Spacecraft Environment Interaction Engineering

Transcription

1 Spacecraft Environment Interaction Engineering Spacecraft Charging Analysis Mengu Cho Laboratory of Spacecraft Environment Interaction Engineering Kyushu Institute of Technology 1

2 Outline What is spacecraft charging Spacecraft charging mechanism Current collection Charging simulation Charging simulation example 2

3 What is spacecraft charging? Satellite is electrically floating in space No ground (earth) in space Plasma serves as the reference of electrical potential 3

4 What is plasma Plasma electron(-) and ion(+) Solar UV O O + e 80km Earth Space is filled with plasma (ions and electrons) Electrical conductivity at LEO is similar to sea water (~0.1Ω m) 4

5 Spacecraft and plasma + e + + e e e e e e + e e + e e + e + e e + e + e + e + e e + e + + e e e e e + + e e e + + e e e e + e Spacecraft is floating in a sea of charged particles (plasma) Spacecraft collects electrons and ions It acquires electrical charge (either + or -) Spacecraft has a potential with respect to the plasma 5

6 Why is spacecraft charging important? Spacecraft surface Made of insulator and conductor Conductor Connected to spacecraft body (metal) Same potential Insulator Possible to have different potentials If the potential difference is big Discharge (arcing) 6 solar array coverglass (insulator)

7 Why is spacecraft charging important? Discharge on solar panel in ground experiment Discharge on spacecraft Sometimes fatal to spacecraft operation 7

8 Why is spacecraft charging important? 41m news/solarcell-02l Galaxy3C (2002) Recent GEO telecom satellites Large size and high power Operate at high (>100V) voltage Single arc may be fatal to the entire satellite operation 8

9 Future of spacecraft charging Spacecraft charging study is important for High-power spacecraft Large (>10kW) telecommunication satellites Space station (>100kW) Space hotel (>1000kW) Solar power satellite (>10 6 kw) New applications Lunar and Martian base (dust charging) Solar sail Electrodynamic tether High-power electric propulsion Satellites with COTS electronic parts (internal charging and radiation) 9

10 Types of spacecraft charging Penetrate satellite skin internal charging Buried in outer skin deep dielectric (bulk) charging Remain on surface surface charging Fig6.4 of SEI Interaction between spacecraft and charged particles depend on energy and thickness 10

11 How is spacecraft charged? A conducting sphere in plasma Electrons and ions collide with the sphere and charge it At the steady state Flux of negative charge = Flux of positive charge 11

12 Current sources to a spacecraft Ambient electrons Secondary electrons Ambient ions Secondary electrons Back-scattered electrons Sunlight Sun Photo-electrons active electron emission 12

13 If a spacecraft is modeled as a conducting sphere Electron-induced secondary electrons I se (φ) Incident - electrons I e (φ) - Incident ions I i (φ) Back-scattered electrons I be (φ) - Ion-induced secondary electrons I si (φ) Photo-electrons I ph (φ) Spacecraft potential φ is determined to satisfy I net = I i (φ) I e (φ) + I se (φ) + I si (φ) + I ph (φ) + I be (φ) =

14 Dominant terms Ambient electrons Secondary electrons Ambient ions Secondary electrons Back-scattered electrons Sunlight Sun Photo-electrons active electron emission Spacecraft potential is determined mostly by Photo-electrons Ambient electrons and their secondaries Ambient ions 14

15 The current balance at a single point on insulator Incident Electrons Incident ions Sunlight Reflected Back-scattered Electrons Secondary Electrons Sheath Photo-Emission V c Isolated Conductor Conduction Deep Dielectric Charging Vd Surface Charging Dielectric Structure 'Ground' V a The surface potential φ s at the steady state is determined by j net =0 The surface potential φ d at the steady state is determined by j net =0 j net = j i (φ s ) j e (φ s ) + j se (φ s ) + j si (φ s ) + j ph (φ s ) + j be (φ s ) j net = j i ) j e ) + j se ) + j si ) + j ph ) + j be ) + j c ) usually we neglect 15 11

