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Simulations of Magnetic Shields for Spacecraft
Simulations of Magnetic Shields for Spacecraft "the nation that controls magnetism will control the universe". -- Dick Tracy Simon G. Shepherd Thayer School of Engineering Patrick Magari and Darin Knaus Creare, Inc. Brian T. Kress Department of Physics and Astronomy Jay C. Buckey, Jr. Dartmouth Medical School Spacecraft Shielding Problem: Radiation from energetic particles is likely to be lethal to astronauts during transit to Mars. Solution: Astronauts must be shielded from energetic particles during flight. Energetic Particle Spectrum Range of energies Protons, Iron (Fe+?) Most concerned about Galactic Cosmic Rays (GCRs) with energies of 2 to 4 GeV per nucleon SEP GCR Spacecraft Shielding How to shield these particles? You don't... -- Robert Zubrin, Mars Society Passive Shields -- Use material/mass to absorb energy simple too much mass required for GCR particles secondary radiation from scattering; could be worse than primary... not very cool. Active Shields -- Use electric/magnetic fields to deflect harmful particles from regions surrounding spacecraft. Electrostatic Shield F =q E Need GV potentials!! Brehmsstrahlung radiation is potentially lethal Charles R. Buhler, ASRC Aerospace Corp. Magnetostatic Shields F =q v × B use magnetic fields to deflect particles Several different strategies Confined magnetic shields Deployed magnetic shields Plasma Magnets Plasma Magnets Mini-Magnetosphere: M2P2 Robert Winglee, UW Create an artificial magnetosphere around spacecraft: Propulsion and protection ● Inflating magnetic field can shield particles with energies 200 times larger than those using just magnetic fields Several criticisms have been voiced about this sort of idea: ● ● There is some skepticism as to whether inflating the magnetic field actually shields better or worse Plasma adds a great deal of complexity... Deployed Magnetic Shields Cocks et al. 1991, 1997, Duke Creare, Inc Dipole magnetic field from a circular loop of wire with radius a creates a shielded region of radius Cst around the spacecraft Based on Stormer Theory, [Stormer, 1955] derived various forbidden regions for particles in the presence of an ideal magnetic dipole M Stormer Theory z showed the existence of a magnetic potential barrier in a dipole magnetic field M 2 r = C st C st cos 3 1 1cos M q 0 1/ 2 = [ ] 4mv Stormer Length r ~ 0.4 Cst at = 0 “40% of particles are shielded from a spherical region of dimension Cst” Deployed Magnetic Shield Cocks et al. 1997 z Magnetic Dipole Moment of Current Loop a 2 M = n I a z M For a given shielded region: C st ~ M 1/ 2 Energy stored in current loop: E ~ LI So: 2 L ~ a ; I ~ a a : I ; E −2 Deployed Magnetic Shields Cocks et al. 1997 Cst = 5 m KE = ?? eV a = 10 km I = “transistor radio battery” Note also that: B ~ I : B as a Magnetic Dipole r 0 I A r = 4 Only if: Expand in powers of: z d l ∮ ∣r −a∣ a M ∣r ∣ ≫ ∣a ∣ a /r ≪ 1 Magnetic Field of a magnetic dipole 0 B r = ∇× A r = 4 [ r r 3 M⋅ −M 3 r r5 ] Magnetic Fields Shepherd and Kress [2007a] Magnetic Field of a current loop is very different from a dipole when r ~ a --> Stormer Theory does not apply to deployed coils... a > Cst Spacecraft Shielding Does the deployed loop provide any type of shielding? Equation of motion for a charged particle in a static magnetic field: d v m = q v × Br dt Rewrite as system of ODEs: d v q = v × B r dt m d r = v dt coupled system of 6 first-order ODEs in x, y, z, vx, vy, vz System of First-Order ODEs Initial value problem: Need initial conditions for: r t=0 Pick initial position: r t =0 Choose energy of particle: ∣v∣ Pick initial direction: v ; v t=0 Advance the solution using any IVP technique from ENGS 91 Lab #6 Euler's Method, modified Euler's Method, Midpoint, Trapezoidal Rule, AB/AM Multistep methods, predictor corrector methods System of First-Order ODEs Runge-Kutta 4th order simple, stable, and accurate ... Adaptive