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Numerical Modeling of Laser-Driven Experiments Aiming to Demonstrate Magnetic Field Amplification Via Turbulent Dynamo P

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Numerical Modeling of Laser-Driven Experiments Aiming to Demonstrate Magnetic Field Amplification Via Turbulent Dynamo P Numerical modeling of laser-driven experiments aiming to demonstrate magnetic field amplification via turbulent dynamo P. Tzeferacos, A. Rigby, A. Bott, A. R. Bell, R. Bingham, A. Casner, F. Cattaneo, E. M. Churazov, J. Emig, N. Flocke, F. Fiuza, C. B. Forest, J. Foster, C. Graziani, J. Katz, M. Koenig, C.-K. Li, J. Meinecke, R. Petrasso, H.-S. Park, B. A. Remington, J. S. Ross, D. Ryu, D. Ryutov, K. Weide, T. G. White, B. Reville, F. Miniati, A. A. Schekochihin, D. H. Froula, G. Gregori, and D. Q. Lamb Citation: Physics of Plasmas 24, 041404 (2017); doi: 10.1063/1.4978628 View online: https://doi.org/10.1063/1.4978628 View Table of Contents: http://aip.scitation.org/toc/php/24/4 Published by the American Institute of Physics Articles you may be interested in Magnetic field production via the Weibel instability in interpenetrating plasma flows Physics of Plasmas 24, 041410 (2017); 10.1063/1.4982044 Particle acceleration in laser-driven magnetic reconnection Physics of Plasmas 24, 041408 (2017); 10.1063/1.4978627 Formation of high-speed electron jets as the evidence for magnetic reconnection in laser-produced plasma Physics of Plasmas 24, 041406 (2017); 10.1063/1.4978883 On the generation of magnetized collisionless shocks in the large plasma device Physics of Plasmas 24, 041405 (2017); 10.1063/1.4978882 A self-consistent analytical model for the upstream magnetic-field and ion-beam properties in Weibel-mediated collisionless shocks Physics of Plasmas 24, 041409 (2017); 10.1063/1.4979187 Development of an inertial confinement fusion platform to study charged-particle-producing nuclear reactions relevant to nuclear astrophysics Physics of Plasmas 24, 041407 (2017); 10.1063/1.4979186 PHYSICS OF PLASMAS 24, 041404 (2017) Numerical modeling of laser-driven experiments aiming to demonstrate magnetic field amplification via turbulent dynamo P. Tzeferacos,1,2,a) A. Rigby,2 A. Bott,2 A. R. Bell,2 R. Bingham,3,4 A. Casner,5 F. Cattaneo,1 E. M. Churazov,6,7 J. Emig,8 N. Flocke,1 F. Fiuza,9 C. B. Forest,10 J. Foster,11 C. Graziani,1 J. Katz,12 M. Koenig,13 C.-K. Li,14 J. Meinecke,2 R. Petrasso,14 H.-S. Park,8 B. A. Remington,8 J. S. Ross,8 D. Ryu,15 D. Ryutov,8 K. Weide,1 T. G. White,2 B. Reville,16 F. Miniati,17 A. A. Schekochihin,2 D. H. Froula,12 G. Gregori,2,1 and D. Q. Lamb1 1Department of Astronomy and Astrophysics, University of Chicago, Chicago, Illinois 60637, USA 2Department of Physics, University of Oxford, Oxford OX1 3PU, United Kingdom 3Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, United Kingdom 4Department of Physics, University of Strathclyde, Glasgow G4 0NG, United Kingdom 5CEA, DAM, DIF, F-91297 Arpajon, France 6Max Planck Institute for Astrophysics, D-85741 Garching, Germany 7Space Research Institute (IKI), Moscow 117997, Russia 8Lawrence Livermore National Laboratory, Livermore, California 94550, USA 9SLAC National Accelerator Laboratory, Menlo Park, California 94025, USA 10Physics Department, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA 11AWE, Aldermaston, Reading, West Berkshire, RG7 4PR, United Kingdom 12Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA 13Laboratoire pour l’Utilisation de Lasers Intenses, UMR7605, CNRS CEA, Universite Paris VI Ecole Polytechnique, France 14Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 15Department of Physics, UNIST, Ulsan 689-798, South Korea 16School of Mathematics and Physics, Queens University Belfast, Belfast BT7 1NN, United Kingdom 17Department of Physics, ETH Zurich,€ CH-8093 Zurich,€ Switzerland (Received 24 October 2016; accepted 3 February 2017; published online 22 March 2017) The universe is permeated by magnetic fields, with strengths ranging from a femtogauss in the voids between the filaments of galaxy clusters to several teragauss in black holes and neutron stars. The standard model behind cosmological magnetic fields is the nonlinear amplification of seed fields via turbulent dynamo to the values observed. We have conceived experiments that aim to demonstrate and study the turbulent dynamo mechanism in the laboratory. Here, we describe the design of these experiments through simulation campaigns using FLASH, a highly capable radiation magnetohydrodynamics code that we have developed, and large-scale three-dimensional simulations on the Mira supercomputer at the Argonne National Laboratory. The simulation results indicate that the experimental platform may be capable of reaching a turbulent plasma state and determining the dynamo amplification. We validate and compare our numerical results with a small subset of experimental data using synthetic diagnostics. Published