16 Total current (A) to spacecraft I net = I i (φ sc ) I e (φ sc ) + I se (φ sc ) + I si (φ sc ) + I ph (φ sc ) + I be (φ sc ) depends on spacecraft body potential φ sc Current density (A/m 2 ) to insulator surface j net = j i ) j e ) + j se ) + j si ) + j ph ) + j be ) + j c ) depends on local insulator surface potential φ d Body potential φ sc Insulator potential φ d During substorm and eclipse 16

17 Conductor in plasma thin sheath high density low temperature plasma sheath conductor thick sheath sheath conductor plasma sheath thickness<radius of curvature Particle motion inside sheath is uni-directional low density high temperature sheath thickness>>radius of curvature Particle motion inside the sheath 17 contains radial and tangential directions

18 Ambient Plasma Current Thin sheath or thick sheath? Plasma density m -3 Electron temperature ev Debye length m Thick/Thin LEO Thin GEO Thick Interplanetary Thick GEO plasma current collection is thick sheath limit 18

19 Thin sheath limit We can approximate the particle motion in one-dimension uniform plasma y particle flow x sheath body z sheath boundary If the body surface has a negative potential, φ collection of ion collection of electron The Earth is round but we model the ground as flat OK 1 only if 2 mv 2 0 > eφ energy at the sheath boundary 19

20 v z dv x v y (v x,v y,v z ) dv z dv y v x At the equilibrium state, the distribution function becomes the Maxwellian distribution 3/2 m f (v x,v y,v z ) = n 2πκT exp m(v 2 x + v y2 + v z2 ) 2κT Imagine a sphere with higher densities inside f (v x,v y,v z )dv x dv y dv z number density (m -3 )of particles with velocity between v x and v x + dv x v y and v y + dv y v z and v z + dv z 20

21 The flux of particles across the y-z plane is given by { } Γ x = v ( x fdv z )dv y 0 dv x After we integrate w/r/t v y and v z Γ x = n m 2πκT 1/2 0 After some algebra, this becomes v x exp mv 2 x 2κT dv x Γ x = 1 4 n 8κT πm or Γ x = n 1 2π κt m 21

22 Flux of repelled particles When plasma outside the sheath is in Maxwellian distribution Incoming flux from y-z plane to presheath Γ x = v x fdv z dv y v * dv x Integrate with respect to v y and v z Γ x = n m 2πkT Integrate over v x 1/2 v * v x exp mv 2 x 2kT dv x 1 2 mv*2 = ev Γ x = 1 4 n 8kT πm ev exp kt Γ x = n 1 or 2π kt m ev exp kt 22

23 Total current(v<0) Sheath boudnary Maxwellian Plasma electron n o, T e ion φ p φ V = φ φ p Ion enters with the Bohm velocity and all reach the conductor I i = 0.61en o A Only electrons with the x-direction energy is larger than ev=e(φ φ p ) reach Total current is given by kt e m i ( ) I e = 1 4 en A 8kT e o exp e φ φ p πm e kt e I = I i I e = en o A 0.61 kt e 1 8kT e m i 4 πm e ( ) exp e φ φ p kt e 23

24 Total current(v<<0) Sheath boundary Maxwellian Plasma electron n o, T e ion φ p φ V = φ φ p As the conductor potential becomes further negative w/r/t the plasma potential, there will be no contribution of the electron current Total current is I = I i = 0.61en o A kt e m i Ion saturation current I si = 0.61en o A kt e m i 24

25 Total current(v>0) Sheath boundary Maxwellian Plasma electron n o, T e ion φ p φ V = φ φ p Ions with the energy larger than e(φ φ p ) can arrive. They are negligible compared to the electron current All the electron can reach the conductor surface Total current is I e = 1 4 en oa 8kT e πm e I = I se = en o A 1 8kT e 4 πm e Electron saturation current 25

26 current ion only j i = j e 0 exp(eφ s / κt) surface potential w/r/t plasma ion+electron electron only 26

27 sheath boundary r s thick sheath sheath boundary r s r p L r p L approximate by cylinder r p << r s L << r s r p << r s L >> r s approximate by sphere It looks a sphere to plasma 27

28 Centripetal force field sheath boundary φ = 0 v o v θo initial velocity φ(r) φ r s s v ro r p r s E r 0 E θ = 0 Between r p and r s Conservation of energy Conservation of angular momentum 1 2 m(v 2 r + v θ2 ) + Zeφ(r) = 1 2 mv 2 o mrv θ = mr s v θo Force is radial only Z=1 positive ion Z=-1 electron 28

