Ion engine for Small Spacecraft
Transcript of Ion engine for Small Spacecraft
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Hiroyuki KOIZUMI
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1. Principle
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Seebeck effect
Peltier effect
Thomson effect
Thermoelectric effect
Δ𝑇
𝐼
Δ𝑉
𝑄
𝐼 𝑄Heattransfer
Current
Voltagedifference
Temperaturedifference
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Seebeck effect
Peltier effect
Thomson effect
Δ𝑉 = −𝑆Δ𝑇
𝑄 = Π𝐴 − Π𝐵 𝐼
𝑄 = −𝜅𝐼Δ𝑇
Thermoelectric effect
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Peltier effect
Thomson effect
𝑄 = Π𝐴 − Π𝐵 𝐼
𝑄 = −𝜅𝐼Δ𝑇
Electricity Heat
Joule heating 𝑄 = 𝑅𝐼2Generation
Transfer (Q>0 = output)
Transfer
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Peltier effect
Thomson effect
𝑄 = Π𝐵 − Π𝐴 𝐼
𝑄 = 𝜅𝐼Δ𝑇
Electricity Heat
Joule heating 𝑄 = 𝑅𝐼2Irreversible
Reversible
Reversible
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Thermoelectric EMF(熱起電力)
Seebeck coefficient or Thermopower (熱電能)
Found by T.J. Seebeck
Seebeck effect (1821)ゼーペック効果
𝑇 𝑇 + Δ𝑇
Δ𝑉
Δ𝑉 = −𝑆 ΔT
𝑇𝐴 𝑇𝐵
𝑉𝐴𝐵
𝑉𝐴𝐵 = − 𝐴
𝐵
𝑆 𝑇 𝑑𝑇
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Seebeck effect (1821)ゼーペック効果
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Thermal equilibrium condition with Electron diffusion
No temperature gradient case
With temperature gradient case
heating
Same temperatures
Charge is carried by electron flow
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MaterialSeebeck
coefficient/(μV/K)
Selenium 895
Tellurium 495
Silicon 435
Germanium 325
Antimony 42
Nichrome 20
Molybdenum 5.0
Cadmium, tungsten 2.5
Gold, silver, copper 1.5
Rhodium 1.0
Tantalum -0.5
Lead -1.0
Aluminium -1.5
Carbon -2.0
Mercury -4.4
Platinum -5.0
Sodium -7.0
Potassium -14
Nickel -20
Constantan -40
Bismuth -77
Wide variety
Dependency on 𝑇
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P-type semiconductor
Carrier: positive hole
Δ𝑉 = −𝑆 Δ𝑇
High 𝑇
Lower hole density(stochastically, by random walk)
Negative potential
Low 𝑇
𝑆 > 0
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N-type semiconductor
Carrier: negative electron
Δ𝑉 = −𝑆 Δ𝑇
High 𝑇
Lower electron density(stochastically, by random walk)
Positive potential
Low 𝑇
𝑆 < 0
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P-N junctionPCarrier: positive hole
NCarrier: negative electron
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Found by J.C.A. Peltier
Peltier effect (1844)ペルチェ効果
Q = Π𝐼
A
ΠA𝐼 Π𝐵𝐼
BQAB = (Π𝐴 − Π𝐵)𝐼
QAB
Π: Peltier coefficient
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Metal N-type P-typeEnergy
Electron energy state in solids
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Metal AEnergy
Electron energy state in solids
Metal Bcurrent
Energy gap
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Metal AEnergyMetal Bcurrent
Energy gap
HeatHeating
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Metal AEnergyMetal Bcurrent
Energy gap
HeatCooling
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N-type
carrier: electron
