Significant relativistic effects in laser–matter interactions require laser fields $\sim{{10}^{11}}\;{\rm V}/{\rm cm}$ to oscillate electrons at relativistic velocities, corresponding to laser intensities $\sim{{10}^{19}}\;{\rm W}/{{\rm cm}^2}$. The Advanced Radiographic Capability laser system at Lawrence Livermore National Laboratory’s National Ignition Facility (ARC [1]) was designed to operate at $\sim{{10}^{18}}\;{\rm W}/{{\rm cm}^2}$, so to observe significant relativistic effects on ARC requires additional focusing. We have achieved this using mm-scale compound parabolic concentrators (CPC).

CPCs were originally described by Winston and Hinterberger in 1966 [2] for the efficient collection of diffuse Cherenkov radiation from high energy physics experiments, and were quickly adopted more widely as light concentrators for solar power production [3]. The surface is a revolved parabola, where the axis has been tilted about a point below the focus and the revolution taken about the original axis as shown in Fig. 1(a). The surface is truncated at the disk defined by the locus of the revolved focus. All rays entering the CPC within the tilt angle θ exit through this disk, the radius of which scales with the distance from the initial parabola focus to the tilt point L as ${\rm r}={\rm L} \sin \theta $. The maximum light concentrating power for uniform irradiation is equal to the ratio of the area of the input and output apertures. In the context of laser plasma interactions, previous attempts to increase the focused intensity have used targets with surfaces described by either linear or exponential cones [4,5]. Both schemes rely on a significant fraction of the energy being deposited at the cone tip with a high-quality focal spot and low intrinsic pre-pulse; the plasma produced by the pre-pulse can otherwise limit performance by filling the cone with plasma before the main pulse arrives, especially near the tip where the focused pre-pulse intensity is highest [6]. For CPC targets, a defocused or otherwise larger focal spot causes the initial interaction to occur further up the wall of the target, at a more grazing angle of incidence and reduced intensity as shown schematically in Fig. 1(b), where a relatively large exit aperture has been used for clarity. CPC targets used on the ARC laser system typically have entrance radii $ \sim{250\;\unicode{x00B5}{\rm m}} $, exit radii $\sim{25\,\,\unicode{x00B5}{\rm m}}$ or less, length $\sim{1.2}\;{\rm mm}$, and are designed to accept the 3.8° half-cone angle envelope of all four ARC beamlets. $\sim{20}\% $ of the encircled energy for each beamlet lies within a 25 µm radius spot while the remainder lies mostly within $\sim{250\,\,\unicode{x00B5}{\rm m}}$ [Fig. 2(a)]. Due to $\sim{35\,\,\unicode{x00B5}{\rm m}}$ ${1}\sigma $ pointing uncertainty, ARC beamlets are not usually overlapped in space. CPC targets on the other hand enable reproducible overlap as geometrically all the rays entering the CPC pass through the exit pupil in a single bounce, mitigating both laser and target alignment error. This is demonstrated in Fig. 2(b), where the hot electron temperature measured from a gold foil target coupled with a CPC was increased ${3.2} \times $ compared to four beamlets onto a foil with no overlap, which by ponderomotive scaling is consistent with raising the intensity on a planar foil $ \gt {10} \times $ [7].

 

Fig. 1. (a) Geometric construction of a CPC. (b) Cutaway schematic of a CPC target showing focus of 3d ray bundle. Large exit aperture diameter shown for clarity. (c) Truncated CPC with annular focal spot and free-standing foil to isolate a point source backlighter from the CPC and reduce confinement of pre-formed plasma.

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Fig. 2. (a) Focal spot for one of the four independent beamlets that comprise ARC. (b) Electron spectra measured from a plane gold foil and a CPC-coupled gold foil target on ARC.

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Laser target interactions are typically accompanied by a pre-pulse interaction and absorption of laser energy in the main pulse can be significantly influenced by the conditions left by the pre-pulse; too little preformed plasma limits coupling efficiency to hot electrons, too much reduces the fraction of energy that makes it to the tip via refraction, absorption and energy transport. We attribute the enhanced performance of the target to a combination of geometric and refractive focusing of the laser pulse by the expanding wall material and enhanced laser absorption due to confinement of the pre-formed plasma near the tip of the CPC. To understand this with a predictive capability requires extensive modeling; hydrodynamic simulations to establish the pre-formed plasma conditions and particle-in-cell (PIC) simulations to accurately model the subsequent high-intensity short pulse interaction. Initial simulations using raytracing through a hydrodynamic simulation of the pre-formed plasma show the CPC continues to concentrate laser energy towards the tip of the target as the wall expands (Fig. 3). In this case the enhanced signal is sharply peaked due to refractive focusing. For this simulation the 10 ps main pulse intensity was reduced $\sim{50} \times $ to avoid relativistic effects which will be addressed in the PIC simulation, while a realistic pre-formed plasma was used to provide a suitable environment for refraction of the main pulse.

 

Fig. 3. (a) 3D hydrodynamic simulation at ${50} \times $ reduced intensity illustrating enhanced focusing expected with a CPC for a sub-relativistic main-pulse. (b) Lineouts at the entrance (red) and exit (blue) of the target at peak intensity.

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By truncating the CPC further from the tip as shown in Fig. 1(c), a localized source can be produced without contamination from wall emission, providing enhanced brightness while maintaining beam pointing error mitigation for both point-projection and areal backlighter sources. Further, with a high-quality wavefront and controlled pre-pulse, an adaptive optic can be used to impose a ${\rm TEM}_{01*}$ “doughnut” mode with optimized intensity in an annular spot. The CPC tilt angle can then be reduced to produce a smaller spot, as rays originating from one side of the axis now always intersect the surface on the same side of the axis versus a poor focal spot, giving higher focused intensity and reduced source size for a structure with similar length and input aperture.

CPC targets have been successfully deployed in experiments on ARC to enhance positron production, proton acceleration and x-ray source temperature and brightness, details of which will be published separately. Hot electron spectra consistent with over an order of magnitude intensity increase compared to flat foil targets have been measured. The CPC targets used in this study were produced by diamond turning. More economical 3D printed targets have recently been produced approaching similar surface quality. CPC targets enhance performance, mitigate laser pointing error and can reduce the barrier of entry to high intensity laser plasma interactions experiments.