February 1, 2005 HYPERIONERAU
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Thermal Analysis of a Radiation Shield for Antimatter Rocketry Concepts
Jon Webb
Embry Riddle Aeronautical University
February 1, 2005 HYPERIONERAU
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Agenda
• Why Hyperion
• Rocket Principles
• Why antimatter
• Velocity Profile and Fundamentals
• Thermal Considerations
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Microgravity Environment
Skeletal and Muscular atrophycan make it impossible toreturn to the surface of Earth!
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Rocket Principles
• Specific Impulse is the fuel efficiency of a rocket engine
• As fuel energy density increases so does Specific Impulse and delta V
• The equation for Specific Impulse is:
g
cI sp
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Rocket Principles
• Thrust is a force
• Thrust is the time rate change of propellant momentum
• Momentum is the mass of fuel ejected multiplied by the exhaust velocity
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Fuel Energy Density
Fuels Energy Release J/kg Converted Mass Fraction
Chemical
LO/LH 1.35 x 107 1.25 x 10-10
Atomic Hydrogen 2.18 x 108 2.40 x 10-9
Metastable Helium 4.77 x 108 5.30 x 10-9
Nuclear Fission238U 8.20 x 1013 9.10 x 10-4
Nuclear Fusion
DT (0.4/0.6) 3.38 x 1014 3.75 x 10-3
CAT-DT (1.0) 3.45 x 1014 3.84 x 10-3
D3He (0.4/0.6) 3.52 x 1014 8.90 x 10-3
pB11 (0.1/0.9) 7.32 x 1013 8.10 x 10-4
Matter-Antimatter 9.00 x 1016 1
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What is antimatter (positrons)
• Produces photons isotropically• Produces photons back to back• 0.511 MeV per photon
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Shield Design (Rad. Lengths)
Absorbed Energy Vs. Radiation Lengths
0
20
40
60
80
100
120
0 1 2 3 4 5
Radiation Lengths (#)
Ab
sorb
ed E
ner
gy
(% o
f in
cid
ent
ener
gy)
Series1
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Shield Design
• Made of Tungsten
• Melting point of 3600 K
• Density of 19.3 gm/cm3
• Radiation length is 0.35 cm
• 5 radiation lengths thick
• Roughly 1.75 cm thick
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Shield Design (Dimension)
Shield Area Vs. Shield Radius
0
1
2
3
4
5
6
7
8
9
10
0 100 200 300 400 500 600
Shield Area (m^2)
Shi
eld
Rad
ius
(m)
Series1
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Shield Design (Mass)
Shield Mass Vs. Inner Area (5 rad lengths)
0
20
40
60
80
100
120
140
160
180
200
0 100 200 300 400 500 600
Shield Area (m^2)
Sh
ield
Mas
s (M
t)
Series1
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Momentum Attenuation
• Compton Scattering• Brehmstralling• Photo-electric Effect- photons/electrons ejected at
random angles- Might reduce
momentum/cosine average
• Monte-Carlo analysis is being developed to research effects
electron
Atom
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Thermal Problem
• Energy is lost as heat in the tungsten shield
• We must find a way to dissipate the heat in order to augment the thrust
• We must find a way to regain the energy lost from the heat to augment efficiency (Isp)
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Shield Thermal Loading
Shield Inner Area Vs. Thermal Loading (Constant 3300 K)
0
10
20
30
40
50
60
70
80
0 100 200 300 400 500 600
Shield Area (m^2)
Th
erm
al E
ner
gy
(GJ)
Series1
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Radiative Cooling
• For highest Isp we must find the steady state condition where blackbody radiation equals input energy.
• This will severely limit the thrust
Eradiated
E thermal , P thrust
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Radiative Cooling
• View Factors must be examined
• The extreme limits of the pi/2 to –pi/2 shield may re-radiate energy into the other side of the shield.
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Radiative Cooling
• We may want to consider making the shield flat and very large, or decrease the angular limits of the shield.
• Annihilate e+ inside shield
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Radiative Cooling
22
2cos
DR
R
D
AP
R
R
22
1sinDR
R
All Values in Radians
minmax sinsincos
max
min
cos1
cos
d
22
2cos
DR
R
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Radiative Cooling
Shield Radius Vs. Cosine Average (Large Shield)
0.6368
0.63682
0.63684
0.63686
0.63688
0.6369
0.63692
0.63694
0.63696
0 2 4 6 8 10 12
Shield Radius (m)
Co
sin
e A
vera
ge
Series1
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Radiative Cooling
Shield Radius Vs. Cosine Average (Small Shield)
0.585
0.59
0.595
0.6
0.605
0.61
0.615
0.62
0.625
0.63
0.635
0.64
0 0.2 0.4 0.6 0.8 1 1.2
Shield Radius (m)
Co
sin
e A
vera
ge
Series1
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Radiative Cooling
Flat Shield Radius Vs. Mass
0
20
40
60
80
100
120
0 2 4 6 8 10 12
Shield Radius (m)
Sh
ield
Mas
s (M
t)
Series1
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Radiative Cooling
1. 7.
