Table 1.
Synopsis of the relevant numerical and physical parameters underlying the PIC simulations.
| Sim. | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| no. | γb | ρ0 | ρ1 | L [Δ] | N0 | N1 | rn | Γ/ωp | ωi, max, sim/ωp | Δωr/ωr | |
| 1 | 26 | 1 | 1 | 104 | 104 | 260 | 0.001 | (5.1 ± 0.5) × 10−4 | (8.7 ± 0.2) × 10−4 | 0.12 ± 0.02 | |
| 2 | 60 | 1 | 1 | 104 | 104 | 600 | 0.001 | (9.6 ± 0.6) × 10−4 | (1.28 ± 0.09) × 10−3 | 0.09 ± 0.02 | |
| 3 | 103 | 1 | 1 | 104 | 104 | 1030 | 0.001 | (1.07 ± 0.04) × 10−3 | (1.34 ± 0.02) × 10−3 | 0.09 ± 0.01 | |
| 4 | 26 | 1 | 1 | 105 | 103 | 1000 | 0.0385 | (3.68 ± 0.03) × 10−3 | (5.24 ± 0.22) × 10−3 | 0.38 ± 0.06 | |
| 5 | 60 | 1 | 1 | 105 | 103 | 1000 | 0.0167 | (3.72 ± 0.09) × 10−3 | (4.61 ± 0.06) × 10−3 | 0.29 ± 0.02 | |
| 6 | 103 | 1 | 1 | 105 | 103 | 1000 | 0.00971 | (2.80 ± 0.02) × 10−3 | (3.40 ± 0.08) × 10−3 | 0.23 ± 0.04 | |
| 7 | 26 | 1 | 10 | 104 | 104 | 260 | 0.001 | (2.76 ± 0.04) × 10−3 | (3.18 ± 0.06) × 10−3 | 0.17 ± 0.03 | |
| 8 | 26 | 1 | 100 | 104 | 104 | 260 | 0.001 | (3.31 ± 0.06) × 10−3 | (3.54 ± 0.09) × 10−3 | 0.19 ± 0.06 | |
| 9 | 26 | 10 | 10 | 104 | 104 | 260 | 0.001 | (7.16 ± 0.07) × 10−3 | (6.83 ± 0.05) × 10−3 | 0.08 ± 0.02 | |
| 10 | 26 | 100 | 100 | 104 | 104 | 260 | 0.001 | (7.02 ± 0.07) × 10−3 | (6.15 ± 0.04) × 10−3 | 0.09 ± 0.04 | |
| 11 | 26 | 10 | 1 | 104 | 104 | 260 | 0.001 | (4.28 ± 0.06) × 10−3 | (4.43 ± 0.06) × 10−3 | 0.07 ± 0.01 | |
| 12 | 26 | 100 | 1 | 104 | 104 | 260 | 0.001 | (5.10 ± 0.06) × 10−3 | (5.39 ± 0.06) × 10−3 | 0.11 ± 0.05 | |
| 13 | 26 | 1 | 1 | 104 | 103 | 2600 | 0.1 | (6.06 ± 0.05) × 10−3 | (7.89 ± 0.11) × 10−3 | 0.65 ± 0.14 | |
| 14 | 26 | 1 | 1 | 104 | 103 | 7800 | 0.3 | (10.33 ± 0.09) × 10−3 | (12.37 ± 0.05) × 10−3 | 0.81 ± 0.20 | |
| 15 | 26 | 1 | 1 | 104 | 103 | 26 000 | 1 | (15.79 ± 0.04) × 10−3 | (17.06 ± 0.10) × 10−3 | 1.16 ± 0.18 | |
Notes. Simulation reference number, beam Lorentz factors γb, inverse background (ρ0) and beam (ρ1) temperatures, simulation length L in number of grid cells (Δ), number of particles per cell per species (electrons and positrons) of the background N0 and of the beam N1, beam-to-background particle density ratio rn, integrated growth rates from PIC simulations Γ, maximum found growth rate in k-space ωi, max, sim, and the fractional bandwidth Δωr/ωr.
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