S. M. Wolfe

A new look at density limits in tokamaks

While the results of early work on the density limit in tokamaks from the ORMAK and DITE groups have been useful over the years, results from recent experiments and the requirements for extrapolation to future experiments have prompted a new look at this subject. There are many physical processes which limit the attainable densities in tokamak plasmas. These processes include: (1) radiation from low Z impurities, convection, charge exchange and other losses at the plasma edge; (2) radiation from low or high Z impurities in the plasma core; (3) deterioration of particle confinement in the plasma core; and (4) inadequate fuelling, often exacerbated by strong pumping by walls, limiters or divertors. Depending upon the circumstances, any of these processes may dominate and determine a density limit. In general, these mechanisms do not show the same dependence on plasma parameters. The multiplicity of processes leading to density limits with a variety of scaling has led to some confusion when comparing density limits for different machines. The authors attempt to sort out the various limits and to extend the scaling law for one of them to include the important effects of plasma shaping, i.e. ;e = k, where ne is the line average electron density (1020 m−3), κ is the plasma elongation and (MAm−2) is the average plasma current density, defined as the total current divided by the plasma cross-sectional area. In a sense, this is the most important density limit since, together with the q-limit, it yields the maximum operating density for a tokamak plasma. It is shown that this limit may be caused by a dramatic deterioration in core particle confinement occurring as the density limit boundary is approached. This mechanism can help explain the disruptions and Marfes that are associated with the density limit.

Nonaxisymmetric field effects on Alcator C-Mod

A set of external coils (A-coils) capable of producing nonaxisymmetric, predominantly n=1, fields with different toroidal phase and a range of poloidal mode m spectra has been used to determine the threshold amplitude for mode locking over a range of plasma parameters in Alcator C-Mod [I. H. Hutchinson, R. Boivin, F. Bombarda, P. Bonoli, S. Fairfax, C. Fiore, J. Goetz, S. Golovato, R. Granetz, M. Greenwald et al., Phys. Plasmas 1, 1511 (1994)]. The threshold perturbations and parametric scalings, expressed in terms of (B21∕BT), are similar to those observed on larger, lower field devices. The threshold is roughly linear in density, with typical magnitudes of order 10−4. This result implies that locked modes should not be significantly more problematic for the International Thermonuclear Experimental Reactor [I. P. B. Editors, Nucl. Fusion 39, 2286 (1999)] than for existing devices. Coordinated nondimensional identity experiments on the Joint European Torus [Fusion Technol. 11, 13 (1987)], DIII-D [Fusion T...

Central impurity toroidal rotation in ICRF heated Alcator C-Mod plasmas

Central impurity toroidal rotation has been observed in Alcator C-Mod ICRF heated plasmas, from the Doppler shifts of argon X ray lines. Rotation velocities of up to 1.3 × 105 m/s in the co-current direction have been observed in H mode discharges with no direct momentum input. There is a strong correlation between the increase in the central impurity rotation velocity and the increase in the plasma stored energy, induced by ICRF heating, although other factors may be involved. This implies a close association between energy and momentum confinement. Co-current rotation is also observed during purely ohmic H modes. In otherwise similar discharges with the same stored energy increase, plasmas with lower current rotate faster. For hydrogen minority (D(H)) heating, plasmas with the highest rotation have an H/D ratio between 5 and 10% and have the resonance location in the inner half of the plasma, i.e. in the same conditions that are conducive to the best ICRF absorption and heating. Comparisons with neoclassical theory indicate that the ion pressure gradient is an unimportant contributor to the central impurity rotation and the presence of a substantial core radial electric field is inferred during the ICRF pulse. An inward shift of ions induced by ICRF waves could give rise to a non-ambipolar electric field in the plasma core.

Observations of Anomalous Momentum Transport in Alcator C-Mod Plasmas with No Momentum Input

Anomalous momentum transport has been observed in Alcator C-Mod tokamak plasmas. The time evolution of core impurity toroidal rotation velocity profiles has been measured with a tangentially viewing crystal x-ray spectrometer array. Following the L-mode to EDA (enhanced Dα) H-mode transition in both Ohmic and ion cyclotron range of frequencies heated discharges, the ensuing co-current toroidal rotation velocity, which is generated in the absence of any external momentum source, is observed to propagate in from the edge plasma to the core with a timescale of the order of the observed energy confinement time, but much less than the neo-classical momentum confinement time. The ensuing steady state toroidal rotation velocity profiles in EDA H-mode plasmas are relatively flat, with V ~ 50 km s−1, and the momentum transport can be simulated using a simple diffusion model. Assuming that the L–H transition produces an instantaneous edge source of toroidal torque (which disappears at the H- to L-mode transition), the momentum transport may be characterized by a diffusivity, with values of ~0.07 m2 s−1 during EDA H-mode and ~0.2 m2 s−1 in L-mode. These values are large compared to the calculated neo-classical momentum diffusivities, which are of the order of 0.003 m2 s−1. Velocity profiles of ELM-free H-mode plasmas are centrally peaked (with V(0) exceeding 100 km s−1 in some cases), which suggests the presence of an inward momentum pinch; the observed profiles are consistent with simulations including an edge inward convection velocity of ~10 m s−1. In EDA H-mode discharges which develop internal transport barriers, the velocity profiles become hollow in the centre, indicating the presence of a negative radial electric field well in the vicinity of the barrier foot. Upper single null diverted and inner wall limited L-mode discharges exhibit strong counter-current rotation (with V(0)~−60 km s−1 in some cases), which may be related to the observed higher H-mode power threshold in these configurations. For plasmas with locked modes, the toroidal rotation is observed to cease (V ≤ 5 km s−1).

