On the electric field screening by electron-positron pairs in a pulsar magnetosphere

Abstract

We present a steady one‐dimensional model for a pulsar polar cap accelerator, where the field‐aligned electric field and flow are solved self‐consistently with a given current density. It is assumed that no particles return to the star. It is known that the space‐charge‐limited flow is accelerated to energies high enough to create electron–positron pairs if the assumed current density is high enough. We find that when pairs are created in such a space‐charge‐limited flow, the accelerating electric field is screened out within a short distance after pair creation, if the pair particle flux is larger than a critical value. We also find that a space charge density wave is excited in the screening region. We find that a pair flux larger than the critical value Mc=103–105 must be reached in a layer with thickness equal to the braking distance for the decelerating component. Therefore, the required multiplicity – the number of pairs created by one primary particle – is too large to be realized in the actual pulsar magnetosphere. We suggest that in order to obtain a localized potential drop along the polar cap magnetic flux, one needs to take into account additional effects such as wave–particle interaction or quasi‐periodic pair creation.

Large‐Amplitude, Pair‐creating Oscillations in Pulsar and Black Hole Magnetospheres

“…In our final example, we take the initial gap structure to be as in the model considered by Shibata et al (1998). To be more precise, the initial electric field is given byẼ k (s; t ¼ 0) ¼ s(1 À s/s 0 ) for s s 0 and E k ¼ 0 for s > s 0 (see Fig.…”

“…Reflecting secondaries ( positrons if the primaries are electrons) provide a net quasistatic charge density, such that the PFF may be regarded as a thin surface with a surface charge density. The resulting additional electrostatic field screens out the initial E k above the PFF (e.g., Fawley et al 1977;Arons & Scharlemann 1979;Shibata et al 1998). In some pulsar models pairs are also assumed to be produced in an ''outer gap'' (Cheng et al 1986), and current conservation can be achieved by the currents through the inner and outer gaps being part of a global circuit (Shibata 1991).…”

“…In some pulsar models pairs are also assumed to be produced in an ''outer gap'' (Cheng et al 1986), and current conservation can be achieved by the currents through the inner and outer gaps being part of a global circuit (Shibata 1991). More recent models differ quantitatively, rather than qualitatively, from earlier models in that the Lorentz factors of the secondary pairs are smaller (Zhang & Harding 2000;Hibschman & Arons 2001;Arendt & Eilek 2002) and the pair creation is over a more extensive region, with the heights of the inner and outer gaps perhaps overlapping (Shibata et al 2002). Despite extensive studies of such models, it remains unclear how and where the radio emission is generated.…”

“…Suppose that E k accelerates electrons upward, so that it accelerates secondary positrons downward. Steady state models that assume the screening of E k above the PFF to be sufficient to prevent reflection of secondary positrons (Shibata et al 1998) require such implausibly large densities that they seem untenable. When trapped positrons are properly accounted for, a steady state solution can be obtained, under certain conditions, in which the number of reflected positrons is small and does not lead to a disruption of the primary electron beam (Arons & Scharlemann 1979;Arons 1981).…”

Theory of pulsar magnetosphere and wind

“…Screening implies an abundance of electron/positron pairs not restricted by any microphysics but only by the requirement to cancel the E component. However, exact electric field screening in the polar caps has been challenged by Shibata, Miyazaki & Takahara (1998 where n represents the quantum number characterising the excitation degree of the level and s = ±1/2 symbolises the electron spin (Daugherty & Ventura 1978). All energy levels are degenerated with an arbitrary choice of spin except for the fundamental level n = 0 for which s = −1/2.…”