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arxiv: 1906.12012 · v1 · pith:ZFRHX6HHnew · submitted 2019-06-28 · ⚛️ physics.plasm-ph · physics.ins-det· physics.optics

Simultaneous polarization transformation and amplification of multi-petawatt laser pulses in magnetized plasmas

Pith reviewed 2026-05-25 13:52 UTC · model grok-4.3

classification ⚛️ physics.plasm-ph physics.ins-detphysics.optics
keywords plasma waveplatemagneto-optical birefringencepetawatt laserspolarization transformationplasma opticslaser amplificationtransverse magnetic fieldhigh intensity laser pulses
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0 comments X

The pith

Magnetized plasma converts a 5-petawatt linearly polarized laser pulse into a circularly polarized pulse exceeding 10 petawatts at 98 percent energy efficiency.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proposes a plasma waveplate that uses magneto-optical birefringence in a transversely magnetized plasma to handle laser powers far beyond the damage limits of solid optics. This device changes the polarization of an incoming laser pulse from linear to circular while increasing its peak power. Numerical results show the conversion of a 5-petawatt input into more than 10 petawatts output in a centimeter-scale structure. The effect arises because the plasma sustains extreme fields and the birefringence produces the required phase shift between polarization components. The required thickness scales inversely with electron density and the square of the magnetic field strength.

Core claim

A plasma waveplate based on magneto-optical birefringence under a transverse magnetic field can simultaneously alter the polarization state and boost the peak laser power, converting an initially linearly polarized 5 petawatt pulse into a circularly polarized pulse with peak power higher than 10 petawatts at an energy conversion efficiency of about 98 percent.

What carries the argument

Magneto-optical birefringence under a transverse magnetic field, which produces different refractive indices for the two orthogonal polarization components of the laser and thereby enables both the polarization change and the intensity amplification in the plasma response.

If this is right

  • The waveplate thickness scales inversely with plasma electron density and the square of the magnetic field.
  • A 1-centimeter thickness suffices at an electron density of 3 times 10 to the 20 per cubic centimeter and a 100-tesla field.
  • The approach supports effective utilization of multi-petawatt laser systems through plasma-based optical components.
  • Similar plasma devices could address other manipulation tasks for high-power lasers.
  • Energy conversion efficiency of the polarization transformation reaches about 98 percent.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the scaling holds, the same birefringence principle could be tested in lower-density plasmas paired with stronger pulsed magnets to reduce the required device size further.
  • The power-boosting feature might allow these waveplates to serve as intensity compressors in laser-plasma acceleration setups that need circular polarization.
  • Integration with other proposed plasma optics could create all-plasma beamlines that avoid solid-state damage thresholds entirely.

Load-bearing premise

The magneto-optical birefringence model and the plasma response remain valid at multi-petawatt intensities without being overtaken by competing instabilities or nonlinear plasma effects.

What would settle it

A simulation or measurement at 5 petawatt peak power that shows filamentation, Raman scattering, or other instabilities preventing the polarization transformation from reaching the predicted 98 percent efficiency within the calculated thickness.

Figures

Figures reproduced from arXiv: 1906.12012 by Hanghang Ma, Min Chen, Paul McKenna, Suming Weng, Xiaolong Zheng, Zhengming Sheng, Zhe Zhang.

Figure 1
Figure 1. Figure 1: FIG. 1. Sketch of the magnetized plasma quarter-wave plate. [PITH_FULL_IMAGE:figures/full_fig_p005_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Stokes parameters of a laser pulse (a) before and (b) a [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. (a) Stokes parameters for a weakly relativistic lase [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Isosurfaces of the electromagnetic field energy dens [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Stokes parameters of a laser pulse after it passes thr [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Stokes Parameters of a short laser pulse after it pass [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
read the original abstract

