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                    Micropropulsion Technologies                                    233


                    and electrical) due to a lack of understanding of the flows in such devices. This is due
                    to the fact that the continuum assumption commonly used in gas and plasma dynam-
                    ics is no longer valid at smaller densities and characteristic dimensions of flow. The
                    Knudsen number is defined as the ratio of the mean free path of gas molecules to a
                    characteristic dimension of flow. As the Knudsen number increases, the collision rate
                    becomes too low to maintain local thermodynamic equilibrium. Furthermore, the
                    expansion of a propellant from chamber conditions to vacuum often involves flow
                    regimes from continuum to transition to free molecular, though the smallest devices
                    may not have any component in the continuum regime. Therefore, fairly complicated
                    models are needed for proper evaluation, which goes beyond the scope of this review.
                    More detailed descriptions of these effects can be found elsewhere. 6,7
                       All these considerations demonstrate that both chemical and electrical propul-
                    sion systems need to be included in this chapter and that a decision between either
                    system has to be made on a case-by-case basis. The emphasis will be put on MEMS
                    and other low-mass systems (i.e., where the total system dry mass is less than
                    1000 g). The principle of operation will be discussed for each system, using few
                    basic equations describing the performance. While simplistic, these basic equations
                    will nevertheless help to understand the operating characteristics of the various
                    micropropulsion technologies and calculate rough estimates of their performance.
                       After describing each system, its key parameters will be discussed and the
                    performance for each system will be summarized in a table. Technologies discussed
                    here include (a) chemical propulsion systems, such as hydrogen peroxide thrusters,
                    cold gas thrusters, solid micro rockets and (b) electric propulsion systems, such as
                    pulsed plasma thrusters, laser-driven plasma thrusters, field effect thrusters, ion
                    engines, and resistojets. While many publications about these types of propulsion
                    systems cite performance specifications of the propulsion device (i.e., the micro-
                    manufactured emission array or the MEMS-valve), this chapter tries to take a look
                    at the complete system, thereby providing information that is needed to successfully
                    design a satellite. Improvements to existing systems and new propulsion technolo-
                    gies will emerge and may well be superior to those mentioned, which also implies
                    that the numbers cited here are by no means absolute limitations. In this light, I
                    would also like to refer to other review articles on micropropulsion, with the most
                    important and complete one authored by Ju ¨rgen Mu ¨eller from NASA JPL. 8
                       Regarding the formality of this chapter, I took the liberty of referring to most
                    publications used in the beginning of each chapter, instead of placing the citations
                    in the body of the text. By doing so, it became much easier to read, digest, and
                    summarize. I hope that none of the original authors will take offense even if a
                    certain thought in the body of the text may have come from a single paper only.

                    Enjoy!


                    11.2 ELECTRIC PROPULSION DEVICES
                    In this review, electric propulsion systems are defined as those where the majority
                    of the energy needed for operation is electrical energy.




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