skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Inferring morphology and strength of magnetic fields from proton radiographs

Abstract

Proton radiography is an important diagnostic method for laser plasma experiments and is particularly important in the analysis of magnetized plasmas. The theory of radiographic image analysis has heretofore only permitted somewhat limited analysis of the radiographs of such plasmas. We furnish here a theory that remedies this deficiency. We show that to linear order in magnetic field gradients, proton radiographs are projection images of the MHD current along the proton trajectories. We demonstrate that in the linear regime (i.e., the small image contrast regime), the full structure of the projected perpendicular magnetic field can be reconstructed by solving a steady-state inhomogeneous 2-dimensional diffusion equation sourced by the radiograph fluence contrast data. Here, we explore the validity of the scheme with increasing image contrast, as well as limitations of the inversion method due to the Poisson noise, discretization errors, radiograph edge effects, and obstruction by laser target structures. We also provide a separate analysis that is suited to the inference of isotropic-homogeneous magnetic turbulence spectra. Finally, we discuss extension of these results to the nonlinear regime (i.e., the order unity image contrast regime).

Authors:
ORCiD logo [1];  [1];  [1];  [2]
  1. Univ. of Chicago, IL (United States). Flash Center for Computational Science, Dept. of Astronomy and Astrophysics
  2. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Plasma Science and Fusion Center
Publication Date:
Research Org.:
Univ. of Chicago, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Fusion Energy Sciences (FES)
OSTI Identifier:
1524603
Alternate Identifier(s):
OSTI ID: 1414330
Grant/Contract Number:  
SC0016566; AC02-06CH11357; B523820; PHY-0903997; PHY-1619573
Resource Type:
Accepted Manuscript
Journal Name:
Review of Scientific Instruments
Additional Journal Information:
Journal Volume: 88; Journal Issue: 12; Journal ID: ISSN 0034-6748
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION TECHNOLOGY

Citation Formats

Graziani, Carlo, Tzeferacos, Petros, Lamb, Donald Q., and Li, Chikang. Inferring morphology and strength of magnetic fields from proton radiographs. United States: N. p., 2017. Web. doi:10.1063/1.5013029.
Graziani, Carlo, Tzeferacos, Petros, Lamb, Donald Q., & Li, Chikang. Inferring morphology and strength of magnetic fields from proton radiographs. United States. doi:10.1063/1.5013029.
Graziani, Carlo, Tzeferacos, Petros, Lamb, Donald Q., and Li, Chikang. Wed . "Inferring morphology and strength of magnetic fields from proton radiographs". United States. doi:10.1063/1.5013029. https://www.osti.gov/servlets/purl/1524603.
@article{osti_1524603,
title = {Inferring morphology and strength of magnetic fields from proton radiographs},
author = {Graziani, Carlo and Tzeferacos, Petros and Lamb, Donald Q. and Li, Chikang},
abstractNote = {Proton radiography is an important diagnostic method for laser plasma experiments and is particularly important in the analysis of magnetized plasmas. The theory of radiographic image analysis has heretofore only permitted somewhat limited analysis of the radiographs of such plasmas. We furnish here a theory that remedies this deficiency. We show that to linear order in magnetic field gradients, proton radiographs are projection images of the MHD current along the proton trajectories. We demonstrate that in the linear regime (i.e., the small image contrast regime), the full structure of the projected perpendicular magnetic field can be reconstructed by solving a steady-state inhomogeneous 2-dimensional diffusion equation sourced by the radiograph fluence contrast data. Here, we explore the validity of the scheme with increasing image contrast, as well as limitations of the inversion method due to the Poisson noise, discretization errors, radiograph edge effects, and obstruction by laser target structures. We also provide a separate analysis that is suited to the inference of isotropic-homogeneous magnetic turbulence spectra. Finally, we discuss extension of these results to the nonlinear regime (i.e., the order unity image contrast regime).},
doi = {10.1063/1.5013029},
journal = {Review of Scientific Instruments},
number = 12,
volume = 88,
place = {United States},
year = {2017},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 5 works
Citation information provided by
Web of Science

Figures / Tables:

FIG. 1 FIG. 1: Illustration of the experimental setup.

