  The finite temperature Casimir effect for a charged, massive scalar field
confined between very large, perfectly conducting parallel plates is studied
using the zeta function regularization technique. The scalar field satisfies
Dirichlet boundary conditions at the plates and a magnetic field perpendicular
to the plates is present. Four equivalent expressions for the zeta function are
obtained, which are exact to all orders in the magnetic field strength,
temperature, scalar field mass, and plate distance. The zeta function is used
to calculate the Helmholtz free energy of the scalar field and the Casimir
pressure on the plates, in the case of high temperature, small plate distance,
strong magnetic field and large scalar mass. In all cases, simple analytic
expressions of the zeta function, free energy and pressure are obtained, which
are very accurate and valid for practically all values of temperature, plate
distance, magnetic field and mass.
