Influence of radiation reaction force on ultraintense laser-driven ion acceleration

The role of the radiation reaction force in ultraintense laser-driven ion acceleration is investigated. For laser intensities $\sim {10}^{23}{\mathrm{W}/\mathrm{cm}}^2$, the action of this force on electrons is demonstrated in relativistic particle-in-cell simulations to significantly enhance the energy transfer to ions in relativistically transparent targets, but strongly reduce the ion energy in dense plasma targets. An expression is derived for the revised piston velocity, and hence ion energy, taking account of energy loses to synchrotron radiation generated by electrons accelerated in the laser field. Ion mass is demonstrated to be important by comparing results obtained with proton and deuteron plasma. The results can be verified in experiments with cryogenic hydrogen and deuterium targets.

Figure 1

(a) Energy transfer to ions (total ion energy normalised to laser energy) as a function of target thickness: red (circles), with RR; black (squares), without RR; green (diamonds), ratio of the two. (b) Maximum ion energy as a function of target thickness.

Figure 2

Total electron energy normalized to laser energy, ${\eta }_e$, as a function of time, for (a) $l=0.8{\lambda }_L$; (b) $l=5{\lambda }_L$; (c) $l=100{\lambda }_L$. (d)–(f) Corresponding plots for radiated energy normalized to laser energy, ${\eta }_{\gamma }$.

Figure 3

Longitudinal electron phase space for (a) $l=0.8{\lambda }_L$, (b) $l=5{\lambda }_L$, and (c) $l=100{\lambda }_L$ at $t$ such that $\partial {\eta }_e/\partial t\approx$ 0. Red, with RR; black, without RR. (d)–(f) Corresponding electron energy spectra: green (thin solid) line, forward electrons with RR; brown (thick dashed) line, forward electrons without RR; blue (thick solid) line, backward electrons with RR; yellow (thin dashed), backward electrons without RR.

Figure 4

Longitudinal ion phase space for (a) $l=0.8{\lambda }_L$, (b) $l=5{\lambda }_L$, and (c) $l=100{\lambda }_L$ at $t$ such that $\partial {\eta }_i/\partial t\approx$ 0: red, with RR; black, without RR. (d)–(f) Corresponding forward-directed deuteron energy spectra. (g)–(i) Corresponding forward-directed proton energy spectra. Color code: red, with RR; black, without RR.

Figure 5

Space-time plots of (a) $\frac{e{E}_x}{m_{e}c{\omega }_L}$ (linear scale), (b) electron, and (c) ion densities [in logarithmic scale: $ln\left(\frac{n}{n_0}\right)]$ for $l=0.8{\lambda }_L$, with RR included. (d)–(f) The corresponding plots without RR inclusion.

Figure 6

Angular distribution of the synchrotron radiation as a function of the polar angle $\theta$ at $t$ such that $\partial {\eta }_{\gamma }/\partial t\approx 0$. Green, deuteron plasma; dashed blue, proton plasma.

Figure 7

Laser intensity dependence of the maximum energy of piston-accelerated (reflected) deuterons. The red line corresponds to the analytical model calculations with RR, respectively, for $l=100{\lambda }_L$. The symbols are simulation results for given parameters.