e^- e⁺ plasma-dark electromagnetism similarity establishes a (nearly) weaker-than-gravity bound on long-range dark matter self-interactions

Dark matter (DM) has been theorized to be charged under its own ``dark electromagnetism" (DEM). Under this hypothesis, DM can behave like a cold collisionless plasma of self-interacting DM particles, and exhibit plasma-like instabilities with observational consequences [1]. Using PIC simulations [2], the nonlinear evolution of such instabilities driven by the interpenetration of two e<sup>-</sup> e<sup>+</sup> plasma clouds that mimic the ``dark plasma" are explored. We show that the clouds slow down due to both oblique and Weibel generated electromagnetic fields, which deflect the particle trajectories, transferring bulk forward momentum into transverse momentum and thermal velocity spread. This process causes the flow velocity (v_fl) to decrease by a factor of √3 in a time interval Δt ω_p∼1/√α (c/v_fl), close to 10 × the instability growth time, where α is the equipartition parameter determined by the non-linear saturation of the instabilities, and ω_p is the plasma frequency. We show that if the typical DM slab length L > v_fl Δt, this slowdown is always expected. Comparison with astronomical observations reveals strong new constraints on DEM with the dark electromagnetic self-interaction Δα_D < 4 × 10^-25. [1] Heikinheimo et. al PRB 749 7 (2015) [2] Fonseca et al., PPCF 50, 124034 (2008)