Dephasingless Laser Wakefield Acceleration

Laser wakefield accelerators (LWFAs) produce extremely high gradients enabling compact accelerators and radiation sources but face design limitations, such as dephasing, occurring when trapped electrons outrun the accelerating phase of the wakefield. Here we combine spherical aberration with a novel cylindrically symmetric echelon optic to spatiotemporally structure an ultrashort, high-intensity laser pulse that can overcome dephasing by propagating at any velocity over any distance. The ponderomotive force of the spatiotemporally shaped pulse can drive a wakefield with a phase velocity equal to the speed of light in vacuum, preventing trapped electrons from outrunning the wake. Simulations in the linear regime and scaling laws in the bubble regime illustrate that this dephasingless LWFA can accelerate electrons to high energies in much shorter distances than a traditional LWFA—a single 4.5 m stage can accelerate electrons to TeV energies without the need for guiding structures.

Figure 1

Energy gain of a DLWFA and traditional LWFA in the (a) linear ($a_0=0.5$) and (b) nonlinear ($a_0=4$) regimes as function of accelerator length compared with a conventional radio-frequency accelerator. The linear regime DLWFA achieves an energy gain of 10 GeV in 10 times less distance than a traditional LWFA. Simulations (dots) show excellent agreement with the theoretical scaling. The nonlinear DLWFA reaches a TeV energy gain in 4.5 m, 40 times less distance than a traditional LWFA. The energy gain for the conventional accelerator is determined by the electric field threshold for material damage $W_C=E_{thr}L$ where $E_{\text{thr}}=100\mathrm{MeV}/\mathrm{m}$. The linear and nonlinear wakefields were driven by a $1\mu \mathrm{m}$ laser with ${\tau }_l=30\mathrm{fs}$ and ${\tau }_l=15\mathrm{fs}$, respectively.

Figure 2

A schematic of the optical configuration enabling the DLWFA. (a),(b) The laser pulse first reflects off of a stepped echelon, which imparts the temporal delay required for a focal velocity equal to the speed of light in vacuum without introducing aberrated focusing. (c),(d) After reflecting from the echelon, the pulse encounters the axiparabola, which focuses different rings in the near field to different axial locations in the far field, stretching the region over which the pulse can sustain a high intensity from the initial focus at $f_0$ to $f_0+L$. (e) The pulse drives a wakefield at the speed of light in vacuum.

Figure 3

(a) The on-axis intensity of a pulse spatiotemporally structured by an axiparabola-echelon pair with $v_f=c$, $f_{\#}=f_0/2R=5$, and $L=8\mathrm{cm}$, orange scale, and the resulting on-axis axial wakefield, gray scale, as a function of propagation distance $z-f_0$ and speed of light frame coordinate $\xi =t-z/c$. The peak intensity of the laser pulse and the phase fronts of the wakefield travel at the speed of light in vacuum ($\xi =\text{const}$). (b) The same quantities for an axiparabola-echelon pair with $v_f=v_g$, which emulates a traditional LWFA with guiding. On account of their subluminal velocity, the peak intensity of the laser pulse and the phase fronts slip backwards in the speed of light frame $\xi \approx ({\omega }_p^2/2c{\omega }_0^2)z$.

Figure 4

Comparison of the maximum energy gain of electrons simulated in a DLWFA with $L=8\mathrm{cm}$ and in a traditional LWFA emulated by a spatiotemporally structured pulse with $v_f=v_g$. For both the DLWFA and traditional LWFA, ${\lambda }_0=1\mu \mathrm{m}$, ${\tau }_l=30\mathrm{fs}$, $a_0=0.5$, and $n_0=3.5\times {10}^{18}{\mathrm{cm}}^{-3}$. In the DLWFA, the electron gains 1.3 GeV over 16 dephasing lengths, while in the traditional LWFA, the electron outruns the laser pulse and only gains a maximum of 75 MeV energy over a single dephasing length.

Figure 5

The spatial profiles (sag functions) of (a) the axiparabola after subtracting the parabolic profile and (b) the echelon used in the simulations.