time-step based on fraction of local gyroperiod t = 10 −3 ⋅ T 2mc T = qB Particle Simulation Specify E, q, m choose r0 ; v0 Launch 10,000 particles toward the origin and determine how close they get 50 km Particle Simulation Dipole Magnetic Field: 0 B r = 4 [ r r 3 M⋅ −M 3 5 r r ] Particle Simulation Point of closest approach to origin M = 1013 A m2 1 GeV Fe+ Cst = 190 m rmin = 75 m M Particle Simulation Stormer was right! Shepherd and Kress [2007b] Particle Simulation r Magnetic field of current loop: z no closed-form solution exists Approximate using Biot-Savart Law 0 I d l × R d B r = 3 4 R 1 degree segments ~ 16 times slower than dipole calculation... Particle Simulation a = 1 km ? Shepherd and Kress [2007a] Particle Simulation a = 1 km Shepherd and Kress [2007a] No Shielding Stormer Theory does not apply to deployed coils... a > Cst Particle Simulation Can a loop of wire shield particles? confined shield Shepherd and Kress [2007b] Stormer-like Shielding is approximately achieved when a << Cst Particle experiences the far field (dipole) along entire trajectory Current Loop What is magnetic field associated with confined shield? Desire: 10 m region shielded from 1 GeV protons a=1m M = 3.3 1010 A m2 n = 100 turns I = 100 MA B>3T Magnetic Shield Dilemma Need a large magnetic field to deflect GCR particles Need a small magnetic field to survive the voyage Is it possible to create a magnetic field such that it achieves both of these goals? Double-Toroidal-Solenoid Superconducting Magnetic Shield Jeffrey Hoffman, MIT Coils generate field to deflect particles from all directions End coils are intended to deflect particles along axis Magnetic field strength in habitat is intended to be small Not clear from their report and analysis that they achieved these goals Other Possibilities? Not Stormer shielding, but some shielding occurs near the wire Move the habitat away from the origin Torus Magnetic Field Cancellation B= 0 I 2R Straight, infinite wire Magnetic Field Cancellation B= 0 I 2R Straight, infinite wires Magnetic Field Cancellation B= 0 I 2R Straight, infinite wires Magnetic Field Cancellation B= 0 I 2R Straight, infinite wires Magnetic Field Cancellation B= 0 I 2R Straight, infinite wires Magnetic Field Cancellation B= 0 I 2R Straight, infinite wires Magnetic Field Cancellation B= 0 I 2R Straight, infinite wires Magnetic Field Cancellation Uniform current in wires Adjust the currents in the wires to create a local field that cancels the field from the other wires I = Iinner +m s s Magnetic Field Cancellation Iinner/Iouter = 1.51 Straight, infinite wires Note that the color scale is logarithmic Magnetic Field Cancellation 32 wires Torus of Wires Magnetic Field Cancellation B 0= Iinner/Iouter = 4.65 0 I 2R Torus of Wires Simon's Dad's Active Shield (SDAS) John P. G. Shepherd, Emeritus Univ. of Wisconsin, River Falls Can it Shield? Toroidal Magnetic Spacecraft Shield (ToMaSS) I SEP: 100 MeV protons B 0= Magnetic field strength 2R inside torus M = 7 x 109 A m2 I = 700 kA : 22 MA 0 < 100 mT Toroidal Magnetic Spacecraft Shield (ToMaSS) I B 0= 0 2R ToMaSS Torus Loop Half Loop Toroidal Magnetic Spacecraft Shield (ToMaSS) I B 0= 0 2R ToMaSS Torus Loop Half Loop Magnetic Spacecraft Shields Magnetic Shields ● require less mass than passive shields; in principle ● no secondary radiation ● less complicated than plasma magnetic shields Toroidal Geometry ● eliminates problem of shielding along axis ● amenable to artificial gravity? ● simpler design – no additional infrastructure ● field cancellation to minimize magnetic field in habitat ToMaSS Is it practical? ● Can it shield GCR particles? with sufficiently low magnetic field (<200 mT) ● Is the energy required too high? 22 MA for SEP protons Wernher Von Braun, “Will Mighty Magnets Protect Voyagers to Planets?”, Popular Science, 1969. Doughnut-shaped manned spaceship, pictured near Mars, wards off lethal solar protons (curved white trails) with huge built-in magnetic coil.