Save / Share:

Works referenced in this record:

The geometry of optimal transportation
journal, January 1996

  • Gangbo, Wilfrid; McCann, Robert J.
  • Acta Mathematica, Vol. 177, Issue 2
  • DOI: 10.1007/bf02392620

Numerical modeling of laser-driven experiments aiming to demonstrate magnetic field amplification via turbulent dynamo
journal, April 2017

  • Tzeferacos, P.; Rigby, A.; Bott, A.
  • Physics of Plasmas, Vol. 24, Issue 4
  • DOI: 10.1063/1.4978628

Proton imaging: a diagnostic for inertial confinement fusion/fast ignitor studies
journal, November 2001


Polar factorization and monotone rearrangement of vector-valued functions
journal, June 1991


Observations of Electromagnetic Fields and Plasma Flow in Hohlraums with Proton Radiography
journal, May 2009


D–3He proton spectra for diagnosing shell ρR and fuel Ti of imploded capsules at OMEGA
journal, June 2000

  • Li, C. K.; Hicks, D. G.; Séguin, F. H.
  • Physics of Plasmas, Vol. 7, Issue 6
  • DOI: 10.1063/1.874099

Charged-Particle Probing of X-ray-Driven Inertial-Fusion Implosions
journal, January 2010


Monoenergetic-Proton-Radiography Measurements of Implosion Dynamics in Direct-Drive Inertial-Confinement Fusion
journal, June 2008


Electric field detection in laser-plasma interaction experiments via the proton imaging technique
journal, May 2002

  • Borghesi, M.; Campbell, D. H.; Schiavi, A.
  • Physics of Plasmas, Vol. 9, Issue 5
  • DOI: 10.1063/1.1459457

Collisionless shock experiments with lasers and observation of Weibel instabilitiesa)
journal, May 2015

  • Park, H. -S.; Huntington, C. M.; Fiuza, F.
  • Physics of Plasmas, Vol. 22, Issue 5
  • DOI: 10.1063/1.4920959

Time evolution of filamentation and self-generated fields in the coronae of directly driven inertial-confinement fusion capsules
journal, January 2012

  • Séguin, F. H.; Li, C. K.; Manuel, M. J. -E.
  • Physics of Plasmas, Vol. 19, Issue 1
  • DOI: 10.1063/1.3671908

A reconstruction of the initial conditions of the Universe by optimal mass transportation
journal, May 2002

  • Frisch, Uriel; Matarrese, Sabino; Mohayaee, Roya
  • Nature, Vol. 417, Issue 6886
  • DOI: 10.1038/417260a

Proton Radiography of a Laser-Driven Implosion
journal, July 2006


An Extended Lagrangian Theory of Semi-Geostrophic Frontogenesis
journal, May 1984


Observation of magnetic field generation via the Weibel instability in interpenetrating plasma flows
journal, January 2015

  • Huntington, C. M.; Fiuza, F.; Ross, J. S.
  • Nature Physics, Vol. 11, Issue 2
  • DOI: 10.1038/nphys3178

Development of an interpretive simulation tool for the proton radiography technique
journal, March 2015

  • Levy, M. C.; Ryutov, D. D.; Wilks, S. C.
  • Review of Scientific Instruments, Vol. 86, Issue 3
  • DOI: 10.1063/1.4909536

Measurements of ρR asymmetries at burn time in inertial-confinement-fusion capsules
journal, August 2002

  • Séguin, F. H.; Li, C. K.; Frenje, J. A.
  • Physics of Plasmas, Vol. 9, Issue 8
  • DOI: 10.1063/1.1492806

