High gradient limits due to single bunch beam breakup in a collinear dielectric wakefield accelerator

A study into the maximum acceleration gradient, E-z(max), in a collinear dielectric wakefield accelerator due to single bunch beam breakup (SBBU) is presented. The longitudinal wakefield is proportional to charge over radius squared (E-z similar to Q/a(2)) which implies small a is favorable for fixed Q. However, when the transverse wakefield (E-perpendicular to similar to Q/a(3)) is also considered then the SBBU instability severely limits the charge that can pass through a long structure as required for a large transfer of energy from the drive bunch to the witness bunch and hence limits the sustained acceleration that can be obtained.