29 Orbital Motion Limited (OML) Theory Fro the case of a cylinder I o 1 Zeφ s κt For the case of a sphere I o = 4en o v o r p ( A / m) I o 1 Zeφ s κt For the case of a plane I o = 4πen o v o r p 2 (A) I o I o = en o v o (A / m 2 ) For an electron current collection I spherical cylindrical exp(eφ s / κt) planar 0 φ s 29

30 Secondary and back-scattered electrons roughly half the original energy same as the incident one Back-scattered Incident electron typically 2 ev Maxwellian Secondary different from the incident one Depends on incident energy incident angle target material 30 4

31 Secondary electrons E i θ surface Secondary electron yield: number of secondary electrons per incident particle E δ ee (E i,θ) = δ e max exp 2 2 E max E E max exp 2(1 cosθ) [ ] As the angle becomes shallow, the yield increases δ ee (E i,π /3)= 2.7δ ee (E i,0) 31 5

32 δ ee δ e max Yield (Number of secondary per primary) E max δ e max E max (ev) Aluminum Aluminum oxide Magnesium oxide Silicon dioxide Teflon Kapton Magnesium E i incident electron energy 6 32

33 Secondary electron current Incident current density to the surface j = e2π vcosθf (v)v 2 sinθdθdv w/r/t v π/2 0 0 w/r/tθ E i v E i = 1 2 mv2 θ using E = 1 2 mv2 and mvdv = de π/2 2E = e2π cosθ sinθf (E)dθ de 0 0 m m = e4π π /2 E cosθ sinθf (E)dθdE m 0 0 For each particle with the angle θ and the energy E,δ ee (E + eφ,θ) secondary electrons are emitted j se = e4π π /2 δ ee (E + eφ,θ)ef (E m 0 e )de cosθ sinθdθ 0 For Maxwellian f (v) = f (E) = m 2πκT 3/2 m 2πκT surface 3/2 exp mv2 2κT exp E κt 33

34 Back-scattered electron current j be = e4π π /2 B(E + eφ)ef (E m 0 e )de cosθ sinθdθ 0 B ( E ) Back-scatter coefficient Usually, j bse 0.2 j see 8 34

35 Photo-electric current j ph = e W(E)S(E)dE 0 W(E) S(E)dE number of photo-electrons per incident photon flux of photons with energy between E and E+dE For the solar flux at 1 AU photon Material Aluminium Oxide j ph (μa / m 2 ) 42 Indium Oxide 30 Gold 29 Stainless steel 20 Graphite 4 typically 2~4eV energy electron 35 10

36 Spacecraft potential in GEO at substorm j e secondary electrons j es antenna solar array j ph j ph j es j ph ambient high-energy electrons photo-electrons antenna j e j ph Sun light j ph j ph j ph shadow caused by antenna j ph j ph j e j es j es j e 36

37 Spacecraft potential in GEO at substorm Potential Onset of substorm φ d φ sc 1~2V Insulator potential φ d Differential voltage spacecraft potential φ sc time Large potential difference builds up between insulator and satellite potential (i.e. interconnector) Arcs occur for V= φ d -φ sc >O(100V) 37

38 What do we do in satellite design? Before launch, we have to check Does the satellite charge to the arc threshold? Computer simulation 1. Detailed 3D simulation 2. Quick check If yes Ground test Make sure that the satellite operates even with arcs 38

39 How do we calculate spacecraft charging? We solve differential equations; dφ sc dt = 1 { I i (φ sc ) I e (φ sc ) + I se (φ sc ) + I si (φ sc ) + I ph (φ sc ) + I be (φ sc )} C sat ( ) dt d φ d φ sc = 1 { j i ) j e ) + j se ) + j si ) + j ph ) + j be ) + j c )} C d The insulator potential φ d is calculated for each insulator on spacecraft C sat : Capacitance of spacecraft body w/r/t plasma (F) C d : Capacitance per unit area of insulator w/r/t spacecraft body (F/m 2 ) 39