P-type
carrier: hole
current
Heat
Energy release
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N-type
carrier: electron
P-type
carrier: hole
current
Heat
Energy injection
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𝜅: Thomson coefficient
(electric specific heat)
Predicted by William Thomson (Lord Kelvin)
Thomson effect (1854)トムソン効果
𝑇 𝑇 + Δ𝑇
Q = −𝜅𝐼Δ𝑇
𝐼
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Current
Energy
𝑇 𝑇 + Δ𝑇
Low energycarrier
High energycarrier
Heat
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Current
Energy
𝑇 𝑇 + Δ𝑇
Low energycarrier
High energycarrier
Heat
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Seebeck effect
Peltier effect
Thomson effect
Δ𝑉 = 𝑆Δ𝑇
𝑄 = Π𝐵 − Π𝐴 𝐼
𝑄 = 𝜅𝐼Δ𝑇
Thermoelectric effectAll the phenomena are caused by the current carriers
They should be related each other
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𝑇 𝑇 + Δ𝑇
Δ𝑉
𝑄in 𝑄out
𝑄ex
𝑄J
𝑄in = Π 𝑇 𝐼
Current𝐼
𝑄out = Π 𝑇 + Δ𝑇 𝐼
𝑄J = −𝐼Δ𝑉
Peltier effect
𝑄J + 𝑄in − 𝑄out − 𝑄ex = 0 Energy balance
Note, voltage drop with current is −Δ𝑉
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Δ𝑉
𝑄in 𝑄out
𝑄ex
𝑄J
Current𝐼
Δ𝑉 = −𝜌Δ𝑥
𝐴𝐼 − 𝑆Δ𝑇
Resistance effect+Seebeck effect
𝜌 : resistivity
𝐴 : cross section
𝑇 𝑇 + Δ𝑇
𝑄ex = 𝜌Δ𝑥
𝐴𝐼2 −
dΠ
𝑑𝑇− 𝑆 Δ𝑇𝐼
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𝑄ex = 𝜌Δ𝑥
𝐴𝐼2 −
dΠ
𝑑𝑇− 𝑆 Δ𝑇𝐼
Thomson effect
𝑄 = −𝜅𝐼Δ𝑇
Joule heating
𝑄 = 𝑅𝐼2
𝜅 =dΠ
𝑑𝑇− 𝑆
The first Thomson relation
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Current𝐼
Two different materials
Temperature difference
Voltage differenceand current flow
Adjusting voltage to neglect 𝐼2 term
Voltage supply
to 𝐼2 ≅ 0
B A
𝑇H
𝑇C𝑉
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Voltage supply
to 𝐼2 ≅ 0
B A
𝑇 + Δ𝑇
𝑇
𝑉 = 𝑆𝐵Δ𝑇 − 𝑆𝐴Δ𝑇 + 𝛿𝑉
𝑉
to flow a little current
to compensate the thermoelectric EMF
𝑄T,𝐵 𝑄T,𝐵
𝑄P,𝐵𝐴
𝑄P,𝐴𝐵
𝑄P,𝐵𝐴 = Π𝐵𝐴 𝑇 + Δ𝑇 𝐼
𝑄P,𝐴𝐵 = Π𝐴𝐵 𝑇 𝐼
𝑄T,𝐵 = −𝜅𝐵Δ𝑇𝐼
𝑄T,𝐴 = 𝜅𝐴Δ𝑇𝐼
Π𝐴𝐵 = Π𝐴 − Π𝐵
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𝑉 ≅ −𝑆𝐴𝐵Δ𝑇
𝑉𝐼 = 𝑄P,𝐵𝐴 + 𝑄P,𝐴𝐵 + 𝑄T,𝐵 + 𝑄P,𝐴
𝑑Π𝐴𝐵𝑑𝑇
− 𝑆𝐴𝐵 = 𝜅𝐴𝐵
𝑆𝐴𝐵 = 𝑆𝐴 − 𝑆𝐵
𝜅𝐴𝐵 = 𝜅𝐴 − 𝜅𝐵
(The first Thomson relation)
Energy balance
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Entropy balanceIrreversible process, Joule heating, is neglected by 𝐼2 ≅ 0
𝑄P,𝐵𝐴𝑇 + Δ𝑇
+𝑄P,𝐴𝐵𝑇
+𝑄T,𝐵
𝑇 + Δ𝑇/2+
𝑄T,𝐴𝑇 + Δ𝑇/2
= 0
Π𝐵𝐴 𝑇 + Δ𝑇
𝑇 + Δ𝑇+Π𝐴𝐵 𝑇
𝑇+
𝜅𝐴𝐵Δ𝑇
𝑇 + Δ𝑇/2= 0
𝑑Π𝐴𝐵𝑑𝑇
−Π𝐴𝐵𝑇= 𝜅𝐴𝐵
Π𝐵𝐴 𝑇 + Δ𝑇
𝑇 + Δ𝑇=Π𝐵𝐴𝑇+dΠ𝐵𝐴d𝑇
Δ𝑇
𝑇−Π𝐵𝐴𝑇2Δ𝑇 + 𝑂 Δ𝑇2
Δ𝑇 → 0
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𝑑Π𝐴𝐵𝑑𝑇
−Π𝐴𝐵𝑇= 𝜅𝐴𝐵
𝑑Π𝐴𝐵𝑑𝑇
− 𝑆𝐴𝐵 = 𝜅𝐴𝐵
Energy balance(The first Thomson relation)Entropy balance
Π𝐴𝐵𝑇= 𝑆𝐴𝐵
The second Thomson relation
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𝑑Π
𝑑𝑇− 𝑆 = 𝜅
Π
𝑇= 𝑆
Seebeck coefficient: 𝑆
Peltier coefficient: Π
Thomson coefficient: 𝜅
Three coefficients
Two relations
One of three coefficientsgives the other two coefficients
The only one directly measurable for individual materials
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Onsager reciprocal relationsin Non-equilibrium thermodynamicsCheck it for more exact and more universal deviation.
