Scaling Law for Ablation of a Hydrogen Pellet in a Plasma

A scaling law is derived which gives the rate of ablation of a frozen hydrogen pellet immersed in a plasma without the presence of a magnetic field or space charge. Plasma particles penetrate the ablating gas-plasma cloud to the evaporating pellet surface and deliver power to the cloud to drive its expansion. The evaporation rate is determined by a "self-regulating" mechanism. The ablation time is shown to be proportional to a5/3¿o-2/3¿o-1/3 where a is the pellet radius, ¿o is the effective penetration depth of the incident particle into solid hydrogen and ¿o is the power flux density of the incident particles. It is found that for ablation in a thermonuclear plasma, the alpha particles significantly affect the ablation rate. For thermonuclear plasma electrons and alpha particles, the energy required to ablate one molecule is shown to be of the order of 10 eV or less. The scaling law is applied to presently available experimental results, and reasonable agreement is found.