Space Environment Impacts on Space Solar Power system

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1 Space Environment Impacts on Space Solar Power system Space Solar Power Workshop Tutorial IEEE WiSEE, December, 2018 T. Vinogradova, PhD NGAS Space System Division, Military and Civil Space

2 Agenda Introduction Space Solar Power (SSP) Satellites, environmental consideration Satellite system hazards in the space environment Space radiation effects on SSP systems Space Radiation Environment and modeling tools Orbits: LEO, HEO, GEO, MEO Environmental effects on Spacecraft (SC) components SSP example: large scale ultra-light system Meteoroids effects on SSP system Meteoroids Environment and modeling tools SSP large scale reduced mass system consideration Conclusions 2

Introduction Space Solar Power Satellites, environmental consideration 3 Credit: US Patent and Trademark Office; Patent No. 5019768 Glaser, Peter.

space and transmit to Earth via RF Numerous funded studies are conducted for proposed system architecture Ultra-light SSP concept (Caltech), sandwich modular system, above 1000 W/kg No program for

3 Introduction Space Solar Power Satellites, environmental consideration 3 Credit: US Patent and Trademark Office; Patent No Glaser, Peter. An Overview of the Solar Power Satellite Option, 1968, original patent JAXA SSP concept, Integrated symmetrical concentrator, ~ 100 W / kg Space Solar Power is the capability to generate power in space and transmit to Earth via RF Numerous funded studies are conducted for proposed system architecture Ultra-light SSP concept (Caltech), sandwich modular system, above 1000 W/kg No program for space demonstration completed up to date due to the cost challenges For economic feasibility it requires breakthrough improvement in power density (kw/kg) Large scale and reduced mass system architecture needs to address shielding and thermal challenges to maintain power performance for desired End Of Life (EOL) period Evaluating environmental effects on SSP system are key for lifetime power delivered per cost prediction and system robustness evaluation

4 Satellite system hazards in the space environment Particle radiation Ionizing and non ionizing dose Degradation of micro-electronics Degradation of optical components Degradation of solar cells Single Event Effects Data corruption Circuit damage System shut-down Noise on the images Plasma environment: Surface charging Internal charging Biasing instrument reading Pulsing Power drains Neutral gas particles Drag effects Torques Orbital decays Ultraviolet and X-rays: Surface erosion: Degradation of thermal, electrical, optical properties Meteoroids and orbital debris: Structural damage, surface area damage Decompression Degradation of optical components Micro-electronics damage 4 Ref.: J. Bart et al., 1997, J. Barth et al., 2004, Lohmeyer et al., 2007

Space Radiation environment Introduction Primary sources of Natural Space Radiation environment Galactic Cosmic Rays Galactic Protons And Heavier Ions Trapped particles Credit:

5 Space Radiation environment Introduction Primary sources of Natural Space Radiation environment Galactic Cosmic Rays Galactic Protons And Heavier Ions Trapped particles Credit: Nikkei Science, Inc. of Japan, by K. Endo Geomagnetically Trapped Particles: Electrons Protons Galactic Cosmic Rays Protons and heavy ions Solar Particle events Protons and Heavy Ions 5

, 1982) Discovered in 1958 (James Van Allen, Explorer 1 and Explorer 3 Spacecraft) Radiation belts: inner and

6 Space Radiation environment Trapped particles: The Van Allen radiation belts The Van Allen Radiation Belts showing electron and proton densities (Anspaugh et al., 1982) Discovered in 1958 (James Van Allen, Explorer 1 and Explorer 3 Spacecraft) Radiation belts: inner and outer electrons belt and the proton belt 6 Inner zone is dominated by the Earth magnetic field and is relatively stable, Outer belt is influences by fluctuations in the geomagnetic tail

7 Space Radiation environment Trapped particles: The Van Allen radiation belts Inner Van Allen Radiation Belt Located between 1.2 and 2 Re (~7,600 km to 12,700 km) Dominated by the Earth magnetic field and is relatively stable Immerse to 200 km at the South Atlantic Anomaly Trapped high energy protons (< 1 GeV) and energetic electrons (~ 100 KeV) [Fennel et al., 2015] High energy protons: Originates primarily from cosmic rays collision with upper atmosphere following by beta decay of neutrons Effects on SC: increased noise in the photonics, TID, SEU, solar panel degradation Low energy electrons: Eject hazardous secondary level of electrons Located in inner zone (below 1Re) and outer zone (above 2Re), overlaps with protons belt Deposit on the surface of SC, not enough energy to penetrate shielding materials Outer Van Allen Radiation Belt Located between ~2.5 and 7 Re (~15,900 km to 44,600 km), can extend up to 10Re (~ 63,700 km) Influences by fluctuations in the geomagnetic tail Trapped high energy electrons up to 1-10MeV [Schulz et al., 1974] 7 High energy electrons: High energy electron flux is controlled by CMEs and CIRs, correlates with solar cycle Effect on SC: penetrate the shielding, contribute to internal charging

