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.

The parallel expansion of a dense, pellet-produced plasmoid is modelled with parameters relevant to pellet fuelling experiments in the Wendelstein7-X stellarator. Good agreement is found between the analytical theory and more detailed modelling. In particular, much of the energy deposited in the pellet by the ambient plasma is transferred to the pellet ions by the ambipolar electric field during the expansion. The validity of the hydrodynamic treatment of the plasmoid and the ambient plasma is discussed.

The problem of the electron dynamics on a closed magnetic field line passing through a high- $Z$ plasmoid is considered. The electron kinetic equation is integrated over bounce motion and pitch angle, reducing the independent variables to a single adiabatic invariant plus time. Integration of the full Landau self-collision operator is carried out exactly, resulting in a nonlinear integro-differential operator in the new invariant. Conservation laws and the $H$ theorem of the integrated self-collision operator are proven. Numerical solutions of the integrated kinetic equation are obtained with a self-consistent quasineutral electric potential, given the initial condition of a cold plasmoid immersed in a hot ambient plasma. The fact that cold electrons are deeply trapped in a potential with a parabolic peak leads to exactly 3/4 the usual rate of collisional heating by the ambient plasma, independent of any other parameters.