Self-consistent model of the global structure of axially-symmetric pulsar magnetosphere in massless approximation

Abstract

The model of the pulsar magnetosphere filled with massless charged particles (rest massm=0) is considered. Such a representation is valid in the case, when e Ф ≫mc ², where Ф is a characteristic potential difference in the pulsar magnetosphere. This inequality takes place almost everywhere in the pulsar magnetosphere. The gas of charged massless particles can be found in two different phases: (1) dynamical phase (DP), when the particles move with nonvanishing energy ε along some base lines, determined by the electromagnetic field only, (2) statical phase (SP), when the particles have vanishing energy ε=0. Even in the simplest axially-symmetric case the pulsar magnetosphere occurs to be divided into regions of different types: (a) the accelerating regions (DP-regions), containing only DP, (b) the capture regions, containing only SP, (c) leaky capture regions, where DP moves through SP. The leaky capture regions are the active regions, which are responsible for the pulsar radio-emission, In the paper the mathematical technique of the massless approximation has been developed. The properties of the capture region has been investigated. The problem of axially-symmetric pulsar magnetosphere has been stated mathematically. The massless approximation permits to substitute some differential equations by the algebraic ones, and to simplify the statement of the problem.