On the internal structure of the current sheet in the pulsar wind

TL;DR

This paper models the internal structure of the pulsar wind's current sheet using force-free and two-fluid MHD approximations, providing new analytical solutions and insights into particle acceleration and sheet dynamics.

Contribution

It presents the first analytical asymptotic solution for the current sheet structure in pulsar winds and analyzes time-dependent effects and particle acceleration within the sheet.

Findings

Derived general asymptotic solution for the Grad-Shafranov equation.

Determined the shape of the current sheet independent of latitudinal magnetic field structure.

Estimated the efficiency of particle acceleration inside the current sheet.

Abstract

We investigate the internal structure of the current sheet in the pulsar wind within force-free and two-fluid MHD approximations. Within the force-free approximation we obtain general asymptotic solution of the Grad-Shafranov equation for quasi-spherical pulsar wind up to the second order in small parameter $\varepsilon = (\Omega r/c)^{-1}$. The solution allows an arbitrary latitudinal structure of the radial magnetic field, including that obtained in the numerical simulations of oblique rotators. It is also shown that the shape of the current sheet does not depend on the latitudinal structure. For the internal region of the current sheet outside the fast magnetosonic surface where the force-free approximation is not valid we use two-fluid MHD approximation. Carrying out calculations in the comoving reference frame we succeed in determining intrinsic electric and magnetic fields of a sheet. It allows us to analyze time-dependent effects which were not investigated up to now. In particular, we estimate the efficiency of the particle acceleration inside the sheet. Finally, after investigating the motion of individual particles in the time-dependent current sheet, we find self-consistently the width of the sheet and its time evolution.