First Measurements of Rayleigh-Taylor-Induced Magnetic Fields in Laser-Produced Plasmas
journal, June 2012


From Nash to Cournot–Nash equilibria via the Monge–Kantorovich problem
journal, November 2014

  • Blanchet, Adrien; Carlier, Guillaume
  • Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 372, Issue 2028
  • DOI: 10.1098/rsta.2013.0398

FLASH MHD simulations of experiments that study shock-generated magnetic fields
journal, December 2015


Macroscopic Evidence of Soliton Formation in Multiterawatt Laser-Plasma Interaction
journal, March 2002


Optimal Mass Transport for Registration and Warping
journal, December 2004


Two Numerical Methods for the elliptic Monge-Ampère equation
journal, February 2010

  • Benamou, Jean-David; Froese, Brittany D.; Oberman, Adam M.
  • ESAIM: Mathematical Modelling and Numerical Analysis, Vol. 44, Issue 4
  • DOI: 10.1051/m2an/2010017

Measuring E and B Fields in Laser-Produced Plasmas with Monoenergetic Proton Radiography
journal, September 2006


Partial Differential Equations and Monge-Kantorovich Mass Transfer
journal, January 1997


Intense High-Energy Proton Beams from Petawatt-Laser Irradiation of Solids
journal, October 2000


Observation of Collisionless Shocks in Laser-Plasma Experiments
journal, July 2008


D3He-proton emission imaging for inertial-confinement-fusion experiments (invited)
journal, October 2004

  • Séguin, F. H.; DeCiantis, J. L.; Frenje, J. A.
  • Review of Scientific Instruments, Vol. 75, Issue 10
  • DOI: 10.1063/1.1788892

Invited Article: Relation between electric and magnetic field structures and their proton-beam images
journal, October 2012

  • Kugland, N. L.; Ryutov, D. D.; Plechaty, C.
  • Review of Scientific Instruments, Vol. 83, Issue 10
  • DOI: 10.1063/1.4750234

Observation of Megagauss-Field Topology Changes due to Magnetic Reconnection in Laser-Produced Plasmas
journal, August 2007


Saturation Mechanisms for the Generated Magnetic Field in Nonuniform Laser-Matter Irradiation
journal, January 1997


Proton Radiography of Inertial Fusion Implosions
journal, February 2008


Python for Scientific Computing
journal, January 2007


    Works referencing / citing this record:

    Proton imaging of stochastic magnetic fields
    journal, December 2017


    Laboratory evidence of dynamo amplification of magnetic fields in a turbulent plasma
    journal, February 2018


    Numerical simulation of magnetized jet creation using a hollow ring of laser beams
    journal, February 2019

    • Lu, Y.; Tzeferacos, P.; Liang, E.
    • Physics of Plasmas, Vol. 26, Issue 2
    • DOI: 10.1063/1.5050924

    Design of a new turbulent dynamo experiment on the OMEGA-EP
    journal, March 2019

    • Liao, Andy Sha; Li, Shengtai; Li, Hui
    • Physics of Plasmas, Vol. 26, Issue 3
    • DOI: 10.1063/1.5081062

    Characterizing filamentary magnetic structures in counter-streaming plasmas by Fourier analysis of proton images
    journal, October 2019

    • Levesque, Joseph; Kuranz, Carolyn; Handy, Timothy
    • Physics of Plasmas, Vol. 26, Issue 10
    • DOI: 10.1063/1.5100728

    MPRAD: A Monte Carlo and ray-tracing code for the proton radiography in high-energy-density plasma experiments
    journal, December 2019

    • Lu, Yingchao; Li, Hui; Flippo, Kirk A.
    • Review of Scientific Instruments, Vol. 90, Issue 12
    • DOI: 10.1063/1.5123392

    Retrieving fields from proton radiography without source profiles
    journal, September 2019


    Dynamics of the Electromagnetic Fields Induced by Fast Electron Propagation in Near-Solid-Density Media
    journal, January 2019