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We study with a two-dimensional particle-in-cell simulation the stability ofa discontinuity or piston, which separates an electron-positron cloud from acooler electron-proton plasma. Such a piston might be present in therelativistic jets of accreting black holes separating the jet material from thesurrounding ambient plasma and when pair clouds form during an X-ray flare andexpand into the plasma of the accretion disk corona. We inject a pair plasma ata simulation boundary with a mildly relativistic temperature and mean speed. Itflows across a spatially uniform electron-proton plasma, which is permeated bya background magnetic field. The magnetic field is aligned with one simulationdirection and oriented orthogonally to the mean velocity vector of the paircloud. The expanding pair cloud expels the magnetic field and piles it up atits front. It is amplified to a value large enough to trap ambient electrons.The current of the trapped electrons, which are carried with the expandingcloud front, drives an electric field that accelerates protons. A solitary wavegrows and changes into a piston after it saturated. Our simulations show thatthis piston undergoes a collision-less instability similar to a Rayleigh-Taylorinstability. The undular mode grows and we observe fingers in the protondensity distribution. The effect of the instability is to deform the piston butit cannot destroy it.

Collisionless Rayleigh-Taylor-like instability of the boundary between a hot pair plasma and an electron-proton plasma: the undular mode