Magnetization around mix jets entering inertial confinement fusion fuel

Sadler, James; Li, Hui; Haines, Brian

doi:10.1063/5.0012959

Cited by 14 publications

(8 citation statements)

References 37 publications

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“…Numerical simulations have predicted |B| ≃ 5 kT in current national ignition facility (NIF) experiments 23 . Separate post-processing 24 of radiation-hydrodynamic simulations with the xRAGE code was in agreement with this value. Recently, a much simpler and faster post-processing technique was developed 25 .…”

Section: Introductionsupporting

confidence: 79%

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Role of self-generated magnetic fields in the inertial fusion ignition threshold

Sadler,

Walsh,

Zhou

et al. 2022

Preprint

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Magnetic fields spontaneously grow at unstable interfaces around hot-spot asymmetries during inertial confinement fusion implosions. Although difficult to measure, theoretical considerations and numerical simulations predict field strengths exceeding 5 kT in current national ignition facility experiments. Magnetic confinement of electrons then reduces the hot-spot heat loss by > 5%. We demonstrate this via magnetic post-processing of two-dimensional xRAGE hydrodynamic simulation data at bang time. We then derive a model for the self-magnetization, finding that it varies with the square of the stagnation temperature and inversely with the areal density. The self-magnetized Lawson analysis then gives a slightly reduced ignition threshold. Time dependent hot-spot energy balance models corroborate this finding, with the magnetic field quadrupling the fusion yield for near threshold parameters. The inclusion of magnetized multi-dimensional fluid instabilities could further alter the ignition threshold, and will be the subject of future work.

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Section: Introductionsupporting

confidence: 79%

“…To answer this question, in section two we extend our previous analysis of the data from a two-dimensional radiationhydrodynamic simulation 24 . We now go further, and use the post-processed magnetic field profile to quantify the reduc-tion in hot-spot heat loss.…”

Section: Introductionmentioning

confidence: 99%

Role of self-generated magnetic fields in the inertial fusion ignition threshold

Sadler,

Walsh,

Zhou

et al. 2022

Preprint

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“…Although there are many subtle effects arising from plasma composition gradients 28,29 , magnetic instabilities have barely been explored, since the Z dependence of β ⊥ is often neglected. Further study 20,30 has found that in low Z plasma regions with steep gradients in Z, this thermal force source term is actually of similar magnitude to the Biermann battery source term. This was previously verified via a kinetic simulation 30 .…”

Section: Extended Mhd Modelmentioning

confidence: 91%

“…Further study 20,30 has found that in low Z plasma regions with steep gradients in Z, this thermal force source term is actually of similar magnitude to the Biermann battery source term. This was previously verified via a kinetic simulation 30 .…”

Section: Extended Mhd Modelmentioning

confidence: 91%

Thermomagnetic instability of plasma composition gradients

Sadler,

2020

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We show that, under Braginskii magneto-hydrodynamics, anti-parallel gradients in average ion charge state and electron temperature can be unstable to the growth of self-generated magnetic fields. The instability is analogous to the fieldgenerating thermomagnetic instability, although it is driven by the collisional thermal force magnetic source term rather than the Biermann battery term. The gradient in ion charge state causes a gradient in collisionality, which couples with temperature perturbations to create a self-generated magnetic field. This magnetic field deflects the electron heat flux in a way that reinforces the temperature perturbation. The derived linearized growth rate, typically on hydrodynamic timescales, includes the resistive and thermal smoothing. It increases with large ion composition gradients and electron heat flux, conditions typical of the hohlraum walls or contaminant mix jets in inertial confinement fusion implosions. However, extended magneto-hydrodynamic simulations indicate that the instability is usually dominated and stabilized by the nonlinear Nernst advection, in a similar manner to the standard thermomagnetic instability.

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“…The evolution of B is found via Faraday's law ∂ t B = −∇ × E. In order of appearance, the terms in eqn. ( 6) are then responsible for advection of B with velocity u B , resistive diffusion of B, the Biermann battery source term, and the Z-gradient source term 20,21 . This form of Ohm's law has the advantage that the sole appearance of the ExMHD effects, that is, the ⊥ and ∧ coefficients, is within modifications to the magnetic advection velocity u B in eqn.…”

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confidence: 99%

Symmetric set of transport coefficients for collisional magnetized plasma

Sadler,

Walsh,

2020

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In Braginskii extended magneto-hydrodynamics (ExMHD), applicable to collisional astrophysical and high energy density plasmas, the electric field and heat flow are described by the α, β and κ transport coefficients. We show that magnetic transport relies primarily on β − β ⊥ and α ⊥ − α , rather than α ⊥ and β ⊥ themselves. However, commonly used coefficient fit functions [Epperlein and Haines, Phys. Fluids 29, 1029 (1986)] cannot accurately calculate these quantities. This means that many ExMHD simulations have significantly overestimated the cross-gradient Nernst advection, resulting in artificial magnetic dissipation and discontinuities. We repeat the kinetic analysis to provide fits that rectify this problem. Use of these in the Gorgon ExMHD code resolves the known discrepancies with kinetic simulations in the literature. Recognizing the fundamental importance of α ⊥ − α and β − β ⊥ , we re-cast the set of coefficients to find that each of them now shares the same underlying properties. This makes explicit the symmetry of the magnetic and thermal transport equations, as well as the symmetry of the coefficients themselves.Treatment of collisional magnetized plasma with the electron-ion two-fluid approach leads to a theory of magnetic transport 1 as a function of the fluid properties. This collisional extended magneto-hydrodynamic (ExMHD) theory is based on the assumption that, since electrons are much lighter than the ions, they will quickly form a sheath around the ion fluid. The electric field E of this sheath leads to transport of the magnetic field. In ideal MHD, E = 0 in the fluid rest frame. This implies that the magnetic field B is simply advected with the fluid flow, although advection along B has no effect.Other processes in the electron momentum equation, however, lead to greater complexity. Coulomb collisions give rise to Ohmic resistance. Electron temperature gradients produce thermoelectric forces, since hotter electrons are less susceptible to collisions. Subsequently, it was recognized 1 that the resistive and thermoelectric processes should be described by tensors dependent on the direction of B. Typically, ExMHD modelling uses an implementation given in ref. 2 , in which E was numerically calculated from kinetic theory and then fitted with tabulated functions for the resistive (α , α ⊥ , α ∧ ) and thermoelectric (β , β ⊥ , β ∧ ) transport coefficients. The transport coefficients describe how currents and heat flux are inhibited and deflected by the magnetic field 3 .These additional ExMHD effects are most important in high energy density (HED) plasmas such as Z-pinches 4 , laser plasmas 3,5 , fast ignition fusion concepts 6 , dense fusion fuel hot-spots 7 and laser ablation fronts 8 . The ExMHD magnetic field advection can greatly exceed that due to the ideal advection with the fluid 9 . Studies using the ExMHD codes Gorgon 7 and Hydra 10 found that heat insulation from self-generated magnetic fields can significantly change HED plasma temperature profiles. Accurate transport coefficients are ...

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Magnetization around mix jets entering inertial confinement fusion fuel

Cited by 14 publications

References 37 publications

Role of self-generated magnetic fields in the inertial fusion ignition threshold

Role of self-generated magnetic fields in the inertial fusion ignition threshold

Thermomagnetic instability of plasma composition gradients

Symmetric set of transport coefficients for collisional magnetized plasma

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