Abstract
A plasma flow behind a relativistic electron bunch propagating through a cold plasma is found assuming that the transverse and longitudinal dimensions of the bunch are small and the bunch can be treated as a point charge. In addition, the bunch charge is assumed small. A simplified system of equations for the plasma electrons is derived and it is shown that, through a simple rescaling of variables, the bunch charge can be eliminated from the equations. These equations have a unique solution, with an ion cavity formed behind the driver. The equations are solved numerically and the scaling of the cavity dimensions with the driver charge is obtained. A numerical solution for the case of a positively charged driver is also found.
Highlights
Over the past two decades, plasma wakefield acceleration (PWFA) has demonstrated record accelerating gradients and high efficiency in a series of experiments that used short bunches of relativistic electrons focused to a small spot size in plasma [1,2]
Other, modern experiments the acceleration occurs in a highly nonlinear “blowout” regime [3] produced by a dense driver bunch—the regime that considerably differs from the original linear model of acceleration studied in the pioneering papers on PWFA [4,5,6]
While linearized plasma equations have led to a fully analytical treatment of the problem in Refs. [4,5,6], not much can be done analytically for a highly nonlinear plasma flow in the blowout regime
Summary
We study propagation of a relativistic electron bunch through a cold plasma assuming that the transverse and longitudinal dimensions of the bunch are much smaller than the plasma collisionless skin depth. Treating the bunch as a point charge and assuming that its charge is small, we derive a simplified system of equations for the plasma electrons and show that, through a simple rescaling of variables, the bunch charge can be eliminated from the equations. The equations demonstrate an ion cavity formed behind the driver. They are solved numerically and the scaling of the cavity parameters with the driver charge is obtained. A numerical solution for the case of a positively charged driver is found
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