8 Space Radiation environment Transient particles Solar Particle Events Cyclical behavior (Solar Max, Solar Min) 11 year average cycle (Solar Max is more active period) Two types of events: Impulsive (Solar Flares), heavy ions rich Gradual (Coronal Mass Ejection), proton rich Dependent on radial distance from Sun Particles are partially ionized Penetrate Magnetosphere Generate neutrons in the atmosphere Galactic Cosmic Rays (GCR) or Heavy Ions Charged particles (H, He, Fe, etc) Found in free space with energies ranges from Mev to GeV 8

Radiation environment SSP satellites potential orbits 9 LEO (Low Earth Orbit) ~400 1200 km altitude above Earth orbit Located in the Inner Van Allen Belt; Earth magnetic field shields and deflects

9 Radiation environment SSP satellites potential orbits 9 LEO (Low Earth Orbit) ~ km altitude above Earth orbit Located in the Inner Van Allen Belt; Earth magnetic field shields and deflects low energy particles Low radiation environment (Order of magnitude less intense environment then GEO orbit for low energy electron ) Note: In polar-regions, particles enter along the magnetic field lines causing danger to LEO polar spacecraft GEO (Geostationary Orbit) Circular equatorial orbit, 36,000km altitude Resides In the outer radiation belt Region is dominated by high energy electrons and energetic solar protons from solar events [Baker, 1998] Injection of high energy plasma near local midnight (surface charging) SC risk: TID induced anomaly, surface and internal charging Van Allen radiation belts showing electron and proton densities with examples of orbiting spacecraft's MEO (Medium Earth Orbit) km altitude above Earth orbit Nearly in the center of outer radiation belt Intense radiation environment HEO (Highly Elliptical Orbit) Above 35,389 km altitude At apogee it is outside of radiation belt, is in the flux of low energy particles At or near perigee resides in Van Allen Radiation belt twice a day; intense radiation environment

10 10 Space Radiation environment Modeling tools / Definitions Flux is the rate of the number of particles that pass through a unit of crosssectional area in units of particles/cm 2 /s. Fluence (Φ) is the number of particles that pass through a unit of cross-sectional area over a finite period of time. Fluence is the integral of flux over the radiation exposure duration, measured in particles/cm2 Linear energy transfer (LET) is the energy per unit path length absorbed/transferred locally by/to the target material through the process of ionization. TID is the total energy per unit mass of material, transferred to the material via ionization from all ionizing radiation TID= Lm,e (integral over fluence) = 1ρdEeledx NIEL is defined as the part of the energy loss per unit length by a particle moving in the material, through Coulomb (elastic), nuclear elastic, and nuclear inelastic interactions thereby producing the initial displacement damage and excited phonons

11 11 System degradation effects Notional Summary of environmental hazards and SC impacts Hazard Particle Type / particle source Impact Total Ionizing Dose (TID) Displacement Damage Dose (DDD) Single-Event Effects (SEE) High energy trapped protons High energy trapped electrons Solar protons Trapped protons Trapped electrons Solar protons Neutrons Trapped protons Solar protons and heavy ions High energy neutrons Galactic cosmic rays Degradation of microelectronics Degradation of solar cells and optical components Data corruption, image noise, system shutdowns, electronic components damage Internal charging High energy trapped electrons Biasing of instrument Readings, electrical discharges causing physical damage Surface Erosion Trapped protons and electrons Ultraviolet, Atomic Oxygen micrometeoroids; contamination Degradation of thermal, electrical, optical properties, degradation of structural Integrity Surface charging Cold and hot plasma Bias in the instrument reading, power drains, physical damage

Integral fluence, [e- cm 2 ] Space Radiation environment Modeling Models, trapped particles: The standard flux models are the AE-9 and AP-9 (AE8/AP8 update) Modeling tools:

spectra Trapped El,GEO orbit,10 year 10 16 10 14 AE8, 10 years AP8, 10 years ASP8, 10 years Figure.

