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A two-fluid single-column model of turbulent shallow convection. Part II: Single-column model formulation and numerics

The two-fluid single-column model of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) is extended to include moisture and horizontal wind shear. Turbulent kinetic energy is introduced as a prognostic variable, dependence on a diagnosed boundary-layer height is removed, and subfilter fluxes are approximated using a two-fluid version of a Mellor–Yamada scheme. Three mechanisms for entrainment and detrainment processes are introduced, which represent entrainment of unstable air at the surface, forced detrainment of air at the top of the boundary/cloud layers, and turbulent mixing that relaxes the convective fluid to a reference profile. A semi-implicit Eulerian discretization replaces the semi-implicit semi-Lagrangian implementation of Thuburn et al. (Quart. J. R. Meteorol. Soc., 2019, 145, 1535–1550) to improve numerical stability and conservation. The equations for the implicit time step are solved using a quasi-Newton method, which is shown to perform well in numerical tests for conservation and convergence. The two-fluid single-column model presented in this article will be applied to simulations of shallow cumulus convection in Part III.

54 ENVIRONMENTAL SCIENCES↗

Boiling and cavitation caused by transient heat transfer in superfluid helium-4

Superfluid helium-4 (He II) has been widely utilized as a coolant in various scientific and engineering applications due to its superior heat transfer capability. An important parameter required in the design of many He II based cooling systems is the peak heat flux $q^*$, which refers to the threshold heat flux above which boiling spontaneously occurs in He II. Past experimental and numerical studies showed that $q^*$ increases when the heating time $t_h$ is reduced, which leads to an intuitive expectation that very high $q^*$ may be achievable at sufficiently small $t_h$. Knowledge on how $q^*$ actually behaves at small $t_h$ is important for applications such as laser ablation in He II. Furthermore we present a numerical study on the evolution of the thermodynamic state of the He II in front of a planar heater by solving the He II two-fluid equations of motion. For an applied heat flux, we determine the heating time beyond which the He II near the heater transits to the vapor phase. As such, a curve correlating $q^*$ and $t_h$ can be obtained, which nicely reproduces some relevant experimental data. Surprisingly, we find that there exists a critical peak heat flux $q^*_c$, above which boiling occurs nearly instantaneously regardless of $t_h$. We reveal that the boiling in this regime is essentially cavitation caused by the combined effects of the first-sound and the second-sound waves in He II. Based on this physical picture, an analytical model for $q^*_c$ is developed, which reproduces the simulated $q^*_c$ values at various He II bath temperatures and hydrostatic head pressures. This work represents a major progress in our understanding of transient heat transfer in He II.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Boiling peak heat flux for steady inhomogeneous heat transfer in superfluid He 4

Superfluid helium-4 (He II) is a widely adopted coolant in scientific and engineering applications owing to its exceptional heat transfer capabilities. However, boiling can spontaneously occur on a heating surface in He II when the heat flux exceeds a threshold value $q^*$, referred to as the peak heat flux. While the parameter $q^*$ holds paramount importance in the design of He II based cooling systems, extensive research has primarily focused on its behavior in steady homogeneous heat transfer from a flat heating surface. For inhomogeneous heat transfer from curved surfaces, $q^*$ exhibits intricate dependance on parameters such as the He II bath temperature $T_b$, the immersion depth $h$, and the curvature radius $R_0$ of the heating surface. A comprehensive understanding on how $q^*$ depends on these parameters remains elusive. In this paper, we report our systematic study on $q^*$ for steady heat transfer from cylindrical and spherical heaters in He II. We compute $q^*$ for a wide range of parameter combinations $(T_b, h, R_0)$ by solving the He II two-fluid equations of motion. The generated data have allowed us to develop a robust correlation that accurately reproduces $q^*$ for all the parameter combinations we explored. Furthermore, our findings, particularly the establishment of the correlation, carry valuable implications for emergent applications that involve steady inhomogeneous heat transfer in He II systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Heat pump via charge incompressibility in a collisional magnetized multi-ion plasma

Stratification due to ion-ion friction in a magnetized multiple-ion species plasma is shown to be accompanied by a heat pump effect, identified for the first time here, transferring heat from one ion species to another as well as from one region of space to another. Here, the heat pump is produced via newly identified heating mechanisms associated with charge incompressibility and the Ettingshausen effect. Besides their academic interest, these new effects may have useful applications to plasma technologies that involve rotation or compression.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Observations of heteroclinic bifurcations in resistive magnetohydrodynamic simulations of the plasma response to resonant magnetic perturbations

