Because experiment/model comparisons in magnetic confinement fusion have not yet satisfied the requirements for validation as understood broadly, a set of approaches to validating mathematical models and numerical algorithms are recommended as good practices. Previously identified procedures, such as verification, qualification, and analysis of error and uncertainty, 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.

[1] On July 24, 2003, when the Cluster 4 satellite crossed the magnetic equator at about 4.5 R E radial distance on the dusk side (∼15 MLT), whistler wave emissions were observed below the local electron gyrofrequency (f ce ) in two bands, one band above one-half the gyrofrequency (0.5f ce ) and the other band below 0.5f ce . A careful analysis of the wave emissions for this event has shown that Cluster 4 passed through the wave source region. Simultaneous electron particle data from the PEACE instrument in the generation region indicated the presence of a mid-energy electron population (∼100 s of eV) that had a highly anisotropic temperature distribution with the perpendicular temperature 10 times the parallel temperature. To understand this somewhat rare event in which the satellite passed directly through the wave generation region and in which a free energy source (i.e., temperature anisotropy) was readily identified, a linear theory and particle in cell simulation study has been carried out to elucidate the physics of the wave generation, wave-particle interactions, and energy redistribution. The theoretical results show that for this event the anisotropic electron distribution can linearly excite obliquely propagating whistler mode waves in the upper frequency band, i.e., above 0.5f ce . Simulation results show that in addition to the upper band emissions, nonlinear wave-wave coupling excites waves in the lower frequency band, i.e., below 0.5f ce . The instability saturates primarily by a decrease in the temperature anisotropy of the mid-energy electrons, but also by heating of the cold electron population. The resulting wave-particle interactions lead to the formation of a high-energy plateau on the parallel component of the warm electron velocity distribution. The theoretical results for the saturation time scale indicate that the observed anisotropic electron distribution must be refreshed in less than 0.1 s allowing the anisotropy to be detected by the electron particle instrument, which takes several seconds to produce a distribution.

An assessment is made of Krook collisional models used to describe the kinetic behavior of collective oscillations, i.e., when Landau damping and collisions must be considered, as is often the case for low-frequency waves. The study focuses on an early energy-conserving model [B. D. Fried, A. N. Kaufman, and D. L. Sachs, Phys. Fluids 9, 292 (1966)] that is shown to be identical to a more modern version used in drift-wave stability studies [G. Rewoldt, W. M. Tang, and R. J. Hastie, Phys. Fluids 29, 2893 (1986)]. The inadequacy of the simpler, and often used, nonconserving model is illustrated. Comparisons are established with recent collisional studies of ion acoustic waves [V. Yu. Bychenkov, J. Myatt, W. Rozmus, and V. T. Tikhonchuk, Phys. Plasmas 1, 2419 (1994)] and electron plasma waves [C. S. Ng, A. Bhattacharjee, and F. Skiff, Phys. Rev. Lett. 83, 1974 (1999)]. A connection is also established with contemporary studies of condensed matter and quantum liquids [K. Morawetz and U. Fuhrmann, Phys. Rev. E 61, 2272 (2000); 62, 4382 (2000)]. A useful empirical fit is found that corrects the Braginskii susceptibility to incorporate the kinetic behavior associated with the Krook kinetic susceptibility.

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.

The local dispersion relation for shear and kinetic Alfvén waves is derived for arbitrary alpha particle distribution functions and analyzed for a set of representative distribution functions. Including both the velocity dependence of magnetic drift and temperature gradients is found to have the most striking effect on the partial growth rate associated with alpha particles for shear Alfvén waves. Parallel electric field effects are included and found to make significant changes in the damping associated with electrons and ions. The formalism parallels that used in reduced magnetohydrodynamics, so that it can be readily extended to calculations incorporating more detailed and realistic equilibrium geometry.