Analysis of a Lunar Base Electrostatic Radiation Shield
Concept
Charles Buhler, PIJohn Lane, Co-PI
ASRC Aerospace CorporationKennedy Space Center, Florida 32899
INTERPLANETARY RADIATION ENVIRONMENT
Main Components:(Atomic Nuclei)
Galactic Cosmic Rays (GCRs)
• Median energy ~1800 MeV/nuc• Continuous flux, varies with
the solar cycle
Solar Energetic Particles (SEPs)
• Sporadic, lasting hours to days• Soft spectra with highly
variable composition
ni~ne~ 6 cm-3
Galactic Cosmic Ray Spectra
0
500
1000
1500
2000
2500
3000
3500
4000
10 100 1000 10000 100000Energy (MeV/nucleon)
#/m
2 -s-s
terr
adia
n Solar MaximumSolar Minimum
From Francis Cucinotta, NASA JSCSpace Radiation Health Project(private communication)
Lunar
Shielding Solutions must
• Reduce radiation exposure• Be lightweight• Safe• Practical• Achievable in time for Moon Missions
There are two basic types: Active and Passive Shields
Polyethylene
Solar Minimum
John W. Wilson et al.NASA Technical Paper 3682 (1997)
Passive shielding can reduce the exposure by only about a factor of two due to weight constraints.
Spacecraft Limitations
Active Shielding Solutions• Electromagnetic Shields
– Magnets (>73 papers since 1961)– Plasma (>18 papers since 1964)– Electrostatic (>16 papers since 1962)
ShieldingVolume
Ea
b
CosmicRay
++ +
+
+
+
+
Traditional Spacecraft Design
Concentric, oppositely charged spherical electrodes for shielding against galactic heavy ions. Electrostatic generator keeps ‘a’at a high voltage with respect to ‘b’.
Slides provided by Jim Adams, Langley
Why Not Electrostatics?
– Debye Length ~11.5m• Assumption: The charge on a
conductor is much lower than the charge in the surrounding volume.
– Extreme voltages are required and surrounding a spacecraft or lunar base with a conducting shell is not realistic
• The same effect can be generated using an alternate
NASA Design
- V1 - V1-3 V1-3 V1
5 at -2 V1
2 spheres at +2V22 spheres at +3V2
5 at -2V1
“Protected Zone”Center Sphere
at +V0
+2V2+2V2
30 m 100 m
5 m radius
geometry.
Radiation Fluence: No ShieldingR
adia
tion
Inte
nsity
SPE
GCRFrom Space
From the Sun
0.1 1 100 1000 1000010Particle Energy [MV]
Radiation Fluence: No Shielding
SPE
GCR
Solar “Storm” –lasting hours to days
Rad
iatio
n In
tens
ity
0.1 1 100 1000 1000010Particle Energy [MV]
Radiation Fluence: No Shielding
SPE
GCR
Solar “Storm” –lasting hours to days
Rad
iatio
n In
tens
ity
0.1 1 100 1000 1000010Particle Energy [MV]
Radiation Fluence: No ShieldingR
adia
tion
Inte
nsity
SPE
GCR
0.1 1 100 1000 1000010Particle Energy [MV]
Radiation Fluence: No ShieldingR
adia
tion
Inte
nsity
SPE
GCR
0.1 1 100 1000 1000010Particle Energy [MV]
An Electrostatic Shield Design
Some Possible Electrode Geometries
Thin Film Polymer with Conductive Inner Coating
Conductive Mesh Screen
Conductive Wire Mesh
Sphere
Arbitrary Geometry
Electrode Geometry Used in ASRC Lunar Electrostatic Shield Model (LESM)
Thin Film Polymer Balloon with Conductive Inner Coating
Theory of Design
Lorentz Force
BvEF ×+= qq
Theory of Design
Coulomb Force
BvF ×E += qq
Theory of Design
Coulomb Force
EF q=
Electrostatic Shield: Use only a time independent electric field, i.e., 0=E&
Design Strategy
Determine an Ideal Electric Field to Repel Charged Particle Radiation (primarily positive
ions and electrons)
STEP 1:
),,( zyxE
Design StrategyFind a Way to Generate an Approximation
of the Ideal FieldSTEP 2:
Design StrategyPerform Mathematical Modeling and Computer
Simulation of Proposed ConfigurationsSTEP 3:
Design StrategyPerform Experiments and Testing on a Scale ModelSTEP 4:
Particle Detector
Lunar Shield Model Under Test
High Vacuum Chamber[torr] }10,10{ 105 −−∈P
Accelerator Grid[volts] }10,10{ 42∈∆V
Ion Selector
Ion Source
Broad-Band Energy Distribution to Simulate SPE Distribution
An Electrostatic Shield Design
Electrostatic Shield Design ConstraintsElectrical
• Electric Field Strength everywhere must remain well below a breakdown threshold value: In the case of non-conductors, EB(x, y, z) is related to the Dielectric Strength of the materials subjected to E(x, y, z).
