Self-similar expansion of a plasmoid supplied by pellet ablation

Abstract

Cryogenic pellet injection is an important means of refuelling and terminating fusion plasmas, with fuel pellets exhibiting a range of phenomena beneficial to confinement and the energy balance between ions and electrons. In this investigation we consider the self-similar expansion along magnetic field lines of the plasmoid produced by a small pellet. In particular, we consider the case when the expansion timescale is comparable to the time taken for the pellet gas cloud to cross a field line. It is shown that plasmoid ions acquire a significant fraction of the energy that is transferred to plasmoid electrons via collisions with the ambient plasma. It is found that the expansion is insensitive to the profile of the gas cloud and details of the ionisation of the gas—the plasma flux emerging from the gas cloud is the only quantity that affects the expansion.

Electron kinetics in a high-Z plasmoid

“…Arnold et al. (2021, § 2) contains the corresponding analysis of how the W7-X pellet gas cloud deposits plasma on a field line, as well as estimates of line-integrated densities according to transverse gas cloud sizes observed by survey cameras (Baldzuhn et al. 2019, HFS in figure 4(2)).…”

“…Previous work on plasmoid dynamics in one dimension assumed the electrons to be in either global Boltzmann equilibrium (Gurevich et al 1966;Mora 2003;Aleynikov et al 2019;Arnold et al 2021) or in local equilibrium with spatially dependent temperature (Runov et al 2021). The difference in the temperatures of plasmoid electrons and ambient electrons was accounted for by introducing a collisional heating term to the equation governing plasmoid electron temperature.…”

“…This 1D description is ubiquitously employed in the description of plasmoids, particularly those in the context of fuel pellet injection in magnetic confinement fusion (MCF) devices (Gurevich, Pariiskaya & Pitaevskii 1966; Mora 2003; Aleynikov et al. 2019; Arnold, Aleynikov & Helander 2021; Runov et al. 2021).…”

“…2019; Arnold et al. 2021) or in local equilibrium with spatially dependent temperature (Runov et al. 2021).…”

Pellet Core Fueling in Tokamaks, Stellarators and Reversed Field Pinches

“…These cloudlets homogenize in the discharge by expanding along the field lines (see e.g. [16]). Nevertheless, since the parallel energy transport (∼ at the thermal electron velocity) is much faster than the density parallel transport (∼ at the sound velocity), the temperatures in the cloudlet and the background plasma equilibrate much faster than the densities, leading to a localized overpressure in the cloudlet.…”