  Sufficiently strong electric fields in plasmas can accelerate charged
particles to relativistic energies. In this paper we describe the dynamics of
positrons accelerated in such electric fields, and calculate the fraction of
created positrons that become runaway accelerated, along with the amount of
radiation that they emit. We derive an analytical formula that shows the
relative importance of the different positron production processes, and show
that above a certain threshold electric field the pair production by photons is
lower than that by collisions. We furthermore present analytical and numerical
solutions to the positron kinetic equation; these are applied to calculate the
fraction of positrons that become accelerated or thermalized, which enters into
rate equations that describe the evolution of the density of the slow and fast
positron populations. Finally, to indicate operational parameters required for
positron detection during runaway in tokamak discharges, we give expressions
for the parameter dependencies of detected annihilation radiation compared to
bremsstrahlung detected at an angle perpendicular to the direction of runaway
acceleration. Using the full leading order pair production cross section, we
demonstrate that previous related work has overestimated the collisional pair
production by at least a factor of four.
