Proton driven plasma wakefield generation in a parabolic plasma channel

An analytical model for the interaction ofcharged particle beams and plasma for a wakefield generationin a parabolic plasma channel is presented. In thesuggested model, the plasma density profile has a minimumvalue on the propagation axis. A Gaussian proton beam isemployed to excite the plasma wakefield in the channel.While previous works investigated on the simulationresults and on the perturbation techniques in case of laserwakefield accelerations for a parabolic channel, we havecarried out an analytical model and solved the acceleratingfield equation for proton beam in a parabolic plasmachannel. The solution is expressed by Whittaker (hypergeometric)functions. Effects of plasma channel radius,proton bunch parameters and plasma parameters on theaccelerating processes of proton driven plasma wakefieldacceleration are studied. Results show that the higheraccelerating fields could be generated in the PWFAscheme with modest reductions in the bunch size. Also, themodest increment in plasma channel radius is needed toobtain maximum accelerating gradient. In addition, thesimulations of longitudinal and total radial wakefield inparabolic plasma channel are presented using LCODE. It isobserved that the longitudinal wakefield generated by thebunch decreases with the distance behind the bunch whiletotal radial wakefield increases with the distance behind thebunch.