12 Integral fluence, [e- cm 2 ] Space Radiation environment Modeling Models, trapped particles: The standard flux models are the AE-9 and AP-9 (AE8/AP8 update) Modeling tools: NOVICE, SPENVIS, OMERE Models, Solar Particles, Galactic Cosmic Rays Doses: SOLPRO, JPL, NRL Single event Effects CRÈME96 (Protons and Heavier Ions) Simulated integral spectra Trapped El,GEO orbit,10 year AE8, 10 years AP8, 10 years ASP8, 10 years Figure. Galactic Cosmic rays flux simulation Energy, [Mev] 12 Figure. Trapped particles, Integral Fluence, GEO orbit, 10 years Figure. Solar protons flux simulation Ref: J. Barth, Radiation environment, NASA TM, 2005

Solar cells ground testing GaAs / Ge example to predict the effect of space particle spectrum Normalized max power is a function of N variables, there are two methods to reduce N variable

13 Solar cells ground testing GaAs / Ge example to predict the effect of space particle spectrum Normalized max power is a function of N variables, there are two methods to reduce N variable dependencies The JPL method: Calculates an equivalent 1 MeV electron fluence for mission Relative displacement coefficient (RDC) is determined empirically Read EOL power from measured 1MeV electron curve The NRL method: Calculates the displacement damage dose for mission Read EOL power from measured characterization curve JPL method NRL method 13 Ref: Messenger et all, 2004 For typical solar panels, 15 years GEO orbit, 5E+14 1 Mev Equivalent El Fluence, 4 mils of coverglass, 87% EOL 3J GaAs on Ge

14 Solar cell degradation analysis Figure. Solar cell efficiency as a function of displacement damage Ref: Jonson et al., Space-based Solar Power: Possible Defense application 14

Technology development: flexible light solar arrays Light and ultra-light solar arrays Enabling technologies of new generation for flexible solar arrays are demonstrated for reduced mass, efficient

15 Technology development: flexible light solar arrays Light and ultra-light solar arrays Enabling technologies of new generation for flexible solar arrays are demonstrated for reduced mass, efficient packaging and deployability in space. Parameter Solar Power Collection System Type Mega Flex ROSA SLASR Flat panel Flat panel Concentrat ors Power density, [kw/kg] Typical thickness of cover glass is 3-4 mils ( microns); it completely blocks out the harmful effects of lowenergy electrons and trapped protons in GEO, with energies less than 1 MeV [Tauke et al., 1967; Messenger et al., 2001] For any SSP design cover glass protection presents substantial weight Stretched challenge (due Lens to Array the system SquareRigger size and (SLASR) therefore prototype, weight limitations) ATK, NASA, ENTECH, follow on SCARLET design For ultra-light SSP design the challenge is to reduce shielding weight while maintaining power generation over mission lifetime ATK, MegaFlex DSS ROSA 15 Images credit: NASA SSP ultra-light approach is to develop system and deployable space structures to reach breakthrough power density

16 SSP ultra-light approach NG-Caltech SSPI project, 2017 How to achieve power density above 1 kw/kg? Radiation shielding required for conventional space solar cells limits specific power to <1 W/g Concentrating PV to reduce cell area and required shielding Flat design with thin radiation tolerant PV technology 16 Ref: M. Kelzenberg et al., Space Solar Power Project, WiSEE, IEEE, 2017

17 SSP trade studies Example: Ultra-light approach, PV design SSP Concentrating Photovoltaic Tile Concept Pro: Reduced mass and PV cost Con: Radiation and Thermal management challenge 17 Advanced radiation coating and new generation of rad. hard solar cells Cover glass development Rad hard cell design Thermal management material development Advanced Concentrators and concentrators thermal and management technology thermal management development Thermal Management Challenge: Heat path from the solar cell with thin, light weight structures Solution: High reflectance in-band, high emissivity out-of-band, high thermal conductivity materials Radiation Challenge: Major weight addition Solution: Reducing cell size via concentrators or radiation resistant cells for flat design Technology focus areas: III-V Multi Junction Solar cells advanced design, perovskite Advanced glass coating options Concentrators design Flexible thin film specular reflectors optical properties and long term performance Thermal management solution

