the nation that controls magnetism will control the...
TRANSCRIPT
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Simulations of Magnetic Shields for Spacecraft
Simon G. ShepherdThayer School of Engineering
Brian T. KressDepartment of Physics
and Astronomy
Jay C. Buckey, Jr.Dartmouth Medical School
"the nation that controls magnetism will control the universe". -- Dick Tracy
Patrick Magari and Darin KnausCreare, Inc.
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Problem: Radiation from energetic particles is likelyto be lethal to astronauts during transit toMars.
Spacecraft Shielding
Solution: Astronauts must be shielded from energeticparticles during flight.
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Energetic ParticleSpectrum
SEP GCR
Range of energies
Protons, Iron (Fe+?)
Most concerned aboutGalactic Cosmic Rays(GCRs) with energiesof 2 to 4 GeV per nucleon
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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 deflectharmful particles from regions surrounding spacecraft.
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Charles R. Buhler, ASRC Aerospace Corp.
Electrostatic Shield
F=q E
Need GV potentials!!
Brehmsstrahlung radiation is potentially lethal
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Magnetostatic Shields
F=qv×B
Several different strategies
use magnetic fields to deflect particles
Plasma Magnets
Confined magnetic shields
Deployed magnetic shields
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Mini-Magnetosphere: M2P2
Robert Winglee, UW
Create an artificial magnetosphere aroundspacecraft: Propulsion and protection
● Inflating magnetic field can shield particleswith energies 200 times larger thanthose using just magnetic fields
● There is some skepticism as to whether inflating the magnetic field actually shields better or worse
● Plasma adds a great deal of complexity...
Several criticisms have been voiced aboutthis sort of idea:
Plasma Magnets
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Cocks et al. 1991, 1997, DukeCreare, Inc
Dipole magnetic field from a circular loopof wire with radius a creates a shieldedregion of radius Cst around thespacecraft
Deployed Magnetic Shields
Based on Stormer Theory, [Stormer, 1955]
derived various forbidden regions for particles in the presence of an ideal magnetic dipole M
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Stormer Theory
C st = [M q04mv
]
1/2
r = C stcos2
11cos3
showed the existence of amagnetic potential barrierin a dipole magnetic field
z
M
r ~ 0.4 Cst at = 0
“40% of particles are shielded from a spherical region of dimension Cst”Stormer Length
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Deployed Magnetic Shield
C st ~ M 1/2
M = n I a2 z
Cocks et al. 1997z
Ma
For a given shielded region:
Magnetic Dipole Moment of Current Loop
Energy stored in current loop:
E ~ L I 2 L ~ a ; I ~ a−2
a : I ; E So:
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Deployed Magnetic Shields
Cocks et al. 1997
a = 10 km
KE = ?? eV
Cst = 5 m
I = “transistor radio battery”
Note also that:
B ~ I : B as a
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Magnetic Dipole
Only if:
Ar =0 I4
∮ d l∣r−a∣
zr
Ma
∣r∣ ≫ ∣a∣
Expand in powers of:
a /r ≪ 1
B r = ∇×Ar =04 [− M
r33 M⋅r r
r 5 ]Magnetic Field of a magnetic dipole
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Shepherd and Kress [2007a]
Magnetic Fields
Magnetic Field of a current loop is very different froma dipole when r ~ a
--> Stormer Theory does not apply to deployed coils... a > Cst
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Spacecraft Shielding
Does the deployed loop provide any type of shielding?
Equation of motion for a charged particle in a staticmagnetic field:
md vdt
= qv×Br
d vdt
=qm
v×B r
d rdt
= v
coupled system of 6 first-order ODEs in
x, y, z, vx, vy, vz
Rewrite as system of ODEs:
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Initial value problem:
System of First-Order ODEs
Need initial conditions for: r t=0 ; v t=0
Pick initial position:
Choose energy of particle: ∣v∣
r t=0
Pick initial direction: v
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
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Runge-Kutta 4th order
System of First-Order ODEs
simple, stable, and accurate ...
