Eduardo Ahedo

A two-dimensional hybrid model of the Hall thruster discharge

Particle-in-cell methods are used for ions and neutrals. Probabilistic methods are implemented for ionization, charge-exchange collisions, gas injection, and particle-wall interaction. A diffusive macroscopic model is proposed for the strongly magnetized electron population. Cross-field electron transport includes wall collisionality and Bohm-type diffusion, the last one dominating in most of the discharge. Plasma quasineutrality applies except for space-charge sheaths, which are modeled taking into consideration secondary-electron-emission and space-charge saturation. Specific weighting algorithms are developed in order to fulfil the Bohm condition on the ion flow at the boundaries of the quasineutral domain. The consequence is the full development of the radial plasma structure and correct values for ion losses at lateral walls. The model gains in insight and physical consistency over a previous version, but thrust efficiency is lower than in experiments, indicating that further model refinement of some...

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.

Effects of the radial plasma-wall interaction on the Hall thruster discharge

The interaction of the plasma discharge with the ceramic walls of a Hall thruster leads to plasma recombination, energy losses, and extra electron collisionality. These three phenomena are included in a one-dimensional axial model of the discharge through source terms obtained from an auxiliary model of the radial dynamics. Spatial solutions are presented for different discharge voltages and wall materials, and agree satisfactorily with experimental data. The parameters related to wall effects are investigated extensively. The energy balance among Joule heating, wall-losses cooling, and heat conduction shapes the temperature profile; three different profile types are identified depending on the wall material and the discharge voltage. For long chambers, the main source of energy losses is the plasma interaction with the walls, even for zero secondary electron emission. By contrast, wall collisionality due to primary/secondary exchanges of electrons is negligible always. The current utilization is related directly to the total energy losses. The propellant utilization is set by the balance between gas ionization and wall recombination in the acceleration region. The rate of wall recombination suggested by the axial solution is much lower than the values given by radial models based on a Maxwellian electron distribution function.

Plasmas for space propulsion

Plasma thrusters are challenging the monopoly of chemical thrusters in space propulsion. The specific energy that can be deposited into a plasma beam is orders of magnitude larger than the specific chemical energy of known fuels. Plasma thrusters constitute a vast family of devices ranging from already commercial thrusters to incipient laboratory prototypes. Figures of merit in plasma propulsion are discussed. Plasma processes and conditions differ widely from one thruster to another, with the pre-eminence of magnetized, weakly collisional plasmas. Energy is imparted to the plasma via either energetic electron injection, biased electrodes or electromagnetic irradiation. Plasma acceleration can be electrothermal, electrostatic or electromagnetic. Plasma–wall interaction affects energy deposition and erosion of thruster elements, and thus is central for thruster efficiency and lifetime. Magnetic confinement and magnetic nozzles are present in several devices. Oscillations and turbulent transport are intrinsic to the performances of some thrusters. Several thrusters are selected in order to discuss these relevant plasma phenomena.

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.

Presheath/sheath model with secondary electron emission from two parallel walls

A macroscopic model of the interaction of a plasma with two parallel, electron-emitting walls is presented. Zero Debye-length and total thermalization of the secondary electron emission (SEE) are assumed. The SEE is treated as a free beam within each thin, collisionless sheath, but as part of a single electron population within the presheath. Plasma models with three and two species result in sheath and presheath, respectively. The ion flow at the presheath/sheath transition is sonic, and the sound speed there determines the relation between the temperature of the confined electron populations in sheath and presheath. For the general case of a plasma flowing axially between two annular walls the complete dimensionless solution depends on five parameters. Potential drops in the presheath can be larger than in the sheaths, mainly when charge-saturation is reached in the sheath or for a large effective ion friction in the presheath. The losses of plasma current to the walls are determined totally by the pres...

Model of the plasma discharge in a Hall thruster with heat conduction

The inclusion of heat conduction into a one-dimensional, macroscopic model of the plasma inside a Hall thruster and in the near plume is found to smooth the temperature profile of previous solutions with a nonconductive model. The spatial structure still consists of reverse-flow, ionization, and acceleration regions. Conductive energy flow, being of the same order of convective flow, has significant effects on the rear part of the channel where it can make impossible the establishment of a steady anode sheath. As a result, there is an upper bound on the plasma reverse flow for the existence of stationary solutions. The analysis of inertial effects on the electron dynamics concludes that the main contribution is the azimuthal electron motion, which can produce extra collisionality, mainly in the near plume. The different contributions to the effective axial diffusion of electrons and the ion temperature are evaluated. A parametric investigation yields the basic scaling laws of the thruster stationary perfo...

Helicon thruster plasma modeling: Two-dimensional fluid-dynamics and propulsive performances

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.

Parametric analysis of a magnetized cylindrical plasma

The relevant macroscopic model, the spatial structure, and the parametric regimes of a low-pressure plasma confined by a cylinder and an axial magnetic field is discussed for the small-Debye length limit, making use of asymptotic techniques. The plasma response is fully characterized by three-dimensionless parameters, related to the electron gyroradius, and the electron and ion collision mean-free-paths. There are the unmagnetized regime, the main magnetized regime, and, for a low electron-collisionality plasma, an intermediate-magnetization regime. In the magnetized regimes, electron azimuthal inertia is shown to be a dominant phenomenon in part of the quasineutral plasma region and to set up before ion radial inertia. In the main magnetized regime, the plasma structure consists of a bulk diffusive region, a thin layer governed by electron inertia, a thinner sublayer controlled by ion inertia, and the non-neutral Debye sheath. The solution of the main inertial layer yields that the electron azimuthal ene...

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.