A class of topological magnetic island bifurcations that has not previously been observed in toroidal plasmas is described. Increasing an externally applied three-dimensional magnetic field in resistive magnetohydrodynamic simulations results in the asymmetric elongation of resonant island flux surfaces followed by a sequence of heteroclinic bifurcations. Here, these bifurcations produce new sets of hyperbolic-elliptic fixed points as predicted by the Poincaré-Birkoff fixed point theorem. Field line calculations verify that the new fixed points do not connect to those of the prebifurcated islands as required for heteroclinic bifurcations on a torus with winding numbers composed of common integer factors.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Three-dimensional modeling of a plasma in a strong azimuthal magnetic field

Three-dimensional magnetohydrodynamic (MHD) simulations are able to model the generation of disc-shaped plasma, driven by laser ablation from a current carrying rod in a pulsed-power machine producing azimuthal magnetic fields of 2–3 MG. The plasma at such extreme conditions is unique in that the parameter space for the plasma β and Hall parameter χ transition from below unity to greater than unity at different stages of the plasma generation. In simulations, the formation of the plasma disc in the azimuthal direction, is driven by heat flux from the laser spot and depends on the set of transport coefficients used in simulations. The most recent set of transport coefficients leads to the formation of plasma ejecta at the back end of the rod, that qualitatively matches experiments. Specifically, the cross-gradient Nernst effect, which twists magnetic field, is shown to have a large effect on the shape of the back end ejecta. In the direction along the axis of the rod there is propagation of perturbations from the disc as observed in experiments. In simulations the period of temperature perturbations is in good agreement with experimental results. Furthermore, an instability due to coupling of heat flux and the magnetic field advection provides a possible explanation for perturbation growth along the axis of the rod, and the instability growth rate is consistent with experimental results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonequilibrium effects in high-gain inertial confinement fusion

Recent experimental demonstrations of ignition and target gain in inertial confinement fusion (ICF) have stimulated interest in exploring the fundamental physics of violent deuterium-tritium (DT) burn in high-gain ICF targets. A significant DT-burn fraction is a necessary condition for high energy gain and large neutron yields (>100MJ). Using classical molecular-dynamics (MD) simulations and a hybrid fluid-kinetic model, we examine how a large fraction of low-energy 𝛼 particles can kick D and T ions out of equilibrium in high-gain ICF targets. The MD results suggest that (1) temperatures of 𝑇 𝐷 and 𝑇 𝑇 can differ by as much as ∼20% of their mean temperature and (2) the deviation of the DT energy distribution from the Maxwell-Boltzmann function can exceed ∼30%. Some of these MD observations, such as the preferential heating of D ions by low-energy 𝛼 particles and the temperature separation, can be explained by a proposed hybrid fluid-kinetic model. Furthermore, the implication of such nonequilibrium effects on the DT reactivity is also discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Higher Harmonics in Multipactor Induced Plasma Ionization Breakdown near a Dielectric Surface

In this Letter, the novel physics of higher harmonic (HH) generation of the normal electric field near a dielectric surface is reported in multipactor induced plasma ionization breakdown, as determined by kinetic particle-in-cell simulations. The observed HH frequency is around ten times the fundamental rf driving frequency, but lower than the electron plasma frequency. A theory is constructed which indicates that stream plasma interaction-induced instability is the mechanism of HH generation in the collisional regime. The HH frequency and its corresponding growth rate of the HH oscillation amplitude from the theory are in good agreement with kinetic particle-in-cell simulations.

60 APPLIED LIFE SCIENCES↗

Combined Influence of Rotation and Scrape-Off Layer Drifts on Recycling Asymmetries in Tokamak Plasmas

Coupled 2D fluid-kinetic simulations of a DIII-D high confinement tokamak plasma show that plasma rotation coupled with drift effects near the plasma edge play a significant role in the creation of the observed poloidal distribution of neutrals. It is observed that including either drift or rotation effects enhances particle flux at the inner target in the case of ion 𝐵×∇𝐵 drift toward the 𝑋-point. However, the particle flux asymmetry is significantly higher with the combination of drifts and rotation than either effect alone. The heightened particle flux asymmetry allows for improved simulation of the strong in-out asymmetry of the Lyman-𝛼 brightness profiles measured in the experiment. Enhancement of radial transport of parallel momentum changes the upstream scrape-off layer flow pattern, increasing the fraction of deuterium flux that reaches the inboard divertor entrance while lowering that which arrives at the outboard. In conclusion, this Letter indicates that by combining drifts, rotation, and viscous coupling, existing boundary plasma models can achieve a satisfactory agreement with experimentally measured neutral asymmetries.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