With increasing laser peak power, the generation and manipulation of high-power laser pulses becomes a growing challenge for conventional solid-state optics due to their limited damage threshold. As a result, plasma-based optical components which can sustain extremely high fields are attracting increasing interest. Here, we propose a type of plasma waveplate based on magneto-optical birefringence under a transverse magnetic field, which can work under extremely high laser power. Importantly, this waveplate can simultaneously alter the polarization state and boost the peak laser power. It is demonstrated numerically that an initially linearly polarized laser pulse with 5 petawatt peak power can be converted into a circularly polarized pulse with a peak power higher than 10 petawatts by such a waveplate with a centimeter-scale diameter. The energy conversion efficiency of the polarization transformation is about $98\%$. The necessary waveplate thickness is shown to scale inversely with plasma electron density $n_e$ and the square of magnetic field $B_0$, and it is about 1 cm for $n_e=3\times 10^{20}$ cm$^{-3}$ and $B_0=100$ T. The proposed plasma waveplate and other plasma-based optical components can play a critical role for the effective utilization of multi-petawatt laser systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript proposes a plasma waveplate based on magneto-optical birefringence in a transversely magnetized plasma slab that simultaneously converts the polarization of an initially linearly polarized multi-petawatt laser pulse to circular while amplifying its peak power, with a numerical demonstration claiming conversion of a 5 PW pulse to >10 PW circular at ~98% energy efficiency in a ~1 cm thick plasma at ne=3×10^20 cm^{-3} and B0=100 T; the required thickness scales inversely with ne and B0^2.

Significance. If the linear birefringence model and numerical results hold under the stated conditions, the work could enable plasma-based optical components for multi-petawatt laser systems that exceed the damage thresholds of solid-state optics, providing both polarization control and power amplification with a simple scaling law for design.

major comments (2)
  1. [Abstract / numerical demonstration] Abstract and numerical demonstration section: the central quantitative claims (98% efficiency, power doubling from 5 PW linear to >10 PW circular) rest on a numerical demonstration, but no details are supplied on the simulation method, spatial/temporal resolution, convergence tests, or explicit verification that competing instabilities (filamentation, Raman/Brillouin scattering, ponderomotive density perturbations) remain negligible over the ~1 cm length and ~ps timescales at these intensities.
  2. [Scaling relation] Scaling relation (thickness ~1/(ne B0^2)): this is derived under the linear cold-fluid magneto-optical response; the manuscript must demonstrate or bound the intensity threshold at which relativistic or ponderomotive nonlinearities invalidate the linear phase-shift accumulation, as this directly limits applicability to the claimed 5–10 PW regime.
minor comments (1)
  1. [Abstract] The abstract states the result is 'demonstrated numerically' without naming the code, dimensionality, or boundary conditions, which would improve clarity and reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive review. We address each major comment below, indicating revisions to strengthen the manuscript.

read point-by-point responses
  1. Referee: Abstract and numerical demonstration section: the central quantitative claims (98% efficiency, power doubling from 5 PW linear to >10 PW circular) rest on a numerical demonstration, but no details are supplied on the simulation method, spatial/temporal resolution, convergence tests, or explicit verification that competing instabilities (filamentation, Raman/Brillouin scattering, ponderomotive density perturbations) remain negligible over the ~1 cm length and ~ps timescales at these intensities.

    Authors: We agree that the numerical demonstration requires additional supporting details for full credibility. The simulations underlying the 98% efficiency and power-doubling claims were performed with a specific method and resolution, but these were omitted from the manuscript. In the revised version we will add a dedicated subsection describing the simulation approach, grid and time-step resolutions, convergence tests performed, and quantitative checks (growth-rate estimates or auxiliary runs) confirming that filamentation, Raman/Brillouin, and ponderomotive perturbations remain negligible over the stated length and duration. revision: yes

  2. Referee: Scaling relation (thickness ~1/(ne B0^2)): this is derived under the linear cold-fluid magneto-optical response; the manuscript must demonstrate or bound the intensity threshold at which relativistic or ponderomotive nonlinearities invalidate the linear phase-shift accumulation, as this directly limits applicability to the claimed 5–10 PW regime.

