Application of optimal control theory to laser heating of a plasma in a solenoidal magnetic field

Laser heating of a plasma column confined by a solenoidal magnetic field is studied via modern optimal control techniques. A two temperature, constant pressure model is used for the plasma so that the temperature and density are functions of time and location along the plasma column. The localized behavior of the plasma heating dynamics is first studied and conventional optimal control theory applied. On a localized basis, the temperature and density are functions of time only so the heating dynamics model reduces to a set of ordinary but non-linear differential equations. Typical numerical cases are presented and some plasma parameters are varied in order to study the design tradeoffs. The distributed parameter optimal control problem is next considered with minimum time to reach a specified final ion temperature criterion as the objective.