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

Abstract

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....

Kinetic modeling of Nernst effect in magnetized hohlraums

“…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.…”

“…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.…”

Heat flux viscosity in collisional magnetized plasmas

“…11 Finally, recent simulations including multiple laser-produced plasma plumes have shown that the Nernst effect can drive magnetic reconnection of the self-generated magnetic fields. 12 These results call for a detailed theoretical understanding of the role of the heat-flux on magnetic fields in such plasmas. The evolution of the magnetic field is ultimately derived from Faraday's law in association with the generalized Ohm's law, which in High Energy Density (HED) plasma conditions may be written schematically as 4…”

“…16 Indeed in the results from Joglekar et al, which studied reconnection in heat-fluxdriven regimes, it was found that reconnection in the reconnection layer was supported by the pressure tensor. 12 The pressure tensor was calculated from first principles within a Vlasov-Fokker-Planck code, but the ultimate origins were not studied.…”

Enhancement of pressure perturbations in ablation due to kinetic magnetized transport effects under direct-drive inertial confinement fusion relevant conditions

“…Under such conditions the electron distribution function deviates from its equilibrium Maxwellian form and the classical (Braginskii) heat transport model [9] breaks down [10].Experimental measurements have demonstrated that non-local heat transport effects are important in nanosecond time scale laser-solid interactions [11,12], and must be taken into account to align ICF simulations with experimental predictions [13][14][15]. It has been shown that there can be a significant interplay between the non-local heat flux effects and the magnetic field dynamics [16,17].Self-generated magnetic fields have been measured in ablation phase ICF experiments [18,19] and are predicted to be important in a variety of ICF relevant conditions [16,20]. Crossed number density, n e , and temperature, T e , gradients, that occur at perturbations in the laser energy deposition, generate magnetic fields through the Biermann battery mechanism, ∂ t B = −∇n e × ∇T e /(|e|n e ) [21,22].…”