The document describes an analysis of using an electrostatic shield concept to protect a lunar base from radiation. It discusses the radiation environment, types of radiation and their energy spectra. It then examines passive and active shielding solutions, focusing on electrostatic shields. The document outlines an electrostatic shield design using charged spheres to generate an electric field, and models this using a Lunar Electrostatic Shield Model (LESM) simulation to analyze particle trajectories with and without an applied field. The simulation results suggest the shield design can effectively deflect energetic particles and protect a region near the lunar surface.

1. Analysis of a Lunar Base Electrostatic Radiation Shield ConceptCharles Buhler, PIJohn Lane, Co-PIASRC Aerospace CorporationKennedy Space Center, Florida 32899

2. INTERPLANETARY RADIATION ENVIRONMENT
Main Components:
(Atomic Nuclei)
¾Galactic Cosmic Rays (GCRs)
•Median energy ~1800 MeV/nuc
•Continuous flux, varies with
the solar cycle
¾Solar Energetic Particles (SEPs)
•Sporadic, lasting hours to days
•Soft spectra with highly
variable composition
ni~ne~ 6 cm-3Galactic Cosmic Ray Spectra0500100015002000250030003500400010100100010000100000Energy (MeV/nucleon) #/m2-s-sterradian Solar MaximumSolar Minimum

3. From Francis Cucinotta, NASA JSCSpace Radiation Health Project(private communication) Lunar

4. 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

5. PolyethyleneSolar MinimumJohn 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

6. Active Shielding Solutions
•Electromagnetic Shields
–Magnets (>73 papers since 1961)
–Plasma (>18 papers since 1964)
–Electrostatic (>16 papers since 1962) ShieldingVolumeEabCosmicRay+ ++ + + + + 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

7. Why Not Electrostatics?
–DebyeLength ~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 V15 at -2 V12 spheres at +2V22 spheres at +3V25 at -2V1“Protected Zone” Center Sphere at +V0+2V2+2V230 m100 m5 m radius
geometry.

8. Radiation Fluence: No Shielding
Radiation Intensity SPEGCRFrom SpaceFrom the Sun
0.1
1
100
1000
10000
10
Particle Energy [MV]

9. Radiation Fluence: No ShieldingSPEGCRSolar “Storm”– lasting hours to days
Radiation Intensity
0.1
1
100
1000
10000
10
Particle Energy [MV]

10. Radiation Fluence: No ShieldingSPEGCRSolar “Storm”– lasting hours to days
Radiation Intensity
0.1
1
100
1000
10000
10
Particle Energy [MV]

11. Radiation Fluence: No Shielding
Radiation Intensity SPEGCR
0.1
1
100
1000
10000
10
Particle Energy [MV]

12. Radiation Fluence: No Shielding
Radiation Intensity SPEGCR
0.1
1
100
1000
10000
10
Particle Energy [MV]

13. An Electrostatic Shield Design

14. Some Possible Electrode Geometries
Thin Film Polymer with Conductive Inner Coating
Conductive Mesh Screen
Conductive Wire Mesh Sphere
Arbitrary Geometry

15. Electrode Geometry Used in ASRC Lunar Electrostatic Shield Model(LESM)
Thin Film Polymer Balloon with Conductive Inner Coating

16. Theory of Design
LorentzForceBvEF×+=qq

17. Theory of Design
Coulomb ForceBvF×E+=qq

18. Theory of Design
Coulomb Force
EFq= ElectrostaticShield: Use only a time independent electric field, i.e., 0=E&

19. Design Strategy
Determine an Ideal Electric Field to Repel Charged Particle Radiation (primarily positive ions and electrons) STEP 1: ),,(zyxE

20. Design Strategy
Find a Way to Generate an Approximation of the Ideal Field
STEP 2:

21. Design Strategy
Perform Mathematical Modeling and Computer Simulation of Proposed Configurations
STEP 3:

22. Design Strategy
Perform Experiments and Testing on a Scale Model
STEP 4: Particle DetectorLunar Shield Model Under TestHigh Vacuum Chamber[torr] }10,10{105−−∈PAccelerator Grid[volts] }10,10{42∈ΔVIon SelectorIon SourceBroad-Band Energy Distribution to Simulate SPE Distribution

