1AE6450 Rocket PropulsionElectricmagnetic Propulsion-1Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Forces on a Charged Particle• To examine how to use electrical energy to accelerate a propellant, consider acceleration of a particle with mass m and charge q()pBuqEqdtudmrrrrr+×+=Electrostatic ForceLorentzForceCollisional Force (Momentum Transfer)ErqeFr+BrqmFr+ur`urBrmFrElec. FieldMag. Field(1)AE6450 Rocket PropulsionElectricmagnetic Propulsion-2Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Motion of Charged Particle in E&B Fields• How does charged particle move in electric and magnetic fields• Electric field only– electron lighter, higher accel.• Magnetic field only– particle gyrates(centripedal accel.)– radius of gyration– frequency of gyration–No work; Band FperpendicularEmqdtudrr=()Bumqdtudrrr×=Er+-urBrrg2qBBumrgrr×=mqBg=ω2AE6450 Rocket PropulsionElectricmagnetic Propulsion-3Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.JrBrInduced Magnetic Fields• In general, current flow induces a B field– B field induced bylinear current– B field inducedby coilBrFrom Space Propulsion Analysis and Design, Humble, Henry and Larson, 1995AE6450 Rocket PropulsionElectricmagnetic Propulsion-4Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Motion of Charged Particle in E&B Fields• Crossed E and B fields– E field acceleratesparticle upward– B field causesaccelerationperpendicular to u– overall result is driftvelocity normal to Eand BErBrdurheavylight2BBEudrrr ×=mrg∝mg1∝ω3AE6450 Rocket PropulsionElectricmagnetic Propulsion-5Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Plasmas• Gas composed of equal “amount” of negatively and positively charged particles– electrically neutral– negative particles usually e-– positive particles are positive ions– typically most of gas molecules remain neutral• Momentum equation for plasmaBjpuuturrrrr×+−∇=∇⋅+∂∂ρCurrent Density (A/m2)()321,, uuuu ∇∇∇≡∇rAE6450 Rocket PropulsionElectricmagnetic Propulsion-6Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Induced E Fields – Hall Effect• Electron acceleration– lighter e-accelerate more quicklyand accommodate to flow field (most of j)– collisional coupling (momentum) of electrons and heavies (ions and neutrals) is weak plasma resistivity (Ωm)enpenBjBujEeee∇−×+×−=⇒rrrrrrηHall Effectaccelerates heavyparticles in chargeneutral plasma2envmecee=η(2)InducedE field dueto plasmamotion electronpressuretermcollision freq.electrons with heavies4AE6450 Rocket PropulsionElectricmagnetic Propulsion-7Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Hall Thruster• Hall effect most noticeable at low particle densities• Stationary Plasma Thruster (SPT)– developed in Russia– 10’s kW– axial current flowacross radial Bgenerates azimuthalelectron flow– induced (axial) Hall Eaccelerates ions– also called “gridless”(neutral) ion thruster– 1500-2000 s Isp with >50% efficiency using Xe and no oscillations like MPDSpace Propulsion Analysis and Design, Humble, Henry and Larson, 1995AE6450 Rocket PropulsionElectricmagnetic Propulsion-8Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Electromagnetic Propulsion Systems • Use applied or induced magnetic fields to produce acceleration of propellant– high currents/powers requiredto produce significant induced fields– high power availableonly (normally) inpulsed operationSpace Propulsion Analysis and Design, Humble, Henry and Larson, 19955AE6450 Rocket PropulsionElectricmagnetic Propulsion-9Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Pulsed Plasma Thruster• Propellant produced by vaporizing solid material with discharge• B field induced by discharge also acts to accelerate vaporized propellant• Advantage of simplicity• Accelerationforce~ j2(discharge current)Space Propulsion Analysis and Design, Humble, Henry and Larson, 1995AE6450 Rocket PropulsionElectricmagnetic Propulsion-10Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.Magnetoplasmadynamic (MPD) Thrusters• Resemble arcjets• Lower flow densities to attain higher exhaust velocity• Diffuse discharge,low erosion• Self field requires high J• Applied B field– allows higher Vat lower discharge currents– increase accel.– larger Hall effectSelf-Field MPD ThrusterApplied-Field MPD ThrusterSpace Propulsion Analysis and Design, Humble, Henry and Larson, 19956AE6450 Rocket PropulsionElectricmagnetic Propulsion-11Copyright © 2003-2004 by Jerry M. Seitzman. All rights reserved.MPD Thrusters (con’t)• Most efforts focused on applications with exhaust velocities (Isp) greater than arc jets• Typically require higher powers than currently available on in-space vehicles• Exhaust speed– limited by erosionand oscillations at high