  The initial beam emittance determines the maximum wakefield amplitude that
can be reached as a result of beam self-modulation in the plasma. The wakefield
excited by the fully self-modulated beam decreases linearly with the increase
of the beam emittance. There is a value of initial emittance beyond which the
self-modulation does not develop even if the instability is initiated by a
strong seed perturbation. The emittance scale at which the wakefield is twice
suppressed with respect to the zero-emittance case (the so called critical
emittance) is determined by inability of the excited wave to confine beam
particles radially and is related to beam and plasma parameters by a simple
formula. The effect of beam emittance can be observed in several discussed
self-modulation experiments.
