Non-local transport in Radiation-Hydrodynamics codes for ICF by efficient coupling to an external Vlasov-Fokker-Planck code

TL;DR

Non-local electron transport in ICF/MCF is poorly captured by flux limiters; the authors propose VFP-Driven Hydrodynamics, coupling a kinetic VFP solver to rad-hydro codes to modify the electron heat flux through a multiplier $M = q_{VFP}/q_{SNB}$ and by rescaling the zeroth-harmonic distribution $f_0$ to preserve $n$ and $E= frac{3}{2}nT$. They validate the method with Epperlein-Short, Tanh ramp, and hohlraum tests in 1D, showing accuracy comparable to full kinetic runs and superior to flux-limited SNB/Spitzer in dynamic ICF-like conditions. The approach is general and can be extended to 2D/3D and to other transport relations such as Ohm's law, enabling broader application to kinetic-fluid coupling in fusion plasmas. This VFP-Driven Hydrodynamics framework offers a computationally efficient, accurate pathway to incorporate non-local kinetic effects into fluid codes across fusion-relevant regimes.

Abstract

Accurately incorporating non-local transport into radiation-hydrodynamics codes, and indeed any fluid system, has long been elusive. To date, a simplified and accurate theory that can be easily integrated has not been available. This limitation affects modeling in inertial confinement fusion and magnetic confinement fusion systems, among others, where non-local transport is well-known to be present. Here, we present a coupling methodology between a full Vlasov-Fokker-Planck (VFP) electron kinetic code and radiation-hydrodynamics (rad-hydro) codes. The VFP code is used to adjust native electron transport in the rad-hydro code, thus enabling improved transport without the need to integrate a full electron VFP solver into the rad-hydro code. This approach necessitates only occasional invocation of the VFP code, reducing computational intensity compared to following the dynamic evolution entirely with the VFP code on fluid time scales. We illustrate that the methodology is more accurate than other simplified methods in thermal decay systems relevant to inertial confinement fusion and can replicate standard theoretical results with high accuracy.

Figures (5)

• Figure 1: Illustrations of $\nabla\cdot q=const$ coupling techniques and its respective failure modes.
• Figure 2: Illustration of Spitzer-Harm multiplier coupling technique and its respective failure modes - formation of a growing numerical artifact.
• Figure 3: Epperlein-Short test for the maintain method. Standard SOL-KiT results are included from Mijin2021comp. Easily noted that the maintain method is able to get within some margin of error to the expected $\kappa / \kappa^{B}$ for all values of $k\lambda^B_{ei}$ except at $k\lambda^B_{ei} = 2$, this can be explained by not having converged fully. The fit is based on the highest harmonic result from the Mijin2021comp.
• Figure 4: Smooth Tanh ramp thermal decay test. Left) Initial conditions for the test problem; ionisation remains constant, and the system is run as a single temperature system. Right) relative L1 error of three different models, flux-limited Spitzer with $f=0.15$, SNB and VFP-Driven Method. Note that the error growth in the VFP-Driven method is inconsistent and slow compared with SNB & $f = 0.15$, which both grow roughly linearly over time.
• Figure 5: Hohlraum thermal decay test. Left: Initial conditions for the test problem. Ionization remains constant, and the system is run as a single temperature system. Right) relative L1 error for three different models: flux-limited Spitzer with $f=0.15$, SNB, and the VFP-Driven method. Note that error growth in the VFP-Driven method is inconsistent and slow, while both SNB and $f=0.15$ grow approximately linearly over time.