Fig. 3: Derivation of the parabolic ion channel properties.

a, Energy spectra and transverse distributions of the driving and trailing probe bunches after interaction with the same perturbed plasma sampled in Fig. 2b. Differences between the spectra and transverse distributions of Fig. 2b arise from modification to the probe bunches made to enhance the strength of the experimental signatures. b, Curvature and on-axis ion-density values derived from the first two experimental signatures (Methods) highlighted in a. The line fits were calculated with a cubic spline. The error bars reflect the experimental uncertainties, which are dominated by the fits to measurements of the relative trailing beam size and the position of the focal lines. Values derived from separations with significant charge loss (>50%), which therefore carry an additional systematic uncertainty beyond the fitting errors shown, are highlighted in grey. This primarily occurs (1) at short timescales for both probe bunches due to their interaction with the decreasing off-axis focusing forces of the on-axis density spike and (2) at approximately 20 ns for the highly divergent trailing probe bunch owing to clipping in the capturing quadrupoles downstream of the plasma capillary.