by AIP Publishing. [http://dx.doi.org/10.1063/1.4978628] I. INTRODUCTION salient agents in astrophysical and cosmological phenomena. This, in conjunction with their ubiquity, has led naturally to Magnetic fields are encountered throughout the uni- the two-fold question of their origin: (1) how are magnetic verse.1 Observational methods based on Faraday rotation fields generated and (2) how do they reach and maintain and polarization measurements, Zeeman effect, and such large values? magneto-bremsstrahlung, even in situ measurements in the The answer to this question is commonly expressed in case of proximal astrophysical objects, have revealed the 2 terms of dynamo action that operates on seed magnetic broad range of values of cosmical magnetic fields: from a 1,3,4 femtogauss in the tenuous voids between galaxy cluster fila- fields. Cosmological seed magnetic fields can be gener- ments, to several microgauss in galaxies and galaxy clusters, ated via a number of mechanisms, such as plasma instabil- ities and thermal electromotive forces,2 the Biermann battery a milligauss in molecular clouds, a few gauss in planets, tens 5 of kilogauss in ordinary stars and accretion disks, a mega- effect that arises from misaligned electron pressure and den- sity gradients, or the Weibel instability6 that can occur in gauss in white dwarfs, and many teragauss in the vicinity of 7 black holes and neutron stars. Astrophysical fields are often collisionless shocks. These seed fields are then amplified by “strong,” in the sense that their energy can amount to a sub- the hydromagnetic dynamo mechanism which achieves a stantial fraction of system’s energy budget, making them sustained conversion of kinetic energy into magnetic energy throughout the bulk of an electrically conducting fluid. This mechanism was first invoked almost a century ago for solar 8 a)Electronic mail: petros.tzeferacos@flash.uchicago.edu magnetic fields. 1070-664X/2017/24(4)/041404/14/$30.00 24, 041404-1 Published by AIP Publishing. 041404-2 Tzeferacos et al. Phys. Plasmas 24, 041404 (2017) An attractive feature of dynamos is that the requirements turbulence and large magnetic Reynolds numbers needed for their operation are modest. The two key ingredients are for turbulent dynamo to operate. The simulations were also fluid motions that are not too symmetric9,10 and high electri- necessary to determine when to fire the diagnostics since cal conductivity.11,12 Both of these requirements are amply the experiments last tens of nanoseconds, but the strongly satisfied by the turbulent motions and high magnetic amplified magnetic fields persisted for only a fraction of Reynolds numbers prevalent in most astrophysical situa- this time. tions,2 supporting the expectation that dynamo action is In Sec. II, we describe the high energy density labora- widespread in astrophysics.1,2,13 While astrophysical dyna- tory plasma (HEDLP) capabilities of the FLASH code that mos come in many flavors,14 they are often distinguished15 was used in the simulations we performed. In Sec. III,we between large-scale (or mean-field) dynamos, in which the discuss the key elements of the platforms we used in previ- magnetic field grows at scales larger than those of the fluid ous experiments. These platforms informed the design of the motion, and small-scale (or fluctuation) dynamos, where the experiments that we describe here. In Sec. IV, we describe growth occurs at or below the outer scales of motion. In this the simulations that we performed and that led to the fielded article, we will concern ourselves with small-scale dynamo, experimental platform, as well as the final design. In Sec. V, at magnetic Prandtl numbers (i.e., magnetic-to-fluid we discuss the simulation results, as well as their validation 15 Reynolds number ratio) smaller than unity. Astrophysical against a subset of experimental data. environments with small magnetic Prandtl numbers include planetary cores, stellar convection zones, the galactic disk, II. SIMULATION CODE 2 and parts of the interstellar medium. 31,32 Even though conditions favorable for dynamos are com- We use the FLASH code to carry out the large-scale simulations of our laser experiments to study the origin of mon in astrophysics, they are extremely difficult to realize in 33 laboratory experiments.16 Thus, so far, our physical intuition cosmic magnetic fields. FLASH is a publicly available, in the working of dynamos is mostly based on theoretical con- parallel, multi-physics, adaptive mesh refinement (AMR), siderations and numerical modeling.14,17–21 The reasons for finite-volume Eulerian hydrodynamics, and MHD code. this state of affairs can be easily explained. The two natural FLASH scales well to over 100,000 processors and uses a working fluids for laboratory dynamo experiments are liquid variety of parallelization techniques including domain metals22–24 and strongly ionized gases,
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