Parameters for quantifying beam halo

Two different parameters for the quantitative description of beam halo are introduced, both based on moments of the particle distribution. One parameter is a measure of spatial halo formation and has been defined previously by Wangler and Crandall, termed the profile parameter. The second parameter relies on kinematic invariants to quantify halo formation in phase space; we call it the halo parameter. The profile parameter can be computed from experimental beam profile data. The halo parameter provides a theoretically more complete description of halo in phase space, but is difficult to obtain experimentally.