Time-dependent kinetic analysis of trapped electrons in a magnetically expanding plasma

A deep understanding of the kinetic properties of the electrons in a magnetic nozzle (MN), which is attracting attention as an acceleration stage for thrusters, is of great significance as it directly contributes to the development of the MN performance. In the sense that a conversion of the electron momentum to the ion kinetic energy determines the characteristics of the MN, fundamental research on the kinetic feature of a magnetically expanding plasma has focused on the spatial distribution of the electron properties and proposed directions to the desired application. Unlike the common perception of this importance, various research groups have proposed contradictory arguments based on their theoretical approaches regarding the ion beam acceleration from the viewpoint of heat flow of electrons. We point out that the main reason for the absence of a theoretical consensus for the nozzle efficiency improvements arises from the lack of the clear interpretation of the plasma properties by focusing only on the final state of the electrons. In this Letter, time-resolved measurement of the electron energy distributions has been performed to grasp a detailed series of expansion processes. It has been revealed that the effective potential well gradually formed by the self-generated electric field acts as a limiting factor in the motion of electrons; this effect attributes to the changes of the electron energy distribution represented as the accumulation of the trapped electrons. The accumulation over the entire region diminishes the degree of the cooling rate of a system and decreases the electric field in the downstream region initially generated by the adiabatic expansion. The present study emphasizes that the kinetic features of an MN are strongly affected by the non-stationary motion of the trapped electrons; thus, the temporal behavior of the trapped electrons must be considered for prediction and analysis of nozzle performances.