1AE6450 Rocket PropulsionElectric Propulsion-1Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic PropulsionIon EnginesAE6450 Rocket PropulsionElectric Propulsion-2Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic Thrusters• Ion engine example• Near vacuum required• Ion source–usually electronbombardmentplasma–also ion contact: propellant flowingthrough hot poroustungsten – field emission: chargedspray droplets/particles• Electrons added toneutralize exhaust– thermionic emittersSpace Propulsion Analysis and Design, Humble, Henry and Larson, 1995LAAccelerator2AE6450 Rocket PropulsionElectric Propulsion-3Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatics - Definitions• V – potential or voltage(sometimes φ) (Volts)• E – electric field (V/m, N/Coulomb)• q – charge (C) (qe-=1.602×10-19C)•Force• Potential Energy• J – current (A, Coulomb/s)• j – charge current density(A/m2, Coulomb/m2s )• n – charge density (C/m3)−=−∇=dxdVVErxVErnquj=qEFrr=VqqEdxFdx ∆==∫∫∆VAE6450 Rocket PropulsionElectric Propulsion-4Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic Thruster Performance - ue• Specific impulse• Find exhaust velocity fromenergy balance• So maximum specific impulse limited by voltage difference across accelerator()inletexiteVVmqu −= 2smMWV )volts(800,13∆=for singlyionizedVqmue∆=221ueoespguI =3AE6450 Rocket PropulsionElectric Propulsion-5Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic Thruster Performance - ττττ•Thrust• Mass flow rate related to current• Maximum thrust limited by achievable current density• For ion engine, ion current limitedby space-charge– field from denseions creates “shield”from applied E field223max294LVmqjo∆=εmeterFarado1210854.8−×=εpermittivityof free spaceChild-LangmuirLawaccelerator electrode spacing()22238maxm)volts(1044.5mAmpsLMWVj∆×=−for singly ionizedeum&=τmnρ=qmjAm =⇒&enquj =+++++++++++++++++AE6450 Rocket PropulsionElectric Propulsion-6Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic Thruster Thrust - ττττ• Maximum thrust• High τ requires high ∆V and aspect ratio– space charge⇒D/L ~1– use many small ion beams toget more thrust()eeuqmjAum ==&τeuqmAjmaxmax=τVmqqmALVmqo∆∆=2294223ε()22max98 LVAo∆=ετA=cross-sectional area flowfor circular cross-sectionof diameter, D()()22max92 VLDo∆=επτ()NewtonsVLD in1018.62212∆×=−DL≠≠≠≠f(q/m)4AE6450 Rocket PropulsionElectric Propulsion-7Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic Thruster Thrust - Propellant• For fixed specific impulse – best propellant for high thrust• heavy molecules (particles)• xenon (Xe) good choice (MW=131.3)• also macro particles possible (colloidal thrusters)qmA∝maxτ∆====spacceloospospeIqmLVmqgIqmjAgIqmjuqmjA223maxmax294εττCs,Hg: but storage issuesAE6450 Rocket PropulsionElectric Propulsion-8Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic Thruster Power• Jet power• at maximum current• Accelerator electrical power• Power supplied to thrusterspoejIgumPτ21212==&thjthPPη=225294accelacceloLVmqA∆=εVjAVJPaccelelec∆=∆=5AE6450 Rocket PropulsionElectric Propulsion-9Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electrostatic Thruster Power - Losses• Ionization losses– must account for energy used to create ions (e.g., Xe→Xe+)– minimum loss given by ionization potential (εI) for atom times current (units of electron volts, eV)• Beam divergence, multiple ionization, sputtering/heating (ion impacts on grid)• Propellant utilization efficiency • Neutralization losses()qmmJPionionlossion&εε==γupropellantbeammmη=&&IεneutV∆AE6450 Rocket PropulsionElectric Propulsion-10Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Nonideal Performance and Typical Values• Nonideal performance equations• Typical values–εionεIup to 100-300 eV/ion–γ0.8-0.95–ηu0.8-0.95–∆Vneut10-20VidealspuspII,γη=()neutaccelionththVVVJVJP ∆+∆+∆=∆=uospebgImumητ&&==()accelneutionuththbthjthVVVVJqmJVJmPP∆∆+∆+=∆=∆==122222γηττη&∆Vaccel, Ispηth∆Vbeamdominateslow Isp ion engines are inefficient6AE6450 Rocket PropulsionElectric Propulsion-11Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Ionization Chambers• Electron bombardment– most common– 1) thermionic production of seed e-, 2) accel. e-(static field), 3) bombard neutral gas molec. and ionize them• hollow cathode or separate thermionic source • mag. field to gyrate e-for increased collisions with neutrals • RF discharges• For liquid metals (e.g. Cs), can flow over another metal (e.g., Tu) to ionizeAE6450 Rocket PropulsionElectric Propulsion-12Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Ionization Chamber (1)• Hollow cathode7AE6450 Rocket PropulsionElectric Propulsion-13Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.• Thermionic e-emission from filament• Magnetic field induced e-gryrationIonization Chamber (2)AE6450 Rocket PropulsionElectric Propulsion-14Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Electron Bombardment Xe+Engine Example• Operating conditions– ∆Vaccel=700 V, L=2.5 mm, 2200 holes (grids) each with D=2.0 mm– MW(Xe)=131.3, εI(Xe)=12.08 eV• Determine– τ, –ue, Isp– m– power required including only minimum needed for ionization and neutralization (10 V).8AE6450 Rocket PropulsionElectric Propulsion-15Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Solution()2212max1018.6 VLD ∆×=−τ()gridN /1094.17005.2/21018.662212−−×=×=()mNgridNgridstotal3.4/1094.122006,max=×=−τsmsmMWVue3.131700800,13800,13 =∆=smue860,31=sIsp3248=⇒sgume41034.1−×==τ&()mmqVumPPPPneutIeneutionjet&&∆++=++=ε22kgkgMWm25271019.21067.1−−×=×=Cq1910602.1−×=for singly ionized molec.WW 16.29.67 +=WP 1.70=maximum effic. =67.9/70.1= 97%AE6450 Rocket PropulsionElectric Propulsion-16Copyright © 2003-2006 by Jerry M. Seitzman. All rights reserved.Child-Langmuir Law Derivation• Poisson’s Eqn.–1-doiioqqnVεερ−=−=∇2ooiiujqndxVdεε−=−=22()xVVqmjoo−−=12ε+