Effect of pellet fuelling on energy transport in ohmically heated alcator C plasmas

Time-dependent transport analysis calculations have been carried out, using experimentally determined plasma parameters to obtain the variation of electron and ion thermal diffusivities following pellet injection into moderate-density Alcator C discharges. The ion thermal diffusivity, which is typically higher than neoclassical predictions by a factor of three to five in the gas-fuelled target plasma, is found to decrease after pellet injection to approximately the neoclassical value. The electron thermal conductivity is not reduced after pellet injection. The improvement in ion transport correlates with the peaking of the density profile and may be related to the reduction in the quantity ηi ≡ d ln Ti/d ln n, which is inferred to lie close to the critical value for stability of drift modes driven by the ion temperature gradient. Extrapolation of these results to higher-density plasmas, for which the electron and ion losses cannot be unambiguously measured, is consistent with previously reported increases in global energy confinement time accompanying pellet injection.

Observations of impurity toroidal rotation suppression with ITB formation in ICRF and ohmic H mode Alcator C-Mod plasmas

Co-current central impurity toroidal rotation has been observed in Alcator C-Mod plasmas with on-axis ICRF heating. The rotation velocity increases with plasma stored energy and decreases with plasma current. Very similar behaviour has been seen during ohmic H modes, which suggests that the rotation, generated in the absence of an external momentum source, is not mainly an ICRF effect. A scan of ICRF resonance location across the plasma has been performed in order to investigate possible influences on the toroidal rotation. With a slight reduction of toroidal magnetic field from 4.7 to 4.5 T and a corresponding shift of the ICRF resonance from r/a = -0.36 to -0.48, the central toroidal rotation significantly decreased together with the formation of an internal transport barrier (ITB). During the ITB phase, electrons and impurities peaked continuously for |r/a| ≤ 0.5. Comparison of the observed rotation and neoclassical predictions indicates that the core radial electric field changes from positive to negative during the ITB phase. Similar rotation suppression and ITB formation have been observed during some ohmic H mode discharges.

Scaling of the power exhaust channel in Alcator C-Mod

Parametric dependences of the heat flux footprint on the outer divertor target plate are explored in EDA H-mode and ohmic L-mode plasmas over a wide range of parameters with attached plasma conditions. Heat flux profile shapes are found to be independent of toroidal field strength, independent of power flow along magnetic field lines and insensitive to x-point topology (single-null versus double-null). The magnitudes and widths closely follow that of the “upstream” pressure profile, which are correlated to plasma thermal energy content and plasma current. Heat flux decay lengths near the strike-point in H- and L-mode plasmas scale approximately with the inverse of plasma current, with a diminished dependence at high collisionality in L-mode. Consistent with previous studies, pressure gradients in the boundary scale with plasma current squared, holding the magnetohydrodynamic ballooning parameter approximately invariant at fixed collisionality—strong evidence that critical-gradient transport physics plays ...

Pedestal profiles and fluctuations in C-Mod enhanced D-alpha H-modes

High resolution measurements on the Alcator C-Mod tokamak [I. H. Hutchinson et al., Phys. Plasmas 1, 1551 (1994)] of the transport barrier in the “Enhanced Dα” (EDA) regime, which has increased particle transport without large edge localized modes, show steep density and temperature gradients over a region of 2–5 mm, with peak pressure gradients up to 12 MPa/m. Evolution of the pedestal at the L-H transition is consistent with a large, rapid drop in thermal conductivity across the barrier. A quasi-coherent fluctuation in density, potential, and Bpol, with f0∼50–150 kHz and kθ∼4 cm−1, always appears in the barrier during EDA, and drives a large particle flux. Conditions to access the steady-state EDA regime in deuterium include δ>0.35, q95>3.5, and L-mode target density ne>1.2×1020 m−3. A reduced q95 limit is found for hydrogen discharges.

High frequency gyrotrons and their application to tokamak plasma heating

Abstract High frequency (⩾ 200 GHz) gyrotrons are potentially useful for several important applications, including plasma heating and radar. For electron cyclotron resonance heating of a moderate-size, high power density tokamak power reactor to ignition temperatures, a gyrotron frequency around 200 GHz appears to be necessary. The design of high frequency gyrotrons is discussed. Analysis of overall gyrotron efficiency indicates that high efficiency may be obtained in fundamental electron cyclotron frequency (ω c ) emission at high frequencies. The linear theory of a gyrotron operating at the fundamental frequency is derived for the TE mpq modes of a right circular cylinder cavity. An analytic expression is given for the oscillator threshold or starting current versus magnetic field.

X-ray imaging crystal spectroscopy for use in plasma transport research

This research describes advancements in the spectral analysis and error propagation techniques associated with x-ray imaging crystal spectroscopy (XICS) that have enabled this diagnostic to be used to accurately constrain particle, momentum, and heat transport studies in a tokamak for the first time. Doppler tomography techniques have been extended to include propagation of statistical uncertainty due to photon noise, the effect of non-uniform instrumental broadening as well as flux surface variations in impurity density. These methods have been deployed as a suite of modeling and analysis tools, written in interactive data language (IDL) and designed for general use on tokamaks. Its application to the Alcator C-Mod XICS is discussed, along with novel spectral and spatial calibration techniques. Example ion temperature and radial electric field profiles from recent I-mode plasmas are shown, and the impact of poloidally asymmetric impurity density and natural line broadening is discussed in the context of the planned ITER x-ray crystal spectrometer.