  Josephson current between two one-dimensional nanowires with proximity
induced $p$-wave superconducting pairing is calculated in the presence of
Rashba spin-orbit interaction, in-plane and normal magnetic fields. We show
that Andreev retro-tunneling is realized by means of three channels. The main
contribution to the Josephson current gives a scattering in a conventional
particle-hole channel, when an electron-like quasiparticle reflects to a
hole-like quasiparticle with opposite spin yielding a current which depends
only on the order parameters' phase differences $\varphi$ and oscillates with
$4\pi$ period. Second anomalous particle-hole channel, corresponding to the
Andreev reflection of an incident electron-like quasiparticle to an hole-like
quasiparticle with the same spin orientation, survives only in the presence of
the in-plane magnetic field. The contribution of this channel to the Josephson
current oscillates with $4\pi$ period not only with $\varphi$ but also with
orientational angle of the in-plane magnetic field $\theta$ resulting in a
magneto-Josephson effect. Third anomalous particle-particle channel, which
represents a reflection of an electron-like (hole-like) quasiparticle to a
electron-like (hole-like) quasiparticle with opposite spin-orientation,
oscillates only with the in-plane magnetic field orientation angle $\theta$. We
present a detailed theoretical analysis of both DC and AC Josephson effects in
such a system showing contributions from all these channels and discuss
experiments which can test our theory.
