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

A model of a pulsar magnetosphere filled with massless charged particles (rest mass m = 0) is considered. Such representation is valid in the case, when e Phi is much greater than mc-squared, where Phi 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) a dynamical phase (DP), when the particles move with nonvanishing energy epsilon along some base lines, determined by the electromagnetic field only; and (2) a static phase (SP), when the particles have vanishing energy epsilon = 0. Even in the simplest axially-symmetric case the pulsar magnetosphere occurs to be divided into regions of different types: (1) the accelerating regions (DP-regions), containing only DP; (2) the capture regions, containing only SP; and (3) 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 have been investigated. The problem of an axially-symmetric pulsar magnetosphere has been stated mathematically. The massless approximation permits differential equations to be substituted by the algebraic ones, and the statement of the problem to be simplified. (Author)