Potential: 𝜙
Its conjugate: 𝑝
Its flow: 𝐽
𝐽1𝐽2⋮𝐽𝑁
=𝐿11 ⋯ 𝐿1𝑁⋮ ⋱ ⋮𝐿𝑁1 ⋯ 𝐿𝑁𝑁
∇𝜙1𝛻𝜙2⋮𝛻𝜙𝑁
𝐿𝑖𝑗 = 𝐿𝑗𝑖 Onsager reciprocal relations
𝑇, 𝜙𝑒 , 𝑃, 𝜇,⋯
𝑠, 𝑞, 𝑉,𝑚,⋯
(𝑝𝜙 has the unit of energy)
Intensive variables
Extensive variables
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2. Thermocouple
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Thermocouple thermometer
Thermocouple“very basic” temperature measurement way.Using Seebeck effect
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𝑉
𝑉𝐴𝐵 = − 𝐵
𝐴
𝑆 𝑇 𝑑𝑇
Thermocouple“very basic” temperature measurement way.Using Seebeck effect
Unknown
𝑇𝐴
Known
𝑇𝐵
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Unknown
𝑇𝐴
Known
𝑇𝐵
Thermocouple“very basic” temperature measurement way.Using Seebeck effect
𝑉 Meter
Wire
Connection is (usually) necessary
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Thermocouple
𝑉 Meter
𝑉𝑀𝐴 = − 𝑀
𝐴
𝑆w 𝑇 𝑑𝑇
𝑉𝐵𝑀 = − 𝐵
𝑀
𝑆w 𝑇 𝑑𝑇
Unknown
𝑇𝐴
Known
𝑇𝐵
What you measure is 𝑉𝐵𝐴 − 𝑉𝑀𝐴 − 𝑉𝐵𝑀
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Thermocouple
𝑉
𝑉 = 𝐵
𝐴
𝑆+ 𝑇 − 𝑆− 𝑇 𝑑𝑇
Unknown
𝑇𝐴
Known
𝑇𝐵
What you measure is
Uniform temperature
Material-
Material+
𝑉
Use two materials(no other way)
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Thermocouple
𝑉 = 𝐵
𝐴
𝑆+ 𝑇 − 𝑆− 𝑇 𝑑𝑇
Coupled propertiesare important
Type Materials𝑆±/
(𝜇𝑉/℃)
K Chromel Alumel 41
J Iron Constantan 50
N Nicrosil Nisil 39
R 87%Pt/13%Rh
Platinum 10
T Copper Constantan 43
E Chromel Constantan 68
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Thermocouple
T Range/℃ Remarks
-200 +1350High sensitivityHigh linearity
-40 +750High sensitivityEasily rusting
-270 +1300Wide range
stability
0 +1600High temperature
Expensive
-200 350Low temperature
Thermal noise
-110 +140Highest
sensitivity
Type Materials𝑆±/
(𝜇𝑉/℃)
K Chromel Alumel 41
J Iron Constantan 50
N Nicrosil Nisil 39
R 87%Pt/13%Rh
Platinum 10
T Copper Constantan 43
E Chromel Constantan 68
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Thermocouple
Type Materials𝑆±/
(𝜇𝑉/℃)
K Chromel Alumel 41
J Iron Constantan 50
N Nicrosil Nisil 39
R 87%Pt/13%Rh
Platinum 10
T Copper Constantan 43
E Chromel Constantan 68
Color code
IEC BS
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3. ThermoelectricPower Generation
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Semiconductor thermoelectric circuit
Small heat engines Non-mechanical engine(Radioisotope generators) Recovery of waste heat (Energy Harvesting)
Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Ptype
Ntype
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Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Generated power W
Excited current IPtype
Ntype
Current𝐼
𝐼 =𝑉
𝑅 + 𝑟=𝑆 𝑇𝐻 − 𝑇𝐶𝑟 𝑚 + 1
𝑚 =𝑅
𝑟
𝑊 = 𝐼2𝑅 =𝑆2 𝑇𝐻 − 𝑇𝐶
2
𝑟 𝑚 + 1 2
h : hightA : cross section ρ : resistivity λ : thermal conductance
𝑟 =ℎp𝜌p
𝐴p+ℎn𝜌n𝐴n
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Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Ptype
Ntype
Current𝐼
Ohmic heating
Heat conduction
Peltier heat
h : hightA : cross section ρ : resistivity λ : thermal conductance
𝑄𝑂 = 𝑟𝐼2 𝑟 =
ℎp𝜌p
𝐴p+ℎn𝜌n𝐴n
𝑄𝐻 = Λ(𝑇𝐻 − 𝑇𝐶)Λ =
𝜆p𝐴p
