Investigation of the trajectory uniformity in water dissolution ultraprecision continuous polishing of large-sized KDP crystal

Large-sized potassium dihydrogen phosphate(KDP)crystals are an irreplaceable nonlinear optical component in an inertial confinement fusion project.Restricted by the size,previous studies have been aimed mainly at the removal principle and surface roughness of small-sized KDP crystals,with less research on flatness.Due to its low surface damage and high machining efficiency,water dissolution ultraprecision continuous polishing(WDUCP)has become a good technique for processing large-sized KDP crystals.In this technique,the trajectory uniformity of water droplets can directly affect the surface quality,such as flatness and roughness.Specifically,uneven trajectory distribution of water droplets on the surface of KDP crystals derived from the mode of motion obviously affects the surface quality.In this study,the material removal mechanism of WDUCP was introduced.A simulation of the trajectory of water droplets on KDP crystals under different eccentricity modes of motion was then performed.Meanwhile,the coefficient of variation(CV)was utilized to evaluate the trajectory uniformity.Furthermore,to verify the reliability of the simulation,some experimental tests were also conducted by employing a large continuous polisher.The results showed that the CV varied from 0.67 to 2.02 under the certain eccentricity mode of motion and varied from 0.48 to 0.65 under the uncertain eccentricity mode of motion.The CV of uncertain eccentricity is always smaller than that of certain eccentricity.Hence,the uniformity of trajectory was better under uncertain eccentricity.Under the mode of motion of uncertain eccentricity,the initial surface texture of the100 mm×100 mm×10 mm KDP crystal did achieve uniform planarization.The surface root mean square roughness was reduced to 2.182 nm,and the flatness was reduced to 22.013μm.Therefore,the feasibility and validity of WDUCP for large-sized KDP crystal were verified.

Ergodicity and asymptotic stability of Feller semigroups on Polish metric spaces

We provide some sharp criteria for studying the ergodicity and asymptotic stability of general Feller semigroups on Polish metric spaces. As an application, the 2D Navier-Stokes equations with degenerate stochastic forcing will be simply revisited.