),,(),,( zyxEzyxE B<
Non-Electrodes
• Surface Charge Distribution must remain well below a threshold breakdown value: In the case of conductors, when σ (x, y, z) exceeds σB(x, y, z), the Coulomb force expels charge from the surface of the conductor.
),,(),,( zyxzyx Bσσ <
Electrodes
Electrostatic Shield Design Constraints
),,(),,( zyxEzyxE B>
Electrostatic Shield Design ConstraintsThis Geometry
Violates Physical Constraints),,(),,( zyxEzyxE B>
Electrostatic Shield Design ConstraintsMechanical
Forces• The Coulomb forces between electrodes must not exceed
the mechanical strength of the materials. In the case of thin film polymers, for example, the tensile strength can not be exceeded.
• Size and weight are limited by considerations related to transportation to the lunar surface and by practical assembly and construction activities.
Size and Weight
Electrostatic Shield Design ConstraintsPower, Dust, and X-Rays
Power• Collision of charged particles with electrodes leads to a
current, which must be minimized in order to constrain power requirements.
• The design must avoid attraction of surface dust and electrons to the high voltage electrodes.
Surface Dust and Free Electrons
• Solar wind electrons accelerated by high voltage positive electrodes, must not be allowed to decelerate due to collisions with the electrodes.
Brehmsstrahlung X-Rays
Four Positive Sphere Electrodes
Front View of Lunar Habitat and Positive High Voltage Shield
[MV] )(zΦ
[m] z 0
100
100−
1050100
Voltage Potential Profile – Assume: Grounded Surface
[MV] )(zΦ
[m] z 0
100
100−
1050100
Voltage Potential Profile – Assume: Grounded Surface
SPE Shield (little effect on GCRs)
Radiation Flux: Grounded Lunar Surface
0.1 10 1001 1000 10000Particle Energy [MV]
SPE
GCR
+100 MV ShieldR
adia
tion
Inte
nsity
[MV] )(zΦ
[m] z 0
100
100−
50100
Voltage Potential Profile – Assume: Floating Surface
[MV] )(zΦ
[m] z 0
100
100−
50100
Voltage Potential Profile – Assume: Floating Surface
SPE & Miminal GCR Shield (some effect on GCRs)
Radiation Flux: Floating Lunar Surface
0.1 10 1001 1000 10000Particle Energy [MV]
SPE
GCR
+100 MV ShieldR
adia
tion
Inte
nsity
[MV] )(zΦ
[m] z 0
100
100−
1050100
Voltage Potential Profile – Ground Ground Shield
[MV] )(zΦ
[m] z 0
100
100−
1050100
Voltage Potential Profile – Ground Ground Shield
SPE Shield only – best for dust?
