  Transverse ionization cooling of muons is modeled as a Brownian motion of the
muon beam as it traverses a Li or Be rod. A Langevin like equation is written
for the free particle case (no external transverse magnetic field) and for the
case of a harmonically bound beam in the presence of a focusing magnetic field.
We demonstrate that the well known muon cooling equations for short-absorbers
can be extrapolated to the useful case of a long absorber rod with a focusing
magnetic field present.
