## Thesis etd-12102013-202735 |

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Thesis type

Tesi di dottorato di ricerca

Author

GIANNELLI, SEBASTIANO

URN

etd-12102013-202735

Thesis title

Plasma generation and stability in high-power electric thrusters

Academic discipline

ING-IND/07

Course of study

INGEGNERIA

Supervisors

**tutor**Prof. Andrenucci, Mariano

**tutor**Prof. Walker, Mitchell L. R.

**controrelatore**Prof.ssa Salvetti, Maria Vittoria

Keywords

- electric propulsion
- helicon sources
- MPD thruster
- onset

Graduation session start date

19/12/2013

Availability

Full

Summary

Stability and efficiency are two fundamental requirements for any component to be used in space applications, and electric thrusters are no exception. This Thesis consists of two parts, each of which addresses a topic concerning the two cited aspects.

In the first part we investigate an unstable operating regime of a specific class of high-power plasma thrusters, the magnetoplasmadynamic (MPD) thrusters. These thrusters potentially offer unique values of thrust density and specific impulse which make them suitable for space missions in which both mass savings and mission duration are a concern. The operation of these devices is strongly limited by the inception of the cited critical phenomenon, which is known simply as "onset" in the literature.

Despite the onset regime has been extensively investigated, with both theoretical and experimental approaches, a complete and clear theoretical framework in which to fit all the experimental results is still missing. To this scope we first start with a detailed and critical review of the last 50 years of research on the topic, aiming at providing a classification of the main results starting from the different thruster configurations.

The main contribution of the first part is then the development of a complete and physically plausible theory in which we provide explanations for the different aspects of the onset phenomenology in self-field MPD thrusters. We address the problem of the breaking of the azimuthal symmetry of the discharge, explaining the underlying physical mechanism and providing a quantitative criterion for this to occur. We then show that this azimuthal instability is also at the base of the formation of the filamentary plasma structures which have been observed in experimental investigations. The nature of the unstable dynamics of these filaments is then addressed and finally we propose a mechanism which explains the connection between the plasma dynamics and the electrical response of the thruster.

We conclude the first part by looking at possible design choices which could help improve the stability of these devices. Among others, particular attention is given to an alternative concept developed by A.I. Morozov, the Quasi-Steady Plasma Accelerator, which requires a staging strategy in which the ionization of the propellant is separated from the acceleration phase. A technical solution for the implementation of this concept in MPD thrusters would be the development of an efficient annular plasma source.

In the second part of this work we focus on the possibility of developing an annular helicon plasma source. Helicon sources have undergone a rapid diffusion in practically all the branches of research on low-temperature plasmas, as a consequence of their simplicity and potentially high ionization efficiency. The use of these sources as ionization stages in high-power plasma thrusters can potentially lead to an increase of the overall efficiency of the device and contribute to widen its operational envelope, as well as help in creating favorable conditions for stable operation. The goal of this work is to provide a basis of knowledge to help and guide future developments and designs of this kind of sources.

First we investigate the problem of the excitation and propagation of helicon waves, which are bounded modes of whistler waves, in an annularly bounded homogeneous plasma. Finite electron mass effects and all possible combinations of boundary conditions are included in the study, for which closed form analytical solutions are provided. A parametric analysis of the solution as a function of the main driving parameters is performed.

The problem of the radial equilibrium of a magnetized plasma in annular configurations is then addressed. By making use of a two-fluid model in a non-dimensional form, the most important parameters affecting both the plasma equilibrium and the wall losses are illustrated. As a result of a parametric study, the interplay between magnetic confinement and collisional effects is stressed to be the most important mechanism, and the effects induced by other parameters such as a finite ion temperature, plasma beta and geometry of the source are illustrated.

Given the relative importance of collisional effects in the radial equilibrium problem, in which neutral particles can play a major role at low ionization levels, we then report the results of a joint experimental and numerical activity aiming at the validation of a procedure that allows to calculate the neutral particle background in a helicon source. The results of this activity also give indication of a possible role played by the propellant injection system in the neutral pumping phenomenon, which is known to be a potential limiting factor of the efficiency of these devices.