23. An Electrostatic Shield Design

24. Electrostatic Shield Design Constraints
Electrical
•Electric Field Strengtheverywhere must remain well below a breakdown threshold value: In the case of non-conductors, EB(x, y, z) is related to the Dielectric Strengthof the materials subjected to E(x, y, z). ),,(),,(zyxEzyxEB< Non-Electrodes•Surface Charge Distributionmust 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. ),,(),,(zyxzyxBσσ< Electrodes

25. Electrostatic Shield Design Constraints),,(),,(zyxEzyxEB>

26. Electrostatic Shield Design ConstraintsThis Geometry Violates Physical Constraints),,(),,(zyxEzyxEB>

27. Electrostatic Shield Design Constraints
MechanicalForces•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

28. Electrostatic Shield Design Constraints
Power, Dust, and X-RaysPower•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. BrehmsstrahlungX-Rays

29. Four Positive Sphere Electrodes

30. Front View of Lunar Habitat and Positive High Voltage Shield

32. [MV] )(zΦ[m] z0100100− 1050100Voltage Potential Profile –Assume:Grounded Surface

33. [MV] )(zΦ[m] z0100100− 1050100Voltage Potential Profile –Assume:Grounded SurfaceSPE Shield (little effect on GCRs)

34. Radiation Flux: Grounded Lunar Surface0.1101001100010000Particle Energy [MV] SPEGCR+100 MV Shield
Radiation Intensity

35. [MV] )(zΦ[m] z0100100− 50100Voltage Potential Profile –Assume:Floating Surface

36. [MV] )(zΦ[m] z0100100− 50100Voltage Potential Profile –Assume:Floating SurfaceSPE & MiminalGCR Shield (some effect on GCRs)

37. Radiation Flux: Floating Lunar Surface0.1101001100010000Particle Energy [MV] SPEGCR+100 MV Shield
Radiation Intensity

38. [MV] )(zΦ[m] z0100100− 1050100Voltage Potential Profile –GroundGround Shield

39. [MV] )(zΦ[m] z0100100− 1050100Voltage Potential Profile –GroundGround ShieldSPE Shield only –best for dust?

40. [MV] )(zΦ[m] z0100100− 1050100Voltage Potential Profile –Use BField to Shield Electrons

41. Passive Shield to Stop Low Angle Particle TrajectoriesIf the lunar surface is zero potential, i.e., electrical ground

42. Radiation Fluence, Shield Transmission, Biological Response, and Dosage
SPE
Biological ResponseShield Efficiency)(EF)(Eξ )(ER)(1Eξ−Shield Transmission
Radiation Intensity
0.1
1
100
1000
10000
10
Particle Energy [MV]

43. Radiation Fluence, Shield Transmission, Biological Response, and Dosage
SPEShield Efficiency)(EF)(ER∫≈dEEREFD)()(0Dosage (without Shielding):
Biological Response
Radiation Intensity
0.1
1
100
1000
10000
10
Particle Energy [MV]

44. Radiation Fluence, Shield Transmission, Biological Response, and Dosage
SPE)(EF)(ER)(1Eξ− ()∫−≈dEEREFED)()()(1ξ Dosage with Shielding:
Biological Response
Radiation Intensity
0.1
1
100
1000
10000
10
Particle Energy [MV]

45. Define a Shielding Quality Factor
SPE)(EF)(ER)(1Eξ− 01DDQS−≡ Shielding Quality Factor:
Biological Response
Radiation Intensity
0.1
1
100
1000
10000
10
Particle Energy [MV]

46. Test Configuration -50 MV-50 MV-50 MV-50 MV-50 MV-50 MV+150 +150

47. Simulation Run of Lunar Electrostatic Shield Model (LESM v1.2) –User Interface and Sphere Configuration File20 Number of SpheresV [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 0.016.0-50.0 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

48. 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-yprojections of unpoweredelectrostatic spheres. x-y, z= 0 plane

49. 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-yprojections of unpoweredelectrostatic spheres. Yellow-gray trails are particle trajectory paths. x-yviewProtected Region

50. Shield OFF (unpowered)
y-zviewLunar surfaceImage SpheresProtected Region0=Φ0=ΦSimulation 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-zprojections of unpoweredelectrostatic spheres. Yellow-gray trails are particle trajectory paths.