40 3D spacecraft charging simulation dφ sc dt = 1 { I i (φ sc ) I e (φ sc ) + I se (φ sc ) + I si (φ sc ) + I ph (φ sc ) + I be (φ sc )} C sat ( ) dt d φ d φ sc = 1 { j i ) j e ) + j se ) + j si ) + j ph ) + j be ) + j c )} C d Calculate the currents by following trajectories of charged particles to each point on spacecraft 3D geometry of spacecraft Massive computer memory Long computation time (~day) 40

41 How to calculate potentials of spacecraft body and surface 1. Calculate electron and ion fluxes to each part of spacecraft Determined by potential structure around spacecraft 2. Calculate flux of photoelectron, secondary electrons and secondary ions (if any) from spacecraft surface Determined by potential structure around spacecraft 3. Add each current to calculate the total current to spacecraft body 4. Add each current to an insulator surface element to calculate the total current density 5. Calculate the temporal variation of charge on spacecraft body and each surface element 6. Calculate potentials from the capacitance of spacecraft body and surface element 41

42 3D spacecraft charging simulation NASCAP (NASA Charging Analyzer Program) 1970s NASCAP-2K 2000s MUSCAT (Multi-Utility Spacecraft Charging Analysis Tool) Under Development at KIT with JAXA since December 2004 Spacecraft charging of LEO, PEO, GEO satellites Final release in spring

43 etc etc MUSCAT (PIC 43

44 Schematic of Algorithm GUI Sheath formation (LEO, PEO) Current collection Sub-functions Upgrade spacecraft potential 44

45 MUSCAT Example Modeling 3-D satellite geometry 45

46 MUSCAT Example Converting to computational grids 46

47 MUSCAT Example Definition of material property 47

48 MUSCAT Example Derivation of potential distribution around spacecraft 48

49 Particle simulation method Compuational domain Calculate motion of each particle inside grids PIC (Particle In Cell) / PT (Particle Tracking) 49

50 Three-dimensional PIC 1 timestep Q1 Distribute charge to each grid q Q1 = Divided volume(weight) q Total volume of grid Renew electric field at grid points (Maxwell equation) Interpolate electric field to particles Weight Solve equation of motion of particles 50

51 1 time step Three-dimensional particle tracking Distribute charge to each grid Q1 = Divided volume(weight) q Total volume of grid When particle motions gives little effect on electric field Renew electric field at grid points (Maxwell equation) Interpolate electric field to particles PT (Particle Tracking) method Decrease of CPU time Solve equation of motion of particles 51

52 PIC/PT method Only particles that reach spacecraft surface contribute to charging PIC/PT method is used by MUSCAT, NASCAP-2K, SPIS 52

53 MUSCAT Example Derivation of current distribution on each surface element 53

54 MUSCAT Example Derivation of temporal profile of surface potential 54

55 MUSCAT Example Derivation of potential distribution on each surface element 55

56 3D spacecraft charging simulation Accuracy depends on 1. Material property data Secondary electron, photo-electron, conductivity, etc 2. Environment data Plasma density, temperature 3. Satellite geometry dφ sc dt = 1 { I i (φ sc ) I e (φ sc ) + I se (φ sc ) + I si (φ sc ) + I ph (φ sc ) + I be (φ sc )} C sat ( ) dt d φ d φ sc = 1 { j i ) j e ) + j se ) + j si ) + j ph ) + j be ) + j c )} C d 56

57 Quick spacecraft charging simulation Analytical formula of each current Calculate only a limited number of points Numerically integrate the differential equations Runge-Kutta, etc. dφ sc dt = 1 { I i (φ sc ) I e (φ sc ) + I se (φ sc ) + I si (φ sc ) + I ph (φ sc ) + I be (φ sc )} C sat ( ) dt d φ d φ sc = 1 { j i ) j e ) + j se ) + j si ) + j ph ) + j be ) + j c )} C d 57

58 QUSCAT (QUick Spacecraft Charging Analysis Tool) Body dimension R Solar panel area = A panel Consider a GEO satellite Calculate three potential body potential, φ sc coverglass potential φ cg insulator patch potential φ d insulator patch (Dielectric material) 58

