G.H. Neilson

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.

Control of the Vertical Instability in Tokamaks

The problem of control of the vertical instability is studied for a massless filamentary plasma with finite resistivity included for the shell and active control coil. Stability boundaries are determined. The system can be stabilized up to a critical decay index, which is predominantly a function of the geometry of the passive stabilizing shell. A second, smaller, critical index, which is a function of the geometry of the control coils, determines the limit of stability in the absence of derivative gain in the control circuit. The system is also studied numerically in order to incorporate the non-linear effects of power supply dynamics. The power supply bandwidth requirement is determined by the open-loop growth rate of the instability. The system is studied for a number of control coil options which are available on the DIII-D tokamak. It is found that many of the coils will not provide adequate stabilization and that the use of inboard coils is advantageous in stabilizing the system up to the critical index. A hybrid control system which utilizes such inboard coils on a time-scale which is faster than the vessel L/R time is proposed. Experiments carried out on DIII-D confirm the appropriateness of the model. Using the results of the model study, DIII-D plasmas with decay indices exceeding 90% of the critical index have been stabilized. Measurement of the plasma vertical position is also discussed.

External inductance of an axisymmetric plasma

The external inductance of an axisymmetric toroidal plasma with an arbitrary aspect ratio and cross section is obtained using a Green’s function method. By varying an equivalent skin current density over the plasma surface, while keeping the total toroidal current fixed, the plasma boundary is made to coincide with a magnetic surface. Numerical computations of the self‐inductance and mutual inductance as functions of aspect ratio and elongation are fitted to simple analytic formulas. The effect of distributed plasma current on the volt‐seconds required to reach a prescribed net current is considered.

The beryllium limiter experiment in ISX-B

An experiment to test beryllium as a limiter material has been performed in the ISX-B tokamak. The effect of the plasma on the limiter and the effect of the limiter on the plasma were studied in detail. Heat and particle fluxes to the limiter were measured, and limiter damage by melting was documented as a function of power flux. Strong melting and evaporation of the limiter caused beryllium gettering of the vacuum vessel. Postmortem analysis of the limiter was performed to document the amount of retained hydrogen and the erosion and impurity deposition on the limiter. The effect of the limiter on the plasma performance was studied in terms of parameter space, impurity content, and confinement for the ungettered and gettered cases. Operational experience with beryllium in a fusion experiment is discussed.

Electron beam and magnetic field mapping techniques used to determine field errors in the ATF torsatron

The beam from an electron gun was used to trace flux surfaces in the Advanced Toroidal Facility (ATF) torsatron. The ATF magnetic field was run steady state at 0.1 T, and the electron beam was detected optically with an image‐intensified, solid‐state camera when it impinged on a phosphor‐coated screen. Closed flux surfaces and islands at several low‐order resonances were observed. The largest island, located at the ι= 1/2 surface, was from 5 to 6 cm in width, and its presence implied the existence of magnetic field errors. To determine if these error fields could be traced to small misalignments of the magnetic coils, a device capable of accurately measuring the radial and vertical magnetic field components of individual coil sets was placed in the center of ATF. This device allowed for a determination of the precise location of each of the coils that make up the ATF coil set. No significant coil misalignments were found. A further investigation of the coil configuration led to the identification of dipol...

Confinement improvement in beam heated ISX-B discharges with low-z impurity injection

Abstract Results are reported on improved confinement in the Impurity Study Experiment (ISX-B) neutral beam heated plasmas when a small amount of neon is injected shortly after the start of beam heating. The scaling of energy confinement is modified by the introduction of a dependence on line-averaged density. Calculations show the improvement is primarily caused by a reduction in electron heat conduction.

Equilibrium and stability studies for an iron core tokamak with a poloidal divertor

A study of plasma equilibrium and stability in a tokamak with an unsaturated iron cpre is presented. A spool model is developed for the iron core. Both a simplified force balance code and a Grad-Shafranov solver are used to study the plasma equilibrium. It is observed that the iron can strongly modify the conditions for equilibrium and stability, and in some cases an infinite cylinder model for the iron core is not adequate. Corrected criteria for plasma position stability in the presence of an iron core are introduced.

Particle removal with pump limiters in ISX-B

Abstract The first pump limiter experiments were performed on ISX-B. Two pump limiter modules were installed in the top and bottom of one toroidal sector of the tokamak. The modules consist of inertia cooled, TiC-coated graphite heads and ZrAl getter pumps each with a pumping speed of 1000–2000 l/s. The objective of the initial experiments was the demonstration of plasma particle control with pump limiters. The first set of experiments were performed in ohmic discharges (OH) in which the effect of the pump limiters on the plasma density was clearly demonstrated. In discharges characterized by Ip = 110 kA, B T = 15 kG , n e = 1−5 × 10 13 cm −3 and t = 0.3 s, the pressure rise in the pump limiters was typically 2 mTorr with the pumps off and 0.7 mTorr after activating the pumps. When the pumps were activated, the line-average plasma density decreased by up to a factor 2 at identical gas flow rates. The second set of measurements were performed in neutral beam heated discharges (NBI) with injected powers between 0.6 MW and 1.0 MW. Due to a cooling problem on one of the ZrAl pumps, the NBI experiments were carried out with one limiter only. The maximum pressure observed in NBI-discharges was 5 mTorr without activating the pumps, i.e., approximately twice as high as in OH-discharges. The exhaust efficiency, which is defined as the removed particle flux divided by the total particle flux in the scrape-off layer, is estimated to be 5%.

Second stability in the ATF torsatron—Experiment and theory

Access to the magnetohydrodynamic (MHD) second stability regime has been achieved in the Advanced Toroidal Facility (ATF) torsatron [Fusion Technol. 10, 179 (1986)]. Operation with a field error that reduced the plasma radius and edge rotational transform resulted in peaked pressure profiles and increased Shafranov shift that lowered the theoretical transition to ideal MHD second stability to β0≊1.3%; the experimental β values (β0≤3%) are well above this transition. The measured magnetic fluctuations decrease with increasing β, and the pressure profile broadens, consistent with the theoretical expectations for self‐stabilization of resistive interchange modes. Initial results from experiments with the field error removed show that the pressure profile is now broader. These later discharges are characterized by a transition to improved (×2–3) confinement and a marked change in the edge density fluctuation spectrum, but the causal relationship of these changes is not yet clear.

Finite-beta equilibrium magnetic field perturbations in stellarator plasmas

Magnetic field perturbations due to finite-beta operation in stellarators have been simulated by using the three-dimensional free-boundary equilibrium code VMEC to overcome the limitations imposed by averaged equilibrium and fixed-boundary methods. Results of these computations have been compared with analytic predictions for cylindrical stellarator models and confirm a linear relationship between the average beta and the plasma dipole moment. Only a weak sensitivity of the computations to details of the pressure profile is found. The distortion of the magnetic surfaces can be significant even at moderate beta, so that careful modelling is required when analysing the data.