(a) Measured lateral extent of Cu Kα emission, half-width-at-half-maximum (HWHM), as a function of target thickness (front Al transport layer), L. Black symbols are data from the present experiment (Al-Cu-Al). Red symbols are measurements made with similar laser pulse parameters on Cu targets, reproduced from Lancaster et al.; 8 (b) Maximum proton energy, Emax , as a function of target thickness. Black squares are data from the present experiment (Al-Cu-Al) and white squares are measurements made with similar laser pulse parameters and Al targets, reproduced from Yuan et al. 14 Blue circles are theoretical estimates of Emax , calculated using a plasma expansion model together with estimates of the rear-surface fast electron density inferred from the Cu Kα measurements shown in (a). See main text for details.
(a) Fast electron beam injection half-angle as a function of electron energy. The dashed black curve is the distribution function derived by Moore et al., 31 in which , where γ is the electron Lorentz factor and with giving a mean half-angle in the example shown. The red line corresponds to electrons injected uniformly within a cone with half-angle equal to at all electron energies. The green curve is the initial fast electron energy spectrum for a beam temperature of 6 MeV; (b) Example temporal evolution profile of the maximum fast electron density at the target rear side, extracted from a hybrid-PIC simulation of electron transport within a 200 μm-thick target, with ; (c) Fast electron energy spectra extracted from the hybrid simulations at the front side ("initial spectrum") and rear side of 100 μm and 200 μm-thick targets. The dashed line is a Boltzmann distribution with kTe = 6 MeV.
(a) Fast electron density at the target rear side, averaged over the temporal peak, as a function of target thickness L, extracted from the hybrid simulations, for given ; (b) Corresponding ion acceleration time, extracted from the FWHM temporal width of the density peak, as a function of L.
((a)-(c)) False-color 2D maps of the z-component of the self-generated resistive B-field (in units of Tesla); ((d)-(f)) Corresponding false-color 2D profiles of the fast electron beam density ( ( )). Note that the y-axis scale is different in the two sets of plots to enable small-scale features in the resistive B-field to be viewed. The results are for a 200 μm-thick Al target and 1 ps runtime, at given injection half-angles specified in ((a)-(c)). The fast electrons are injected at position (0,0,0) and the beam propagates in the direction of the x-axis. The grid size for these example simulations was equal to 1 μm × 1 μm × 1 μm to enable small-scale features to be resolved.
(a) False-color 2D profiles of the fast electron density distribution ( ( )) at given depths for a 200 μm-thick Al target for and 0.8 ps simulation time; (b) Same as (a), but with the B-field growth artificially suppressed in the simulation.
Fast electron beam diameter, , as a function of target thickness. Black squares correspond to the experimental data. Coloured symbols correspond to the lateral extent of the electron beam as determined from the simulations for given injection parameters. Unless otherwise stated, the B-field evolution is included in the simulation and . The beam size is extracted from the simulation results before refluxing at the rear surface boundary at time step equal to 0.4 ps for L = 100 μm, 0.6 ps for L = 150 μm, 0.9 ps for L = 200 μm, and 1 ps for L = 250 μm.
Maximum proton energy as a function of L. As in Figure 1(b) , black squares are data from the present experiment (Al-Cu-Al) and white squares are the measurements from Yuan et al. 14 Colored symbols are plasma expansion model calculations of Emax using electron densities and ion acceleration times deduced from the hybrid simulation resultsof electron transport: (a) for fixed and given injection half-angles, ; (b) illustrating the effect of B-field suppression (for fixed and given ); and (c) for given and .
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