Plasma wakefield acceleration

A driver excites charge-density oscillations in a plasma whose longitudinal electric field transfers energy to a trailing witness beam. Density fixes a characteristic plasma frequency and wavelength, while driver shape and loading determine the actual field and transfer efficiency.

A full pulse duration of roughly half a plasma period and a Gaussian rms duration of order the inverse plasma frequency are different conventions for a short resonant driver. Numerical estimates should state which width is meant. Maximum cold-wave fields also need not be produced by a specified driver with normalized amplitude below unity.

The cold nonrelativistic plasma field scale $E_0=m_{e}c{\omega }_p/e$. It provides an order-of-magnitude density-gradient relation, not a complete nonlinear or relativistic wave-breaking criterion.

The ratio of the witness accelerating field to the driver decelerating field, with peak or loaded-field conventions stated. Under ideal common-length depletion, it also relates witness energy gain to driver energy loss.