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.
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