ℎp+𝜆n𝐴nℎn
𝑄𝑃 = 𝑆𝑇𝐻𝐼
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Thermoelectric power generation
Load
resistance: 𝑅
Heat input
𝑄𝑇H
𝑇C
Ptype
Ntype
Current𝐼
Heat balance on hot side
𝑄 +1
2𝑄𝑂 − 𝑄𝐻 − 𝑄𝑃 = 0
𝑄 = 𝑆𝑇𝐻𝐼 + Λ 𝑇𝐻 − 𝑇𝐶 −1
2𝑟𝐼2
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Thermoelectric power generation
Theoretical thermal efficiency
𝑚opt = 1 +𝑍
2𝑇𝐻 − 𝑇𝐶
𝜂 =𝑇𝐻 − 𝑇𝐶𝑇𝐻
𝑚opt − 1
𝑚opt + 𝑇𝐶/𝑇𝐻
𝜂 =𝑊
𝑄= 𝑓(𝑇𝐻 , 𝑇𝐶 , 𝑚, 𝑍)
Maximum efficiency (impedance matching)
𝑍opt = S2 𝜆𝑝𝜌𝑝 + 𝜆𝑛𝜌𝑛
−2
𝑍 =𝑆2
Λ𝑟Figure-of-merit (熱電素子対の性能指数 )
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Thermoelectric materials
49
Temperature dependence of ZT (dimensionless parameter)
p-type (left) and n-type (right) semiconductors
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Design example
50
Specifications
p n
e [mV/K] 210 ‐170
r [mWm] 18 14
l [W/mK] 1.1 1.5
h [cm] 1.0 1.0
S [cm2] 1.3 1.0
TH=1,000K and TC=400K(S has been optimized)
Thermal efficiency
Output =4.5[W]
6
p n 380 10 [V/K]e e e
2
2 -1
max p p n n 0.00177[K ]Z e l r l r
opt 1.5m R r
max
1000 400 1.5 10.6 0.26 0.16
1000 1.5 400 1000
2 2
opt opt
opt
0.2280.004127
0.006886
TW R
R r
e
2.8mr W
=
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Radioisotope Generator: RTG 原子力電池
Energy from the decay of a radioactive isotope to generate electricity(different from nuclear reactor)
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Nuclear ReactorUse of nuclear chain reaction
Natural decay Chain reaction
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Control the rateby the material and environment
Chain reactionUse of nuclear chain reaction
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Electron
Nucleus
= Protons+ neutrons
Atom
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Chemical energyUse of electron energy states
Electron
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Radioactive decayUse of nucleus energy
Plutonium 238
He
Uranium 234
x 94
x 144
x 94
x 92
x 142
x 92
x 2
x 2
x 2Half decayby 88 years
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Radioactive decayUse of nucleus energy
Plutonium 238
He
Uranium 234
x 94
x 144
x 94
x 92
x 142
x 92
x 2
x 2
x 2Half decayby 88 years
540 W/kg
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RTG~5 W/kg
SAP~50 W/kg(1 AU)
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59
Radioisotope-Thermoelectric Generator
Electric output 290W/250W
Thermal Output 4,234Wt
TH 1000℃
Total mass 55kg
Pu mass 7.561kg
size 114cm×f42cm
Galileo RTG
Radioisotope Generator: RTG 原子力電池
Energy from the decay of a radioactive isotope to generate electricity(different from nuclear reactor)
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VoyagerRTG was located with a distance from the main body.Power would be 73% of BOL after 39 years.
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CuriosityRTG on the back (hip)
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CassiniThree RTGswith a cover for each
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New HorizonsThe latest RTG
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Thank you