Illustration of laser generated proton beam formation and expansion.
(a) Targets and experimental setup. The cone target (expanded) consists of a 10μm thick spherical foil, attached to an Al cone structure. A Cu mesh (200 LPI) is positioned 1.5 mm from the apex of the hemisphere and the RCF stack is at 4 cm. Representative RCF data from a cone structure target is shown. Upper right images are the full and partial hemi targets. (b) Typical proton unfold spectra for a partial hemi target (solid) and full hemi target (dashed).
Illustration of the ray tracing technique. The ray bundle is formed by projecting back from the RCF film though the mesh. The D80 (z) profile is determined by finding the diameter at position z which encompasses 80% of the rays.
(a) D80 diameter for each target geometry. Cone (blue triangles) and cylinder (red squares) enclosed geometries show significantly smaller D80 values at most proton energies compared to the freestanding partial and full hemi shells. (b) Focal z-position of the proton beam at different proton energies. The inside surface of the foil is z = 0.
Proton density map at t = 7.3 ps for the case of a partial hemisphere target. Note that the expanded radial scale. Trajectories of test proton particles are also shown, with solid lines to t < 7.3 ps and broken lines from 7.3 ps < t < 19.2 ps. The kinetic energy gained by two sample particles is also shown (in red).
Comparisons of experimental and simulation results of D80 (z) for (a) freestanding partial hemisphere targets and (b) cone targets. The circles along with the appropriate error bars represent the minimum D80. The simulation curves (black) include all protons with E > 9 MeV.
Simulation of the electric fields Ez (z) for the partial hemi target showing the evolution of the accelerating axial field. Ez is generated from the hot electron pressure gradient that decays as the beam expands away from the surface.
The radial electric fields in the frame of a few trace particles that originate from equally spaced positions along the partial hemi target surface: r = 2 μm (purple), r = 45 μm (blue), r = 90 μm, r = 135 μm (red). Initially, the off-axis protons experience a negative radial field component from the target curvature. Within a few picoseconds, the protons experience a net positive radial field that persists for ≈20 ps.
Δ80 (z) curves for proton energies >3 MeV for the partial hemi and the cone target. Also, shown are results with a uniformly illuminated cone target (cone 2) as described in the text.
Hot electron density profiles and radial electric field contours for a cone target showing the rapid transport of the electrons from the laser spot region after the pulse (t > 0.5 ps). The hot electrons transport along the surface and create the sheath field on the inner cone wall directed radially inward (blue contours Er < 0).
Proton beam propagation and focusing with a spatially uniform target illumination. The laser pulse τpulse = 3 ps and Thot ≈ 1 MeV. The converging beam focusing diameter < 20 μm. The radial profile (c) is averaged between z = 280 μm and 330 μm, while the axial profile (d) is averaged between r = 0 and 10 μm.
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