The design of a cryogenic dark matter detector based on the detection of the recoil direction of target nuclei

We discuss the design of a cryogenic detector for a WIMP dark matter search based on single crystal absorbers and using Series Arrays of Superconducting Tunnel Junctions (SASTJs). The distribution of recoil vectors of target nuclei from WIMP interactions are affected by the motion of the laboratory through the dark matter halo. The angular distribution of recoil directions is skewed due to the motion of the solar system around the galaxy and is modulated by the diurnal and annual rotation of the earth. We discuss the kinematics of the recoil events and how a directional signal might be identified in our cryogenic detectors using the fast response of SASTJs to the ballistic phonons arising in the absorber from WIMP interactions. We consider how the anisotropy of a dark matter recoil distribution can be used to place statistical limits on its component relative to the isotropic background signal. We also consider how the dark matter limit is altered if only the axis of the nuclear recoil, rather than the full recoil direction is available. We also briefly consider the effect of phonon focusing within single crystal absorbers. Focusing will modulate strongly the signal detected by the SASTJs, on the crystal surface, as the position of the interaction within the crystal varies. A comparison is made between the behaviour of phonons in strongly focusing crystals, such as Nb, Si and LiF, and their near isotropic propagation in BaF2.