fusion 41, 1301 (2001)]. The DIII-D NTM control system has demonstrated many elements of an eventual ITER solution, including general algorithms for robust detection of q-surface/ECCD alignment and for real-time maintenance of alignment following the disappearance of the mode. This latter capability, unique to DIII-D, is based on real-time reconstruction of q-surface geometry by a Grad-Shafranov solver using external magnetics and internal motional Stark effect measurements. Alignment is achieved by varying either the plasma major radius (and the rational q surface) or the toroidal field (and the deposition location). The requirement to achieve and maintain q-surface/ECCD alignment with accuracy on the order of 1cm is routinely met by the DIII-D Plasma Control System and these algorithms. We discuss the integrated plasma control design process used for developing these and other general control algorithms, which includes physics-based modeling and testing of the algorithm implementation against simulations of actuator and plasma responses. This systematic design/test method and modeling environment enabled successful mode suppression by the NTM control system upon first-time use in an experimental discharge.

ITER will rely on electron cyclotron stabilization of neoclassical tearing mode islands. The large size and low torque applied in ITER imply slow plasma rotation and susceptibility to island locking by the resistive wall; locking is likely to lead to a loss of the high confinement H-mode, a beta collapse and possibly disruption. ‘Front’ steering of the launcher, with narrower electron cyclotron current drive (ECCD), has resolved the issue in ‘remote’ steering of the driven current being too broad and relatively ineffective. However, narrower current drive places demands on alignment of the current drive on the rational surface that is being stabilized. DIII-D alignment techniques with and without (preemptive) an island are reviewed. The results are used to check models for the effect of misalignment and are then applied to ITER. Criteria for accuracy of alignment as a function of injected power and for the necessary time response of the controller are presented.