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Fundamentals of Plasma Acceleration

Fundamentals of Plasma Acceleration. Plasma Thrusters. Unified approach based on acknowledgement that different types of electric thruster can all be described as Plasma Thrusters. Plasma?. • small Debye length. Plasma Thrusters.

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Fundamentals of Plasma Acceleration

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  1. Fundamentals of Plasma Acceleration

  2. Plasma Thrusters • Unified approach based on acknowledgement that different types of electric thruster can all be described as Plasma Thrusters Plasma? Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  3. • small Debye length Plasma Thrusters • Unified approach based on acknowledgement that different types of electric thruster can all be described as Plasma Thrusters Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  4. • low neutral collisionality Plasma Thrusters • Unified approach based on acknowledgement that different types of electric thruster can all be described as Plasma Thrusters Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  5. • plasma parameter large Plasma Thrusters • Unified approach based on acknowledgement that different types of electric thruster can all be described as Plasma Thrusters Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  6. Plasma Thrusters • Unified approach based on acknowledgement that different types of electric thruster can all be described as Plasma Thrusters • Main implication: quasi-neutrality assumption • We shall call Plasma Thrusters all devices in which the working fluid remains quasi-neutral throughout all phases of the process • Hall Thrusters, Self-field MPD Thrusters and Applied Field MPD Thrusters belong in this cathegory • This definition leaves out ion thrusters, which inherently involve charge separation as a basic feature of the acceleration process Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  7. collisions Interaction with particles of other types change of momentum Lorentz emf electromotive force pressure, viscosity interactions with particles of the same type Momentum Equation • To generate thrust we must transfer momentum to a working fluid. How can momentum be transfered to a plasma? •   Under very general assumptions we can obtain the following Momentum Equation for the generic species Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  8. Isotropic pressure terms non-isotropic (viscous) terms friction between the two fluids small m, negligible Two-fluid Model • By considering only the electronic and ionic components of the plasma the following two-fluid model is obtained Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  9. Two-fluid Model • By neglecting the electron inertial term in the second equation and with the substitution we finally obtain Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  10. With the further useful substitutions from the electron equation we obtain the Generalized Ohm’s Law electric field Hall’s emf back emf thermionic emf Generalized Ohm’s Law Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  11. Ohmic term Back emf Hall’s emf Thermionic emf No useful contribution in the velocity direction Electric Field By rearranging the generalized Ohm’s law we obtain the expression for the self-consistent electric field in the quasi-neutral plasma Resistive heating is exploited in arcjets This is exploited in different ways in MPD and HET thrusters Usually small Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  12. Momentum increase of the ion fluid Electric field contribution Collisional contribution B General Vector Diagram Going back to the two-fluid model, let us visualize the vector diagram of fields and currents (neglect the pressure gradient contributions) Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  13. Momentum transfer to the ions Electric field contribution Collisional contribution B Electric field effect on the electron fluid in the ion comoving frame Electric field effect due to electrons relative velocity Collisional momentum loss General Vector Diagram Going back to the two-fluid model, let us visualize the vector diagram of fields and currents (neglect the pressure gradient contributions) Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  14. Lorentz force General Vector Diagram Thus, the vector diagram of fields and currents for the two-fluid model (neglecting the pressure gradient contributions) can be visualized as shown here By combining and posing we finally have Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  15. The increase in the flow directed kinetic energy can be obtained by taking the dot product of the momentum equations for the two species by and respectively: Collisional terms Joule heating Energy Equations which can be rewritten as Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  16. Energy Equations Adding up the two equations above the collisional terms cancel out, and we are left with Once again we can explicitly highlight the role of the overall Lorentz force. With a few passages we would obtain but it should be remembered that the increase in the ion fluid kinetic energy is either drawn from the energy transferred by the electrons through collisions, or from direct action of the electric field on the ions Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  17. Hall parameter Power transfer efficiency Thus we see that - neglecting again the pressure gradient terms - the useful energy transfered to the plasma can utimately be computed in terms of power delivered by the electric field minus power dissipated as Ohmic heating. We are thus prompted to define a power transfer efficiency as and remembering that we finally obtain being is the angle formed by the Lorentz force with the local flow direction Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  18. Example I : large Hall parameter Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  19. Example I : large Hall parameter Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  20. Example I : large Hall parameter Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  21. Example I : large Hall parameter Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  22. Example II : Hall parameter ~ 1 Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  23. Example II : Hall parameter ~ 1 Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  24. Example II : Hall parameter ~ 1 Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  25. Example II : Hall parameter ~ 1 Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  26. Hall-effect Thrusters Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  27. Self-field MPD Thrusters Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  28. Applied-field MPD Thrusters Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

  29. Applied-field MPD Thrusters Including effect of self-field Advanced Course: Electric Propulsion Concepts and Systems M. Andrenucci

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