  We demonstrate a qualitatively new aspect of the dynamics of Gamma-Ray Burst
(GRB) fireballs: the development of a substantial dispersion in the proton
component in fireballs in which neutron decoupling occurs and is sufficiently
pronounced. This effect depends sensitively on the neutron to proton ratio in
the fireball, becoming more dramatic with increasing neutron excess. Simple
physical arguments and transport calculations indicate that the dispersion in
Lorentz factor of the protons can be of order the final mean Lorentz factor of
the fireball. We show how plasma instabilities could play an important role in
the evolution of the fireball and how they might ultimately govern the
development of such a velocity dispersion in the proton component. The role of
these instabilities in setting/diminishing a proton Lorentz factor dispersion
represents a new and potentially important venue for the study of plasma
instabilities. Significant dispersion in the proton velocities translates into
fewer protons attaining the highest Lorentz factors. This is tantamount to a
reduction in the total energy required to attain a given Lorentz factor for the
highest energy protons. As well, a proton component dispersion can have
consequences for the electromagnetic and neutrino signature of GRBs.
