Table 1.

Laser, plasma and beam parameters for the simulated case at $n_p\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em}\times \hspace{0.17em}{10}^{18}\hspace{0.17em}{\mathrm{cm}}^{-3}$ and the extrapolated case at $n_p\hspace{0.17em}=\hspace{0.17em}2\hspace{0.17em}\times \hspace{0.17em}{10}^{17}\hspace{0.17em}{\mathrm{cm}}^{-3}$.

plasma density	np	$2\hspace{0.17em}\times \hspace{0.17em}{10}^{18}\hspace{0.17em}{\mathrm{cm}}^{-3}$	$2\hspace{0.17em}\times \hspace{0.17em}{10}^{17}\hspace{0.17em}{\mathrm{cm}}^{-3}$
laser peak intensity	$a_0\propto 1$	3.18	3.18
laser spot size (norm.)	$w_0\propto n_p^{\hspace{0.17em}-\hspace{0.17em}1/2}$	17 μm (4.5)	54 μm (4.5)
laser pulse duration (norm.)	${\tau }_0\propto n_p^{\hspace{0.17em}-\hspace{0.17em}1/2}$	27 fs (2.15)	85 fs (2.15)
laser power	$P_0\propto n_p^{-1}$	98 TW	980 TW
laser energy	$E_0\propto n_p^{\hspace{0.17em}-\hspace{0.17em}3/2}$	2.8 J	88 J
acceleration distance	$L_{\mathrm{acc}}\propto n_p^{\hspace{0.17em}-\hspace{0.17em}3/2}$	2.0 mm	6.3 cm
accelerating field	$E_z^{\mathrm{w}}\propto n_p^{1/2}$	185 GV m−1	58 GV m−1
beam energy (mean)	${\overline{\gamma }}_{\mathrm{w}}\propto n_p^{-1}$	370 MeV mc−2	3.7 GeV mc−2
beam charge	$Q_{\mathrm{w}}\propto n_p^{\hspace{0.17em}-\hspace{0.17em}1/2}$	190 pC	601 pC
beam current	$I_{\mathrm{w}}\propto 1$	30 kA	30 kA
beam duration (fwhm)	${\tau }_{\mathrm{w}}\propto n_p^{\hspace{0.17em}-\hspace{0.17em}1/2}$	6 fs	19 fs
beam norm. emittance	${ϵ}_{n,\mathrm{w}}\propto n_p^{\hspace{0.17em}-\hspace{0.17em}1/2}$	5 μm	16 μm
beam rel. energy spread	${\sigma }_{\gamma }^{\mathrm{w}}/{\overline{\gamma }}_{\mathrm{w}}\propto 1$	2.5%	2.5%