[MV] )(zΦ
[m] z 0
100
100−
1050100
Voltage Potential Profile – Use B Field to Shield Electrons
Passive Shield to Stop Low Angle Particle Trajectories
If the lunar surface is zero potential, i.e., electrical ground
Radiation Fluence, Shield Transmission, Biological Response, and Dosage
SPE
Biological Response
Shield Efficiency
)(EF)(Eξ
)(ER
)(1 Eξ− Shield Transmission
Rad
iatio
n In
tens
ity
0.1 1 100 1000 1000010Particle Energy [MV]
Radiation Fluence, Shield Transmission, Biological Response, and Dosage
SPE
Shield Efficiency
)(EF
)(ER∫≈ dEEREFD )()(0
Dosage (without Shielding):
Biological Response
Rad
iatio
n In
tens
ity
0.1 1 100 1000 1000010Particle Energy [MV]
Radiation Fluence, Shield Transmission, Biological Response, and Dosage
SPE)(EF
)(ER
)(1 Eξ−
( )∫ −≈ dEEREFED )()()(1 ξDosage with Shielding:
Biological Response
Rad
iatio
n In
tens
ity
0.1 1 100 1000 1000010Particle Energy [MV]
Define a Shielding Quality Factor
SPE)(EF
)(ER
)(1 Eξ−
0
1DD
QS −≡
Shielding Quality Factor:
Biological Response
Rad
iatio
n In
tens
ity
0.1 1 100 1000 1000010Particle Energy [MV]
Test Configuration
-50 MV
-50 MV-50 MV
-50 MV
-50 MV
-50 MV+150 +150
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – User Interface and Sphere Configuration File
20 Number of Spheres
V [MV] R [m] x [m] y [m] z [m]==========================================150.0 3.0 5.0 0.0 8.0150.0 3.0 -2.5 4.33 8.0150.0 3.0 -2.5 -4.33 8.0-50.0 4.0 10.0 0.0 12.0-50.0 4.0 -5.0 8.66 12.0-50.0 4.0 -5.0 -8.66 12.0-50.0 5.0 0.0 0.0 16.0-50.0 4.0 -15.0 0.0 8.0-50.0 4.0 7.5 12.99 8.0-50.0 4.0 7.5 -12.99 8.0
-150.0 3.0 5.0 0.0 -8.0-150.0 3.0 -2.5 4.33 -8.0-150.0 3.0 -2.5 -4.33 -8.050.0 4.0 10.0 0.0 -12.050.0 4.0 -5.0 8.66 -12.050.0 4.0 -5.0 -8.66 -12.050.0 5.0 0.0 0.0 -16.050.0 4.0 -15.0 0.0 -8.050.0 4.0 7.5 12.99 -8.050.0 4.0 7.5 -12.99 -8.0
==========================================
Shield OFF (unpowered)
Sphere Configuration FileShaded Entries Correspond To Image
Charges Below Lunar Surface
Shield OFF (unpowered)
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – Red dots are intersection of electrons and blue dots are intersection of protons with lunar surface
(z = 0). Gray circles are x-y projections of unpowered electrostatic spheres.
x-y, z = 0 plane
Shield OFF (unpowered)
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – Red dots are intersection of electrons and blue dots are intersection of protons with a 4 [m] radius
sphere (protected area) centered at x = 0, y = 0, z = 0. Gray circles are x-y projections of unpowered electrostatic spheres. Yellow-gray trails are particle trajectory paths.
x-y viewProtected Region
Shield OFF (unpowered)
y-z view
Lunar surface
Image Spheres
Protected Region 0=Φ
0=Φ
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – Red dots are intersection of electrons and blue dots are intersection of protons with a 4 [m] radius
sphere (protected area) centered at x = 0, y = 0, z = 0. Gray circles are y-z projections of unpowered electrostatic spheres. Yellow-gray trails are particle trajectory paths.
