J.‐N. Leboeuf

Validation in fusion research : Towards guidelines and best practices

Because experiment/model comparisons in magnetic confinement fusion have not yet satisfied the requirements for validation as understood broadly, approaches to validating mathematical models and numerical algorithms are recommended as good practices. Previously identified procedures, such as, verification, qualification, and analysis of errors from uncertainties and deficiencies, remain important. However, particular challenges intrinsic to fusion plasmas and physical measurement therein lead to identification of new or less familiar concepts that are also critical in validation. These include the primacy hierarchy, which tracks the integration of measurable quantities, and sensitivity analysis, which assesses how model output is apportioned to different sources of variation. The use of validation metrics for individual measurements is extended to multiple measurements, with provisions for the primacy hierarchy and sensitivity. This composite validation metric is essential for quantitatively evaluating comparisons with experiments. To mount successful and credible validation in magnetic fusion, a new culture of validation is envisaged.

Computational modeling of physical processes during laser ablation

Abstract A combined theoretical and experimental effort to model various physical processes during laser ablation of solids using a variety of computational techniques is described. Currently the focus of the modeling is on the following areas: (a) rapid transformations through the liquid and vapor phases under possibly nonequilibrium thermodynamic conditions induced by laser-solid interactions; (b) breakdown of the vapor into a plasma in the early stages of ablation through both electronic and photoionization processes; (c) hydrodynamic behavior of the vapor/plasma during and after ablation; and (d) the effects of initial conditions in the vapor, in particular, the nature of the initial velocity distribution, on the characteristics of subsequent vapor expansion. The results from the modeling will be compared with experimental observations where possible.

Modeling of plume dynamics in laser ablation processes for thin film deposition of materials

The transport dynamics of laser-ablated neutral/plasma plumes are of significant interest for film growth by pulsed-laser deposition of materials since the magnitude and kinetic energy of the species arriving at the deposition substrate are key processing parameters. Dynamical calculations of plume propagation in vacuum and in background gas have been performed using particle-in-cell hydrodynamics, continuum gas dynamics, and scattering models. Results from these calculations are presented and compared with experimental observations.

Theory of drift-thermal instability-induced turbulence

A simple model for drift‐thermal instability‐induced turbulence is derived and studied both analytically and numerically. Both nonlocal, nonlinear analytical calculations and three‐dimensional computations are used. Potential and temperature fluctuation levels and radial correlation lengths are calculated and compared to numerical results. The saturation mechanism and the role of a fluctuation‐generated shear flow are elucidated. The numerical calculations are used to obtain spectra and correlation lengths. A detailed comparison of analytical and numerical results is given.

Landau fluid equations for electromagnetic and electrostatic fluctuations

Closure relations are developed to allow approximate treatment of Landau damping and growth using fluid equations for both electrostatic and electromagnetic modes. The coefficients in these closure relations are related to approximations of the plasma dispersion function by ratios of polynomials. Thirteen different numerical sets of coefficients are given and explicitly related to previous fits to the plasma dispersion function. The application of the techniques presented in this paper is illustrated with the specific example of resistive g modes. Comparisons of full kinetic and approximate results are made for the solutions to the dispersion relation, radially resolved modes in sheared magnetic geometry, and the plasma dispersion function itself.

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.

Recent results from the ATF torsatron

Recent experiments in the Advanced Toroidal Facility (ATF) torsatron [Plasma Physics and Controlled Nuclear Fusion Research 1990 (IAEA, Vienna, in press)] have emphasized the role of magnetic configuration control in transport studies. Long‐pulse plasma operation up to 20 sec has been achieved with electron cyclotron heating (ECH). With neutral beam injection (NBI) power of ≥1 MW, global energy confinement times of 30 msec have been obtained with line‐average densities up to 1.3×1020 m−3. The energy confinement and the operational space in ATF are roughly the same as those in tokamaks of similar size and field. The empirical scaling observed is similar to gyro‐reduced Bohm scaling with favorable dependences on density and field offsetting an unfavorable power dependence. The toroidal current measured during ECH is identified as the bootstrap current. The observed currents agree well with predictions of neoclassical theory in magnitude and in parametric dependence. Variations of the magnetic configuration ...

Ideal low-n and Mercier mode stability boundaries for ℓ = 2 torsatrons

The relationship between the stability properties of ideal low-n internal modes and the threedimensional (3-D) ideal Mercier criterion for l = 2 torsatron configurations is discussed. A broad range of aspect ratios and pressure profiles are considered. It is found that the low-n modes with resonant surfaces lying in a Mercier unstable region are unstable in most of the cases studied and that the critical beta given by the Mercier criterion is always lower than the critical beta for the lowest-n unstable mode. This is verified even in the cases where global n = 1 modes are unstable. Therefore, the 3-D Mercier criterion is a useful guide in mapping the ideal stability beta limits for these torsatron configurations.

Shear flow effects on the nonlinear evolution of thermal instabilities

In the weak radiation drive regime, the coupling between the thermal instability driven by impurity radiation and the self‐consistent flow profile modification leads to a simple dynamical system that can be approximated by the Volterra–Lotka equations. In this system the shear flow acts as a predator and the temperature fluctuations act as prey. The solutions are oscillatory, and their behavior resembles that of edge‐localized modes (ELM’s). The solutions of the simplified model are compared with the three‐dimensional and two‐dimensional nonlinear numerical results for this instability.

Low‐n stability calculations for three‐dimensional stellarator configurations

A set of reduced magnetohydrodynamic (MHD) equations to study linear stability in general toroidal configurations is presented. The equations are derived by applying the averaging method to an equilibrium represented in a straight‐field‐line coordinate system. They permit the calculation of the low‐n stability of fully three‐dimensional (3‐D) equilibria for stellerator configurations with either a planar or a helical magnetic axis. Numerical solutions are shown to agree well with marginal stability boundaries given by the classical stellerator expansion when average stellarator equilibria with a planar magnetic axis are used as input.