Heating and Ablation of High-Z Cryogenic Pellets in High Temperature Plasmas

A kinetic model is developed to determine the power deposition from energetic electrons into the neutral gas shield of an ablating high-Z pellet. For high-Z, the velocity distribution of the hot electrons is nearly isotropic, and we use this feature to develop solutions to the kinetic equation. In contrast to pre-existing models, we consider the effect of gyro-motion as well as elastic scattering of the hot electrons. Two limits are considered: when the gyro-frequency is much greater than the elastic collision frequency, the hot electrons diffuse longitudinally along the field lines as they slow down; but if the gyro-frequency is much less than the elastic collision frequency, the hot electrons diffuse radially. In both limits, it is possible to express the kinetic equation describing the hot electrons independently of the gas density profile, and therefore, the power deposition model is universal in this respect. The emphasis on elastic scattering yields an ablation rate which scales as Z(-7/6) which is different than Z(-2/3) shown in Sergeev et al (2006 Plasma Phys. Rep. 32 5). It is also shown that the sheath potential required to maintain ambipolarity in the cloud scales as Z(-1/3). Fluid simulations yield ablation rates that scale with the four-thirds power of the pellet radius in agreement with [2].