在圆柱内爆情况下质子射线照相直接反演的评价
Evaluation of direct inversion of proton radiographs in the context of cylindrical implosions
摘要：
偏转测量数据的直接反演，如质子射线照片和阴影照片，是一个适定的问题，如果它们的轨迹不相交，每个粒子或射线的横向偏转具有唯一的解决方案。当轨迹相交时，存在无限多个解。在质子射线照相术中，直接反演确定线积分横向洛伦兹力。为了分析OMEGA激光器上圆柱内爆的质子射线照片，我们测试了五个公开可用的直接反演例程;四个Monge-Ampère求解器[github.com/flash-center/PRaLine，github.com/flash-center/PROBLEM，github.com/mfkasim1/invert-shadowgraphy/tree/fast-inverse，github.com/OxfordHED/proton-radiography-no-source]和一个幂图方法[github.com/mfkasim1/invert-shadowgraphy]。测试问题产生了使用四个字段配置文件，三个圆柱形和一个球形，不同的字段振幅在质子跟踪例程。两个Monge-Ampère解算器没有运行，另外两个在轨迹交叉时未能再现射线照片，尽管对于一个场剖面，解只是在边界处偏离原始解。功率图方法是成功的，即使当质子轨迹交叉，给出了一个解决方案，最大限度地减少质子偏转，但失败的配置文件，产生一个单一的，足够尖锐的峰值。对于轨迹不相交的情况，Monge-Ampère解算器的优势是比幂图程序快得多，在我们的测试中高达$1000$倍。测试问题在pradformat的补充信息中提供[github.com/phyzicist/pradformat]。
英文摘要：
Direct inversion of deflectometry data, such as proton radiographs and shadowgraphs, is a well-posed problem with a unique solution for the transverse deflection of each particle or ray if their trajectories do not cross. When trajectories cross, there exists an infinite set of solutions. In proton radiography direct inversion determines the line-integrated transverse Lorentz force. We have tested five publicly available direct inversion routines with a view to analyzing proton radiographs of cylindrical implosions on the OMEGA laser; four Monge-Ampère solvers [github.com/flash-center/PRaLine, github.com/flash-center/PROBLEM, github.com/mfkasim1/invert-shadowgraphy/tree/fast-inverse, github.com/OxfordHED/proton-radiography-no-source], and a power-diagram method [github.com/mfkasim1/invert-shadowgraphy]. Test problems were generated using four field profiles, three cylindrical and one spherical, with varying field amplitudes in proton-tracing routines. Two Monge-Ampère solvers did not run, the other two failed to reproduce radiographs when trajectories crossed, although for one field profile the solutions only diverged from the original at the boundary. The power-diagram method was successful even when proton trajectories crossed, giving a solution that minimized proton deflection, but failed for profiles that produced a single, sufficiently sharp peak. For cases where trajectories do not cross, the Monge-Ampère solvers have the advantage of being considerably faster than the power-diagram routine, up to $1000$ times in our tests. The test problems are provided in the supplementary information in pradformat [github.com/phyzicist/pradformat].
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