    Authors: The scaling law follows directly from the linear cold-fluid dispersion relation. To bound its validity we will insert a short paragraph that derives an intensity threshold by requiring the normalized vector potential a0 to remain ≪1 and the ponderomotive density perturbation to be small compared with the background density. Using the stated parameters (ne=3×10^20 cm^{-3}, B0=100 T) we will explicitly state the maximum intensity (and corresponding power for a given focal spot) below which the linear phase accumulation remains accurate, thereby confirming that the 5 PW demonstration lies inside the reported regime. revision: yes

Circularity Check

0 steps flagged

Derivation self-contained; no circular reductions identified

full rationale

The paper proposes a plasma waveplate effect based on standard magneto-optical birefringence under transverse B0, with the thickness scaling derived from linear phase-shift accumulation (inversely with ne and B0 squared) and the 5 PW to >10 PW conversion plus 98% efficiency obtained as direct numerical outputs of the model for stated parameters. No equations reduce the claimed power amplification or efficiency to a fitted parameter defined from the same simulation; the result is not self-definitional, not a renamed known result, and does not rely on load-bearing self-citations or smuggled ansatzes. The linear-regime assumption is a validity question outside circularity analysis.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The claim rests on the standard cold-plasma or fluid response to a transverse magnetic field plus the assumption that the laser-plasma interaction remains in the linear birefringence regime at petawatt intensities. No new particles or forces are introduced.

free parameters (2)
  • plasma electron density n_e
    Example value 3e20 cm^-3 is chosen to set the required thickness; it is an input parameter rather than derived.
  • magnetic field B_0
    Example value 100 T is chosen to set the required thickness; it is an external input.
axioms (2)
  • domain assumption Magneto-optical birefringence arises from the difference in refractive indices for left- and right-circular polarization in a magnetized plasma.
    Invoked to justify the waveplate function; standard result in plasma physics but not re-derived here.
  • domain assumption The plasma slab remains uniform and stable over the interaction length at the stated intensities.
    Required for the centimeter-scale device to function as described.

pith-pipeline@v0.9.0 · 5778 in / 1635 out tokens · 26285 ms · 2026-05-25T13:52:24.934136+00:00 · methodology

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages

  1. [1]

    Strickland and G

    D. Strickland and G. Mourou, Compression of amplified chirped optical pulses, Opt. Commun. 55, 447-449 (1985)

  2. [2]

    Danson, D

    C. Danson, D. Hillier, N. Hopps, and D. Neely, Petawatt class lasers worldwide, High Power Laser Sci. Eng. 3, e3 (2015)

  3. [3]

    G. A. Mourou, T. Tajima, and S. V. Bulanov, Optics in the relativistic regime, Rev. Mod. Phys. 78, 309-371 (2006)

  4. [4]

    Gibbon, Short Pulse Laser Interactions with Matter (Imperial College Press, 2005)

    P. Gibbon, Short Pulse Laser Interactions with Matter (Imperial College Press, 2005)

  5. [5]

    B. C. Stuart, M. D. Feit, S. Herman, A. M. Rubenchik, B. W. Shore, and M. D. Perry, Nanosecond-to-femtosecond laser-induced breakdown in dielectrics, Phys. Rev. B 53, 1749-1761 (1996)

  6. [6]

    Cotel, B

    A. Cotel, B. Villier, and C. Gombaud, Conference on Lasers and Electro-Optics , OSA Technical Digest SM2M.2 (2016)

  7. [7]

    Suckewer, Ultra-intense lasers: Beyond a petawatt, Nat

    S. Suckewer, Ultra-intense lasers: Beyond a petawatt, Nat. Phys. 7, 11-12 (2011)

  8. [8]

    Doumy, F

    G. Doumy, F. Qu\' e r\' e , O. Gobert, M. Perdrix, Ph. Martin, P. Audebert, J. C. Gauthier, J.-P. Geindre, and T. Wittmann, Complete characterization of a plasma mirror for the production of high-contrast ultraintense laser pulses, Phys. Rev. E 69, 026402 (2004)

  9. [9]