18 SSP ultra-light design, trade studies example Solar cell performance GEO orbit, 10 years of operation 18 Figure. Integral spectra for trapped electrons and protons and solar protons at PV component for ultralight SSP design as a function of solar cell shielding (SiO2) simulated using AP9, AE9 and SPM (JPL91) fluxes and NOVICE SW Figure. 1 MeV equivalent fluence experienced by the solar cells as a function of thicknesses of cover glass for flat panel design and concentrator design of ultralight SSP approach Ref: P. Espinet-Gonzalez, et al., Impact of radiation environment on concentrator photovoltaic system, PVSC conference, 2016

19 SSP ultra-light design, trade studies example Solar cell degradation Calculated impact of simulated radiation environment on XTJ triple junction solar cells in ultra-light SSP design Trade studies included flat panel and parabolic concentrator mirror design A concentrator design provided an additional shielding against protons and low energy electrons due to geometry To maintain 85% of BOL power flat plate design needs 85 um of SiO2 shielding (vs 25 um of SiO2 for concentrator system) Results are used in the trade studies for SSP system design optimization Figure. Remaining power after 10 years of operation on GEO orbit for solar cells as a function of different SiO2 shielding 19 Ref: P. Espinet-Gonzalez et al., Impact of radiation environment on concentrator photovoltaic system, PVSC conference, 2016

20 TID analysis, SSP ultralight approach GEO orbit, 10 years of operation, Solar cell performance Commercial CMOS transistor, TID effect del V exceeds 100 mv at 300 krad(si) Assuming close to 30 Mrad is the possibility for commercial IC We have ~10 years at mils of shielding Figure. Simulated Total Ionizing Dose Versus Ceramic Shield Thickness, 10 years, GEO orbit Ref : Improving Integrated Circuit Performance Through the Application of Hardness-by-Design Methodology, IEEE TRANSACTIONS ON NUCLEAR SCIENCE, VOL. 55, NO. 4, AUGUST 2008, Ronald C. Lacoe, Member, IEEE Different commercial CMOS processes: del V is less then 5 mv up to 30 Mrad(Si) 20

21 SSP Space Radiation Environment Summary Introduced the radiation environment and its effect on SSP system with potential operations on LEO, MEO, GEO and HEO orbits Efficient and robust design lies in understanding how to quantify effect of space weather on SC components Summarized challenges on large scale and reduced mass SSP satellite in the space radiation environment Less protected if compared to currently flying systems due to the reduced weight (shielding) Large amount of SSP component need to be radiation hardened or shielded Challenges to fly consumer electronics or manufacture required amount of radiation hardened parts due to scale of the system System shielding is a trade study parameter to maintain light SC mass and power performance over time Key technology development with high payoff for system design Radiation resistant solar cells: III-V Multi Junction Solar cells advanced design, perovskite solar cell Advanced glass coating options Resilient solar array technologies Radiation tolerant advanced material development for structural support (composite materials), concentrating mirrors, flexible thin film materials Radiation hardened electronic in mass production 21 SSP challenges are manufacturing with specialty materials at the large scale; technologies are broadly applicable outside of SSP areas

22 Meteoroids Environment Introduction Meteoroids / Micrometeoroids (MM) Environment Small, solid particles considerably larger then molecule and smaller than an asteroid Originated mainly from collision between asteroids and the decay of comets (natural sources) Extensive debate on the size limits for meteoroid term (1 micron to 10 cm): Low mass limit are the solid particles on unbound orbits due to radiation pressure from sun Upper limit are infrequent meteoroids (negligible impacts, to SC compared to orbital debris**) Meteoroids damage depends on mass, velocity, impact angles, density 22 Modeling approach: Several primary methods for flux, velocity and physical properties estimation: Ground-base radar and optical measurements, in-situ impact detection, zodiacal brightness measurements Modeling tool: Meteoroids Engineering Model, NASA, MEM a stand-alone SW, (NASA, MEMR2) describes meteoroid environment along user-supplied spacecraft trajectory (Moorhead, 2018) ** No orbital debris will be considered in the current chapter, similar logic for analysis formalism Figure. Flux of meteoroids at the top of Earth s atmosphere as reported by different authors (Ref: An Assessment of NASA Meteoroids and Orbital debris programs (2011))

