Observations have shown weak interaction between dark matter clouds in collisions of galaxy clusters. Dark matter may undergo a ``dark electromagnetic'' interaction, behaving like a non-relativistic collisionless plasma of self-interacting dark matter particles. Under this hypothesis, dark matter could exhibit plasma-like instabilities with observational consequences. We investigate this interaction by simulating the collision between two e-e+ plasma slabs that mimics this "dark-electromagnetic" interaction. We use a particle-in-cell code and explore the instabilities driven by the interpenetration of two e-e+ plasma clouds. We show that in both hot and cold regimes, the clouds exhibit significant slowdown after passing through each other unless there is an extremely weak interaction. A significant slowdown due to the Weibel instability invariably slows down the clouds, yielding an extraordinary new constraint on the interaction strength compared to constraints based on collisions.
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