2.
3. 8.
4.
5.
6.
4TAq 2mcq
42 TAmc 42 TAcm
42
2TA
cm
2
42
c
TAm
cmF 2
cos
c
TAF
4cos
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Radiative CoolingRadiated Power Vs. Shield Inner Area
0
200
400
600
800
1000
1200
0 100 200 300 400 500 600
Shield Inner Area (m^2)
Rad
iate
d P
ower
(M
W)
Series1
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Radiative Thrust
Shield Inner Area Vs. Thrust (Radiative Cooling)
0
0.2
0.4
0.6
0.8
1
1.2
0 100 200 300 400 500 600
Shield Area (m^2)
Th
rust
(N
)
Series1
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Convective Cooling
• Use liquid Hydrogen or Ammonia to absorb excess heat
• Allow fluid to expand across the shield to produce thrust with a decreased Isp
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Convective Cooling
LH2 Properties
- Cp = 10,000 J/ (kg.K)- h = 210 W/(m2.K)- TLH2 = 16 K- Tshld = 3300 K
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Convective Power Transfer
1. 2. 2LHshield TThAQ 2
689640m
WxAQ
Energy Transfer Rate to LH2 Vs. Shield Inner Area
0
50
100
150
200
250
300
350
400
0 100 200 300 400 500 600
Shield Inner Area (m^2)
Po
wer
(M
W)
Power
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LH2 Mass Flow Rate
3.
4.
5.
22
LHshieldpLH TTC
Qm
pLH C
hAm 2
s
kgxAmLH 021.02
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LH2 Mass Flow Rate
Mass Flow Rate Vs. Shield Inner Area
0
2
4
6
8
10
12
0 100 200 300 400 500 600
Shield Inner Area (m^2)
Mas
s F
low
Rat
e (k
g/s
)
Mass Flow Rate
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Convective Thrust from LH2
6.
7.
9.
10.
222 HHH VxmF
22
2
LHH m
EV
22 2 LHshieldpH TTCV
s
mVH 32.81042
22 2 Hshieldpp
H TTCC
AhF
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Convective Thrust from LH2
Thrust due to expanding Hydrogen Vs. Shield Area
0
10
20
30
40
50
60
70
80
90
100
0 100 200 300 400 500 600
Shield Area m^2
Th
rust
(kN
)
Thrust
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Shield Thrust to Weight Ratio
Acceleration Vs. Shield Area
0.48
0.485
0.49
0.495
0.5
0.505
0 200 400 600 800 1000 1200
Shield Area (m^2)
Acc
eler
atio
n (
m/s
^2)
Series1
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Convective Specific Impulse
11.
12.
13.
14.
222
cosHshieldp
peeT TTC
C
AhcmF
gm
FI
LHspH
22
g
TTCI
Hshieldp
spH
222
sIHsp
8262 gmm
FFI
eeLH
eeHsp
2
2
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Specific Impulse vs. Shield Temp.
Specific Impulse vs. Shield Temperature
0
200
400
600
800
1000
1200
0 1000 2000 3000 4000 5000 6000
Shield Temperature (K)
Sp
ecif
ic I
mp
uls
e (s
)
Series1
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Thrust Augmentation
• Shield Mass: 170 Mt• 10 Shields• Shield Area: 10,000m2
• Thrust: 1.70 MN• Isp: 826 seconds
5 rad. lengths
10 sub-shields
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Convective Case Study 1
• MS/C = 40 Mt
• F = 1.70 MN• A = 10,000 m2
• P = 6,896 MW
• Msh = 170 Mt
• Md = 210 Mt
• Mdote+ = 7.662 x 10-8 kg/s
• MdotH2 = 210 kg/s
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Convective Case Study 1
Initial Mass in Low Earth Orbit/Hydrogen Propellant Mass Vs. dV (400 Mt Payload)
0
500
1000
1500
2000
2500
3000
0 5 10 15 20 25
Change in Velocity (km/s)
IML
EO
/Hyd
rog
en M
ass
(Mt)
IMLEO
Liquid Hydrogen Mass
f
isp M
MgIV ln
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Convective Case Study 1
Positron Mass Vs. Burnout Velocity
0
50
100
150
200
250
300
350
400
450
0 5 10 15 20 25
Change in Velocity (km/s)
Po
sitr
on
Mas
s (m
icro
-gra
ms)
Series1
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Convective Case Study 2
• MS/C = 40 Mt
• F = 261.9 kN• A = 1130.4 m2
• P = 780 MW
• Msh = 19.2 Mt
• Md = 66.113 Mt
• Mdote+ = 4.33 x 10-9 kg/s
• MdotH2 = 23.7 kg/s
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Convective Case Study 2
Initial Mass in Low Earth Orbit/H2 Propellant Mass Vs. dV (400 Mt Payload)
0
100
200
300
400
500
600
700
800
900
0 5 10 15 20 25
Change in Velocity (km/s)
IML
EO
/H2
