Table 1 Simulation parameters in both real and normalised simulation units for the 2D3V simulations. Solid aluminium has a density of 2.7 \({\hbox {g}}\;{\hbox {cm}}^{-3}\).

From: Attosecond and nano-Coulomb electron bunches via the Zero Vector Potential mechanism

Laser (2D, p-polarised)

Parameters

Real

Sim

Wavelength, \(\lambda\) (nm)

1060

2\(\pi\)

Angular frequency, \(\omega _\mathrm{L}\) (fs\(^{-1}\))

1.8

1

Beam width, \(L_0\) (nm)

6\(\lambda\)

12\(\pi\)

Focal point, (\(x_\mathrm{f}\), \(y_\mathrm{f}\)) (nm)

(2\(\lambda\), 5\(\lambda\))

(4\(\pi\), 10\(\pi\))

Spatial envelope, \(E_y\)

\(E_y \sim e^{-(y-f_y)^2/L_0^2}\)

Temporal envelope, \(E_t\)

\(E_t \sim e^{-(t-4\lambda /c)^2/((4\lambda /3c)^2\ln 2)}\)

Simulation box

Size, \(x \times y\) (nm)

\(4\lambda \times 10\lambda\)

\(8\pi \times 20\pi\)

Sim length (fs)

35.22

20\(\pi\)

Spatial resolution, \(\Delta x\) (nm)

\(\lambda /128\) = 8.28

0.0491

Temporal resolution, \(\Delta t\) (as)

\(\Delta x/11c\) = 2.51

0.00446

Plasma (collisionless, fully pre-ionised aluminium plasma)

Electron x profile, n(x)

\({\left\{ \begin{array}{lll} n_\mathrm{e} \text { for} \; 2\lambda \le x \le 3\lambda ,\\ n_\mathrm{e}e^{(x-2\lambda )/0.2\lambda } \text { for} \; x \le 2\lambda , \\ 0 \text{ otherwise.}\\ \end{array}\right. }\)

Electron y profile, n(y)

\({\left\{ \begin{array}{ll} 1 \quad \text { for } 2\lambda \le y \le 8\lambda ,\\ 0 \quad \text { otherwise.}\\ \end{array}\right. }\)

Ion profile, \(n_\mathrm{i}\)

\(n_\mathrm{i} = n(x)n(y)/13\)

Ion charge

13e

Macro-electrons per cell

484

Macro-ions per cell

25

 

Parameter scan

Plasma density, \(n_\mathrm{e}\) (\({\hbox {gcm}}^{-3}\))

0.003–7

1–1000

Peak laser E-field & \(a_0\) (\({\hbox {V}}\,{\hbox {m}}^{-1}\))

\(10^{10}\)–\(10^{16}\)

0.01–5000