W. A. Houlberg

Bootstrap current and neoclassical transport in tokamaks of arbitrary collisionality and aspect ratio

A multi-species fluid model is described for the steady state parallel and radial force balance equations in axisymmetric tokamak plasmas. The bootstrap current, electrical resistivity, and particle and heat fluxes are evaluated in terms of the rotation velocities and friction and viscosity coefficients. A recent formulation of the neoclassical plasma viscosity for arbitrary shape and aspect ratio (including the unity aspect ratio limit), arbitrary collisionality, and orbit squeezing from strong radial electric fields is used to illustrate features of the model. The bootstrap current for the very low aspect ratio National Spherical Torus Experiment [J. Spitzer et al., Fusion Technol. 30, 1337 (1996)] is compared with other models; the largest differences occur near the plasma edge from treatment of the collisional contributions. The effects of orbit squeezing on bootstrap current, thermal and particle transport, and poloidal rotation are illustrated for an enhanced reverse shear plasma in the Tokamak Fusi...

Baldur: A one-dimensional plasma transport code

Abstract A version of the BALDUR plasma transport code which calculates the evolution of plasma parameters is documented. This version uses an MHD equilibrium which can be approximated by concentric circular flux surfaces. Transport of up to six species of ionized particles, of electron and ion energy, and of poloidal magnetic field is computed. A wide variety of source terms are calculated including those due to neutral gas, fusion and auxiliary heating. The code is primarily designed for modelling tokamak plasmas.

THE AMBIPOLAR ELECTRIC FIELD IN STELLARATORS

In a three-dimensional device like a stellarator, the ambipolar electric field must be determined self-consistently from the ambipolarity constraint and can have a significant effect on transport through the diffusion coefficients. A differential formulation and an algebraic formulation for the electric field are solved, together with the density and temperature equations. The results are compared, and in both cases multiple electric field solutions can exist, with bifurcations occurring between different solutions. It is shown that heating of the electrons encourages bifurcation to the more favourable positive electric field root.

Pellet fuelling and control of burning plasmas in ITER

Pellet injection from the inner wall is planned for use in ITER as the primary core fuelling system since gas fuelling is expected to be highly inefficient in burning plasmas. Tests of the inner wall guide tube have shown that 5 mm pellets with up to 300 m s−1 speeds can survive intact and provide the necessary core fuelling rate. Modelling and extrapolation of the inner wall pellet injection experiments from present days smaller tokamaks leads to the prediction that this method will provide efficient core fuelling beyond the pedestal region. Using pellets for triggering of frequent small edge localized modes is an attractive additional benefit that the pellet injection system can provide. A description of the ITER pellet injection systems capabilities for fuelling and ELM triggering is presented and performance expectations and fusion power control aspects are discussed.

Toroidal rotation in DIII-D in electron cyclotron heating and Ohmic H-mode discharges

Spatially and temporally resolved toroidal rotation measurements have been made in DIII-D [J. L. Luxon, Nucl. Fusion 42, 614 (2002)] discharges with no externally applied torque. The velocity measurements are made using the charge exchange recombination (CER) technique viewing emission from the intrinsic carbon impurity in deuterium discharges. Three cases have been studied: L mode and H mode with Ohmic heating and H mode with electron cyclotron heating (ECH). The ECH H mode has carbon counter-rotation in the center of the plasma, and co-rotation outside, where co- and counter- are relative to the direction of the toroidal plasma current. The Ohmic H mode has carbon rotation everywhere in the co-direction. Neoclassical theory is applied to compute the deuterium toroidal velocity and it is found that the counter-rotation measured for carbon in the core of the ECH H mode is also thus predicted for the bulk deuterium species. Short blips of neutral beams (NB) must be used for the CER technique and these blip...

