Asymmetric wakes and hosing theory in PWFA

In PWFA and LWFA experiments, the wakefields are generally made by asymmetric beams and the beams may have some transverse offset or tilt. Yet little theoretical work has been done in understanding wake structures in these scenarios. Here, we will investigate using 3D QuickPIC simulations the wake structure excited by particle beams (a two-bunch PWFA scenario) where there is transverse spot size asymmetry in the drive or witness beam, or where the witness beam has some offset or tilt with respect to the drive beam. In the back of the nonlinear wake, i.e., bubble, where the witness bunch experiences the highest acceleration, there may be severe hosing. In this regime, we modify the non-linear hosing equations where some of the original assumptions break down. An alternative derivation for these equations using an azimuthal mode expansion may be discussed.