Scaling of maximum electron energy gain in laser wakefield acceleration with ionization injection

The phenomenological nonlinear wakefield theory, developed by W. Lu et al.,¹ includes an expression for the maximum energy gain of self-trapped electrons achievable in laser wakefield acceleration (LWFA). This theory also gives the acceleration distance (“dephasing length”) required to achieve this maximum energy gain. These expressions have been widely adopted by LWFA experimentalists; however, the expressions have not yet been systematically compared with experimental results for available laser and plasma parameters. In this work, we report on the scaling of the maximum energy gain of electrons produced via LWFA in thin gas cells of varied lengths. In previous LWFA experiments, the dephasing process has been inferred from the observation of spectral narrowing of the self-trapped plasma electrons. It is assumed that the phase-space rotation of the trapped electrons as they dephase leads to their bunching and spectral narrowing and thus gives an estimate of the maximum energy gain. In this study, we used ionization injection to continuously inject electrons into the wake to ensure that some electrons are always close to the dephasing-limited energy when the plasma length is longer than the dephasing distance. Ionization injection can occur when the laser intensity is above the threshold for ionization of inner-shell electrons of dopant atoms in the gas. This process greatly reduces the need for laser pulse evolution before self-trapping can occur. Gas cells were used rather than gas jets because the density profile of the gas tends to be more axially uniform and more reproducible in gas cells. By using gas cells with variable thicknesses from 180-1100 microns, electron energies up to 160 MeV were measured for laser powers between 3.5 TW and 6.8 TW and for plasma densities between 8 × 10¹⁸ cm^-3 and 2.5 × 10¹⁹ cm^-3. Measured electron energies were carefully compared with nonlinear- wakefield theory and with the results of 2D OSIRIS PIC simulations using the experimental parameters.