  The Fermi acceleration model was introduced to describe how cosmic ray
particles are accelerated to great speeds by interacting with moving magnetic
fields. We identify a new variation of the model where light ions interact with
a moving wall while undergoing pitch angle scattering through Coulomb
collisions due to the presence of a heavier ionic species. The collisions
introduce a stochastic component which adds complexity to the particle
acceleration profile and sets it apart from collisionless Fermi acceleration
models. The unusual effect captured by this simplified variation of Fermi
acceleration is the non-conservation of phase space, with the possibility for a
distribution of particles initially monotonically decreasing in energy to
exhibit an energy peak upon compression. A peaked energy distribution might
have interesting applications, such as to optimize fusion reactivity or to
characterize astrophysical phenomena that exhibit non-thermal features.
