1. Electrodynamic Tether System Analysis Comparing Various Mission Scenarios Keith R Fuhrhop and Brian E. Gilchrist University of Michigan

2. Introduction Electron Emission Theory & Space Charge Limits –Thermionic Cathodes –Field Emitters –Hollow Cathodes ED Tethers System Integration System Simulations

3. Thermionic Emission Thermionic Emitter 2 Step Process – Thermionic Emitter then Electron Gun –EG emission To Overcome SCL EG needs more E –TC production Overcome Fermi Energy Boils off Low E Electron Electron Gun Richardson Eq.

4. Field Emission Quantum Mechanical Tunneling Effect –10 8 - 10 9 V/m E-field –10 7 tips / cm 2 No Heaters or Gas Required Many Emitter Types –Spindt type, carbon nanotubes, BN nanostructure (UM) Fowler-Nordheim Eq.

5. Hollow Cathodes Setup –TC Emission –Xe Ionized Gas Stats –Fuel Flow Rate (4–14 sccm) –Potentials (10-40 V) –Diameter of Keeper (1-12 cm) Double Sheath Possible –2 Potential Drops Across the Xe gas then Sheath

6. Space Charge Limit 1-d C-L Law (vacuum gap) 3-d C-L Law (vacuum gap) Only so many Electrons can emitted at a time Plasma Parameters Determine –Sheath –Emission Area –Emission e- Energy

7. De-boost Tether Example Tether electromotive force (EMF) drives current through tether –V emf = (v x B North ) l –Geomagnetic field, B North (0.18 - 0.32 Gauss) –Orbital velocity, v (~7500 m/s @ 300 km alt) –V emf (35 – 250 V/km) along tether of length l Electrons collected from ionosphere along positively biased upper bare tether and returned to ionosphere at lower end Current I produces magnetic force (drag thrust) dF on each tether section of length dl: dF = dlI x B North. –Current magnitude varies along tether Current magnitude determined by –Available EMF and tether resistance –Bare-tether electron collection efficiency –Electron ejection efficiency at lower end

8. Configurations Grounded Cathode (HC’s) –S/C Surface is negative by HC bias Grounded Gate (TC & FEA) –S/C at floating potential –V emf powers emitter –If can’t emit current then emmiter cathode or spacecraft pulled very negative Series - Bias Grounded Gate (TC & FEA) –S/C at floating potential –Emitter not Powered by V emf –Easily Control Emitter Potential –Requires non-tether power source –If can’t emit current then emitter spacecraft pulled very neg. Grounded TipGrounded Gate Series – Bias Grounded Gate

9. EDT Simulation System Setup Differences in Mission Objective –Tether length: 5005 m –Geometry: Single Line –Bare vs. Insulated: 50% Bare –Boost vs. De-boost: Both cases –Orbital Parameters: 0 o Latitude, 35 o Inclination –HVPS:2000 V –S/C Surface area: Next Slide –Emission device: TC, FEA, or HC –Models:IRI-2001, MSIS-86, IGRF-91 –Test Dates:1-1-06 (Min) & 7-15-01 (Max)

10. EDT Simulation System Setup 2 Delta 2 PayloadTether SectionEndmass / Emitter Surface Area [m 2 ] 8.086.75680.7854 Total Section Mass [kg] 9805520 Total Mass = 1055 kgTotal SA = 15.622 m 2 Ballistic Coeff. = 30.697

11. Simulation Analysis 1 Max boost [N]: –High Density: ~0.56 HC, ~0.51 FEA, ~0.076 TC –Low Density: ~0.048 HC, ~0.046 FEA, ~0.033 TC Fewer TC Emitters: Potential near Max –System correspondingly reacts

12. Simulation Analysis 2 Total Power ( = P HVPS ) [W]: –High Density: ~7800 HC, ~7300 FEA, ~1700 TC –Low Density: ~418 HC, ~ 421 FEA, ~462 TC TC has weakest boost & uses most power (Min) Same issue with Fewer Emitters in Max Case

13. Simulation Analysis 3 Efficiency = Orbit Power / Supplied Power Identical (Min) Dip being investigated (Max)

14. Simulation Analysis 4 Boost / Power [N/W] HC most Efficient Within 25% of max value through 2000 km Investigating max density case

15. Simulation Analysis 5 Max boost [N]: –High Density: -0.57 HC, -0.52 FEA, -0.11 TC –Low Density: -0.038 HC, -0.036 FEA, -0.024 TC Fewer TC Emitters: Potential near Max –System correspondingly reacts

16. Simulation Analysis 6 Total Power ( = P EMF ) [W]: –High Density: ~7390 HC, ~6760 FEA, ~1580 TC –Low Density: ~330 HC, ~320 FEA, ~280 TC Near equivalent power (Min) Same issue with Fewer Emitters in Max Case

17. Simulation Analysis 7 Boost / Power [N/W] TC most efficient until 400 km in high density case Efficiency reaches min at 500 km then goes up FEA highest after ~1300 km in low density case

18. Conclusion TC’s –Not Very Effective FEA’s –Nearly identical to HC performance HC’s –Proven, Most Powerful & Efficient –Requires use of a consumable gas! Future Work: –Analysis on Other EDT Mission Objectives –Further analysis on current work