  Spider pulsars are compact binary systems composed of a millisecond pulsar
and a low-mass companion. Their X-ray emission - modulated on the orbital
period - is interpreted as synchrotron radiation from high-energy electrons
accelerated at the intrabinary shock. We perform global two-dimensional
particle-in-cell simulations of the intrabinary shock, assuming that the shock
wraps around the companion star. When the pulsar spin axis is nearly aligned
with the orbital angular momentum, we find that the magnetic energy of the
relativistic pulsar wind - composed of magnetic stripes of alternating field
polarity - efficiently converts to particle energy at the intrabinary shock,
via shock-driven reconnection. The highest energy particles accelerated by
reconnection can stream ahead of the shock and be further accelerated by the
upstream motional electric field. In the downstream, further energization is
governed by stochastic interactions with the plasmoids / magnetic islands
generated by reconnection. We also extend our earlier work (Cort\'es & Sironi
2022) by performing simulations that have a larger (and more realistic)
companion size and a more strongly magnetized pulsar wind. We confirm that our
first-principles synchrotron spectra and lightcurves are in good agreement with
X-ray observations.
