Electron acceleration and short-wavelength radiation generation by an intense, short, linearly polarized laser pulse in an external magnetic field parallel to that of the light wave is investigated classically. It is found that enhanced electron acceleration by the laser can occur. After the pulse has passed, much of the energy gained by the electron is retained in its relativistic cyclotron motion. The electron emits radiation at high harmonics of the cyclotron frequency until the static magnetic field decays.