Fast time averaged equations are derived for the motion of particles a
nd the generation of electromagnetic wake fields under the action of t
he ponderomotive potential of an ultraintense laser pulse propagating
through a tenuous plasma. Based on these averaged equations, a new par
ticle code is designed which calculates the particle trajectories on t
he plasma period time scale. The regime of total cavitation of the pla
sma is investigated. It is found that stable propagation over a long d
istance is possible in this regime, and that energetic electrons are p
roduced with a simple characteristic dependence of their angle of defl
ection on energy. This new code allows for computationally efficient m
odeling of pulse propagation over great distances. (C) 1997 American I
nstitute of Physics.