An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields

Kingham, R. J.; Bell, A. R.

doi:10.1016/j.jcp.2003.08.017

Journal of Computational Physics

2004

DOI: 10.1016/j.jcp.2003.08.017

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An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields

R. J. Kingham

A. R. Bell

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Cited by 89 publications

(83 citation statements)

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“…Higher orders are successively smaller perturbations, f 0 f 1 f 2 etc. In the classical limit that f 0 is a Maxwell-Boltzmann velocity distribution, Impacta has been shown to agree with Braginskii's transport equations [24]. These simulations, however, are collisional enough such that f 2 is neglected to an error…”

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confidence: 93%

“…While these may modify the magnitude of the electron temperature near the high density plasma, the conclusions presented here primarily arise as a result of the non-local dynamics prevalent within the low density, optically thin, gas fill where the radiation effects will be negligible [23]. With the use of Impacta [24,25], we studied the effect of non-equilibrium electron kinetics on thermal energetic and magnetic field dynamics of a Omega-scale hohlraum with an externally imposed 7.5 T magnetic field. We found that significant proportions of the total heat flow are non-local.…”

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confidence: 99%

“…The code we use, Impacta [24,25], uses a Cartesian tensor expansion, with the distribution function expanded as…”

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confidence: 99%

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Kinetic modeling of Nernst effect in magnetized hohlraums

et al. 2016

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We present nanosecond timescale Vlasov-Fokker-Planck-Maxwell modeling of magnetized plasma transport and dynamics in a hohlraum with an applied external magnetic field, under conditions similar to recent experiments. Self-consistent modeling of the kinetic electron momentum equation allows for a complete treatment of the heat flow equation and Ohm's Law, including Nernst advection of magnetic fields. In addition to showing the prevalence of non-local behavior, we demonstrate that effects such as anomalous heat flow are induced by inverse bremsstrahlung heating. We show magnetic field amplification up to a factor of 3 from Nernst compression into the hohlraum wall. The magnetic field is also expelled towards the hohlraum axis due to Nernst advection faster than frozen-in-flux would suggest. Non-locality contributes to the heat flow towards the hohlraum axis and results in an augmented Nernst advection mechanism that is included self-consistently through kinetic modeling.There has been recent interest in the role of applied magnetic fields in high-energy-density plasmas [1-3] for inertial fusion energy applications [4]. The MagnetoInertial Fusion Electric Discharge System has been developed to provide steady state magnetic fields for long time-scales relative to the experiments. An experiment on the Omega Laser Facility with a 7.5 T external axial magnetic field imposed on an Omega-scale hohlraum measured a rise in observed temperature along the hohlraum axis [5] and modeling showed that external fields can guide hot electrons from laser-plasma interactions [6] through the hohlraum, rather than the capsule [7]. From Ohm's Law, it has been shown that electron heat transport advects such magnetic fields through the Nernst effect [8][9][10][11][12][13][14] in addition to well-known processes like "frozen-in-flow" and resistive diffusion. Dimensionless numbers comparing the ratio of the magnitudes of the Nernst term to the bulk plasma flow term, R N 1 [10], and the Hall term, H N 1 [13], suggest that Nernst convection should be the dominant mechanism for magnetic field transport in a hohlraum. Such a hot and semi-collisional environment is, however, rich in nonequilibrium effects that may complicate the magnetic field dynamics.Laser heating of the plasma results in steep temperature gradients, typically O(3 keV/50 µm). The collisional * archis@ucla.edu † agrt@umich.edu mean-free-path of a 3 keV electron is O(10 µm), depending on the plasma density. Since λ mfp /L < 100, nonlocality can be expected to be important [15]. The steep temperature gradients caused by intense laser heating in a hohlraum have been shown to result in non-local heat flow [16,17]. Careful consideration of the electron population with 2v th < v < 4v th is required as these carry most of the heat. Additionally, inverse-bremsstrahlung heating of a plasma [18,19] not only leads to deviations from Braginskii transport [20], but also new transport terms [21,22]. Both non-locality and laser heating result in modifications to the distribution function an...

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Kinetic modeling of Nernst effect in magnetized hohlraums

et al. 2016

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“…The code we use, Impacta [25,26], uses a Cartesian tensor expansion [27], with the distribution function expanded as f (t, r, v) = f 0 +f 1 ·v+f…”

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Magnetic Reconnection in Plasma under Inertial Confinement Fusion Conditions Driven by Heat Flux Effects in Ohm’s Law

