Appears in collection : CEMRACS : Numerical modeling of plasmas / CEMRACS : Modèles numériques des plasmas

This series of 4 lectures discusses the key physical processes in fusion-relevant plasmas, the equations used to describe them, and the interrelationships between them. The focus is on developing comprehensive equations and models for magnetically-confined fusion plasmas on a hierarchy of time scales. The relevant plasma equations for inertial fusion are also briefly mentioned. The pedagogical development begins with the very short time scale microscopic charged-particle-based Coulomb collision processes in a plasma. This microscopic description is then used to develop a comprehensive plasma kinetic equation, fluid moment, magnetohydrodynamic (MHD) and hybrid kinetic/fluid moment plasma descriptions, and finally the long time scale equations for plasma transport across the confining magnetic field. The present grand challenge in magnetic fusion is to develop a "predictive capability" for deuteron-triton (D-T) burning plasmas in ITER (http://www.iter.org). Individual .pdf files of the final, corrected sets of viewgraphs are available via http://homepages.cae.wisc.edu/~callen/plasmas.

This initial lecture first discusses the wide range of characteristic length and time scales involved in modeling fusion plasmas. Next, the Coulomb scattering of a charged test particle's velocity and the differences between the ensemble-averaged electron and ion collisional scattering and relaxation rates are discussed. Then, the mathematical properties of these collisional scattering processes are used to develop a Fokker-Planck collision operator. Finally, a general plasma kinetic equation (PKE) is developed and its general properties discussed.