Physics of confinement improvement of plasmas with impurity injection in DIII-D

External impurity injection into L mode edge discharges in DIII-D has produced clear confinement improvement (a factor of 2 in energy confinement and neutron emission), reduction in all transport channels (particularly ion thermal diffusivity to the neoclassical level), and simultaneous reduction of long wavelength turbulence. Suppression of the long wavelength turbulence and transport reduction are attributed to synergistic effects of impurity induced enhancement of E × B shearing rate and reduction of toroidal drift wave turbulence growth rate. A prompt reduction of density fluctuations and local transport at the beginning of impurity injection appears to result from an increased gradient of toroidal rotation enhancing the E × B shearing. Transport simulations carried out using the National Transport Code Collaboration demonstration code with a gyro-Landau fluid model, GLF23, indicate that E × B shearing suppression is the dominant transport suppression mechanism.

Plasma and momentum transport processes in the vicinity of a magnetic island in a tokamak

In the vicinity of a magnetic island in tokamaks, the toroidal symmetry in the magnitude of the magnetic field |B| is broken. This leads to enhanced radial transport fluxes and momentum dissipation. The radial electric field can be determined from the quasineutrality condition, or equivalently the momentum equation, on the island magnetic surface. The equation that governs the radial electric field is nonlinear and can have bifurcated solutions. This may suppress turbulence fluctuations and improve plasma confinement. The theory remains valid for a rotating island with an appropriate re-interpretation of the radial electric field.

Physics aspects of the Compact Ignition Tokamak

The Compact Ignition Tokamak (CIT) is a proposed modest-size ignition experiment designed to study the physics of alpha particle heating. The basic concept is to achieve ignition in a modest-size minimum cost experiment by using a high plasma density to achieve nT{sub E} {approx} 2 x 10{sup 20}s/m{sup 3} required for ignition. The high density requires a high toroidal field (10 T). The high toroidal field allows a large plasma current (10 MA) which provides a high level of ohmic heating, improves the energy confinement, and allows a relatively high beta ({approx} 6%). The present CIT design also has a high degree of elongation (k {approx} 1.8) to aid in producing the large plasma current. A double null poloidal divertor and pellet injection are part of the design to provide impurity and particle control, improve the confinement, and provide flexibility for improving the plasma profiles. Auxiliary heating is expected to be necessary to achieve ignition, and 10-20 MW of ICRF is to be provided.

Influence of fast alpha diffusion and thermal alpha buildup on tokamak reactor performance

The effect of fast alpha diffusion and thermal alpha accumulation on the confinement capability of a candidate Engineering Test Reactor plasma (Tokamak Ignition/Burn Experimental Reactor) in achieving ignition and steady-state driven operation has been assessed using both global and 1-1/2-dimensional transport models. Estimates are made of the threshold for radial diffusion of fast alphas and thermal alpha buildup. It is shown that a relatively low level of radial transport, when combined with large gradients in the fast alpha density, leads to a significant radial flow with a deleterious effect on plasma performance. Similarly, modest levels of thermal alpha concentration significantly influence the ignition and steady-state burn capability.

Magnetic flux evolution in highly shaped plasmas

The resistive evolution of magnetic flux in toroidal devices is studied. The formulation is applicable to general nonaxisymmetric (three-dimensional) toroidal configurations. In particular, it can treat highly shaped, high β, three-dimensional stellarator configurations, as well as two-dimensional (axisymmetric) tokamak plasmas. The time evolution of the poloidal magnetic flux is posed in terms of the rotational transform, ι, and allows for a transparent inclusion of stellarator specific current-free contributions to ι. Strong diamagnetic and paramagnetic contributions to toroidal magnetic flux, as evident in spherical tokamaks and similar concepts, are calculated by direct iteration with an equilibrium solver. The nonlinear evolution equation is derived using a susceptance matrix formulation originally introduced by Grad and co-workers [Bateman, Nucl. Fusion 13, 227 (1973)]. Here, it is extended to general, nonstraight field line coordinate systems. The basic equations are described, explicit expressio...