et al. 2014

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In the interaction of high-power laser beams with solid density plasma there are a number of mechanisms that generate strong magnetic fields. Such fields subsequently inhibit or redirect electron flows, but can themselves be advected by heat fluxes, resulting in complex interplay between thermal transport and magnetic fields. We show that for heating by multiple laser spots reconnection of magnetic field lines can occur, mediated by these heat fluxes, using a fully implicit 2D VlasovFokker-Planck code. Under such conditions, the reconnection rate is dictated by heat flows rather than Alfvènic flows. We find that this mechanism is only relevant in a high β plasma. However, the Hall parameter ωcτei can be large so that thermal transport is strongly modified by these magnetic fields, which can impact longer time scale temperature homogeneity and ion dynamics in the system. Understanding the O 10 2T magnetic fields that can develop in high-power-laser interactions with soliddensity plasma [1][2][3][4][5] is important because such fields significantly modify both the magnitude and direction of electron heat fluxes [6]. The dynamics of such fields evidently has consequences for inertial fusion energy applications [7][8][9], as the coupling of the laser beams with the walls or pellet and the development of temperature inhomogeneities are critical to the uniformity of the implosion. There is a significant interplay between heat fluxes and magnetic fields: in semi-collisional plasmas heat flux can be the dominant mechanism for transporting magnetic fields in addition to currents or bulk ion flow [10]. This effect, arising due to an electric field analogous to the Nernst-Ettingshausen effect in metals [11], has been shown to be significant in laser heated plasma [12][13][14]. The Nernst effect in plasma [10] arises as a consequence of the velocity dependent collision frequency of electrons in plasma. Since the faster, "hot", population of electrons are essentially collisionless, the magnetic field is "frozen" to them, whereas the collisional, "cold", portion of the distribution function is able to diffuse across field lines. Hence, magnetic fields can be advected with close to zero net current by "hot" electrons.In heating plasma with a finite laser spot, an azimuthal magnetic field about the heated region arises through the Biermann battery effect [15]. For multiple spots in close proximity, as in inertial fusion, these magnetic fields will be in a configuration with oppositely directed field lines. Under such conditions, magnetic reconnection of field lines may be expected to arise. Magnetic reconnection has been intensely studied in space plasmas, but more recently, laser inertial fusion relevant scenarios have been investigated [16][17][18].In Sweet-Parker theory, a resistive region between plasma inflows with resistivity η allows magnetic field lines to diffuse and change topology, leading to jets outflowing at Alfvènic speeds, v A [19,20]. However, observed reconnection rates are rarely well described by this model....

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“…The effects of frozen-in flow and Nernst advection on the magnetic field profile are separated in order to determine which is more important. This novel investigation has been made possible by the development of IMPACT [17] the first twodimensional Vlasov-Fokker-Planck (VFP) code including magnetic fields, hydrodynamic ions and the ability to run over nanosecond timescales. This solves the VFP equation in two cartesian spatial dimensions and three velocity space dimensions.…”

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Magnetic Cavitation and the Reemergence of Nonlocal Transport in Laser Plasmas

2008

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We present the first fully kinetic Vlasov-Fokker-Planck simulations of nanosecond laser-plasma interactions including self-consistent magnetic fields and hydrodynamic plasma expansion. For the largest magnetic fields externally applied to long-pulse laser-gas jet experiments (12T). A significant degree of cavitation of the B-field (>40%) will be shown to occur from the laser heated region in under half a nanosecond. This is due to the Nernst effect and leads to the re-emergence of nonlocality even if the initial value of the magnetic field strength is sufficient to localize the transport. PACS numbers: Valid PACS appear hereRecent interest in inertial confinement fusion (ICF) with the near-completion of the National Ignition Facility (NIF) [1], and in magnetic-reconnection in the novel high energy-density regime [2,3], has brought longpulse laser solid interactions back to the forefront of plasma physics. Magnetohydrodynamics (using Braginskii's classical transport theory [4,5]) is the most commonly employed theoretical model in the simulation of such experiments. The validity of this model to many of these experiments is poorly understood. This is of particular interest to indirect drive ICF [1]. In this scheme a deuterium-tritium fusion capsule is placed in a hohlraum (hollow chamber) of high Z material. This hohlraum generally contains an initially homogeneous under-dense gasfill. The hohlraum wall and gas-fill are heated by many long-pulse lasers creating a plasma. This emits x-rays which drive the compression of the capsule. Whether the heat flow in the plasma is given by Braginskii directly affects the uniformity of the hohlraum conditions which, in turn, can affect the drive uniformity of the capsule and so the fusion yield. The break down of classical heat transport in laser plasmas has been shown to be important in experimental measurements by Hawreliak et al [6] and Gregori et al [7] over nanosecond time-scales.Large magnetic fields -ranging from tens of kilogauss to a megagauss -have been inferred to be important in indirect drive ICF experiments [8,9]. Thus the effect of B-fields on the heat transport in long-pulse laser plasma interactions must be better characterized. Magnetic fields can act to suppress heat flow (by reducing the mobility of the heat-carrying electrons as the Larmor radius becomes smaller than the mean free path) and redirect it. However, this letter is concerned with the fact that B-fields may suppress the breakdown of Braginskii's transport theory. This has recently been addressed in an experiment relevant to a hohlraum gas-fill [10]. The evolution of the magnetic field determines in which regions classical theory is valid at a given time. Under the conditions investigated by Froula et al [10] the B-field may evolve by advecting by 'frozen-in' flow at the plasma's bulk flow velocity or by the Nernst effect [11] (with a velocity v N = 2q e /5n e T e which is proportional to the heat flow [12]). The Nernst effect is often not considered in the modeling of long-pulse interactions an...

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An implicit Vlasov–Fokker–Planck code to model non-local electron transport in 2-D with magnetic fields

Cited by 89 publications

References 63 publications

Kinetic modeling of Nernst effect in magnetized hohlraums

Kinetic modeling of Nernst effect in magnetized hohlraums

Magnetic Reconnection in Plasma under Inertial Confinement Fusion Conditions Driven by Heat Flux Effects in Ohm’s Law

Magnetic Cavitation and the Reemergence of Nonlocal Transport in Laser Plasmas

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