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – User Interface and Sphere Configuration File
Shield ON (powered)
Sphere Configuration FileShaded Entries Correspond To Image
Charges Below Lunar Surface
20 Number of Spheres
V [MV] R [m] x [m] y [m] z [m]==========================================150.0 3.0 5.0 0.0 8.0150.0 3.0 -2.5 4.33 8.0150.0 3.0 -2.5 -4.33 8.0-50.0 4.0 10.0 0.0 12.0-50.0 4.0 -5.0 8.66 12.0-50.0 4.0 -5.0 -8.66 12.0-50.0 5.0 0.0 0.0 16.0-50.0 4.0 -15.0 0.0 8.0-50.0 4.0 7.5 12.99 8.0-50.0 4.0 7.5 -12.99 8.0
-150.0 3.0 5.0 0.0 -8.0-150.0 3.0 -2.5 4.33 -8.0-150.0 3.0 -2.5 -4.33 -8.050.0 4.0 10.0 0.0 -12.050.0 4.0 -5.0 8.66 -12.050.0 4.0 -5.0 -8.66 -12.050.0 5.0 0.0 0.0 -16.050.0 4.0 -15.0 0.0 -8.050.0 4.0 7.5 12.99 -8.050.0 4.0 7.5 -12.99 -8.0
==========================================
Shield ON (powered)
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – Red dots are intersection of electrons and blue dots are intersection of protons with lunar surface
(z = 0). Gray circles are x-y projections of powered electrostatic spheres.
x-y, z = 0 plane
MV 50−=Φ
MV 150=Φ
Shield ON (powered)
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – Red dots are intersection of electrons and blue dots are intersection of protons with a 4 [m] radius
sphere (protected area) centered at x = 0, y = 0, z = 0. Gray circles are x-y projections of powered electrostatic spheres. Yellow-gray trails are particle trajectory paths.
x-y viewProtected Region
MV 50−=Φ
MV 150=Φ
Shield ON (powered)
y-z view
Lunar surface
Image Spheres
Protected Region 0=Φ
0≠Φ
MV 50=Φ
MV 150−=Φ
MV 50−=Φ
MV 150=Φ
Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) – Red dots are intersection of electrons and blue dots are intersection of protons with a 4 [m] radius
sphere (protected area) centered at x = 0, y = 0, z = 0. Gray circles are y-z projections of powered electrostatic spheres. Yellow-gray trails are particle trajectory paths.
Model Simulation ResultsFour Electrostatic Spheres and One Magnetic Field Coil
Spherical Solenoid
Simulation Run of Lunar Electrostatic Shield Model (LESM v2.3) – User Interface and Sphere Configuration File
Shield ON (powered)
Sphere Configuration FileShaded Entries Correspond To Image
Charges Below Lunar Surface
8 Number of Spheres
V [MV] R [m] x [m] y [m] z [m]========================================100 4.0 0.0 0.0 25.050 4.0 8.66 5.0 20.050 4.0 -8.66 5.0 20.050 4.0 0.00 -10.0 20.0
-100 4.0 0.0 0.0 -25.0-50 4.0 8.66 5.0 -20.0-50 4.0 -8.66 5.0 -20.0-50 4.0 0.00 -10.0 -20.0
========================================
Model Simulation Results: x-y Plane
Two 30 MeV Protons and Two 1 MeV Electrons
E ≠ 0 B ≠ 0
Model Simulation Results: x-z Plane
E ≠ 0 B ≠ 0
Two 30 MeV Protons and Two 1 MeV Electrons
Lunar Surface
Model Simulation Results: y-z Plane
E ≠ 0 B ≠ 0
Two 30 MeV Protons and Two 1 MeV Electrons
Lunar Surface
E = off
B = off
E = off
B = off
E = on
B = off
E = on
B = on
E = off
B = on
Model Simulation Results: x-y Plane
30 MeV Protons, 1 MeV Electrons
