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

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 M-c= 10(3)-10(5) 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.