Radial equilibrium of relativistic particle bunches in plasma wakefield accelerators

Drive particle beams in linear or weakly nonlinear regimes of the plasma wakefield accelerator quickly reach a radial equilibrium with the wakefield, which is described in detail for the first time. The equilibrium beam state and self-consistent wakefields are obtained by combining analytical relationships, numerical integration, and first-principles simulations. In the equilibrium state, the beam density is strongly peaked near the axis, the beam radius is constant along most of the beam, and longitudinal variation of the focusing strength is balanced by varying beam emittance. The transverse momentum distribution of beam particles depends on the observation radius and is neither separable nor Gaussian.