E = 0 B = 0
Model Simulation Results: x-z Plane
Lunar Surface
Image Spheres
30 MeV Protons, 1 MeV Electrons
E = 0 B = 0
Model Simulation Results: y-z Plane
Lunar Surface
Image Spheres
30 MeV Protons, 1 MeV Electrons
E = 0 B = 0
Model Simulation ResultsOne +100 MV Sphere and
Three +50 MV Spheres
Habitat Habitat --Protected Protected VolumeVolume
25 m
20 m
8 m
Model Simulation Results30 MeV Protons, 1 MeV Electrons
electrons protons
Habitat Habitat --Protected Protected VolumeVolume
E = 0 B = 0
Model Simulation Results30 MeV Protons, 1 MeV Electrons
E ≠ 0B = 0
electrons protons
Habitat Habitat --Protected Protected VolumeVolume
+50 MV+50 MV
+50 MV
+100 MV
Model Simulation Results
E ≠ 0B = 0
electrons protons
Habitat Habitat --Protected Protected VolumeVolume
+50 MV+50 MV
+50 MV
+100 MV
Brehmsstrahlung X-ray Emission
Model Simulation Results30 MeV Protons, 1 MeV Electrons
electrons protons
Habitat Habitat --Protected Protected VolumeVolume
E ≠ 0 B ≠ 0
+50 MV+50 MV
+50 MV
+100 MV i = 1000 A
Bmax ≈ 0.5 [T]
Mathematical ModelElectric Field Due to a System of Conducting Spheres
The field due to a system of N point charges at a field point r is:
∑= −
−=
N
i i
iiq
13
041
)(rrrr
rEπε
(1)
where ri is the location of the ith point charge qi
If the ith point charge qi is implemented as a sphere with radius Ri and a uniform charge distribution at potential Ri, Equation (1) can be rewritten as:
∑= −
−=
N
i i
iii RV
13)(
rrrr
rE (2)
Mathematical Model
A particle of charge Q, velocity v and rest mass m0 in combined static electric and magnetic fields, is:
where,
(3)
Equation of Motion of a Charged Particle
( )
⎟⎠⎞
⎜⎝⎛ ⋅
+=
=
=×+
vvv
v
v
prBvrE
22
0
0
)()(
cm
mdtd
&&
&
γγ
γ
( ) 2/122 /1 −−≡ cvγ
Mathematical ModelSolution to Particle Equation of Motion
The acceleration of the particle, va &≡ , of the particle is calculated by re-writing Equation (3):
( ))()( 0
rBvrEaC ×+=⋅mQ
γ
where,
⎟⎟⎟⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜⎜⎜⎜
⎝
⎛
+
+
+
=⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
2
22
22
22
22
2
22
22
22
22
2
22
333231
232221
131211
1
1
1
cv
cvv
cvv
cvv
cv
cvv
cvv
cvv
cv
ccccccccc
zyzxz
zyyxy
zxyxx
γγγ
γγγ
γγγ
C (5)
(4)
Mathematical ModelSolution to Particle Equation of Motion
Solving for a in Equation (4),
where,
(6)
( )
⎟⎟⎟
⎠
⎞
⎜⎜⎜
⎝
⎛=
×+⋅= −
z
y
x
AAA
A
mQ
0
1
0
1
)()(
rBvrECaγ
( ) γ03322113321123223113221133123123122130 mccccccccccccccccccA −++−−= (7)
( )QFccFccFccFccFccEccA zzyyxxx 231222133312321333223223 −++−−=
( )QFccFccFccFccFccFccA zzyyxxy 231121133311311333213123 +−−++−=( )QFccFccFccFccFccFccA zzyyxxz 221121123211311232213122 −++−−=
yzzyxx BvBvEF −+≡
zxxzyy BvBvEF −+≡
xyyxzz BvBvEF −+≡
(8a)
(8b)
(8c)
(8d)
(8e)
(8f)
Mathematical ModelTrajectory Difference Equations of Particle Motion
Based on a Taylor series expansion about time point k, a set of difference equations for position and velocity can be expressed as:
(9a)tt
kk
kkk
∆+≈∆+≈+
avvvv &1
221
221
1
tt
tt
kkk
kkkk
∆+∆+≈
∆+∆+≈+
avr
rrrr &&&(9b)
where ∆t a constant time step.