23 Meteoroids Impact Effects Meteoroid hazard to SC Hypervelocity impacts of solid meteoroid particles onto spacecraft surfaces Partial penetration and/or surface damage, cratering Surface erosion (impact on thermal and electrical properties) Optical and sensor s properties degradation Structural damage Perforation, secondary fractures SC walls, damage of inner subsystems Cables damage, short circuits Catastrophic ruptures Generation of impact plasma at extreme conditions Electrical interfaces, current flow, electrostatic discharge Momentum transfer Figure. Multi-layer penetration mechanisms Ref. N. C. Elfer, Structural Damage Prediction and Analysis of Hypervelocity Impacts, NASA,

24 Meteoroid impact Modeling and simulation Parameters to estimate meteoroid hazard to SC : The flux of meteoroids above specific mass or size The velocity distribution The density of impacting meteoroids Directionality relative to SC surface Payload (PL) / Spacecraft (SC) material properties Shielding relative to impact location MM Parameters: Flux (mass, density, velocity) Debris parameters** Orbital parameters Payload / SC viewing angle PL/SC material properties: Young module, density, sonic velocity, surface hardness shielding design PL/SC geometric properties: plate thickness, plate geometry (single / double wall, viewing geometry, system s size Analysis formalism: Hydrodynamic theory for semi finite body, thin plates, separate plates, SC structures Analysis results / damage assessment The area damaged per lifetime Optical contamination / degradation EOL cleanness Probability of failure Probability of surviving Shielding design Redundancy considerations 24 ** No orbital debris will be considered in the current chapter, similar logic for analysis formalism

25 Meteoroid s Flux Baseline model MM flux model (Grϋn et al., 1985) is used as baseline for flat plate facing the meteor shower at 1AU: F m = c 0 ((c 1 m c 2 ) γ1 +c 3 (m + c 4 m 2 + c 5 m 4 ) γ2 + c 6 (m + c 7 m 2. ) γ3 ) where the coefficients are: c 0 =3.16e7, c 1 =2.2e3, c 2 =15,, c 3 =1.3e-9, c 4 =1.0e11, c 5 =1.0e27, c 6 =1.30 e-16, c 7 =1.0e6, γ 1 =-4.38, γ 2 =-0.36, γ 2 =-0.85 Average total micrometeoroids flux F(m) - # of particles with mass > m per m2 per year Empirical formalism includes streamed and sporadic meteoroid components Omnidirectional wrt Earth / Directional relative to SC 25

26 Meteoroids impact parameters Ballistic limit, Critical diameter for penetration Cour Palais equation (1979) for ballistic limit and critical diameter, single wall penetration: f d c = 0.65d c ρ p 0.52 V Modified Cour Palais equation (Schmidt Holsapple, single wall): d c = 2.06 f( ρ p ) ( 2.68F t ρ t ρ p V 2 n ) Modified Cour Palais equation (Hayashida & Robinson), single wall penetration: d c = f H ( ρ t ρ p ) ( c V n ) where f is target thickness with complete particle penetration, d c critical diameter of impacting particle, ρ p is the particle density, ρ t is the target density V is a normal component of impacting velocity, c is sonic velocity in the target material, F is ultimate tensile strength for the plate, H is Brinnel hardness of the target 26

): D = ( ρ p ) 1/3 V 2/3 d c ρ t where D is an impact crater diameter, ρ p, is the particle density, ρ

27 Meteoroids impact parameters Critical diameter for penetration, Crater diameter Crater and Particle diameter (Erickson, Hemp et al.): D = ( ρ p ) 1/3 V 2/3 d c ρ t where D is an impact crater diameter, ρ p, is the particle density, ρ t is the target density, V is a normal component of impacting velocity Hypervelocity impact on an Al plate (ESA, 2006) Hypervelocity impact on an brittle material (ESA, 2006) 27

28 Meteoroids impact parameters Material properties examples SC /PL part: material Beryllium mirror Young module, [N/m2] Density, [kg/m3] Surface hardness, [kg/mm2] Plate thickness [cm] Min D for penetration, [cm] **N MM / year / m2 2.87E E-09 Silicon 1.31E E-07 SiO2 glass (typical solar panel) SSP collector, SiO2 glass, ultra-light 7.40E E E E+01 Mylar / kapton (solar sails) 3.80E E+02 ** Assuming identical orbital viewing factor 28 If compared to known systems, there is an order of magnitude meteoroid flux increase of the particles able to penetrate thinner materials Specific system geometry needs to be considered to design a shielding and redundancy approach

