Time-dependent pair cascades in magnetospheres of neutron stars - I. Dynamics of the polar cap cascade with no particle supply from the neutron star surface

Abstract

I argue that the problem of electromagnetically driven electron–positron cascades in magnetospheres of neutron stars must be addressed starting from first principles. I describe a general numerical algorithm for doing self‐consistent kinetic simulations of electron–positron cascades – wherein particle acceleration, pair creation and screening of the electric field are calculated simultaneously – and apply it to model the Ruderman & Sutherland cascade in one dimension. I find that pair creation is quite regular and quasi‐periodic. In each cycle a blob of ultra‐relativistic electron–positron plasma is generated; it propagates into the magnetosphere leaving a tail of less relativistic plasma behind, and the next discharge occurs when this mildly relativistic plasma leaves the polar cap. A short burst of pair formation is followed by a longer quiet phase when accelerating electric field is screened and no pairs are produced. Some of freshly injected electron–positrons pairs get trapped in plasma oscillations creating a population of low‐energy particles. The cascade easily adjusts to the current density required by the pulsar magnetosphere by reversing some of the low‐energy particles. Each discharge generates a strong coherent superluminal electrostatic wave, which may be relevant for the problem of pulsar radioemission.

Two modes of partially screened gap

“…The calculations took into account particle acceleration, pair creation and screening of the electric field by newly created pairs. Timokhin (2010) found that the backstreaming particles would be responsible for heating of the polar cap to temperature T s ∼ 4 × 10 6 f −0.25 K, where (R dp /c) f is the time between two successive discharges. According to the calculations of the cohesive energy (Medin & Lai 2007) for such a high temper- (c) Figure 9.…”

“…In the accompanying paper (Szary et al 2014a) we apply the PSG model to explain the radio emission of magnetars. Timokhin (2010) applied the model of Ruderman & Sutherland (1975) to one dimensional self-consistent kinetic simulations of electron-positron cascades. The calculations took into account particle acceleration, pair creation and screening of the electric field by newly created pairs.…”

Gamma-ray pulsars: A gold mine

“…These steady-state cascades yield pair multiplicities up to 10 4 [73] that are a strong function of pulsar period and surface magnetic-field strength. However, recent studies of time-dependent polar-cap pair cascades [149,150] . Pplar view of the current density distributions (current density j relative to the Goldreich-Julian current density jGJ) on the polar cap in a force-free magnetosphere for different pulsar inclination angles α B .…”

Scenarios for Ultrafast Gamma-Ray Variability in AGN

“…However, the process of the pair creation is expected to be highly non-stationary (see, e.g., Levinson et al 2005;Timokhin 2010 for theoretic and numerical considerations of the pair creation in vacuum gaps, respectively), thus even if anelectric-field-free state of themagnetosphere is possible, it cannot be stable (Sturrock 1971). The gaps, i.e., regions in whichthe charge density isnot sufficient for the electric field screening, may appear sporadically in the magnetosphere, for example, in the vicinity of the stagnation surface, i.e., at the boundary that separates acretion and ejection trends in the flow.…”