Transient effects in the plasma-wake-field acceleration scheme

We reformulate the theory of the acceleration of charged particles in the recently proposed plasma-wake-field acceleration scheme. Our treatment makes manifest the transient effects. To illustrate, we consider a point-charge driving beam traversing a semi-infinite plasma. We show that it takes a few plasma wavelengths for transient effects to dissipate and give the wake-field solutions currently discussed in the literature. Thus our treatment provides needed justification for the existing theoretical discussions since they neglect transient effects.