Ionisation of Hydrogen for Plasma Wakefield Accelerators

In order to describe the electron density of a hydrogen plasma generated via anultrashort laser pulse, it is necessary to understand the underlying ionisation processof the pulse interacting with H2. Simulations and calculations based on thesimplest ADK ionisation thresholds are likely to overestimate the ionisation fractionsince the molecular dynamics in H2 are not included.The tunnelling barrier-suppression (TBSI) model combines atomic ADK theory [2]with an empirical correction far into the barrier-suppression ionisation regime [46],[38], and can also be applied to calculate molecular ionisation rates [39]. Electrondensities are computed from either a measured or simulated focus scan, basedon a laser intensity distributions perpendicular to the laser propagation direction,describing ionisation within the TBSI model under the assumption of a static temporalshape (EDDIT).EDDIT is benchmarked against the electron density obtained from a plasma interferometryexperiment, determined by performing an Abel inversion on theplasma-induced phase shift. In addition, the dissociation behaviour of H2 is exploredby solving the classical equations of motion in the electromagnetic field ofthe laser pulse in one dimension.The molecular structure especially affects the ionisation behaviour of H2 in ultrashortpulses on femtosecond time scale with peak intensities on the order of 1013 –1015Wcm2.The presented EDDIT approach shows a dependence on laser pulse duration owingto the characteristic time scale to break the molecular bond. EDDIT allows to examinethe influence of realistic laser pulse parameters e.g. pulse duration, beam powerand gas density, on plasma generation, and thus enables to tailor the focussinggeometry and laser-power-profile evolution to the needs of specific experiments. Inorder to quantitatively predict electron densities, additional laser-plasma interactioneffects, such as plasma-induced beam refraction, need to be incorporated