51. 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 Surface20 Number of SpheresV [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 0.016.0-50.0 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==========================================

52. 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-yprojections of powered electrostatic spheres. x-y, z= 0 planeMV 50−=ΦMV 150=Φ

53. 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-yprojections of powered electrostatic spheres. Yellow-gray trails are particle trajectory paths. x-yviewProtected RegionMV 50−=ΦMV 150=Φ

54. Shield ON (powered)
y-zviewLunar surfaceImage SpheresProtected Region0=Φ0≠ΦMV 50=ΦMV 150−=ΦMV 50−=ΦMV 150=ΦSimulation 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-zprojections of powered electrostatic spheres. Yellow-gray trails are particle trajectory paths.

55. Model Simulation Results
Four Electrostatic Spheres and One Magnetic Field CoilSpherical Solenoid

56. 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 Surface8 Number of SpheresV [MV] R [m] x [m] y [m] z [m] ======================================== 100 4.0 0.0 0.025.050 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========================================

57. Model Simulation Results: x-yPlaneTwo 30 MeVProtons and Two 1 MeVElectronsE ≠0 B ≠0

58. Model Simulation Results: x-zPlane
E ≠0 B ≠0Two 30 MeVProtons and Two 1 MeVElectronsLunar Surface

59. Model Simulation Results: y-zPlane
E ≠0 B ≠0Two 30 MeVProtons and Two 1 MeVElectronsLunar Surface

60. E =offB =off

61. E =offB =off

62. E =onB =off

63. E =onB =on

64. E =offB =on

65. Model Simulation Results: x-yPlane30 MeVProtons, 1 MeVElectrons
E =0 B = 0

66. Model Simulation Results: x-zPlaneLunar SurfaceImage Spheres30 MeVProtons, 1 MeVElectrons
E =0 B = 0

67. Model Simulation Results: y-zPlaneLunar SurfaceImage Spheres30 MeVProtons, 1 MeVElectrons
E =0 B = 0

68. Model Simulation Results
One +100 MV Sphere and Three +50 MV SpheresHabitat Habitat -- Protected VolumeVolume 25 m20 m8 m

69. Model Simulation Results
30 MeVProtons, 1 MeVElectronselectrons protonsHabitat Habitat -- Protected VolumeVolumeE =0 B = 0

70. Model Simulation Results
30 MeVProtons, 1 MeVElectronsE ≠0B = 0electrons protonsHabitat Habitat -- Protected VolumeVolume+50 MV+50 MV+50 MV+100 MV

71. Model Simulation ResultsE ≠0B = 0electrons protonsHabitat Habitat -- Protected VolumeVolume+50 MV+50 MV+50 MV+100 MVBrehmsstrahlungX-ray Emission

72. Model Simulation Results
30 MeVProtons, 1 MeVElectronselectrons protonsHabitat Habitat -- Protected VolumeVolumeE ≠0 B ≠0+50 MV+50 MV+50 MV+100 MVi= 1000 A
Bmax≈0.5 [T]

73. Mathematical Model
Electric Field Due to a System of Conducting SpheresThe field due to a system of Npoint charges at a field point ris: Σ= − − = Niiiiq13041)( rrrrrE πε (1) where riis the location of the ithpoint chargeqiIf the ithpoint charge qiis implemented as a sphere with radius Riand a uniform charge distributionat potential Ri, Equation (1) can be rewritten as: Σ= − − = NiiiiiRV13)( rrrrrE(2)

74. Mathematical ModelA particle of charge Q, velocityvand rest mass m0in combined static electric and magnetic fields, is: where, (3) Equation of Motion of a Charged Particle () ⎟⎠ ⎞ ⎜⎝ ⎛⋅ += = =×+ vvvvvprBvrE2200 )()( cmmdtdQQ& & & γγγ ()2/122/1−−≡cvγ

75. Mathematical Model
Solution to Particle Equation of MotionThe acceleration of the particle,va&≡, of the particle is calculated by re-writing Equation (3): ())()( 0rBvrEaC×+=⋅ mQ γ where, ⎟⎟⎟⎟⎟⎟⎟ ⎠ ⎞ ⎜⎜⎜⎜⎜⎜⎜ ⎝ ⎛ + + + = ⎟⎟⎟ ⎠ ⎞ ⎜⎜⎜ ⎝ ⎛ = 222222222222222222222333231232221131211111cvcvvcvvcvvcvcvvcvvcvvcvccccccccczyzxzzyyxyzxyxx γγγγγγγγγ C(5) (4)

