Effect of Thermal Conductivity on the Knudsen Layer at Ablative Surfaces (Preprint)

In this paper we develop an analytical model of Knudsen layer at the ablative wall taking into account the temperature gradient in the bulk gas. The region of validity of the existing models and effect of the temperature gradient on the Knudsen layer properties are calculated. 1 Electronic address: [email protected] Distribution A: Approved for public release; distribution unlimited 2 The formation of the Knudsen layer, the non-equilibrium (kinetic) layer, near the vaporizing surface and subsequent ablation is of great interest for a number of applications such as capillary discharges [1,2], plasma thrusters [3,4], high-pressure discharges [5], vacuum arcs [6], electroguns [7] and laser ablation [8]. Anisimov [9] was the first to consider details of the vaporization process for a case of vaporization of a metal exposed to laser radiation. He used a bimodal velocity distribution function in the kinetic layer, assuming no absorption of laser radiation in the ablated gas. The primary result of his work was the calculation of the maximal flux of returned atoms to the evaporating surface, which was found to be about 18% of the flux of vaporized atoms. This result was obtained under the assumption that the atom flow velocity is equal to the sound velocity at the external boundary of the Knudsen layer and the temperature of the gas in the equilibrium region (beyond Knudsen Layer) is constant, i.e. no conductive heat flux to the ablative wall surface. However, in many physical situations, the vapor leaving the non-equilibrium layer cannot be described by using a speed of sound approximation. For example, in ablative capillary discharges, the gas motion in the capillary chamber is not "free"; it is restricted by the capillary wall, leading to a more dense gas (plasma) in the discharge volume and therefore, larger backflux to evaporating surface and smaller flow velocity at the outer boundary of the Knudsen layer. Beilis [10,11], was the first to consider ablation into a dense plasma. He studied the case of metal vaporization into discharge plasmas in a vacuum arc cathode spot. He concluded that the parameters at the outer boundary of the Knudsen layer are close to their equilibrium values and that the velocity at the outer boundary of the kinetic layer is much smaller than the sound velocity. Later these models were applied for the case of dielectric ablation into the discharge plasma in the capillary discharge conditions [12, 13] and for the case of strong plasma acceleration [14]. All those analytical models neglected the conductive heat flux to the ablative surface. This can be significant because the temperature in the plasma core is assumed in the models to be much greater than the temperature of the ablative surface. In particular, neglecting the conductive heat flux leads results in the calculated gas temperature at the outer boundary of the Knudsen layer to appears to be smaller than the temperature of the evaporating surface. This consequently leads to the heat flux through the Knudsen Layer being directed