Cartesian Tensor Scalar Product and Spherical Harmonic Expansions in Boltzmann's Equation

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 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…”

mentioning

confidence: 99%

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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“…Here, the more detailed VFP treatment, over a 50 ps timescale, resulted in magnetization of the plasma for linear polarization of over an order of magnitude greater than with the hydrodynamic calculation. Additionally, the growth rate of the fields was significantly less than 10 ps, which is within the typical coherence time of a laser speckle, when the Cartesian tensor distribution 3 function expansion [23] included terms up to order 2. When a reduced model for the full rank 3 heat-flux tensor was included, the growth rate was damped but remained significant in terms of the long-time evolution of the system.…”

Section: Introductionmentioning

confidence: 75%

“…Various methods can be used to reduce the problem. Here a Cartesian tensor expansion [23] is employed, with the distribution function expanded as f (t, r , v) = f 0 + f…”

Section: The Model and Set-upmentioning

confidence: 99%

Rapid self-magnetization of laser speckles in plasmas by nonlinear anisotropic instability

2009

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View the article online for updates and enhancements. Abstract. Presented here are the first kinetic two-dimensional VlasovFokker-Planck calculations of inertial confinement fusion-related laser-plasma interactions, to include self-consistent magnetic fields, hydrodynamic plasma expansion and anisotropic electron pressure. An underdense plasma, reminiscent of the gas fill of a hohlraum, is heated by a laser speckle with I λ 2 = 1.0 × 10 15 W cm −2 µm 2 and radius w 0 = 5 µm. Inverse bremsstrahlung absorption of the laser and non-local electron transport lead to the development of a collisional analogue of the Weibel electromagnetic instability. The instability is seeded by magnetic fields, generated in an initial period of linear growth due to the anisotropic electron distribution arising in a laser speckle. Using the circular polarization does not generate significant fields. For linear polarization, the field generally saturates when the magnetization is ωτ ei > 1, and the effective growth rate is similar to the coherence time of typical laser speckles. The presence of these magnetic fluctuations significantly affects the heat fluxes and hydrodynamics in the plasma. Contents

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“…This is formally equivalent to the Cartesian tensor expansion used in the previous section [30]. Without loss of generality, the driving force s ∈ {E, ∇T } can be specified to be in the x-direction, with the magnetic field B in the z-direction, as before.…”

Section: Plasmas With Arbitrary Atomic Number: Numerical Solutionmentioning

confidence: 99%

Transport coefficients of a relativistic plasma

Pike

Rose

2016

Phys. Rev. E

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In this work, a self-consistent transport theory for a relativistic plasma is developed.Using the notation of Braginskii [S. I. Braginskii, in Reviews of Plasma Physics, ed. M. A. Leontovich (1965), Vol. 1, p.174], we provide semi-analytical forms of the electrical resistivity, thermoelectric and thermal conductivity tensors for a Lorentzian plasma in a magnetic field.This treatment is then generalized to plasmas with arbitrary atomic number by numerically solving the linearized Boltzmann equation. The corresponding transport coefficients are fitted by rational functions in order to make them suitable for use in radiation-hydrodynamic simulations and transport calculations. Within the confines of linear transport theory and on the assumption that the plasma is optically thin, our results are valid for temperatures up to a few MeV. By contrast, classical transport theory begins to incur significant errors above k B T ∼ 10 keV, e.g., the parallel thermal conductivity is suppressed by 15% at k B T = 20 keV due to relativistic effects.

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Cartesian Tensor Scalar Product and Spherical Harmonic Expansions in Boltzmann's Equation

Cited by 84 publications

References 7 publications

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

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

Rapid self-magnetization of laser speckles in plasmas by nonlinear anisotropic instability

Transport coefficients of a relativistic plasma

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