## Publica

Hier finden Sie wissenschaftliche Publikationen aus den Fraunhofer-Instituten. # Contribution to the theory of surface deformation on light valve control layers

**Abstract**

An analytical method is developed for the determination of the deformation of a viscous fluid in a vacuum tube being scanned by an electron beam. Assuming a sinusoidal surface charge pattern, the resulting electrostatic boundary value problem is solved and the electrostatic forces are thereby determined. Assuming again a sinusoidal surface deformation and using the linearized Navier-Stokes differential equation, the resulting hydrodynamic boundary value problem is solved. In steady state conditions between electrostatic and hydrodynamic forces, closed-form expressions are obtained for the deformation, the dependence of which on system parameters are shown in diagrams.