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.

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.

Energetic ParticleSpectrum

SEP GCR

Range of energies

Protons, Iron (Fe+?)

Most concerned aboutGalactic Cosmic Rays(GCRs) with energiesof 2 to 4 GeV per nucleon

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.

Charles R. Buhler, ASRC Aerospace Corp.

Electrostatic Shield

F=q E

Need GV potentials!!

Brehmsstrahlung radiation is potentially lethal

Magnetostatic Shields

F=qv×B

Several different strategies

use magnetic fields to deflect particles

Plasma Magnets

Confined magnetic shields

Deployed magnetic shields

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

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

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

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:

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

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

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

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:

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

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

Specify E, q, m

Particle Simulation50 km

Launch 10,000particles toward the origin and determine how close they get

choose r 0 ; v0

Particle Simulation

Dipole Magnetic Field: B r =04 [− M

r 33 M⋅r r

r5 ]

Particle Simulation

M1 GeV Fe+

M = 1013 A m2

Cst = 190 m

Point of closest approachto origin

rmin = 75 m

Particle Simulation

Stormer was right!Shepherd and Kress [2007b]

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...

Particle Simulation

Shepherd and Kress [2007a]

a = 1 km

?

Particle Simulation

Shepherd and Kress [2007a]

No Shielding

a = 1 km

Stormer Theory does not apply to deployed coils... a > Cst

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

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

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?

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

Other Possibilities?

Not Stormer shielding,but some shieldingoccurs near the wire

Move the habitat awayfrom the origin

Torus

Straight, infinite wire

B=0 I

2 R

Magnetic Field Cancellation

Straight, infinite wires

B=0 I

2 R

Magnetic Field Cancellation

Straight, infinite wires

B=0 I

2 R

Magnetic Field Cancellation

Straight, infinite wires

B=0 I

2 R

Magnetic Field Cancellation

Straight, infinite wires

B=0 I

2 R

Magnetic Field Cancellation

Straight, infinite wires

B=0 I

2 R

Magnetic Field Cancellation

Straight, infinite wires

B=0 I

2 R

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

Note that the color scale is logarithmic

Iinner

/Iouter

= 1.51 Straight, infinite wires

Magnetic Field Cancellation

Magnetic Field Cancellation

Torus of Wires32 wires

Iinner

/Iouter

= 4.65

B0=0 I

2 R

Torus of Wires

Magnetic Field Cancellation

Simon's Dad's Active Shield (SDAS)

Can it Shield?

John P. G. Shepherd, EmeritusUniv. of Wisconsin, River Falls

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

B0=0 I

2 R

Toroidal Magnetic Spacecraft Shield (ToMaSS)

ToMaSS

Loop

Torus

HalfLoop

B0=0 I

2 R

Toroidal Magnetic Spacecraft Shield (ToMaSS)

ToMaSS

Loop

Torus

HalfLoop

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

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.