Transverse expansion of the electron sheath during laser acceleration of protons

The transverse expansion of the electrostatic sheath during target normal sheath acceleration of protons is investigated experimentally using a setup with two synchronized laser pulses. With the pulses spatially separated by less than three laser spot diameters, the resulting proton beam profiles become elliptical. By introducing a small intensity difference between the two pulses, the ellipses are rotated by a certain angle, except if the spatial separation of the two laser pulses is in the plane of incidence. The rotation angle is shown to depend on the relative intensity of the two pulses. The observed effects are found to require high temporal contrasts of the laser pulses. A simple model describing how the transverse shape of the electron sheath on the rear of the target depends on the relative intensity between the foci is presented. The model assumptions are verified, and the unknown dependence of the transverse extents of the sheaths are estimated self-consistently through a series of high resolution, two-dimensional particle-in-cell simulations. The results predicted by the model are also shown to be consistent with those obtained from the experiment.