  The zeta function regularization technique is used to study the finite
temperature Casimir effect for a massless Majorana fermion field confined
between parallel plates and satisfying bag boundary conditions. A magnetic
field perpendicular to the plates is included. An expression for the zeta
function is obtained, which is exact to all orders in the magnetic field
strength, temperature and plate distance. The zeta function is used to
calculate the Helmholtz free energy of the Majorana field and the pressure on
the plates, in the case of weak magnetic field and strong magnetic field. In
both cases, simple analytic expressions are obtained for the free energy and
pressure which are very accurate and valid for all values of the temperature
and plate distance.
