Design Considerations for Permenant Magnetic Quadrupole Triplet for Matching Into Laser Driven Wake Field Acceleration Experiment at SINBAD

SINBAD (Short and INnovative Bunches and Accelerators at DESY) facility aims to produce ultrashort bunches (sub-fs) at ~100 MeV, suitable for injection into novel accelerators e.g. dielectric Laser acceleration (DLA) and Laser Driven Wakefield acceleration (LWFA). The LWFA experiment demands β functions to be of the order of 1 mm to reduce energy spreads and emittance growth from nonlinearities. Matching such a space charge dominated beam to such constraints with conventional electromagnets is challenging. A Permanent Magnetic Quadrupole (PMQ) triplet is one promising focusing strategy. In this paper, we investigate the performance of a PMQ triplet to fit the requirements of the electron beam properties in a plasma cell and discuss the realizable phase spaces for the LWFA experiment planned at SINBAD