L.D. Pearlstein

Experimental vertical stability studies for ITER performance and design guidance

United States Department of Energy (DE-FC02-04ER54698, DEAC52- 07NA27344, and DE-FG02-04ER54235)

MHD equilibria in a spheromak sustained by coaxial helicity injection

Spheromaks sustained by coaxial helicity injection differ from unsustained spheromaks in the profiles of the ratio of current to magnetic field and of the safety factor. Ideal MHD modelling with Taylor relaxed profiles in the injector predicts that the safety factor in the confined region will generally lie between 0.5 and 1, with a divergence on the separatrix since the open field lines carry current from the injector. The safety factor can be single or double valued, depending on the current profile. The modelling predicts that there are no mode rational surfaces with m = 1 except very near the separatrix; this is expected to determine the unstable resistive tearing modes associated with the dynamo which drives the discharge current. The resulting low magnetic shear has a beta (~2%) at the Mercier limit, which can be improved by current profiles differing significantly from the Taylor state or by other effects such as plasma flow. Examples are presented for the Sustained Spheromak Physics Experiment recently constructed at LLNL.

The super X divertor (SXD) and a compact fusion neutron source (CFNS)

A new magnetic geometry, the super X divertor (SXD), is invented to solve severe heat exhaust problems in high power density fusion plasmas. SXD divertor plates are moved to the largest major radii inside the TF coils, increasing the wetted area by 2–3 and the line length by 2–5. Two-dimensional fluid simulations with SOLPS (Schneider et al 2006 SOLPS 2-D edge calculation code Contrib. Plasma Phys. 46) show a several-fold decrease in divertor heat flux and plasma temperature at the plate. A small high power density tokamak using SXD is proposed, for either (1) useful fusion applications using conservative physics, such as a component test facility (CTF) or fission–fusion hybrid, or (2) to develop more advanced physics modes for a pure fusion reactor in an integrated fusion environment.

Radial transport calculations for tandem mirrors

The existence of a non-axisymmetric magnetic field in the transition regions between the central cell and end-plugs of a tandem mirror device can lead to significant radial transport of central-cell ions. Self-consistent calculation of the consequences of this non-ambipolar process requires the solution of a highly non-linear charge balance equation for the ambipolar potential. In this paper, radial transport in tandem mirrors is studied, with particular emphasis on the charge balance equation and its consequences. A time-dependent radial transport code is presented. Simulations of the Tandem Mirror Experiment (TMX) are performed. Generally, good agreement between code and experiment is obtained. The phenomenon of quenching of radial transport is analysed and demonstrated numerically.

Theoretical investigation of field-line quality in a driven spheromak

Theoretical studies aimed at predicting and diagnosing field-line quality in a spheromak are described. These include nonlinear three-dimensional MHD simulations and analyses of confinement in spheromaks dominated by either open (stochastic) field lines or approximate flux surfaces. Three-dimensional nonlinear MHD simulations confirm that field lines are predominantly open when there is a large-amplitude toroidal-mode-number n = 1 mode. However, an appreciable volume of good flux surfaces can be obtained either during the drive-off phase of a scheme with periodic pulsed drive or for an extended period under driven conditions, with oscillating volume, when the odd-n modes are suppressed. If a configuration with radially localized perturbations can be achieved, a scaling analysis for a Rosenbluth?Bussac spheromak equilibrium indicates a favourable (1/Lundquist number) scaling to larger, higher-field devices. A hyper-resistivity analysis, which also assumes small-scale perturbations, reproduces well magnetic probe data in the sustained spheromak physics experiment, while an analysis of the same experiment based on one-dimensional transport along open field lines contradicts experimental observations in several key ways. The scaling analysis is also applied to reversed-field pinches and indicates that a completely determined scaling can be obtained with less approximation to the resistive MHD equations than indicated in the previous literature.