29 29 SSP Meteoroids Environment Summary Introduced the meteoroid environment and modeling approach to evaluate the effect on SSP system Summarized meteoroid hazard to large scale and reduced mass SSP satellite Less protected if compared to currently flying systems due to the reduced weight and increased scale, order of magnitude meteoroid flux increase of the particles able to penetrate thinner materials System shielding against the damage is a trade study parameter to maintain light SSP mass and power generation performance Evaluation of surface erosion due to cratering effect, optical degradation, structural damage is dependent on material and geometric properties of proposed SSP design and will benefit from technology development in both areas Experimental testing will be beneficial to understand effect on light SSP design material and system effect Thin solar cell technology Thin and flexible optical components Structural support Flexible thin film materials

30 30 Closing notes Particle radiation and meteoroids environment addressed in the current tutorial are two initial areas to evaluate large scale reduced mass SSP system performance under space effects to propose an efficient and robust design The next key environmental area to consider are: Thermal performance and related advanced technologies to address its challenges Plasma environment and its effect on instrument charging UV and X-ray radiation and its effect on the surface erosion Cross-correlation between several environment are a challenge to predict by simulation and ideally need to be tested to evaluate overall system robustness

32 Space Radiation environment Modeling tools Modeled particle fluxes are combined with an orbit generator and geomagnetic field computation to produce orbit average fluxes for SC degradation analysis Trapped Particles: Includes Protons (E ~ MeV), Electrons (E ~.04 - ~7MeV) and heavy ions Fluxes are omni-directional as functions of idealized geomagnetic dipole with continuous Energy Spectra The trapped particle models represent omnidirectional, integral intensities expected to accumulate on average over a six months period of time [Bart 97]. Models: The standard flux models are the AE-9 and AP-9 Modeling tools: NOVICE, SPENVIS, OMERE Solar Particles, Galactic Cosmic Rays: Energies: Protons 100s of MeV; Heavy ions 100s of GeV Models: Doses: SOLPRO, JPL, NRL Single event Effects CRÈME96 (Protons and Heavier Ions) 32

33 Solar cell degradation JPL method (Eq. 1) : Integrate differential fluence with relative damage coefficient (RDC) empirically determined φ 1 MeV electron = RDC(Ee, t) dφ(ee) dee + Cpe RDC(Ep, t) dφ(ep) dep dee dep (1) DDD (NRL) method (Eq. 2) : Integrate differential fluence with NIEL, n is empirically determined R ep D D = dφ(ee) dee dφ(ep) dep d φ Ep NIEL Ep dep + S(Ee) d φ Ee NIEL Ee [ ] (n 1) S(E ref ) (2) Ref: Messenger et all, Both methods are well defined, characterization curves exist for widely used cells and system configurations (usually given thickness of the cover glass and assuming infinite backside shielding)

34 Meteoroids analysis formalism 34 Meteoroids flux Flux as function of density and velocity Empirical compilation of several sources for meteoroids flux (Grun et al., 1985) A physics-based model, the Meteoroid Environment Model (MEM), NASA SC / PL properties Materials properties (Young module, density, sonic velocity, surface hardness) Geometric properties (plate thickness, plate geometry (single / double wall, viewing geometry, system s size) Derived parameters, degradation analysis Mechanical damage: ballistic limit (Cour-Palais eq), Minimum diameter for penetration, damage diameter, number of penetrating particles per year, damaged area Single Plate penetrating equation Double Plate Penetration Equations Ratio of the pit diameter Optical contamination Probability of surviving / probability of failure per mission time System design update for desired probability of SC surviving Experimental techniques / verification Light gas gun, shock tube, electric-arc lithium plazma, ets

35 Probability analysis Failure due to micro-meteoroids Probability of impact by meteoroids is based on Poisson distribution equation: P x n = r=n r=0 [ e NAτ (NAτ) r ] r! Where P x n is a probability of n or fewer impacts; Nis expected flux, A is exposed area, τ is an exposure time (in correspondent units). Probability of no impact (can be defined as reliability): P x=0 = e NAτ Probability of failure for structure with redundancy degree (s) (MacNeal, R. H. Meteoroid damage to filamentary structures. NASA CR-869,1967) P x=0 = (1 e NAτ ) s 35

A New JPL Interplanetary Solar HighEnergy Particle Environment Model

A New JPL Interplanetary Solar HighEnergy Particle Environment Model Insoo Jun (JPL), Randall Swimm (JPL), Joan Feynman (JPL), Alexander Ruzmaikin (JPL), Allan Tylka (NRL), and William Dietrich (NRL/Consultant)