  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-principle simulations. In the equilibrium
state, the beam density is strongly peaked near the axis, the beam radius is
constant along 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.
