This paper focuses on the process of magnetic flux generation in inertial confinement fusion implosions. Hot-spots are shown to be dominated by fields generated during stagnation when the temperature and density gradients are largest. A scaling of hot-spot magnetic flux is derived and compared with simulations, revealing that perturbations with both larger amplitudes and higher mode numbers generate more magnetic flux. The model allows for greater understanding of which target designs will be susceptible to magnetohydrodynamic effects. For example, the model can be used to ascertain the time when most magnetic flux is generated. If generation is weighted more toward early times, then more high-mode magnetic field loops will be present. A hot-spot with no high-mode perturbations at time of peak neutron production can still contain significant magnetic flux on those scales. By assuming that magnetic flux is deposited at the hot-spot edge by Nernst advection, the model can be used to post-process radiation-hydrodynamics data to estimate magnetic field strengths and magnetizations.
References
1.
O. A.
Hurricane
, D. A.
Callahan
, D. T.
Casey
, P. M.
Celliers
, C.
Cerjan
, E. L.
Dewald
, T. R.
Dittrich
, T.
Döppner
, D. E.
Hinkel
, L. F. B.
Hopkins
, J. L.
Kline
, S.
Le Pape
, T.
Ma
, A. G.
MacPhee
, J. L.
Milovich
, A.
Pak
, H.-S.
Park
, P. K.
Patel
, B. A.
Remington
, J. D.
Salmonson
, P. T.
Springer
, and R.
Tommasini
, “Fuel gain exceeding unity in an inertially confined fusion implosion
,” Nature
506
, 343
–348
(2014
).2.
R.
Betti
, M.
Umansky
, V.
Lobatchev
, V. N.
Goncharov
, and R. L.
McCrory
, “Hot-spot dynamics and deceleration-phase Rayleigh–Taylor instability of imploding inertial confinement fusion capsules
,” Phys. Plasmas
8
(12
), 5257
–5267
(2001
).3.
4.
P. T.
Campbell
, C. A.
Walsh
, B. K.
Russell
, J. P.
Chittenden
, A.
Crilly
, G.
Fiksel
, P. M.
Nilson
, A. G.
Thomas
, K.
Krushelnick
, and L.
Willingale
, “Magnetic signatures radiation-driven double ablation fronts
,” Phys. Rev. Lett.
125
, 145001
(2020
).5.
P. T.
Campbell
, C. A.
Walsh
, B. K.
Russell
, J. P.
Chittenden
, A.
Crilly
, L. G.
Fiksel Gao
, P. M.
Nilson
, A. G. R.
Thomas
, K.
Krushelnick
, and L.
Willingale
, “Measuring Biermann battery flux suppression in high-power laser-plasma interactions
,” Phys. Plasmas
(submitted); arxiv.org/abs/2107.12864.6.
D. T.
Casey
, B. J.
MacGowan
, J. D.
Sater
, A. B.
Zylstra
, O. L.
Landen
, J.
Milovich
, O. A.
Hurricane
, A. L.
Kritcher
, M.
Hohenberger
, K.
Baker
, S. L.
Pape
, T.
Döppner
, C.
Weber
, H.
Huang
, C.
Kong
, J.
Biener
, C. V.
Young
, S.
Haan
, R. C.
Nora
, S.
Ross
, H.
Robey
, M.
Stadermann
, A.
Nikroo
, D. A.
Callahan
, R. M.
Bionta
, K. D.
Hahn
, A. S.
Moore
, D.
Schlossberg
, M.
Bruhn
, K.
Sequoia
, N.
Rice
, M.
Farrell
, and C.
Wild
, “Evidence of three-dimensional asymmetries seeded by high-density carbon-ablator nonuniformity in experiments at the National Ignition Facility
,” Phys. Rev. Lett.
126
(2
), 025002
(2021
).7.
J. P.
Chittenden
, S. V.
Lebedev
, C. A.
Jennings
, S. N.
Bland
, and A.
Ciardi
, “X-ray generation mechanisms in three-dimensional simulations of wire array Z-pinches
,” Plasma Phys. Controlled Fusion
46
, B457
–B476
(2004
).8.
A.
Ciardi
, S. V.
Lebedev
, A.
Frank
, E. G.
Blackman
, J. P.
Chittenden
, C. J.
Jennings
, D. J.
Ampleford
, S. N.
Bland
, S. C.
Bott
, J.
Rapley
, G. N.
Hall
, F. A.
Suzuki-Vidal
, A.
Marocchino
, T.
Lery
, and C.
Stehle
, “The evolution of magnetic tower jets in the laboratory
,” Phys. Plasmas
14
, 056501
(2007
).9.
D. S.
Clark
, C. R.
Weber
, J. L.
Milovich
, A. E.
Pak
, D. T.
Casey
, B. A.
Hammel
, D. D.
