Table 3
Theoretical versus experimental values of the filamentation growth rate τ.
| β 0 | n t | n x | ρ sp | vth/c | Box size in de | Λp |
|
|
|
|
|
|||||||||
| 0.95 | 1000 | 20 | 16 | 0.1 | 3 × 3 × 30 | 0.29 (38%) | 0.21 | ||
| ′′ | ′′ | ′′ | 100 | ′′ | ′′ | 0.27 (29%) | ′′ | ||
| ′′ | 250 | 20 | 16 | 0.1 | 9 × 9 × 30 | 0.27 (29%) | 0.24 (14%) | ′′ | |
|
|
|||||||||
| 0.995 | 1000 | 20 | 4 | 0.1 | 3 × 3 × 30 | 32 | 0.52 (44%) | 0.36 | |
| ′′ | ′′ | ′′ | 16 | ′′ | ′′ | 128 | 0.45 (25%) | ′′ | |
| ′′ | ′′ | ′′ | 80 | ′′ | ′′ | 640 | 0.43 (19%) | ′′ | |
| ′′ | ′′ | ′′ | 160 | ′′ | ′′ | 1280 | 0.43 (19%) | ′′ | |
| ′′ | ′′ | ′′ | 400 | ′′ | ′′ | 3200 | 0.41 (14%) | ′′ | |
| ′′ | ′′ | ′′ | 560 | ′′ | ′′ | 4480 | 0.42 (17%) | ′′ | |
| ′′ | 500 | 20 | 4 | 0.1 | ′′ | 32 | 0.51 (42%) | ′′ | |
| ′′ | ′′ | ′′ | 80 | ′′ | ′′ | 640 | 0.41 (14%) | ′′ | |
| ′′ | ′′ | ′′ | 128 | ′′ | ′′ | 1024 | 0.43 (19%) | ′′ | |
| ′′ | ′′ | ′′ | 200 | ′′ | ′′ | 1600 | 0.42 (17%) | ′′ | |
| ′′ | ′′ | ′′ | 280 | ′′ | ′′ | 2240 | 0.42 (17%) | ′′ | |
| ′′ | 250 | 20 | 4 | 0.1 | ′′ | 32 | 0.51 (42%) | ′′ | |
| ′′ | ′′ | ′′ | 80 | ′′ | ′′ | 640 | 0.41 (14%) | ′′ | |
| ′′ | ′′ | ′′ | 128 | ′′ | ′′ | 1024 | 0.43 (19%) | ′′ | |
| ′′ | ′′ | ′′ | 200 | ′′ | ′′ | 1600 | 0.42 (17%) | ′′ | |
| ′′ | ′′ | ′′ | 280 | ′′ | ′′ | 2240 | 0.42 (17%) | ′′ | |
| ′′ | 1000 | 40 | 80 | 0.1 | ′′ | 5120 | 0.46 (27%) | ′′ | |
| ′′ | 2000 | 40 | 4 | 0.1 | ′′ | 256 | 0.60 (67%) | ′′ | |
| ′′ | ′′ | ′′ | 16 | ′′ | ′′ | 1024 | 0.50 (39%) | ′′ | |
| ′′ | ′′ | ′′ | 48 | ′′ | ′′ | 3072 | 0.46 (27%) | ′′ | |
| ′′ | ′′ | ′′ | 74 | ′′ | ′′ | 4736 | 0.47 (31%) | ′′ | |
| ′′ | ′′ | ′′ | 160 | ′′ | ′′ | 10 024 | 0.43 (19%) | ′′ | |
| ′′ | 2000 | 40 | 16 | 0.075 | ′′ | 432 | 0.52 (44%) | ′′ | |
| ′′ | 2000 | 40 | 16 | 0.05 | ′′ | 128 | 0.58 (61%) | ′′ | |
| ′′ | 250 | 20 | 80 | 0.1 | 4.5 × 4.5 × 15 | 128 | 0.41 (14%) | 0.38 (6%) | ′′ |
| ′′ | 250 | 20 | 4 | 0.1 | 9 × 9 × 30 | 32 | 0.50 (39%) | 0.38 (6%) | ′′ |
| ′′ | ′′ | ′′ | 16 | ′′ | ′′ | 128 | 0.48 (33%) | 0.38 (6%) | ′′ Figs. 4, 5, 7 |
| ′′ | ′′ | ′′ | 80 | ′′ | ′′ | 640 | 0.43 (19%) | 0.39 (8%) | ′′ |
| ′′ | 125 | 10 | 128 | 0.1 | ′′ | 128 | 0.42 (17%) | 0.39 (8%) | ′′ |
| ′′ | 1000 | 20 | 16 | 0.1 | ′′ | 128 | 0.46 (27%) | 0.38 (6%) | ′′ |
| ′′ | 500 | 20 | 16 | 0.1 | ′′ | 128 | 0.46 (27%) | 0.38 (6%) | ′′ |
|
|
|||||||||
| 0.999 | 1000 | 20 | 100 | 0.1 | 3 × 3 × 30 | 0.61 (15%) | 0.53 | ||
| ′′ | 250 | 20 | 16 | 0.1 | 9 × 9 × 30 | 0.70 (32%) | 0.56 (6%) | ′′ | |
Notes. Numbers in parenthesis are the discrepancy with respect to 
, i.e., 
and 
. Tpe is the plasma period comprising all electrons, and de the plasma skin depth based on this period. We recall that de corresponds to nx cells. We also give the PIC plasma parameter 
(see Sect. 5.1).
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