A fully relativistic local dispersion relation for whistler waves has been solved at closely spaced points along the magnetic field lines of a 2:1 magnetic mirror in which a highly anisotropic, spatially inhomogeneous, hot‐electron plasma is confined. The limiting plasma parameters for convective (spatial) growth have been determined numerically and used to identify plasma conditions leading to maximum amplification of input microwave signals introduced in the form of whistler waves. The maximum gain has been evaluated numerically for a range of values of the hot‐electron plasma within which all major stability criteria are satisfied. Very high gains (∼40 dB) are indicated over the entire range of beta investigated.