    Thaury, F

    C. Thaury, F. Qu\' e r\' e , J.-P. Geindre, A. Levy, T. Ceccotti, P. Monot, M. Bougeard, F. R\' e au, P. D'Oliveira, P. Audebert, R. Marjoribanks, and Ph. Martin, Plasma mirrors for ultrahigh-intensity optics, Nat. Phys. 3, 424-429 (2007)

  10. [10]

    Nakatsutsumi, A

    M. Nakatsutsumi, A. Kon, S. Buffechoux, P. Audebert, J. Fuchs, and R. Kodama, Fast focusing of short-pulse lasers by innovative plasma optics toward extreme intensity, Opt. Lett. 35, 2314-2316 (2010)

  11. [11]

    S. V. Bulanov, T. Esirkepov, and T. Tajima, Light Intensification towards the Schwinger Limit, Phys. Rev. Lett. 91, 085001 (2003)

  12. [12]

    Shvets, N

    G. Shvets, N. J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, Superradiant Amplification of an Ultrashort Laser Pulse in a Plasma by a Counterpropagating Pump, Phys. Rev. Lett. 81, 4879-4882 (1998)

  13. [13]

    A. A. Andreev, C. Riconda, V. T. Tikhonchuk, and S. Weber, Short light pulse amplification and compression by stimulated Brillouin scattering in plasmas in the strong coupling regime, Phys. Plasmas 13, 053110 (2006)

  14. [14]

    R. M. G. M. Trines, F. Fi\' u za, R. Bingham, R. A. Fonseca, L. O. Silva, R. A. Cairns, and P. A. Norreys, Simulations of efficient Raman amplification into the multipetawatt regime, Nat. Phys. 7, 87-92 (2011)

  15. [15]

    Chiaramello, F

    M. Chiaramello, F. Amiranoff, C. Riconda, and S. Weber, Role of Frequency Chirp and Energy Flow Directionality in the Strong Coupling Regime of Brillouin-Based Plasma Amplification, Phys. Rev. Lett. 117, 235003 (2016)

  16. [16]

    Turnbull, S

    D. Turnbull, S. Bucht, A. Davies, D. Haberberger, T. Kessler, J. L. Shaw, and D. H. Froula, Raman amplification with a flying focus, Phys. Rev. Lett. 120, 024801 (2018)

  17. [17]

    Z. M. Sheng, J. Zhang, and D. Umstadter, Plasma density gratings induced by intersecting laser pulses in underdense plasmas, Appl. Phys. B: Lasers Opt. 77, 673-680 (2003)

  18. [18]

    H. C. Wu, Z. M. Sheng, Q. J. Zhang, Y. Cang, and J. Zhang, Manipulating ultrashort intense laser pulses by plasma Bragg gratings, Phys. Plasmas 12, 113103 (2005)

  19. [19]

    H. C. Wu, Z. M. Sheng, and J. Zhang, Chirped pulse compression in nonuniform plasma Bragg gratings, Appl. Phys. Lett. 87, 201502 (2005)

  20. [20]

    L. L. Yu, Z. M. Sheng, and J. Zhang, Plasma Bragg density gratings produced by optical-field ionization, J. Opt. Soc, Am. B 26, 2095-2100 (2009)

  21. [21]

    Lehmann and K

    G. Lehmann and K. H. Spatschek, Transient plasma photonic crystals for high-power lasers, Phys. Rev. Lett. 116, 225002 (2016)

  22. [22]

    L. L. Yu, Y. Zhao, L. J. Qian, M. Chen, S. M. Weng, Z. M. Sheng, D. A. Jaroszynski, W. B. Mori, and J. Zheng, Plasma optical modulators for intense lasers, Nat. Commun. 7, 11893 (2016)

  23. [23]

    G.-Izquierdo, R

    B. G.-Izquierdo, R. J. Gray, M. King, R. J. Dance, R. Wilson, J. McCreadie, N. M. H. Butler, R. Capdessus, S. Hawkes, J. S. Green, M. Borghesi, D. Neely, and P. McKenna, Optically controlled dense current structures driven by relativistic plasma aperture-induced diffraction, Nat. Phys. 12, 505-512 (2016)

  24. [24]

    G.-Izquierdo M

    B. G.-Izquierdo M. King, R. J. Gray, R. Wilson, R. J. Dance, H. Powell, D. A. Maclellan, J. McCreadie, N. M. H. Butler, S. Hawkes, J. S. Green, C. D. Murphy, L. C. Stockhausen, D. C. Carroll, N. Booth, G. G. Scott, M. Borghesi, D. Neely, and P. McKenna, Towards optical polarization control of laser-driven proton acceleration in foils undergoing relativist...

