All-optical control of electron trapping in tapered plasmas and channels

The radiation pressure of a multi-terawatt, sub-100 fs laser pulse propagating in an under-dense plasma causes complete electron cavitation. The resulting electron density “bubble” guides the pulse over many Rayleigh lengths, leaving the background ions unperturbed while maintaining GV/cm-scale accelerating and focusing gradients. The shape of the bubble, and, hence, the wakefield potentials, evolve slowly, in lockstep with the optical driver. This dynamic structure readily traps background electrons.¹ The electron injection process can thus be controlled by purely optical means.^{2, 3}Sharp gradients in the nonlinear refractive index produce a large frequency red-shift (Δω ~ ω0), localized at the leading edge of the pulse.^2,3 Negative group velocity dispersion associated with the plasma response compresses the pulse into a relativistic optical shock (ROS). ROS formation slows the pulse (and the bubble), reducing the electron dephasing length and limiting energy gain.⁴ Furthermore, the ponderomotive force due to the ROS causes the bubble to constantly expand, trapping copious unwanted electrons, polluting the electron spectrum with a high-charge, low-energy tail.^1,2 Here, we demonstrate a new, all-optical approach to compensating for the increase in pulse bandwidth, thereby delaying ROS formation and thus producing high quality, GeV-scale electron beams with 10-TW-class (rather than PW-class⁴) lasers in mm-scale (rather than cm-scale4), highdensity plasmas (n_e0 > 5 x 10¹⁸ vs. 10¹⁷ cm^-3). We show that a negatively chirped drive pulse with an ultra-high (~ 400 nm) bandwidth: extends the electron dephasing length; prevents ROS formation through dephasing; and almost completely suppresses continuous injection. Precise compensation of the nonlinear frequency shift can be achieved using a higher-order chirp extracted from reduced simulation models. ROS formation can be further delayed by using a plasma channel to suppress diffraction of the pulse leading edge, minimizing longitudinal variations in the pulse. Plasma density tapering further delays dephasing, providing an additional boost in beam energy.