Novo, AS; Bret, A; Fonseca, RA; Silva, LO

[Novo, A. Stockem] Ruhr Univ Bochum, Inst Theoret Phys, Lehrstuhl Weltraum & Astrophys 4, Bochum, Germany; [Bret, A.] Univ Castilla La Mancha, ETSI Ind, E-13071 Ciudad Real, Spain; [Bret, A.] Inst Invest Energet & Aplicac, E-13071 Ciudad Real, Spain; [Fonseca, R. A.; Silva, L. O.] Univ Lisbon, Inst Super Tecn, Inst Plasmas & Fusao Nucl, GoLP, P-1699 Lisbon, Portugal; [Fonseca, R. A.] Lisbon Univ Inst, ISCTE, DCTI, Lisbon, Portugal

We analyze the full shock formation process in electron-ion plasmas in theory and simulations. It is accepted that electromagnetic shocks in initially unmagnetized relativistic plasmas are triggered by filamentation instability. However, the transition from the first unstable phase to the quasi-steady shock is still missing. We derive a theoretical model for the shock formation time, taking into account filament merging in the nonlinear phase of the filamentation instability. This process is much slower than in electron-positron pair shocks, and so the shock formation is longer by a factor proportional to root m(i)/m(e) ln (m(i)/m(e)).