Ho
, O. S.
Jones
, J. M.
Koning
, A. L.
Kritcher
, M. M.
Marinak
, L. P.
Masse
, D. H.
Munro
, M. V.
Patel
, P. K.
Patel
, H. F.
Robey
, C. R.
Schroeder
, S. M.
Sepke
, and M. J.
Edwards
, “Three-dimensional modeling and hydrodynamic scaling of National Ignition Facility implosions
,” Phys. Plasmas
26
(5
), 050601
(2019
).10.
D. S.
Clark
, C. R.
Weber
, J. L.
Milovich
, J. D.
Salmonson
, A. L.
Kritcher
, S. W.
Haan
, B. A.
Hammel
, D. E.
Hinkel
, O. A.
Hurricane
, O. S.
Jones
, M. M.
Marinak
, P. K.
Patel
, H. F.
Robey
, S. M.
Sepke
, and M. J.
Edwards
, “Three-dimensional simulations of low foot and high foot implosion experiments on the National Ignition Facility
,” Phys. Plasmas
23
(5
), 056302
(2016
).11.
E. M.
Epperlein
and M. G.
Haines
, “Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker-Planck equation
,” Phys. Fluids
29
(4
), 1029
(1986
).12.
C.
Graziani
, P.
Tzeferacos
, D.
Lee
, D. Q.
Lamb
, K.
Weide
, M.
Fatenejad
, and J.
Miller
, “The Biermann catastrophe of numerical MHD
,” J. Phys.
719
, 012018
(2016
).13.
M. G.
Haines
, “Heat flux effects in Ohm's law
,” Plasma Phys. Controlled Fusion
28
, 1705
–1716
(1986
).14.
D. W.
Hill
and R. J.
Kingham
, “Enhancement of pressure perturbations in ablation due to kinetic magnetised transport effects under direct-drive ICF relevant conditions
,” arXiv:1712.02663
(2017
).15.
C.
Jennings
, “Radiation transport effects in wire array Z pinches and magneto-hydrodynamic modelling techniques
,” Ph.D. thesis (University of London
, 2006
).16.
J. D.
Sadler
, H.
Li
, and K. A.
Flippo
, “Magnetic field generation from composition gradients in inertial confinement fusion fuel
,” Philos Trans. R. Soc. A
378
(2184
), 20200045
(2020
).17.
J. D.
Sadler
, H.
Li
, and B. M.
Haines
, “Magnetization around mix jets entering inertial confinement fusion fuel
,” Phys. Plasmas
27
(7
), 072707
(2020
).18.
J. D.
Sadler
, C. A.
Walsh
, and H.
Li
, “Symmetric set of transport coefficients for collisional magnetized plasma
,” Phys. Rev. Lett.
126
(7
), 075001
(2021
).19.
P.
Sharma
and G. W.
Hammett
, “Preserving monotonicity in anisotropic diffusion
,” J. Comput. Phys.
227
(1
), 123
(2007
).20.
M.
Sherlock
and J. J.
Bissell
, “Suppression of the Biermann battery and stabilization of the thermomagnetic instability in laser fusion conditions
,” Phys. Rev. Lett.
124
(5
), 055001
(2020
).21.
B. K.
Spears
, M. J.
Edwards
, S.
Hatchett
, J.
Kilkenny
, J.
Knauer
, A.
Kritcher
, J.
Lindl
, D.
Munro
, P.
Patel
, H. F.
Robey
, and R. P. J.
Town
, “Mode 1 drive asymmetry in inertial confinement fusion implosions on the National Ignition Facility
,” Phys. Plasmas
21
(4
), 042702
(2014
).22.
C. A.
Walsh
, “Extended magneto-hydrodynamic effects in indirect-drive inertial confinement fusion experiments
,” Ph.D. thesis (Imperial College London
, 2018
).23.
C. A.
Walsh
, J. P.
Chittenden
, D. W.
Hill
, and C.
Ridgers
, “Extended-magnetohydrodynamics in under-dense plasmas
,” Phys. Plasmas
27
(2
), 022103
(2020
).24.
C. A.
Walsh
, J. D.
Sadler
, and J. R.
Davies
, “Updated magnetized transport coefficients: Impact on laser-plasmas with self-generated or applied magnetic fields
,” arXiv:2107.12988 (2021
).25.
C. A.
Walsh
, J. P.
Chittenden
, K.
McGlinchey
, N. P. L.
Niasse
, and B. D.
Appelbe
, “Self-generated magnetic fields in the stagnation phase of indirect-drive implosions on the National Ignition Facility
,” Phys. Rev. Lett.
118
(15
), 155001
(2017
).26.
C. A.
Walsh
et al., Nucl. Fusion
60
, 106006
(2020
).© 2021 Author(s). Published under an exclusive license by AIP Publishing.
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