  As long-distance space travel requires propulsion systems with greater
operational flexibility and lifetimes, there is a growing interest in
electrodeless plasma thrusters that offer the opportunity of improved
scalability, larger throttleability, running on different propellants, and
limit device erosion. The majority of electrodeless designs rely on a magnetic
nozzle (MN) for the acceleration of the plasma, which has the advantage of
utilizing the expanding electrons to neutralize the ion beam without the
additional installation of a cathode. The plasma expansion in the MN is nearly
collisionless, and a fluid description of electrons requires a non-trivial
closure relation. Kinetic electron effects, and in particular electron cooling,
play a crucial role in various physical phenomena such as energy balance, ion
acceleration, and particle detachment. Based on the experimental and
theoretical studies conducted in recognition of this importance, the
fundamental physics of the electron cooling mechanism revealed in MNs and
magnetically expanding plasma are reviewed. Especially, recent approaches from
the kinetic point of view are discussed, and our perspective on the future
challenges of electron cooling and the relevant physical subject of MN is
presented.
