Possible re-acceleration regions above the inner gap and pulsar gamma-ray emission

We propose that the violent breakdown of the RudermanSutherland type vacuum gap above the pulsar polar cap region may produce copious primary particles and make the charge density above the gap in excess of the Goldreich-Julian density. Such an excess residue of charge density may arise some re-acceleration regions above the gap due to the space-charge-limited flow mechanism. Such re-acceleration regions, if exist, may accelerate particles to carry away more spin-down energy, and may have some implications for pulsar γ-ray emission. Much has been done to investigate the formation of pulsar inner accelerators near the polar cap region (Ruderman & Sutherland 1975 [RS75]; Arons & Scharlemann 1979; Harding & Muslimov 1998) via various charge deficit mechanisms. Here we propose another possible particle acceleration mechanism in the pulsar inner magnetospheres via a charge excess mechanism. The violent breakdown of the vacuum gap (RS75) may produce extra charges to make the charge density above the gap deviated from the Goldreich-Julian (1969) density, so that the space-charge-limited flow mechanism may result in one or more re-acceleration regions above the gap. Basic idea of the re-acceleration regions Above the gap, the secondaries do not contribute to the pure charge density, so the net contribution of ρ is just the primary charge density. In the previous polar cap acceleration models (RS75; Arons & Scharlemann 1979; Harding & Muslimov 1998), it is assumed that E‖ is completely screened. However, a complete screening of the field requires both E‖ = 0 and dE‖/dz = 0 to be achieved. This is only assumed in the previous models. In reality, both conditions can not be achieved simultaneously at the very beginning, and there must be some oscillation and relaxation processes to readjust ρ and E‖ to achieve final screening. In principle, such a detailed process should be investigated explicitly. Here we present our first attempt to treat such a complicated process within the framework of the vacuum gap model (RS75). We argue that the charge density ρ of the primary particles flowing out from the gap could be considerably in excess of ρgj if the breakdown is very violent, e.g. ρ = ξρgj with ξ > 1. In the near surface regime (RS75), Poisson equation could be approximately treated as one-dimensional, i.e. dE‖/dz = 4π(ρ − ρgj). Within the gap, since ρ = 0, and ρgj > 0, the E‖ gradient is negative, and E‖ ' (2ΩB/c)(h− z) (RS75). Above the gap, the possible excess of the charge density (ρ > ρgj) actually changes the sign of the E‖