We present an exact plane-wave-based analysis of the vacuum acceleration, t
o energy gradients in the TeV/m range, of a single electron, using two lase
r beams crossing at an arbitrary angle. Our analysis of the dynamics evolve
s from analytic solutions to the relativistic equations of motion and predi
cts that, for a given laser intensity, a unique crossing angle maximizes th
e energy gain due to constructive interference. (C) 2000 American Institute
of Physics. [S0003-6951(00)03134-X].