The last part of the thesis concerns an experimental activity carried on an annular helicon source. This activity involved designing and building both the plasma source and a diagnostics setup to perform optical emission spectroscopy measurements. The setup allowed to perform scans of the light emitted by the plasma through a cross section of the device in between adjacent magnets. The occurrence of some calibration issues of the spectrometer did not allow for a quantitative estimate of the plasma parameters (electron temperature and number density), but the recorded spectra give indication of an inductive coupling mode of the source with the RF antenna. Taking into account the results of the model on the radial equilibrium, it is likely that the plasma in the source was collision-dominated. Finally, the linear scans of the emitted light are not in general axi-symmetric, which is not expected given the nominal symmetry of the source, thus indicating the possibility that asymmetric equilibria might exist in these sources.

In the first part we investigate an unstable operating regime of a specific class of high-power plasma thrusters, the magnetoplasmadynamic (MPD) thrusters. These thrusters potentially offer unique values of thrust density and specific impulse which make them suitable for space missions in which both mass savings and mission duration are a concern. The operation of these devices is strongly limited by the inception of the cited critical phenomenon, which is known simply as "onset" in the literature.

Despite the onset regime has been extensively investigated, with both theoretical and experimental approaches, a complete and clear theoretical framework in which to fit all the experimental results is still missing. To this scope we first start with a detailed and critical review of the last 50 years of research on the topic, aiming at providing a classification of the main results starting from the different thruster configurations.

The main contribution of the first part is then the development of a complete and physically plausible theory in which we provide explanations for the different aspects of the onset phenomenology in self-field MPD thrusters. We address the problem of the breaking of the azimuthal symmetry of the discharge, explaining the underlying physical mechanism and providing a quantitative criterion for this to occur. We then show that this azimuthal instability is also at the base of the formation of the filamentary plasma structures which have been observed in experimental investigations. The nature of the unstable dynamics of these filaments is then addressed and finally we propose a mechanism which explains the connection between the plasma dynamics and the electrical response of the thruster.

We conclude the first part by looking at possible design choices which could help improve the stability of these devices. Among others, particular attention is given to an alternative concept developed by A.I. Morozov, the Quasi-Steady Plasma Accelerator, which requires a staging strategy in which the ionization of the propellant is separated from the acceleration phase. A technical solution for the implementation of this concept in MPD thrusters would be the development of an efficient annular plasma source.

In the second part of this work we focus on the possibility of developing an annular helicon plasma source. Helicon sources have undergone a rapid diffusion in practically all the branches of research on low-temperature plasmas, as a consequence of their simplicity and potentially high ionization efficiency. The use of these sources as ionization stages in high-power plasma thrusters can potentially lead to an increase of the overall efficiency of the device and contribute to widen its operational envelope, as well as help in creating favorable conditions for stable operation. The goal of this work is to provide a basis of knowledge to help and guide future developments and designs of this kind of sources.

First we investigate the problem of the excitation and propagation of helicon waves, which are bounded modes of whistler waves, in an annularly bounded homogeneous plasma. Finite electron mass effects and all possible combinations of boundary conditions are included in the study, for which closed form analytical solutions are provided. A parametric analysis of the solution as a function of the main driving parameters is performed.

The problem of the radial equilibrium of a magnetized plasma in annular configurations is then addressed. By making use of a two-fluid model in a non-dimensional form, the most important parameters affecting both the plasma equilibrium and the wall losses are illustrated. As a result of a parametric study, the interplay between magnetic confinement and collisional effects is stressed to be the most important mechanism, and the effects induced by other parameters such as a finite ion temperature, plasma beta and geometry of the source are illustrated.

Given the relative importance of collisional effects in the radial equilibrium problem, in which neutral particles can play a major role at low ionization levels, we then report the results of a joint experimental and numerical activity aiming at the validation of a procedure that allows to calculate the neutral particle background in a helicon source. The results of this activity also give indication of a possible role played by the propellant injection system in the neutral pumping phenomenon, which is known to be a potential limiting factor of the efficiency of these devices.

The last part of the thesis concerns an experimental activity carried on an annular helicon source. This activity involved designing and building both the plasma source and a diagnostics setup to perform optical emission spectroscopy measurements. The setup allowed to perform scans of the light emitted by the plasma through a cross section of the device in between adjacent magnets. The occurrence of some calibration issues of the spectrometer did not allow for a quantitative estimate of the plasma parameters (electron temperature and number density), but the recorded spectra give indication of an inductive coupling mode of the source with the RF antenna. Taking into account the results of the model on the radial equilibrium, it is likely that the plasma in the source was collision-dominated. Finally, the linear scans of the emitted light are not in general axi-symmetric, which is not expected given the nominal symmetry of the source, thus indicating the possibility that asymmetric equilibria might exist in these sources.

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