Effect of beam emittance on self-modulation of long beams in plasma wakefield accelerators

Abstract

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 selfmodulation 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.

Path to AWAKE: Evolution of the concept

“…At low energies (24 GeV), the excited fields turn out to be much lower because of the quick emittance-driven blowup of the beam radius [47,50]. Therefore the SPS proton beam was chosen.…”

Stable bunch trains for plasma wakefield acceleration

“…This is only possible if each bunch resides in the focusing phase of the plasma wave. The bunch train produced by SSM is stable and focused everywhere [15,19], if the self-modulation develops in a longitudinally nonuniform plasma with a ramped-up density [20]. However, the equidistant bunch train produced with conventional techniques is not.…”

Multi-proton bunch driven hollow plasma wakefield acceleration in the nonlinear regime

“…The transverse wakefield of the beam leads to rippling of the beam itself, which further amplifies the plasma waves. Because of this positive feedback, the long proton bunch transforms into a train of micro-bunches that follow equidistantly at the plasma wavelength [19][20][21] . With proper seeding, the axisymmetric mode develops quickly and suppresses destructible non-axisymmetric modes like the hosing instability [22][23][24] .…”