59 QUSCAT dφ sc dt dφ cg dt = 1 { j i (φ sc ) j e (φ sc ) + j se(φ sc )}( A body + A panel )+ j ph (φ sc ) A body 2 C sat + { j i (φ cg ) j e (φ cg ) + j se (φ cg ) + j ph (φ cg )}A panel = 1 { j i (φ cg ) j e (φ cg ) + j se (φ cg ) + j ph (φ cg ) + j c (φ cg )}+ dφ sc C cg dt dφ d dt = 1 C d j i ) j e ) + j se ) + j ph ) + j c ) { }+ dφ sc dt Integrate three differential equations with the initial conditions φ sc (t=0)=φ cg (t=0)=φ d (t=0)=0 Runge-Kutta method Each j(φ) is given by an analytical formula depends on plasma parameters, material selection, sunlight, thickness, 59

60 QUSCAT push this to restart the simulation push this to stop and change the parameters parameter selections Made as JAVA applet 60

61 How do we run QUSCAT? 1. Access 2. Double click the link to the program 3. The program starts running with default set of parameters. If you want to stop, press the suspend button 4. Change the parameters by the pull buttons. Then press the run button 5. Once the graph reaches the horizontal end, the program stops automatically. The horizontal axis is approximately 10 seconds. It takes less than 10 minutes with a typical PC. 6. To run the program again, press the suspend button and press the run button. 61

62 Default parameters Electron Temperature Te (ev) Ion Temperature Ti=1000(eV) Electron density Ne=10 6 (m -3 ) Ion density Ne=10 6 (m -3 ) Body length = 4m Panel area = 20 m 2 Body surface material = ITO (Indium Tin Oxide) Solar panel back surface = CFRP (Carbon Fiber Reinforced Plastic) Solar panel coverglass = CMG Dielectric (Insulator) material = Kapton (Polyimide polymer film) Eclipse? = No (in daytime) Dielectric in shadow? = No (in daytime) Dielectric thickness = 1000 um 62

63 Surface materials ITO (Indium Tin Oxide) Transparent conductive coating Used for plasma displays television, etc. CFRP (Carbon Fiber Reinforced Plastic) Light and strong used as structural material 60% weight of aluminum Thermal expansion coefficient is very small no thermal deformation CMG,CMX,CMZ,s0213 Brand name of coverglas. Thermal expansion coefficient is similar to solar cell Kapton (Polyimide polymer film) High-temperature resistant Teflon used as thermal/electrical insulator very good insulator and little outgassing Black Kapton Used as thermal insulator Carbon filled polyimide OSR Optical solar reflector. Mirror used for thermal control purpose MgF2 Used for anti-reflection coating of glass, e.g. your eyeglass too Thermal control requirement often determines the choice of surface material 63

64 What do we look at? Look at how the body potential and the differential voltage change depending on 1. Electron flux increase Te to 10000eV and N e to 10 7 m -3 (substorm condition) 2. Solar illumination change to Eclipse 3. Solar illumination and electron condition change to Eclipse and increase Te to 2000eV 4. Coverglass Material 1. increase Te to 10000eV and N e to 10 7 m -3 (substorm condition) 2. change to no coated glass Secondary electron coefficient» 11 for CMG (default) because of MgF 2 coating» 2.4 for no-coated glass 5. Dielectric capacitance increase Te to 10000eV and N e to 10 7 m -3 (substorm condition) increase dielectric thickness to 10000um Other parameters should be set to the default value 64

65 Task 1. Run the five cases simulation. Explain the result. Show the graph and the final value of the satellite potential, the solar panel potential and the dielectric potential. 2. Due date July 24,

66 Notes Flux is proportional to n κt Solar illumination m Photo electrons are emitted from surface due to photoelectric effect found by Einstein Secondary electron An electron incident on surface kicks out a certain number of electron secondary electron coefficient = (secondary)/(primary) If it is more than 1, positive charge remains Dielectric capacitance Capacitance is inversely proportional to thickness Thinner dielectric can store more charge 66

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68 PIC (Particle In Cell) / PT (Particle Tracking) 68

69 3 PIC 1 Q1 q Q1 = ( ) q (Maxwell ) 69

70 1 3 PT Q1 = ( ) q (Maxwell ) PT (Particle Tracking) 70

71 PIC/PT PIC/PT MUSCAT, NASCAP-2K, SPIS 71