Mario Merino

Two-dimensional supersonic plasma acceleration in a magnetic nozzle

A two-dimensional model of the expansion of a collisionless, electron-magnetized, low-beta, current-free plasma in a divergent magnetic nozzle is presented. The plasma response is investigated in terms of the nozzle/plasma divergence rate, the magnetic strength on ions, and the Hall current at the nozzle throat. Axial acceleration profiles agree well with those estimated from simple one-dimensional models. A strong radial nonuniformity develops downstream. There is a separation between ion and electron/magnetic streamtubes which leads to the formation of, first, a longitudinal electric current density, which indicates that current ambipolarity is not fulfilled, and, second, a small ion azimuthal current that competes negatively with the electron azimuthal (Hall) current. The analysis of the mechanisms driving thrust, ion momentum, and ion energy unveils the dual electrothermal/electromagnetic character of the magnetic nozzle. In general, the thrust includes the contributions of volumetric and surface Hall currents, this last one formed at the plasma-vacuum interface. Plume efficiency, based on radial expansion losses, is computed. Plasma detachment and the transonic matching with the upstream plasma are not addressed.

On plasma detachment in propulsive magnetic nozzles

Three detachment mechanisms proposed in the literature (via resistivity, via electron inertia, and via induced magnetic field) are analyzed with an axisymmetric model of the expansion of a small-beta, weakly collisional, near-sonic plasma in a diverging magnetic nozzle. The model assumes cold, partially magnetized ions and hot, isothermal, fully magnetized electrons. Different conditions of the plasma beam at the nozzle throat are considered. A central feature is that a positive thrust gain in the nozzle of a plasma thruster is intimately related to the azimuthal current in the plasma being diamagnetic. Then, and contrary to existing expectations, the three aforementioned detachment mechanisms are divergent, that is, the plasma beam diverges outwards of the guide nozzle, further hindering its axial expansion and the thrust efficiency. The rate of divergent detachment is quantified for the small-parameter range of the three mechanisms. Alternative mechanisms for a convergent detachment of the plasma beam are suggested.

Two-dimensional plasma expansion in a magnetic nozzle: Separation due to electron inertia

A previous axisymmetric model of the supersonic expansion of a collisionless, hot plasma in a divergent magnetic nozzle is extended here in order to include electron-inertia effects. Up to dominant order on all components of the electron velocity, electron momentum equations still reduce to three conservation laws. Electron inertia leads to outward electron separation from the magnetic streamtubes. The progressive plasma filling of the adjacent vacuum region is consistent with electron-inertia being part of finite electron Larmor radius effects, which increase downstream and eventually demagnetize the plasma. Current ambipolarity is not fulfilled and ion separation can be either outwards or inwards of magnetic streamtubes, depending on their magnetization. Electron separation penalizes slightly the plume efficiency and is larger for plasma beams injected with large pressure gradients. An alternative nonzero electron-inertia model [E. Hooper, J. Propul. Power 9, 757 (1993)] based on cold plasmas and current ambipolarity, which predicts inwards electron separation, is discussed critically. A possible competition of the gyroviscous force with electron-inertia effects is commented briefly.

Plasma detachment in a propulsive magnetic nozzle via ion demagnetization

Plasma detachment in propulsive magnetic nozzles is shown to be a robust phenomenon caused by the inability of the internal electric fields to bend most of the supersonic ions along the magnetic streamtubes. As a result, the plasma momentum is effectively ejected to produce thrust, and only a marginal fraction of the beam mass flows back. Detachment takes place even if quasineutrality holds everywhere and electrons are fully magnetized, and is intimately linked to the formation of local electric currents. The divergence angle of the 95%-mass flow tube is used as a quantitative detachment performance figure.

Influence of Electron and Ion Thermodynamics on the Magnetic Nozzle Plasma Expansion

A two-fluid 2-D model of the supersonic plasma flow in a propulsive magnetic nozzle (MN) is extended to include simple electron and ion thermodynamics to study the effects of electron cooling and ion thermal energy on the expansion. A faster electron cooling rate is seen to reduce plasma jet divergence, increase radial rarefaction, and enhance detachment from the closed magnetic lines. Ion thermal energy is converted to directed kinetic energy by the MN without the mediation of an ambipolar electric field, and alters the electric response of the plasma.

Plasma detachment mechanisms in a magnetic nozzle

An axisymmetric model of the supersonic expansion of a collisionless, totally ionizedplasma in a divergent magnetic nozzle and the DIMAGNO simulation code are beingused to study the plasma detachment from the guiding magnetic eld, taking into accountthe e ects of the induced magnetic eld generated by the plasma electric currents. Theazimuthal electric currents carried by the plasma from the discharge chamber or createdwithin the nozzle are the central feature for both thrust generation and plasma detachment.These currents are mainly electronic and have a globally diamagnetic character, as theirinduced eld lowers the total eld around the axis and increases nozzle divergence rate.This paper focuses on the role of the plasma-generated magnetic eld and the detachmentissue, particularized for the case of a helicon thruster (although conclusions extracted hereinmight be easily generalizable to other thruster types). A viable alternative detachmentmechanism based on plasma self-demagnetization is investigated.

Two-dimensional plasma acceleration in a divergent magnetic nozzle

The acceleration of a current-free plasma in a divergent magnetic nozzle with fully magnetically guided electrons is discussed. Ion momentum is gained from the electron thermal pressure, via the electrostatic self-field. Except for very large magnetic fields, ion magnetization is weak and ion streamlines deviate from magnetic streamlines. As a consequence the local ambipolar condition does not hold, and local electric currents are formed. Azimuthal ion and electron currents are evaluated. The acceleration efficiency is computed.

Two-dimensional quasi-double-layers in two-electron-temperature, current-free plasmas

The expansion of a plasma with two disparate electron populations into vacuum and channeled by a divergent magnetic nozzle is analyzed with an axisymmetric model. The purpose is to study the formation and two-dimensional shape of a current-free double-layer in the case when the electric potential steepening can still be treated within the quasineutral approximation. The properties of this quasi-double-layer are investigated in terms of the relative fraction of the high-energy electron population, its radial distribution when injected into the nozzle, and the geometry and intensity of the applied magnetic field. The two-dimensional double layer presents a curved shape, which is dependent on the natural curvature of the equipotential lines in a magnetically expanded plasma and the particular radial distribution of high-energy electrons at injection. The double layer curvature increases the higher the nozzle divergence is, the lower the magnetic strength is, and the more peripherally hot electrons are inject...

Simulation of Plasma Flows in Divergent Magnetic Nozzles

Images from the simulation code DIMAGNO illustrate the roles of pressure, electric, and magnetic forces in the 2-D plasma expansion in a magnetic nozzle and the generation of thrust.

Preliminary assessment of detachment in a plasma thruster magnetic nozzle

A magnetic nozzle model for the supersonic expansion of a collisionless, low-beta plasma characterizes the plasma ow for propulsive applications. Thrust gain in the nozzle is achieved by an azimuthal current developed in the plasma. That current is necessarily diamagnetic in character, which disagrees with the current direction assumed in existing theories for resistive, inertial-based, and MHD selfeld detachment.