Current flow and pair creation at low altitude in rotation-powered pulsars’ force-free magnetospheres: space charge limited flow

Abstract

We report the results of an investigation of particle acceleration and electron-positron plasma generation at low altitude in the polar magnetic flux tubes of Rotation Powered Pulsars, when the stellar surface is free to emit whatever charges and currents are demanded by the forcefree magnetosphere. We apply a new 1D hybrid plasma simulation code to the dynamical problem, using Particle-in-Cell methods for the dynamics of the charged particles, including a determination of the collective electrostatic fluctuations in the plasma, combined with a Monte-Carlo treatment of the high energy gamma rays that mediate the formation of the electron-positron pairs. We assume the electric current flowing through the pair creation zone is fixed by the much higher inductance magnetosphere, and adopt the results of force-free magnetosphere models to provide the currents which must be carried by the accelerator. The models are spatially 1D, designed to explore the physics, although of practical relevance to young, high voltage pulsars.We observe novel behavior. a) When the current density j is less than the Goldreich-Julian value (0 < j/ j GJ < 1), space charge limited acceleration of the current carrying beam is mild, with the full Goldreich-Julian charge density being comprised of the charge density of the beam, co-existing with a cloud of electrically trapped particles with the same sign of charge as the beam. The voltage drops are on the order of mc 2 /e, and pair creation is absent. b) When the current density exceeds the Goldreich-Julian value ( j/ j GJ > 1), the system develops high voltage drops (TV or greater), causing emission of curvature gamma rays and intense bursts of pair creation. The bursts exhibit limit cycle behavior, with characteristic time scales somewhat longer than the relativistic fly-by time over distances comparable to the polar cap diameter (microseconds). c) In return current regions, where j/ j GJ < 0, the system develops similar bursts of pair creation. These discharges are similar to those encountered in previous calculations of pair creation when the surface has a high work function and cannot freely emit charge, Timokhin (2010). In cases b) and c), the intermittently generated pairs allow the system to simultaneously carry the magnetospherically prescribed currents and adjust the charge density and average electric field to force-free conditions. We also elucidate the conditions for pair creating beam flow to be steady (stationary with small fluctuations in the rotating frame), finding that such steady flows can occupy only a small fraction of the current density parameter space exhibited by the force-free magnetospheric model. The generic polar flow dynamics and pair creation is strongly time dependent. The model has an essential difference from almost all previous quantitative studies, in that we sought the accelerating voltage (with pair creation, when the voltage drops are sufficiently large; without, when they are small) as a function of the applied current.The 1D results described here char...

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