  25. [25]

    W. Q. Wei, X. H. Yuan, Y. Fang, Z. Y. Ge, X. L. Ge, S. Yang, Y. F. Li, G. Q. Liao, Z. Zhang, F. Liu, M. Chen, L. Zhao, H. B. Zhuo, Y. T. Li, Z. M. Zheng, and J. Zhang, Plasma optical shutter in ultraintense laser-foil interaction, Phys. Plasmas 24, 113111 (2017)

  26. [26]

    Leblanc, A

    A. Leblanc, A. Denoeud, L. Chopineau, G. Mennerat, Ph. Martin, and F. Qu\' e r\' e , Plasma holograms for ultrahigh-intensity optics, Nat. Phys. 13, 440-443 (2017)

  27. [27]

    Michel, L

    P. Michel, L. Divol, E. A. Williams, S. Weber, C. A. Thomas, D. A. Callahan, S. W. Haan, J. D. Salmonson, S. Dixit, D. E. Hinkel, M. J. Edwards, B. J. MacGowan, J. D. Lindl, S. H. Glenzer, and L. J. Suter, Tuning the implosion symmetry of ICF targets via controlled crossed-beam energy transfer, Phys. Rev. Lett. 102, 025004 (2009)

  28. [28]

    J. D. Moody et al., Multistep redirection by cross-beam power transfer of ultrahigh-power lasers in a plasma, Nat. Phys. 8, 344-349 (2012)

  29. [29]

    Michel, L

    P. Michel, L. Divol, D. Turnbull, and J. D. Moody, Dynamic control of the polarization of intense laser beams via optical wave mixing in plasmas, Phys. Rev. Lett. 113, 205001 (2014)

  30. [30]

    Turnbull, P

    D. Turnbull, P. Michel, T. Chapman, E. Tubman, B. B. Pollock, C. Y. Chen, C. Goyon, J. S. Ross, L. Divol, N. Woolsey, and J. D. Moody, High power dynamic polarization control using plasma photonics, Phys. Rev. Lett. 116, 205001 (2016)

  31. [31]

    Lehmann and K

    G. Lehmann and K. H. Spatschek, Plasma-based polarizer and waveplate at large laser intensity, Phys. Rev. E 97, 063201 (2018)

  32. [32]

    S. Weng, Q. Zhao, Z. Sheng, W. Yu, S. Luan, M. Chen, L. Yu, M. Murakami, W. B. Mori, and J. Zhang, Extreme case of Faraday effect: magnetic splitting of ultrashort laser pulses in plasmas, Optica 4, 1086-1091 (2017)

  33. [33]

    F. F. Chen, Introduction to Plasma Physics and Controlled Fusion (Plenum Press, New York, 1984)

  34. [34]

    A. K. Zvezdin and V. A. Kotov, Modern Magnetooptics and Magnetooptical Materials (Taylor & Francis Group, New York,1997)

  35. [35]

    S. E. Segre, A review of plasma polarimetry-theory and methods, Plasma Phys. Control. Fusion 41, R57-R100 (1999)

  36. [36]

    Shorokhov, A

    O. Shorokhov, A. Pukhov, and I. Kostyukov, Self-compression of laser pulses in plasma, Phys. Rev. Lett. 91, 265002 (2003)

  37. [37]

    C. Ren, B. J. Duda, R. G. Hemker, W. B. Mori, T. Katsouleas, T. M. Antonsen, and P. Mora, Compressing and focusing a short laser pulse by a thin plasma lens, Phys. Rev. E 63, 026411 (2001)

  38. [38]

