Abstract
Collisionless shocks are ubiquitous in astrophysics and in the lab. Recent numerical simulations and experiments have shown how they can arise from the encounter of two collisionless plasma shells. When the shells interpenetrate, the overlapping region turns unstable, triggering the shock formation. As a first step towards a microscopic understanding of the process, we analyze here in detail the initial instability phase. On the one hand, 2D relativistic Particle-In-Cell simulations are performed where two symmetric initially cold pair plasmas collide. On the other hand, the instabilities at work are analyzed, as well as the field at saturation and the seed field which gets amplified. For mildly relativistic motions and onward, Weibel modes govern the linear phase. We derive an expression for the duration of the linear phase in good agreement with the simulations. This saturation time constitutes indeed a lower-bound for the shock formation time.
Highlights
Colliding plasma shells are present in a variety of physical settings
Astrophysical jets produced by black holes are expected to generate a shock when interacting with the interstellar medium [1, 2]
The Fireball scenario for Gamma-Rays-Bursts [3, 4] relies on shock particle acceleration [5,6,7], where the shock arises from the encounter of two ultra-relativistic plasma blobs ejected from a central engine
Summary
Colliding plasma shells are present in a variety of physical settings. Astrophysical jets produced by black holes are expected to generate a shock when interacting with the interstellar medium [1, 2]. The instabilities at play can be interpreted in terms of the homogeneous theory for such, the geometry is finite here, since our shells have one contact open boundary As it amplifies a seed field from its initial fluctuation value to saturation, the instability governs this first phase of the shock formation process for a time τs that we labeled “saturation time”. [30, 31] was conducted for counter streaming electron δ ωp v0 c Comparing this value to the growth of the field observed in the overlapping region results in a very satisfactory agreement, as evidenced on Fig. 2.
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