Mas
s (M
t)
IMLEO
H2 Mass
f
isp M
MgIV ln
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Convective Case Study 2
Mass of Positrons Vs. dV
0
20
40
60
80
100
120
140
0 5 10 15 20 25
Change in Velocity (km/s)
Mas
s o
f P
osi
tro
ns
(mic
ro-g
ram
s)
e+ mass
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Convective Case Study
Burn Time Vs. Burnout Velocity
0
20
40
60
80
100
120
140
160
180
200
0 5 10 15 20 25
Change in Velocity (km/s)
Bu
rn T
ime
(min
ute
s)
Series1
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Further Convective Work
• Combine case studies into 3-D graphs (dV vs. IMLEO/H2/e+ mass vs. shield mass/radius/area)
• Research energy/heat deposition as a function of thickness plus H2 gaps
• Increase SA without increasing mass
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Electrical Power Production
• Another option is to use a working fluid that can be expanded through a turbine to produce electricity
• This would allow for low thrust missions and provide the spacecraft with electricity for its subcomponents
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Tri-Modal Operation
• Lastly the engine could be cooled with LH2 when large thrust is needed and operate in a radiative mode to slowly accelerate S/C in interplanetary space.
• When the engine is in a radiative mode, electricity can be produced
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Concluding Remarks
• Antimatter offers extraordinary propulsion capabilities
• Unfortunately thermal challenges are quite daunting
• Production and storage are a whole different challenge
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Concluding Remarks
• Advantages warrant serious look
• Possible high Isp uses as a thermal rocket by increasing the shield surface area
• Best method is to use the reflecting shield
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Antiprotons
• Statistically complicated• Produces massive particles
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Flight TimesMinumum Rendezvous Times Vs. Isp for a 5000 kg Spacecraft (dm/dt = 50 mg/s)
0
50
100
150
200
250
0 20 40 60 80 100 120 140 160 180
Isp (thousand seconds)
Tra
nsfe
r T
ime (
weeks)
0 0.002 0.004 0.006 0.008 0.01 0.012
<cos(theta)>
Mercury
Venus
Mars
Jupiter
Series5
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Flight TimesMinimum Rendezvous Time Vs. Isp for a Spacecraft of 5000 kg (dm/dt = 50 mg/s)
0
50
100
150
200
250
300
350
400
450
500
0 20 40 60 80 100 120 140 160 180
Isp (thousand seconds)
Tra
nsfe
r T
ime (
mo
nth
s)
0 0.002 0.004 0.006 0.008 0.01 0.012
<cos(theta)>
Saturn
Uranus
Neptune
Pluto
Series5
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Flight TimesMinimum Rendezvous Times Vs. Isp for a Spacecraft of 50 mT (dm/dt = 50 mg/s)
0
50
100
150
200
250
0 5 10 15 20 25 30 35
Isp (million seconds)
Tra
nsfe
r T
ime (
days)
0 0.5 1 1.5 2 2.5
<cos(theta)>
Mercury
Venus
Mars
Jupiter
Series5
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Flight TimesMinimum Rendezvous Time Vs. Isp for a Spacecraft of 50 mT (dm/dt = 50 mg/s)
0
200
400
600
800
1000
1200
0 5 10 15 20 25 30 35
Isp (million seconds)
Tra
nsfe
r T
ime (
days)
0 0.5 1 1.5 2 2.5
<cos(theta)>
Saturn
Uranus
Neptune
Pluto
Series5
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Lunar Flight TimesLunar Rendezvous Time and Propellant Mass Vs. <cos (theta)>for a spacecraft of 10 mT
dm/dt = 50 mg/s
0
10
20
30
40
50
60
0 0.002 0.004 0.006 0.008 0.01 0.012
<cos(theta)>
Tra
nsfe
r T
ime (
days)
0
50
100
150
200
250
Pro
pellan
t M
ass (
kg
)
Moon Trip Time
Propellant Mass
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Lunar Flight TimesLunar Rendezvous Time Vs. <cos(theta)> and Propellant Mass for a 10 mT spacecraft, dm/dt
= 50 mg/s
0
10
20
30
40
50
60
70
80
90
0 0.5 1 1.5 2 2.5
<cos(theta)>
Tra
nsfe
r T
ime (
ho
urs
)
0
2
4
6
8
10
12
14
16
18
Pro
pellan
t M
ass (
kg
)
Lunar Trp Time
Propellant Mass
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