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 in 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 suppressed by a factor of two 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. (C) 2015 AIP Publishing LLC.
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