    R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Katsouleas, and J. C. Adam, OSIRIS, a three-dimensional fully relativistic particle in cell code for modeling plasma based accelerators, Lect. Notes Comput. Sci. 2331, 342-351 (2002)

  39. [39]

    B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics (Wiley, 1991)

  40. [40]

    T. C. Wilson, F. Y. Li, M. Weikum, and Z. M. Sheng, Influence of strong magnetic fields on laser pulse propagation in underdense plasma, Plasma Phys. Control. Fusion 59, 065002 (2017)

  41. [41]

    T. C. Wilson, F. Y. Li, S. M. Weng, M. Chen, P. McKenna, and Z. M. Sheng, Laser pulse compression towards collapse and beyond in plasma, J. Phys. B: At. Mol. Opt. Phys. 52, 055403 (2019)

  42. [42]

    Scullion, D

    C. Scullion, D. Doria, L. Romagnani, A. Sgattoni, K. Naughton, D. R. Symes, P. McKenna, A. Macchi, M. Zepf, S. Kar, and M. Borghesi, Polarization dependence of bulk ion acceleration from ultrathin foils irradiated by high-intensity ultrashort laser pulses, Phys. Rev. Lett. 119, 054801 (2017)

  43. [43]

    T.-P. Yu, A. Pukhov, Z.-M. Sheng, F. Liu, and G. Shvets, Bright betatronlike x rays from radiation pressure acceleration of a mass-limited foil target, Phys. Rev. Lett. 110, 045001 (2013)

  44. [44]

    J. H. Bin, W. J. Ma, H. Y. Wang, M. J. V. Streeter, C. Kreuzer, D. Kiefer, M. Yeung, S. Cousens, P. S. Foster, B. Dromey, X. Q. Yan, R. Ramis, J. Meyer-ter-Vehn, M. Zepf, and J. Schreiber, Ion acceleration using relativistic pulse shaping in near-critical-density plasmas, Phys. Rev. Lett. 115, 064801 (2015)

  45. [45]

    X. F. Shen, B. Qiao, H. Zhang, S. Kar, C. T. Zhou, H. X. Chang, M. Borghesi, and X. T. He, Achieving stable radiation pressure acceleration of heavy ions via successive electron replenishment from ionization of a high-material coating, Phys. Rev. Lett. 118, 204802 (2017)

  46. [46]

    Eliezer, The Interaction of High-Power Lasers with Plasmas (Institute of Physics Publishing, 2002)

    S. Eliezer, The Interaction of High-Power Lasers with Plasmas (Institute of Physics Publishing, 2002)

  47. [47]

    M Weng, Z

    S. M Weng, Z. M. Sheng, and J. Zhang, Inverse bremsstrahlung absorption with nonlinear effects of high laser intensity and non-Maxwellian distribution, Phys. Rev. E 80, 056406 (2009)

  48. [48]

    Fujioka, Z

    S. Fujioka, Z. Zhang, K. Ishihara, K. Shigemori, Y. Hironaka, T. Johzaki, A. Sunahara, N. Yamamoto, H. Nakashima, T. Watanabe, H. Shiraga, H. Nishimura, and H. Azechi, Kilotesla magnetic field due to a capacitor-coil target driven by high power laser, Sci. Rep. 3, 1170 (2013)

  49. [49]

    K. F. F. Law, M. Bailly-Grandvaux, A. Morace, S. Sakata, K. Matsuo, S. Kojima, S. Lee, X. Vaisseau, Y. Arikawa, A. Yogo, K. Kondo, Z. Zhang, C. Bellei, J. J. Santos, S. Fujioka, and H. Azechi, Direct measurement of kilo-tesla level magnetic field generated with laser-driven capacitor-coil target by proton deflectometry, Appl. Phys. Lett. 108, 091104 (2016)

  50. [50]

    V. T. Tikhonchuk, M. Bailly-Grandvaux, J. J. Santos, and A. Poy\' e , Quasistationary magnetic field generation with a laser-driven capacitor-coil assembly, Phys. Rev. E 96, 023202 (2017)