  Bow shock pulsar wind nebulae are a large class of non-thermal synchrotron
sources associated to old pulsars, that have emerged from their parent
supernova remnant and are directly interacting with the interstellar medium.
Within this class a few objects show extended X-ray features, generally
referred as "jets", that defies all the expectations from the canonical MHD
models, being strongly misaligned respect to the pulsar direction of motion. It
has been suggested that these jets might originate from high energy particles
that escape from the system. Here we investigate this possibility, computing
particle trajectories on top of a 3D relativistic MHD model of the flow and
magnetic field structure, and we show not only that beamed escape is possible,
but that it can easily be asymmetric and charge separated, which as we will
discuss are important aspects to explain known objects.