Adaptive time-step based on fraction of local gyroperiod
t = 10−3 ⋅ T T =2mcq B
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Specify E, q, m
Particle Simulation50 km
Launch 10,000particles toward the origin and determine how close they get
choose r 0 ; v0
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Particle Simulation
Dipole Magnetic Field: B r =04 [− M
r 33 M⋅r r
r5 ]
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Particle Simulation
M1 GeV Fe+
M = 1013 A m2
Cst = 190 m
Point of closest approachto origin
rmin = 75 m
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Particle Simulation
Stormer was right!Shepherd and Kress [2007b]
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Particle Simulation
no closed-form solution exists
Magnetic field of current loop:
zr
d Br =0 I4
d l×RR3
Approximate using Biot-Savart Law
1 degree segments
~ 16 times slower than dipole calculation...
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Particle Simulation
Shepherd and Kress [2007a]
a = 1 km
?
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Particle Simulation
Shepherd and Kress [2007a]
No Shielding
a = 1 km
Stormer Theory does not apply to deployed coils... a > Cst
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Particle Simulation
Can a loop of wire shield particles?
Stormer-like Shielding is approximately achieved when a << Cst
Particle experiences the far field (dipole) along entire trajectory
Shepherd and Kress [2007b]
confined shield
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Current Loop
What is magnetic field associated with confined shield?
Desire:
10 m region
shielded from 1 GeVprotons
a = 1 mM = 3.3 1010 A m2
n = 100 turnsI = 100 MA
B > 3 T
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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 itachieves both of these goals?
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Jeffrey Hoffman, MIT
End coils are intended todeflect particlesalong axis
Coils generate field todeflect particles fromall directions
Magnetic field strength inhabitat is intended tobe small
Not clear from their report and analysisthat they achieved these goals
Double-Toroidal-Solenoid SuperconductingMagnetic Shield
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Other Possibilities?
Not Stormer shielding,but some shieldingoccurs near the wire
Move the habitat awayfrom the origin
Torus
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Straight, infinite wire
B=0 I
2 R
Magnetic Field Cancellation
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Straight, infinite wires
B=0 I
2 R
Magnetic Field Cancellation
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Straight, infinite wires
B=0 I
2 R
Magnetic Field Cancellation
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Straight, infinite wires
B=0 I
2 R
Magnetic Field Cancellation
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Straight, infinite wires
B=0 I
2 R
Magnetic Field Cancellation
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Straight, infinite wires
B=0 I
2 R
Magnetic Field Cancellation
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Straight, infinite wires
B=0 I
2 R
Magnetic Field Cancellation
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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
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Note that the color scale is logarithmic
Iinner
/Iouter
= 1.51 Straight, infinite wires
Magnetic Field Cancellation
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Magnetic Field Cancellation
Torus of Wires32 wires
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Iinner
/Iouter
= 4.65
B0=0 I
2 R
Torus of Wires
Magnetic Field Cancellation
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Simon's Dad's Active Shield (SDAS)
Can it Shield?
John P. G. Shepherd, EmeritusUniv. of Wisconsin, River Falls
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B0=0 I
2 R
Toroidal Magnetic Spacecraft Shield (ToMaSS)
SEP: 100 MeV protons
M = 7 x 109 A m2
I = 700 kA : 22 MA
Magnetic field strength inside torus
< 100 mT
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B0=0 I
2 R
Toroidal Magnetic Spacecraft Shield (ToMaSS)
ToMaSS
Loop
Torus
HalfLoop
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B0=0 I
2 R
Toroidal Magnetic Spacecraft Shield (ToMaSS)
ToMaSS
Loop
Torus
HalfLoop
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Magnetic Spacecraft Shields
● require less mass than passive shields; in principle
Magnetic Shields
● 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
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Is it practical?
ToMaSS
● Can it shield GCR particles?
● Is the energy required too high?
22 MA for SEP protons
with sufficiently low magnetic field (<200 mT)
Wernher Von Braun, “Will MightyMagnets Protect Voyagers toPlanets?”, Popular Science, 1969.
Doughnut-shaped manned spaceship,pictured near Mars, wards off lethalsolar protons (curved white trails) withhuge built-in magnetic coil.