Fig. 5: Electron beam charge optimization through pulse shaping.

a Surrogate model predicted charge on the β⁽²⁾ − β⁽⁴⁾ plane at the optimal values of β⁽³⁾ and f. Markers show the initial position projected onto this plane, A, and the optimal position, B. Marker C shows the likely end result of sequential 1D optimizations of β⁽²⁾ and β⁽⁴⁾ when starting from position A. The diagonal lines show the combination of β⁽²⁾ and β⁽⁴⁾ modifications that maintain an approximately constant pulse shape. b Snapshots from a PIC simulation showing the laser normalized vector potential a, the electron densities of the background plasma and the electrons released from the two inner ionization levels of nitrogen normalized to n₀ = 1.2 × 10¹⁹ cm⁻³. c Left: axial laser field envelope at the given z positions and (right) maximum laser field, and total electron beam charge as functions of z position from simulations using the input laser pulse spectral phase coefficients from points A and B from a.