1 New runs

All runs have μ_{50} = 10^{6}, λ̃^{1/2} = 7 × 10^{11}, and ν = η = D = 5 × 10^{−8}. Thus, we have

v_{λ} = μ_{50}/λ^{1/2} = 1.4 × 10^{−6},  (1)

and

v_{μ} = μ_{50}η = 5 × 10^{−2},  (2)

corresponding to regime II.

 Figure 1: pcomp_D512_1e5_1e6_49e22_5em8a4

The difference between the four runs is the minimum wavenumber, k_{1}, available in the simulations (ideally, it should be → 0). Figure 1 shows the time traces for those runs. They are all reasonably similar, except for h_{rms} and E_{GW}^{sat}, which drop significantly for large k_{1}.

The chiral chemical potential drops rapidly when the linear phase of the chiral plasma instability is over (t ≈ 1.001). It then levels off near 10^{5}, which

Table 1:

k_{1}  E_{M}^{max}  E_{GW}^{sat}  color
5 × 10^{3} 4.7 × 10^{−13} 1.9 × 10^{−37} black
10^{4}  4.9 × 10^{−13} 1.7 × 10^{−38} red
2 × 10^{4} 4.9 × 10^{−13} 3.4 × 10^{−39} orange
10^{5}  5.0 × 10^{−13} 1.0 × 10^{−41} blue

                                                       Figure 2: EEGW_vs_EEKM

corresponds to the wavenumber where the magnetic energy spectra peak; see below.

Figure 2 compares E_{M}^{max} and E_{GW}^{sat} with those of earlier runs. The efficiency of GW production is very low.

                                            Figure 3:  pspec_sat_D512_1e5_1e6_49e22_
                                            5em8a4_k5e3

Figure 3 compares magnetic and GW energy spectra. As found in our 2021 paper, the GW energy spectra don’t capture the lowest wavenumber and therefore the GW energies are not converged.

2 Next?

It would be useful to have a model of how μ_{5} builds up.