Mathematical ModelMagnetic Field due to a Current Loop
The magnetic field from a single current loop is:
(10a)( ))K()E()(2
),,( 2222222 kkRazxCzyxBx α
βρα−+=
( ))K()E()(2
),,( 2222222 kkRazyCzyxBy α
βρα−+=
( ))K()E()(2
),,( 222222 kkRaCzyxBz αβα
+−=
(10b)
(10c)
where E(k2) and K(k2) are the complete elliptic integrals of the first and second kind, respectively, and:
Circular Current Loop.
z
x
ya
i
ρα aRa 2222 −+≡ 222 /1 βα−≡k222 yx +≡ρ222 zR +≡ ρ ρβ aRa 2222 ++≡ πµ / 0 iC ≡
Mathematical ModelMagnetic Field due to a Spherical Solenoid
(11a)
(11b)
(11c)
( )∑ ∑−
−−=
−
=
−+=
)1(
)1(
1
02
22222
2
21
21
)K()E()(2
),,(z
z
xM
Mm
M
n mnmn
mnmnmmnx
kkRazxCzyxBβα
αρ
( )∑ ∑−
−−=
−
=
−+=
)1(
)1(
1
02
22222
2
21
21
)K()E()(2
),,(z
z
xM
Mm
M
n mnmn
mnmnmmny
kkRazyCzyxBβα
αρ
( )∑ ∑−
−−=
−
=
+−=
)1(
)1(
1
02
2222221
21
)K()E()(2 ),,(
z
z
xM
Mm
M
n mnmn
mnmnmmnz
kkRaCzyxBβα
α
where E(k2) and K(k2) are the complete elliptic integrals of the first and second kind, respectively, and:
222 yx +≡ρ( )222
zm mdzR −+≡ ρ
ρα mnmmnmn aRa 2222 −+≡
ρβ mnmmnmn aRa 2222 ++≡
222 /1 mnmnmnk βα−≡
πµ / 0 iC ≡
The radius of each loop is: 220 )( zxmn mdanda −+≡ (12)
.
0amdz < 021 )1( adM zz <−where, and
Mathematical Model
Total energy of a particle of rest mass m0 is:
where,
(13a)
Initial Particle Velocity calculated from Initial Particle Energy
2mcE =
( ) 2/122 /1 −−≡ cvγ
(13b)Tcm
TEE
+=
+=2
0
0
Total energy is the sum of rest mass energy and kinetic energy:
Solve for T in term of v:(13c)
20
20
20
02
)1( cmcmcm
EmcT
−=−=
−=
γγ
Solve for v in term of T, with : (13d)ξξ
++
=1
21cv
qTcm 2
0≡ξ
Present Radiation Shielding Studies at KSC
Analysis of a Lunar Base Electrostatic Radiation Shield ConceptPhase I: NIAC CP 04-01
Advanced Aeronautical/Space Concept Studies
Charles R. Buhler, Principal Investigator(321) 867-4861
October 1, 2004
ASRC Aerospace CorporationP.O. Box 21087
Kennedy Space Center, Florida 32815-0087
~ $0.07 M / 6 mo~ $1.9 M / 4 yrs
NASA (Spacecraft)NIAC (Lunar)
Software-Mathematical
Modeling
ASRC
Software-Mathematical
Modeling
Field Precision, NM
Problems already being addressed by NASA
Shield Configuration and Design for spacecraftShield EffectivenessMaterial Tensile Strength/Dielectric Strength Other Material Issues-Mechanical (Attachment, etc.)Other Material Issues-Environmental (Temperature, UV resistance)Other Material Issues-Misc. (Leakage current, Gamma resistance, Thickness/Weight,
Crease resistance, Conductive coating (CNT or CVD Au), Aging)Shield Forces Net Shield Charge Shield Discharge Calculations-Leakage, Corona, Plasma. Charge Buildup on outside of Spheres. Power Supply Feasibility-Voltage Power Supply Feasibility-Current Field Extent in a PlasmaParticle Entrapment Safety-Total Stored Energy Safety-Shield Stability Safety-Electron Dosage Issue
Future Work required for a Lunar Solution
• Lunar Shield configuration• Lunar gravity• Lunar surface may or may not act as a
sufficient electrical ground. [Power systems may have the benefit of free charges that a spacecraft will not have access to.]
• Lunar Shield will have to contend with Lunar dust.
Proposed Validation Experiment
Particle Detector
Lunar Shield Model Under Test
High Vacuum Chamber[torr] }10,10{ 105 −−∈P
Accelerator Grid[volts] }10,10{ 42∈∆V
Ion Selector
Ion Source
Broad-Band Energy Distribution to Simulate SPE Distribution