Proton imaging of stochastic magnetic fields
Abstract
Recent laserplasma experiments report the existence of dynamically significant magnetic fields, whose statistical characterization is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a protonimaging diagnostic can be used to determine a range of relevant magneticfield statistics, including the magneticenergy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the imageflux distribution created upon imaging that field. This ‘Kugland imageflux relation’ was previously derived under simplifying assumptions typically valid in actual protonimaging setups. We conclude that, as with regular electromagnetic fields, features of the beam’s final imageflux distribution often display a universal character determined by a single, fieldscale dependent parameter – the contrast parameter $$\unicode[STIX]{x1D707}\equiv d_{s}/{\mathcal{M}}l_{B}$$ – 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 $${\mathcal{M}}$$. For stochastic magnetic fields, we establish the existence of four contrast regimes, under which protonflux 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 characterized. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the pathintegrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magneticenergy 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 contrastregime characterization arising for inhomogeneous, multiscale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one’s ability to extract magneticfield statistics. Furthermore, 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 protonflux images.
 Authors:

 Univ. of Oxford, Oxford (United Kingdom)
 Univ. of Chicago, Chicago, IL (United States)
 Univ. of Oxford, Oxford (United Kingdom); Univ. of Chicago, Chicago, IL (United States)
 Univ. of Oxford, Oxford (United Kingdom); Univ. of Nevada, Reno, NV (United States)
 Merton College, Oxford (United Kingdom); Univ. of Oxford, Oxford (United Kingdom)
 Publication Date:
 Research Org.:
 Univ. of Chicago, IL (United States)
 Sponsoring Org.:
 USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC)
 OSTI Identifier:
 1495713
 Grant/Contract Number:
 NA0002724
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Journal of Plasma Physics
 Additional Journal Information:
 Journal Volume: 83; Journal Issue: 06; Journal ID: ISSN 00223778
 Publisher:
 Cambridge University Press
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; plasma diagnostics
Citation Formats
Bott, A. F. A., Graziani, C., Tzeferacos, P., White, T. G., Lamb, D. Q., Gregori, G., and Schekochihin, A. A. Proton imaging of stochastic magnetic fields. United States: N. p., 2017.
Web. doi:10.1017/S0022377817000939.
Bott, A. F. A., Graziani, C., Tzeferacos, P., White, T. G., Lamb, D. Q., Gregori, G., & Schekochihin, A. A. Proton imaging of stochastic magnetic fields. United States. doi:10.1017/S0022377817000939.
Bott, A. F. A., Graziani, C., Tzeferacos, P., White, T. G., Lamb, D. Q., Gregori, G., and Schekochihin, A. A. Tue .
"Proton imaging of stochastic magnetic fields". United States. doi:10.1017/S0022377817000939. https://www.osti.gov/servlets/purl/1495713.
@article{osti_1495713,
title = {Proton imaging of stochastic magnetic fields},
author = {Bott, A. F. A. and Graziani, C. and Tzeferacos, P. and White, T. G. and Lamb, D. Q. and Gregori, G. and Schekochihin, A. A.},
abstractNote = {Recent laserplasma experiments report the existence of dynamically significant magnetic fields, whose statistical characterization is essential for a complete understanding of the physical processes these experiments are attempting to investigate. In this paper, we show how a protonimaging diagnostic can be used to determine a range of relevant magneticfield statistics, including the magneticenergy spectrum. To achieve this goal, we explore the properties of an analytic relation between a stochastic magnetic field and the imageflux distribution created upon imaging that field. This ‘Kugland imageflux relation’ was previously derived under simplifying assumptions typically valid in actual protonimaging setups. We conclude that, as with regular electromagnetic fields, features of the beam’s final imageflux distribution often display a universal character determined by a single, fieldscale dependent parameter – the contrast parameter $\unicode[STIX]{x1D707}\equiv d_{s}/{\mathcal{M}}l_{B}$ – 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 ${\mathcal{M}}$. For stochastic magnetic fields, we establish the existence of four contrast regimes, under which protonflux 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 characterized. The nonlinear injective regime is distinguished from the caustic regime in manifesting nonlinear behaviour, but as in the linear regime, the pathintegrated magnetic field experienced by the beam can be extracted uniquely. Thus, in the linear and nonlinear injective regimes we show that the magneticenergy 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 contrastregime characterization arising for inhomogeneous, multiscale stochastic fields, which can encompass many contrast regimes, as well as limitations currently placed by experimental capabilities on one’s ability to extract magneticfield statistics. Furthermore, 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 protonflux images.},
doi = {10.1017/S0022377817000939},
journal = {Journal of Plasma Physics},
number = 06,
volume = 83,
place = {United States},
year = {2017},
month = {12}
}
Web of Science
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