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1.
Philos Trans A Math Phys Eng Sci ; 379(2189): 20200017, 2021 Jan 25.
Article in English | MEDLINE | ID: mdl-33280564

ABSTRACT

Magnetic fields can be generated in plasmas by the Biermann battery when the electric field produced by the electron pressure gradient has a curl. The commonly employed magnetohydrodynamic (MHD) model of the Biermann battery breaks down when the electron distribution function is distorted away from Maxwellian. Using both MHD and kinetic simulations of a laser-plasma interaction relevant to inertial confinement fusion we have shown that this distortion can reduce the Biermann-producing electric field by around 50%. More importantly, the use of a flux limiter in an MHD treatment to deal with the effect of the non-Maxwellian electron distribution on electron thermal transport leads to a completely unphysical prediction of the Biermann-producing electric field and so results in erroneous predictions for the generated magnetic field. This article is part of a discussion meeting issue 'Prospects for high gain inertial fusion energy (part 2)'.

2.
Phys Rev Lett ; 124(5): 055001, 2020 Feb 07.
Article in English | MEDLINE | ID: mdl-32083939

ABSTRACT

Magnetic field generated by the Biermann battery is thought to be one of the principal mechanisms behind the inhibition of heat flow in laser-plasma interactions, and is predicted to grow exponentially in some contexts due to the thermomagnetic instability [Tidman and Shanny, Phys. Fluids 17, 1207 (1974)PFLDAS0031-917110.1063/1.1694866]. In contrast to these predictions, however, we have conducted Vlasov-Fokker-Planck simulations of magnetic field dynamics under a range of classically unstable laser-fusion conditions, and find field generation to be strongly suppressed, preventing magnetization of the transport, and stabilizing instability. By deriving new scaling laws, we show that this stabilization is a consequence of (i) heavy suppression of the Biermann battery under nonlocal conditions; (ii) rapid convection of magnetic field by the heat flow; and (iii) comparatively short field length scales. Our results indicate that classical models substantially overestimate the importance of magnetic fields generated by the Biermann battery, and the susceptibility of laser-fusion plasmas to the thermomagnetic instability.

3.
Proc Math Phys Eng Sci ; 472(2195): 20160649, 2016 Nov.
Article in English | MEDLINE | ID: mdl-27956886

ABSTRACT

By substituting the Cattaneo-Christov heat-flow model for the more usual parabolic Fourier law, we consider the impact of hyperbolic heat-flow effects on thermal convection in the classic problem of a magnetized conducting fluid layer heated from below. For stationary convection, the system is equivalent to that studied by Chandrasekhar (Hydrodynamic and Hydromagnetic Stability, 1961), and with free boundary conditions we recover the classical critical Rayleigh number [Formula: see text] which exhibits inhibition of convection by the field according to [Formula: see text] as [Formula: see text], where Q is the Chandrasekhar number. However, for oscillatory convection we find that the critical Rayleigh number [Formula: see text] is given by a more complicated function of the thermal Prandtl number [Formula: see text], magnetic Prandtl number [Formula: see text] and Cattaneo number C. To elucidate features of this dependence, we neglect [Formula: see text] (in which case overstability would be classically forbidden), and thereby obtain an expression for the Rayleigh number that is far less strongly inhibited by the field, with limiting behaviour [Formula: see text], as [Formula: see text]. One consequence of this weaker dependence is that onset of instability occurs as overstability provided C exceeds a threshold value CT(Q); indeed, crucially we show that when Q is large, [Formula: see text], meaning that oscillatory modes are preferred even when C itself is small. Similar behaviour is demonstrated in the case of fixed boundaries by means of a novel numerical solution.

4.
Proc Math Phys Eng Sci ; 471(2175): 20140845, 2015 Mar 08.
Article in English | MEDLINE | ID: mdl-25792960

ABSTRACT

Adoption of the hyperbolic Cattaneo-Christov heat-flow model in place of the more usual parabolic Fourier law is shown to raise the possibility of oscillatory convection in the classic Bénard problem of a Boussinesq fluid heated from below. By comparing the critical Rayleigh numbers for stationary and oscillatory convection, Rc and RS respectively, oscillatory convection is found to represent the preferred form of instability whenever the Cattaneo number C exceeds a threshold value CT≥8/27π2≈0.03. In the case of free boundaries, analytical approaches permit direct treatment of the role played by the Prandtl number [Formula: see text], which-in contrast to the classical stationary scenario-can impact on oscillatory modes significantly owing to the non-zero frequency of convection. Numerical investigation indicates that the behaviour found analytically for free boundaries applies in a qualitatively similar fashion for fixed boundaries, while the threshold Cattaneo number CT is computed as a function of [Formula: see text] for both boundary regimes.

5.
Phys Rev Lett ; 105(17): 175001, 2010 Oct 22.
Article in English | MEDLINE | ID: mdl-21231051

ABSTRACT

The mechanism for a new instability in magnetized plasmas is presented and a dispersion relation derived. Unstable behavior is shown to result purely from transport processes-feedback between the Nernst effect and the Righi-Leduc heat-flow phenomena in particular-neither hydrodynamic motion nor density gradients are required. Calculations based on a recent nanosecond laser gas-jet experiment [D. H. Froula, Phys. Rev. Lett. 98, 135001 (2007)] predict growth of magnetic field and temperature perturbations with typical wavelengths of order 50 µm and characteristic growth times of ∼0.1 ns. The instability yields propagating magnetothermal waves whose direction depends on the magnitude of the Hall parameter.

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