An axisymmetric macroscopic model of the magnetized plasma flow inside the helicon thruster chamber is derived, assuming that the power absorbed from the helicon antenna emission is known. Ionization, confinement, subsonic flows, and production efficiency are discussed in terms of design and operation parameters. Analytical solutions and simple scaling laws for ideal plasma conditions are obtained. The chamber model is then matched with a model of the external magnetic nozzle in order to characterize the whole plasma flow and assess thruster performances. Thermal, electric, and magnetic contributions to thrust are evaluated. The energy balance provides the power conversion between ions and electrons in chamber and nozzle, and the power distribution among beam power, ionization losses, and wall losses. Thruster efficiency is assessed, and the main causes of inefficiency are identified. The thermodynamic behavior of the collisionless electron population in the nozzle is acknowledged to be poorly known and crucial for a complete plasma expansion and good thrust efficiency.

The steady, collisionless, slender flow of a magnetized plasma into a surrounding vacuum is considered. The ion component is modeled as mono-energetic, while electrons are assumed Maxwellian upstream. The magnetic field has a convergent-divergent geometry, and attention is restricted to its paraxial region, so that 2D and drift effects are ignored. By using the conservation of energy and magnetic moment of particles and the quasi-neutrality condition, the ambipolar electric field and the distribution functions of both species are calculated self-consistently, paying attention to the existence of effective potential barriers associated to magnetic mirroring. The solution is used to find the total potential drop for a set of upstream conditions, plus the axial evolution of various moments of interest (density, temperatures, and heat fluxes). The results illuminate the behavior of magnetic nozzles, plasma jets, and other configurations of interest, showing, in particular, in the divergent plasma the collisionless cooling of electrons, and the generation of collisionless electron heat fluxes.

A kinetic paraxial model of a collisionless plasma stationary expansion in a convergent-divergent magnetic nozzle (MN) is analyzed. Monoenergetic and Maxwellian velocity distribution functions of upstream ions are compared, leading to differences in the expansion only on second and higher-order velocity moments. Individual and collective magnetic mirror effects are analyzed. Collective ones are small on the electron population since only a weak temperature anisotropy develops, but they are significant on the ions all over the nozzle. Momentum and energy equations for ions and electrons are assessed based on the kinetic solution. The ion response is different in the hot and cold limits, with the anisotropic pressure tensor being relevant in the first case. Heat fluxes of parallel and perpendicular energies have a dominant role in the electron energy equations. They do not fulfill a Fourier-type law; they are large even when electrons are near isothermal. A crude electron fluid closure based on a constant diffusion-to-convective thermal energy ratio is shown equivalent to the much invoked polytropic law. Analytical dimensionless parameter laws are derived for the nozzle total electric potential fall and the downstream residual electron temperature. Electron confinement and related current control by a thin Debye sheath and a semi-infinite divergent MN are compared.

The dynamics of xenon atoms and ions expanding in the magnetic nozzle (MN) of a helicon plasma thruster is studied by means of near-infrared laser-induced fluorescence spectroscopy on resonant and metastable states. Fluorescence spectra are measured for several operating conditions inside and outside the thruster discharge chamber. In the near-field plume, the relatively intense magnetic field induces Zeeman effect on the probed optical transitions. Hence, modeling of the atomic lineshapes is addressed to accurately compute the Doppler shift and infer the velocity. The first direct measurements of the neutral flow in a MN reveal that atoms are accelerated to supersonic velocities behind the thruster exit. The ions acceleration region extends several centimeters downstream the exit plane. Larger axial ion speeds are attained when the thruster operates at lower mass flow rates and higher levels of input power.

Experiments and simulations are used to analyze a compact helicon plasma thruster with a cusp in its internal magnetic field. The former rely on a compensated Langmuir probe and a Faraday cup, while the latter employ a hybrid PIC/fluid transport model combined with a frequency-domain electromagnetic field model. Measurements serve to tune the anomalous transport parameters of the model and overall show the same trends as the numerical results, including a secondary peak of electron temperature downstream in the magnetic nozzle, where electron cyclotron resonance conditions for the 13.56 MHz excitation frequency are met. The cusp plays a central role in determining the plasma losses to the walls and the profile of electron temperature, which in turn defines the excitation and ionization losses. While losses to the rear wall are reduced, losses to the lateral wall are increased, which, together with the low production efficiency, limit the performance of the device.