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Injection and transport properties of fast electrons in ultraintense laser-solid interactions
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View: Figures


Image of FIG. 1.

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FIG. 1.

(a) Measured lateral extent of Cu Kα emission, half-width-at-half-maximum (HWHM), as a function of target thickness (front Al transport layer), . 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 8 (b) Maximum proton energy, , 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 14 Blue circles are theoretical estimates of , 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.

Image of FIG. 2.

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FIG. 2.

(a) Fast electron beam injection half-angle as a function of electron energy. The dashed black curve is the distribution function derived by Moore , 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 m-thick target, with ; (c) Fast electron energy spectra extracted from the hybrid simulations at the front side ("initial spectrum") and rear side of 100 m and 200 m-thick targets. The dashed line is a Boltzmann distribution with  = 6 MeV.

Image of FIG. 3.

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FIG. 3.

(a) Fast electron density at the target rear side, averaged over the temporal peak, as a function of target thickness , 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 .

Image of FIG. 4.

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FIG. 4.

((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 m-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 m × 1 m × 1 m to enable small-scale features to be resolved.

Image of FIG. 5.

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FIG. 5.

(a) False-color 2D profiles of the fast electron density distribution ( ( )) at given depths for a 200 m-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.

Image of FIG. 6.

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FIG. 6.

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  = 100 m, 0.6 ps for  = 150 m, 0.9 ps for  = 200 m, and 1 ps for  = 250 m.

Image of FIG. 7.

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FIG. 7.

Maximum proton energy as a function of . As in Figure 1(b) , black squares are data from the present experiment (Al-Cu-Al) and white squares are the measurements from Yuan 14 Colored symbols are plasma expansion model calculations of 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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Fast electron injection and transport in solid foils irradiated by sub-picosecond-duration laser pulses with peak intensity equal to is investigated experimentally and via 3D simulations. The simulations are performed using a hybrid-particle-in-cell (PIC) code for a range of fast electron beam injection conditions, with and without inclusion of self-generated resistive magnetic fields. The resulting fast electron beam transport properties are used in rear-surface plasma expansion calculations to compare with measurements of proton acceleration, as a function of target thickness. An injection half-angle of is inferred, which is significantly larger than that derived from previous experiments under similar conditions.


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Scitation: Injection and transport properties of fast electrons in ultraintense laser-solid interactions