Self-modulation of ultra-relativistic SLAC electron and positron bunches

Long (L>>λ
_pe
) charged particle bunches traveling in dense plasmas are subject to a transverse two-stream instability, the self-modulation instability (SMI)
¹
. This instability modulates the bunch in the radial direction with a longitudinal period approximately equal to the plasma wavelength (λ
_pe
~n
_e
^1/2
). The SMI can be used to transform a long bunch into a train of short bunches that can resonantly drive wakefields to large amplitudes. An experiment known as AWAKE
²
was recently approved at CERN to drive GV/m wakefields with 400GeV, ~12cm-long proton bunches in a 10m plasma with λ
_pe
~1mm. In the linear wakefield regime, the plasma response is symmetric for positively and negatively charged bunches. However, once the nonlinear regime is approached the plasma response becomes asymmetric, leading to differences that could be evidenced using the ultra-relativistic electron and positron bunches
³
. This asymmetry makes it more difficult to accelerate positively than negatively charged particle bunches in plasmas.