Phases of the shock formation. Two identical pair plasmas interpenetrate. The overlapping region turns unstable, and two shocks form near the border of each shell. The simulation box contains half of the system.
Integrated density in the direction normal to the flow for 3 instants of a typical shock formation simulation. The last plot shows the growth of the magnetic energy integrated over the transverse direction, and . The dashed line is the theoretical growth-rate. The initial Lorentz factor was . All the field growth plots look qualitatively the same until . The saturation time is . The field at saturation is .
Same as Fig. 2 , but using 800 particles per cell.
Growth-rate in units, in terms of for (left) and (right).
Field at saturation from the simulations (circles), compared with Eqs. (9)–(11) .
Magnetic field energy evolution for different simulation setups and . Black: piston-wall method, Red: full shock picture, Blue: periodic system of counter-streaming beams, Black dashed: theoretical growth rate. A detailed description of the models is given in the text.
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