Vlasov solution describing nonadiabatic plasma heating by magnetic compression

An analytical Vlasov description of a fast magnetic compression is developed with use of the Lewis invariant for the time-dependent harmonic oscillator. Simple formulas for the nonadiabatic heating of an initial rigid rotor Maxwellian distribution are derived, providing a low β kinetic description of the oscillatory state after compression. The role of diamagnetic shielding and orbit stochasticity to relax the oscillations in the plasma after compression is considered. In addition to the adiabatic heating (which is equal to the field ratio B1/B0), a much stronger heating, proportional to (B1/B0)2, can be obtained in a nonturbulent fast compression. The ultimate need to use low initial β to achieve strong nonadiabatic heating and avoid turbulent development of instabilities follows from a formula describing the increase in β during the implosion. An evolution profile for B(t) with a constant nonadiabaticity parameter is considered for optimization of compression time (of order 5--10 μsec) and nonadiabatic heating. The radial extension of the compressed plasma is calculated. Space charge effects can arise from the differential radial motions of electrons and ions in a nonadiabatic compression, which can have important consequences. In straight devices, space charge can be removed by letting magnetic field lines connect to a conducting plate. Special attention is paid to the possibility of creating a ''Migma pinch'' with self-colliding orbits in the MeV range. The model indicates that this high energy can be reached in a compression with large field ratio, i.e., B1/B0∼103