Lithium Droplet Transport in Tokamak Edge Plasmas

Abstract

A lithium droplet transport and evaporation model has been developed within the Direct Simulation Monte Carlo code OpenEdge. This model integrates gravity, collisional ion drag, orbital-motion-limited charging, energy-balance evaporation, and an anisotropic rocket recoil force using a Strang-split integrator. Validation against analytical drag-gravity solutions and independent RK45 evaporation integration demonstrates relative errors below 0.00001 for droplet radii of 1.5, 2.5, and 3.5 mm. Simulations of ensembles containing 100000 droplets, launched from inner and outer divertor surfaces in SOLPS-ITER plasma background for the CAT tokamak reactor concept, indicate that transport outcomes are determined by initial size, velocity, and launch location. Outer-divertor droplets predominantly redeposit locally, whereas inner-divertor droplets reach the low-field-side wall. Smaller droplets lose most of their mass to evaporation before reaching the core, while larger droplets retain their mass and redeposit on nearby tiles. Both one-way and iterative two-way coupling frameworks map the evaporated lithium onto the SOLPS-ITER mesh as volumetric sources, facilitating self-consistent evaluation of lithium droplet impacts on edge-plasma performance.

Figures (9)

• Figure 1: Time-integration scheme for a droplet subject to drag, gravity, evaporation, rocket recoil, and Lorentz forces. Evaporation (with rocket velocity kick) and non-Lorentz forces (drag, gravity) are applied as symmetric half-steps surrounding the Boris pusher, which advances both Lorentz rotation and position advection over the full timestep.
• Figure 2: Evaporation-only verification against RK45 for three droplet sizes ($r_{d0}=1.5,\ 2.5,\ 3.5~\mathrm{mm}$) at uniform heat flux $Q_s=50~\mathrm{MW\,m^{-2}}$. Markers: OpenEdge; solid lines: RK45. Left axis: $r_d/r_{d0}$, right axis: $T_d$. Insets show relative error snippets for radius and temperature.
• Figure 3: Drag-gravity verification for a $2.5~\mathrm{mm}$ lithium droplet. Dotted lines: OpenEdge; solid lines: closed-form solution. All panels use $T_d=773.15~\mathrm{K}$, $r_d=2.5~\mathrm{mm}$, $m_d=3.495\times10^{-5}~\mathrm{kg}$, and no evaporation. Panels show: (a) $v\!\parallel\!g$, $u_g=0$, $\nu_E=1.736\times10^{-2}~\mathrm{s}^{-1}$, $v_{z,0}=+5~\mathrm{m\,s}^{-1}$; (b) $v\!\perp\!g$, $u_g=0$, same $\nu_E$; (c) $v\!\parallel\!g$, $u_g=1~\mathrm{m\,s}^{-1}$, same $\nu_E$; (d) $v\!\parallel\!g$, $u_g=1~\mathrm{m\,s}^{-1}$, higher drag $\nu_E=3.472\times10^{-2}~\mathrm{s}^{-1}$. Insets list $v(t_{\mathrm{end}})$, $v_{\infty}$, and clarify that $t_{\mathrm{end}}/\tau<1$ for these runs.
• Figure 4: Total heat-flux density and main ion parallel flow velocity computed from SOLPS-ITER.
• Figure 5: Rocket-force verification for a $2.5\,\mathrm{mm}$ lithium droplet launched from the outer divertor into a CAT SOLPS-ITER background plasma. Three asymmetry parameters are compared: $\eta=0$ (no recoil), $0.5$, and $1.0$ (fully one-sided evaporation). (a) Trajectories in the $(R,Z)$ plane; filled circle marks the launch point, open circles mark the final position before wall absorption. (b) Radial velocity $v_R(t)$. (c) Normalized radius $r_d/r_{d0}$.