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Table 1 Quantities related to protons obtained in the 2D simulation scan (time selection is explained in Sect. 3) changing foam and substrate thicknesses and in the 3D simulation with nanostructured foam at 300 fs. The reported quantities are the maximum energy \(E_{p}^{\mathrm{max}}\) reached by the protons, their mean energy \(\bar{E}_{p}\) above 0.5 MeV, their temperature \(T_{p}\) coming from the exponential fitting of the spectra, the conversion efficiency η from laser energy to proton energy, and the estimate \(N_{p}\) of the total number of accelerated protons per shot above 0.5 MeV

From: Towards compact laser-driven accelerators: exploring the potential of advanced double-layer targets

Foam thickness

\(E_{p}^{\mathrm{max}}\) (MeV)

\(\bar{E}_{p}\) [MeV]

\(T_{p}\) [MeV]

Efficiency η [-]

Np [-]

Substrate Thickness = 0.2 Î¼m

No foam

5.86

1.32

1.09

0.52%

5.12â‹…109

2 Î¼m

26.24

3.44

5.03

5.48%

2.07â‹…1010

4 Î¼m

31.05

4.2

6.04

8.31%

2.44â‹…1010

8 Î¼m

22.83

3.88

4.07

7.28%

2.57â‹…1010

Substrate Thickness = 0.6 Î¼m

No foam

4.56

1.26

1.03

0.25%

2.58â‹…109

2 Î¼m

21.63

3.55

5.54

3.64%

1.33â‹…1010

4 Î¼m

24.04

4.41

5.91

5.72%

1.76â‹…1010

8 Î¼m

18.73

3.93

4.16

5.33%

1.69â‹…1010

Substrate Thickness = 2 Î¼m

No foam

2.69

0.91

0.61

0.07%

1.0â‹…109

2 Î¼m

17.93

3.27

4.13

2.61%

1.04â‹…1010

4 Î¼m

19.03

4.02

5.24

4.58%

1.63â‹…1010

8 Î¼m

15.92

3.60

3.62

4.50%

1.48â‹…1010

Nanostructured 3D (Substrate Thickness = 0.2 Î¼m)

4 Î¼m

15.05

1.85

2.20

4.58%

4.08â‹…1010