  Most of the rotational luminosity of a pulsar is carried away by a
relativistic magnetised wind in which the matter energy flux is negligible
compared to the Poynting flux. Near the equatorial plane of an obliquely
rotating pulsar magnetosphere, the magnetic field reverses polarity with the
pulsar period, forming a wind with oppositely directed field lines. This
structure is called a striped wind; dissipation of alternating fields in the
striped wind is the object of our study.
  The aim of this paper is to study the conditions required for magnetic energy
release at the termination shock of the striped pulsar wind. Magnetic
reconnection is considered via analytical methods and 1D relativistic PIC
simulations.
  An analytical condition on the upstream parameters for partial and full
magnetic reconnection is derived from the conservation laws of energy, momentum
and particle number density across the relativistic shock. Furthermore, by
using a 1D relativistic PIC code, we study in detail the reconnection process
at the termination shock.
  We found a very simple criterion for dissipation of alternating fields at the
termination shock, depending on the upstream parameters of the flow. 1D
relativistic PIC simulations are in agreement with our criterion.
  Thus, alternating magnetic fields annihilate easily at relativistic highly
magnetised shocks.