Evidence for anomalous effects on the current evolution in the tokamak hybrid operating scenarios

Alternatives to the usual picture of advanced tokamak (AT) discharges are those that form when anomalous thermal conductivity and/or resistivity alter plasma current and pressure profiles to achieve stationary characteristics through self-organizing mechanisms where a measure of desired AT features is maintained without external current-profile control. Regimes exhibiting these characteristics are those where the safety factor (q) evolves to a stationary profile with the on-axis and minimum q ∼ 1. Operating scenarios with fusion performance exceeding H-mode at the same plasma current and where the inductively driven current density achieves a stationary configuration with either small or nonexisting sawteeth should enhance the performance of ITER and future burning plasma experiments. We present simulation results of anomalous current-profile formation and evolution using theory-based hyper-resistive models. These simulations are stimulated by experimental observations with which we compare and contrast the simulated evolution. We find that the hyper-resistivity is sufficiently strong to modify the current-profile evolution to achieve conditions consistent with experimental observations. Modelling these anomalous effects is important for developing a capability to scale current experiments to future burning plasmas.

On the operational ideal magnetohydrodynamic limit in sawtoothing discharges

Magnetohydrodynamic stability calculations of the n = 1 kink mode for equilibria with increasing β and values of the axis safety factor q0 > 1 and q0 1. This provides justification for the usual computational procedure of optimizing β by taking q0 > 1 and applying it to predict the β limit of sawtoothing discharges.

CORSICA modelling of ITER hybrid operation scenarios

The hybrid operating mode observed in several tokamaks is characterized by further enhancement over the high plasma confinement (H-mode) associated with reduced magneto-hydro-dynamic (MHD) instabilities linked to a stationary flat safety factor () profile in the core region. The proposed ITER hybrid operation is currently aiming at operating for a long burn duration (>1000 s) with a moderate fusion power multiplication factor, , of at least 5. This paper presents candidate ITER hybrid operation scenarios developed using a free-boundary transport modelling code, CORSICA, taking all relevant physics and engineering constraints into account. The ITER hybrid operation scenarios have been developed by tailoring the 15 MA baseline ITER inductive H-mode scenario. Accessible operation conditions for ITER hybrid operation and achievable range of plasma parameters have been investigated considering uncertainties on the plasma confinement and transport. ITER operation capability for avoiding the poloidal field coil current, field and force limits has been examined by applying different current ramp rates, flat-top plasma currents and densities, and pre-magnetization of the poloidal field coils. Various combinations of heating and current drive (H&CD) schemes have been applied to study several physics issues, such as the plasma current density profile tailoring, enhancement of the plasma energy confinement and fusion power generation. A parameterized edge pedestal model based on EPED1 added to the CORSICA code has been applied to hybrid operation scenarios. Finally, fully self-consistent free-boundary transport simulations have been performed to provide information on the poloidal field coil voltage demands and to study the controllability with the ITER controllers.

Electron cyclotron heating and current drive for maintaining minimum q in negative central shear discharges

Toroidal plasmas created with negative magnetic shear in the core region offer advantages in terms of MHD stability properties. These plasmas, transiently created in several tokamaks, have exhibited high-performance as measured by normalized stored energy and neutron production rates. A critical issue with extending the duration of these plasmas is the need to maintain the off-axis-peaked current distribution required to support the minimum in the safety factor q at large radii. We present equilibrium and transport simulations that explore the use of electron cyclotron heating and current drive to maintain this negative shear configuration. Using parameters consistent with DIII-D tokamak operation (Strait E et al 1995 Phys. Rev. Lett. 75 4421, Rice B W et al 1996 Nucl. Fusion 36 1271), we find that with sufficiently high injected power, it is possible to achieve steady-state conditions employing well aligned electron cyclotron and bootstrap current drive in fully non-inductively current-driven configurations.

Toward a Design for the ITER Plasma Shape and Stability Control System

A design strategy for an integrated shaping and stability control algorithm for ITER is described. This strategy exploits the natural multi-variable nature of the system so that all poloidal field coils are used to simultaneously control all regulated plasma shape and position parameters. A nonrigid, flux-conserving, linearized plasma response model is derived using a variational procedure analogous to the ideal MHD Extended Energy Principle. Initial results are presented for the non-rigid plasma response model approach applied to an example DIII-D equilibrium. For this example, the nonrigid model is found to yield a higher passive growth rate than a rigid current-conserving plasma response model. Multivariable robust controller design methods are discussed and shown to be appropriate for the ITER shape control problem.