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We propose a method for interpolating divergence-free continuous magnetic fields via vector potential reconstruction using Hermite interpolation, which ensures high-order continuity for applications requiring adaptive, high-order ordinary differential equation (ODE) integrators, such as the Dormand-Prince method. The method provides C(m) continuity and achieves high-order accuracy, making it particularly suited for particle trajectory integration and Poincar\'e section analysis under optimal integration order and timestep adjustments. Through numerical experiments, we demonstrate that the Hermite interpolation method preserves volume and continuity, which are critical for conserving toroidal canonical momentum and magnetic moment in guiding center simulations, especially over long-term trajectory integration. Furthermore, we analyze the impact of insufficient derivative continuity on Runge-Kutta schemes and show how it degrades accuracy at low error tolerances, introducing discontinuity-induced truncation errors. Finally, we demonstrate performant Poincar\'e section analysis in two relevant settings of field data collocated from finite element meshes, Comment: 21 pages, 9 figures

In this work, we propose a data-driven method to discover the latent space and learn the corresponding latent dynamics for a collisional-radiative (CR) model in radiative plasma simulations. The CR model, consisting of high-dimensional stiff ordinary differential equations (ODEs), must be solved at each grid point in the configuration space, leading to significant computational costs in plasma simulations. Our method employs a physics-assisted autoencoder to extract a low-dimensional latent representation of the original CR system. A flow map neural network is then used to learn the latent dynamics. Once trained, the reduced surrogate model predicts the entire latent dynamics given only the initial condition by iteratively applying the flow map. The radiative power loss is then reconstructed using a decoder. Numerical experiments demonstrate that the proposed architecture can accurately predict both the full-order CR dynamics and the radiative power loss rate., Comment: 33 pages, 30 figures

Thermal quench of a nearly collisionless plasma against a cooling boundary or region is an undesirable off-normal event in magnetic fusion experiments, but an ubiquitous process of cosmological importance in astrophysical plasmas. There is a well-known mismatch that what experimentally diagnosed is the drop in perpendicular electron temperature $T_{e\perp},$ but the parallel transport theory of ambipolar-constrained tail electron loss produces parallel electron temperature $T_{e\parallel}$ cooling. Here two collisionless mechanisms, dilutional cooling by infalling cold electrons and wave-particle interaction by two families of whistler instabilities, are shown to enable fast $T_{e\perp}$ cooling that closely tracks the mostly collisionless crash of $T_{e\parallel}.$

The assimilation of ablated high-Z impurities into the hot surrounding plasma along the magnetic field is investigated by first-principles kinetic simulations. It is found that the assimilated impurity ions, primarily driven by the ambipolar electric force, propagate steadily into the surrounding plasmas. The high-Z impurities in different charge states are mostly aligned due to the strong collisional friction among them so that the averaged impurity ions charge $\bar{Z}$ is a deciding factor. Such assimilation is led by an impurity front that is behind the cooling front due to a smaller charge-mass-ratio of the impurity ions $\bar{Z}/m_I$. With the help of a self-similar solution, the speed of the impurity front $U_s$ is shown to be primarily set by the hot surrounding plasma temperature $T_0$ with a weak dependence on the pellet plasma temperature, underscoring the collisionless nature of the impurity assimilation process. Specifically, $U_s\sim \sqrt{\bar{Z}T_0/m_I}$. The ambipolar-constrained electron conduction flux from the hot plasma is primarily responsible for the collisionless impurity assimilation process.

The thermal collapse of a nearly collisionless plasma interacting with a cooling spot, in which the electron parallel heat flux plays an essential role, is investigated both theoretically and numerically. We show that such thermal collapse, which is known as thermal quench in tokamaks, comes about in the form of propagating fronts, originating from the cooling spot, along the magnetic field lines. The slow fronts, propagating with local ion sound speed, limit the aggressive cooling of plasma, which is accompanied by a plasma cooling flow toward the cooling spot. The extraordinary physics underlying such a cooling flow is that the fundamental constraint of ambipolar transport along the field line limits the spatial gradient of electron thermal conduction flux to the much weaker convective scaling, as opposed to the free-streaming scaling, so that a large electron temperature and hence pressure gradient can be sustained. The last ion front for a radiative cooling spot is a shock front where cold but flowing ions meet the hot ions.

We present compatible finite element space discretizations for the ideal compressible magnetohydrodynamic equations. The magnetic field is considered both in div- and curl-conforming spaces, leading to a strongly or weakly preserved zero-divergence condition, respectively. The equations are discretized in space such that transfers between the kinetic, internal, and magnetic energies are consistent, leading to a preserved total energy. We also discuss further adjustments to the discretization required to additionally achieve magnetic helicity preservation. Finally, we describe new transport stabilization methods for the magnetic field equation which maintain the zero-divergence and energy conservation properties, including one method which also preserves magnetic helicity. The methods' preservation and improved stability properties are confirmed numerically using a steady state and a magnetic dynamo test case.

The survivability of dust being transported in the magnetized sheath near the divertor plate of a tokamak and its impact on the desired balance of erosion and redeposition for a steady-state reactor are investigated. Two different divertor scenarios are considered. The first is characterized by an energy flux perpendicular to the plate $q_0\simeq 1$ MW/m$^2$ typical of current short-pulse tokamaks. The second has $q_0\simeq 10$ MW/m$^2$ and is relevant to long-pulse machines like ITER or DEMO. It is shown that micrometer dust particles can survive rather easily near the plates of a divertor plasma with $q_0\simeq 1$ MW/m$^2$ because thermal radiation provides adequate cooling for the dust particle. On the other hand, the survivability of micrometer dust particles near the divertor plates is drastically reduced when $q_0\simeq 10$ MW/m$^2$. Micrometer dust particles redeposit their material non-locally, leading to a net poloidal mass migration across the divertor. Smaller particles (with radius $\sim 0.1$ $\mu$m) cannot survive near the divertor and redeposit their material locally. Bigger particle (with radius $\sim 10$ $\mu$m) can instead survive partially and move outside the divertor strike points, thus causing a net loss of divertor material to dust accumulation inside the chamber and some non-local redeposition. The implications of these results for ITER are discussed., Comment: 35 pages, 7 figures, published