Simulations of Magnetic Shields for Spacecraft

Transcription

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 1cos 
M q 0 1/ 2
= [
]
4mv
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 × 
Br 
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
2mc
T =
qB
Particle Simulation
Specify E, q, m
choose
r0 ; v0
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
2R
Straight, infinite wire
Magnetic Field Cancellation
B=
0 I
2R
Straight, infinite wires
Magnetic Field Cancellation
B=
0 I
2R
Straight, infinite wires
Magnetic Field Cancellation
B=
0 I
2R
Straight, infinite wires
Magnetic Field Cancellation
B=
0 I
2R
Straight, infinite wires
Magnetic Field Cancellation
B=
0 I
2R
Straight, infinite wires
Magnetic Field Cancellation
B=
0 I
2R
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.