Proton imaging of stochastic magnetic fields
Proton imaging of stochastic magnetic fields
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DOI：
10.1017/s0022377817000939
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发表时间：
2017-12-01
影响因子：
2.5
通讯作者：
Schekochihin, A. A.
中科院分区：
文献类型：
--
作者：
Bott, A. F. A.;Graziani, C.;Schekochihin, A. A.
最近的激光等离子体实验（Fox 等人，Phys. Rev. Lett.，第 111 卷，2013，225002；Huntington 等人，Nat. Phys.，第 11(2) 卷，2015，173-176；Tzeferacos 等人，Phys. Plasmas，第 24(4) 卷， 2017a，041404；Tzeferacos 等人，2017b，arXiv：1702.03016 [物理学。等离子体-ph]）报告了动态显着磁场的存在，其统计特征对于完整理解这些实验试图研究的物理过程至关重要。在本文中，我们展示了如何使用质子成像诊断来确定一系列相关的磁场统计数据，包括磁能谱。为了实现这一目标，我们探索随机磁场与对该场成像时产生的图像通量分布之间的解析关系的性质。这种“Kugland 图像-通量关系”先前是根据在实际质子成像设置中通常有效的简化假设推导的（Kugland 等人，Rev. Sci. Instrum. vol. 83(10), 2012, 101301）。我们的结论是，与常规电磁场一样，光束最终图像通量分布的特征通常表现出由单个场尺度相关参数决定的通用特征 - 对比度参数 mu 相当于 d(s)/Ml(B) - 它量化了随机场的相关长度 l(B) 的相对大小、磁偏转引起的质子位移 d(s) 和图像放大率 M。对于随机磁场，我们建立了四个对比度的存在制度，在这种制度下，质子通量图像以定性不同的方式与其母场相关。这些是线性的、非线性的单射、苛性和扩散。扩散机制是新近被识别和描述的。非线性注入状态与苛性状态的区别在于表现出非线性行为，但与线性状态一样，可以唯一地提取光束所经历的路径积分磁场。因此，在线性和非线性注入机制中，我们表明可以在进一步的各向同性统计假设下获得磁能谱。在腐蚀性或扩散体系中情况并非如此。我们讨论了非均匀、多尺度随机场引起的对比度范围表征的复杂性，它可以包含许多对比度范围，以及目前实验能力对提取磁场统计数据的能力所造成的限制。本文提出的结果对于提供随机磁场质子图像的全面描述具有重要意义，并可用于改进质子通量图像的分析。
Recent laser-plasma experiments (Fox et al., Phys. Rev. Lett., vol. 111, 2013, 225002; Huntington et al., Nat. Phys., vol. 11(2), 2015, 173-176; Tzeferacos et al., Phys. Plasmas, vol. 24(4), 2017a, 041404; Tzeferacos et al., 2017b, arXiv: 1702.03016 [physics. plasm-ph]) report the existence of dynamically significant magnetic fields, whose statistical characterisation is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a proton-imaging diagnostic can be used to determine a range of relevant magnetic-field statistics, including the magnetic-energy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the image-flux distribution created upon imaging that field. This 'Kugland image-flux relation' was previously derived (Kugland et al., Rev. Sci. Instrum. vol. 83(10), 2012, 101301) under simplifying assumptions typically valid in actual proton-imaging set-ups. We conclude that, as with regular electromagnetic fields, features of the beam's final image-flux distribution often display a universal character determined by a single, field-scale dependent parameter - the contrast parameter mu equivalent to d(s)/Ml(B) - which quantifies the relative size of the correlation length l(B) of the stochastic field, proton displacements d(s) due to magnetic deflections and the image magnification M. For stochastic magnetic fields, we establish the existence of four contrast regimes, under which proton-flux images relate to their parent fields in a qualitatively distinct manner. These are linear, nonlinear injective, caustic and diffusive. The diffusive regime is newly identified and characterised. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the path-integrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magnetic-energy spectrum can be obtained under a further statistical assumption of isotropy. This is not the case in the caustic or diffusive regimes. We discuss complications to the contrast-regime characterisation arising for inhomogeneous, multi-scale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one's ability to extract magnetic-field statistics. The results presented in this paper are of consequence in providing a comprehensive description of proton images of stochastic magnetic fields, with applications for improved analysis of proton-flux images.