  We calculate the first order maximal acceleration corrections to the
classical electrodynamics of a particle in external electromagnetic fields.
These include additional dissipation terms, the presence of a critical electric
field, a correction to the cyclotron frequency of an electron in a constant
magnetic field and the power radiated by the particle. The electric effects are
sizeble at the fields that are considered attainable with ultrashort $TW$ laser
pulses on plasmas.
