Reflection and transmission of plasma waves at the interface of crystallites

A linearized problem of the reflection and transmission of a plasma wave at the boundary of a half-space (namely, the plane separating two crystallites) is formulated and analytically solved. The electron distribution function and the electric field inside the half-space of a degenerate plasma are found. The reflection and transmission coefficients are determined as functions of the input parameters of the problem. The longwave limit (i.e., the resonance case when the oscillation frequency of the self-consistent electric field is close to the natural (Langmuir) oscillation frequency) is analyzed.