Optimal laser plasma heating in a solenoidal magnetic field

Abstract

Laser heating of a plasma column confined by a solenoidal magnetic field is studied via modern optimal control techniques. Plasma density and temperature at a given axial position along the plasma column are assumed to be uniform in the radial direction but time varying; the (local) laser intensity as a function of time is taken as the control. Classical absorption of laser energy by the electrons through the mechanism of inverse bremsstrahlung is assumed, with ion heating resulting from collisional energy transfer. It is also assumed that electrical conductivity is very large, so that particle diffusion and Ohmic heating are negligible. The theory for determining optimal laser pulse shapes in time, I (t), to achieve specified performance criteria is then developed and applied to the problem of raising the ion temperature from an initial equilibrium value to a prescribed level in minimum time. Constraints on the maximum laser intensity and energy available are imposed and typical numerical results presented.