76. Mathematical ModelSolution to Particle Equation of MotionSolving for ain Equation (4), where, (6) () ⎟⎟⎟ ⎠ ⎞ ⎜⎜⎜ ⎝ ⎛ = ×+⋅=− zyxAAAAmQ0101)()( rBvrECa γ ()γ03322113321123223113221133123123122130 mccccccccccccccccccA−++−−=(7) ()QFccFccFccFccFccEccAzzyyxxx 231222133312321333223223−++−−= ()QFccFccFccFccFccFccAzzyyxxy 231121133311311333213123+−−++−= ()QFccFccFccFccFccFccAzzyyxxz 221121123211311232213122−++−−= yzzyxxBvBvEF−+≡ zxxzyyBvBvEF−+≡ xyyxzzBvBvEF−+≡ (8a) (8b) (8c) (8d) (8e) (8f)

77. Mathematical Model
Trajectory Difference Equations of Particle MotionBased on a Taylor series expansion about time point k, a set of difference equations for position and velocity can be expressed as: (9a)ttkkkkkΔ+≈ Δ+≈+ avvvv&12212211ttttkkkkkkkΔ+Δ+≈ Δ+Δ+≈+ avrrrrr&&& (9b) where Δt a constant time step.

78. Mathematical Model
Magnetic Field due to a Current LoopThe magnetic field from a single current loop is: (10a)())K()E()( 2 ),,(2222222kkRazxCzyxBxαβρα −+= ())K()E()( 2 ),,(2222222kkRazyCzyxByαβρα −+= ())K()E()( 2),,(222222kkRaCzyxBzαβα +−= (10b) (10c) where E(k2) and K(k2) are the complete elliptic integrals of the first and second kind, respectively, and: Circular Current Loop. zxyai ραaRa2222−+≡222/1βα−≡k222yx+≡ρ 222zR+≡ρρβaRa2222++≡πμ/ 0iC≡

79. Mathematical ModelMagnetic Field due to a Spherical Solenoid(11a) (11b) (11c) ()ΣΣ− −−= − = −+ = )1( )1( 1022222222121)K()E()( 2 ),,( zzxMMmMnmnmnmnmnmmnxkkRazxCzyxB βααρ ()ΣΣ− −−= − = −+ = )1( )1( 1022222222121)K()E()( 2 ),,( zzxMMmMnmnmnmnmnmmnykkRazyCzyxB βααρ ()ΣΣ− −−= − = +− = )1( )1( 102222222121)K()E()( 2 ),,( zzxMMmMnmnmnmnmnmmnzkkRaCzyxB βαα where E(k2) and K(k2) are the complete elliptic integrals of the first and second kind, respectively, and: 222yx+≡ρ ()222zmmdzR−+≡ρραmnmmnmnaRa2222−+≡ ρβmnmmnmnaRa2222++≡ 222/1mnmnmnkβα−≡ πμ/ 0iC≡ The radius of each loop is:220)(zxmnmdanda−+≡(12) .0amdz<021)1(adMzz<−where, and

80. Mathematical ModelTotal 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) TcmTEE+= += 200Total energy is the sum of rest mass energy and kinetic energy: Solve for Tin term of v: (13c) 20202002)1( cmcmcmEmcT−=−= −= γγ Solve for vin term of T, with :(13d) ξξ + + = 121cvqTcm20≡ξ

81. Present Radiation Shielding Studies at KSCAnalysis of a Lunar Base Electrostatic Radiation Shield ConceptPhase I: NIAC CP 04-01Advanced Aeronautical/Space Concept StudiesCharles R. Buhler, Principal Investigator(321) 867-4861October 1, 2004ASRC Aerospace CorporationP.O. Box 21087Kennedy Space Center, Florida 32815-0087~ $0.07 M / 6 mo~ $1.9 M / 4 yrsNASA (Spacecraft) NIAC (Lunar) Software- Mathematical ModelingASRCSoftware- Mathematical ModelingField Precision, NM

82. Problems already being addressed by NASA
Shield Configuration and Design for spacecraft
Shield Effectiveness
Material 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 Plasma
Particle Entrapment
Safety-Total Stored Energy
Safety-Shield Stability
Safety-Electron Dosage Issue

83. 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.

84. Proposed Validation ExperimentParticle DetectorLunar Shield Model Under TestHigh Vacuum Chamber[torr] }10,10{105−−∈PAccelerator Grid[volts] }10,10{42∈ΔVIon SelectorIon SourceBroad-Band Energy Distribution to Simulate SPE Distribution