Transcript 90-Day Single-Launch to Mars: A Case Study for The Fusion-Driven Rocket Anthony Pancotti John Slough, David Kirtley, George Votroubek, Christopher Pihl FISO Telecon 09-‐25-‐13 MSNW LLC,

90-Day Single-Launch to Mars:
A Case Study for The Fusion-Driven Rocket
Anthony Pancotti
John Slough, David Kirtley, George
Votroubek, Christopher Pihl
FISO Telecon 09-‐25-‐13
MSNW LLC, Redmond, WA 98052
1.
2.
3.
4.
Background
Mission Architecture Design
Spacecraft Design
Fusion Physics
2
Why We Are Not on Mars Yet?
Takes too long
Costs too much
Safety
Direct cost
Radiation exposure
Cancer risk
Bone & muscle loss
Mental fatigue
Increased risk of
critical failure
Governmental support
Political
Solution:
High
Public interest
Operational costs
Complexity
Pre-‐deploy assets
Space assembly
Launch costs
Large space
Huge fuel
structures
Mass
New method of propulsion is needed
Short trip time
Reduced IMLEO
( )
High Exit Velocity (Isp)
3
The Fusion Driven Rocket
(a) Thin hoops of metal are driven at the proper angle
and speed for convergence onto target plasmoid at
thruster throat. Target FRC plasmoid is created and
injected into thruster chamber.
(b) Target FRC is confined by axial magnetic field from
shell driver coils as it translates through chamber
eventually stagnating at the thruster throat
(c) Converging shell segments form fusion blanket
compressing target FRC plasmoid to fusion
conditions
(d) Vaporized and ionized by fusion neutrons and
alphas, the plasma blanket expands against the
divergent magnetic field resulting directed flow of
the metal plasma out of the magnetic nozzle.
Schematic of the inductively driven metal propellant compression of an FRC
plasmoid for propulsion
4
Magneto-‐Inertial Fusion
Two Approaches
Shell (liner) implosion driven by B from largeLiner implosion from j x B force between
axial currents in shell.
external coil and induced liner currents
Foil Liner Compression
FRC
plasmoid
Magnetic Nozzle
FRC
Injector
MTF
Issues:
FDR
Advantages:
Extremely low inductance load difficult to drive
(massively parallel HV caps and switches)
Close proximity and electrical contact
major
collateral damage with each pulse
Small FRC must be formed close to implosion
marginal B for ignition w injector destruction
Only inefficient 2D compression possible
requires much larger driver energy
Liner
Driver System
Large driver coil easy to power with ample
standoff
Driver electrically isolated from liner and
magnetically from fusion process
Large FRC can be formed external to implosion
with abundant B for ignition
Full 3D compression can be realized for
efficient compression and translation
John Slough, David Kirtley, George Votroubek, and Chris Pihl,
Lithium Liner Compression of an FRC Plasmoid , 20th ANS TOFE, Aug 2012
-‐Driven
5
FDR offers the first realistic
approach to fusion-based propulsion
Benefit
Result
1
Directtransferoffusion
energytothepropellant
Highefficiency,
lowmassengine
2
Usessolidpropellant
Nosignificanttankage
Highexhaustvelocities
(2000-5000sIsp)
Shorttriptime,
highmassfraction
LowIMLEO
Magneticinsulatednozzle
Nosignificantphysicalinteraction
Minimalthermalmass
5
Lowenergyrequirements
toachieveMIF
Lowmass(singlelaunch)andgreatly
reducedcost
6
Fusionenergyyieldhas
beendemonstrated
Fundamentalphysicsisprovenand
understood
3
4
6
1.
2.
3.
4.
Background
Mission Architecture Design
Spacecraft Design
Fusion Physics
7
Mission Studies
350
Fusion Gain
200
0.6
0.5
0.4
0.3
150
0.2
100
50
Mission Assumptions:
0.1
20
40
60
80 100
Trip Time (Days)
120
200
0
0.8
0.7
0.6
150
Total Gain
Mass of Payload= 61 MT
Habitat 31 MT
Aeroshell 16 MT
Descent System 14 MT
Specific Mass of capacitors ~ 1 J/g
Specific Mass of Solar Electric Panels 200 W/kg
Tankage fraction of 10% (tanks, structure,
radiator, etc.)
Payload mass fraction =Payload Mass/Initial
Mass
System Specific Mass = Dry Mass/SEP (kg/kW)
Analysis for single transit optimal transit to Mars
Full propulsive braking for Mars Capture - no
aerobraking
250
0.7
Higher fusion gain
and longer trip times
result in higher
payload mass fraction
0.5
100
Burn time of ~10 days
is optimal
0.4
0.3
0.2
50
0.1
20
40
60
Burn Time (Days)
80
Paylod
PayloadMass
MassFraction
Fraction
Ionization cost is 75 MJ/kg
Coupling Efficiency to liner is 50%
Thrust conversion t ~ 90%
Realistic liner mass are 0.28 kg to 0.41 kg
Corresponds to a Gain of 50 to 500
Ignition Factor of 5
Safety margin of 2: GF =GF(calc.)/2
300
0.8
Paylod Mass
Fraction
Payload
Mass Fraction
Fusion Assumptions:
0
Anthony Pancotti, John Slough, David Kirtley, Micheal Pfaff,
Christopher Pihl, George Votroubek,
Design Architecture
for the Fusion Driven
, AIAA 48th JPC, July 2012
8
Determining the Optimal Mars Mission
Opposition-class
short surface stay times at Mars
typically 30 to 90 days
relatively short total round-trip mission times
500 to 650 days
Conjunction-class
long-duration surface stay times
500 days or more
long total round-trip times
approximately 900 days
minimum-energy solutions for a given launch
opportunity
Both options are well outside the current permissible exposure limit of radiation
(1) shortest overall mission to reduce the
associated human health and reliability
risks
(2) adequate time on the surface in which
to maximize the return of mission
objectives and science
(3) low mission mass, which, in turn,
reduces the overall cost and mission
complexity
mission does not
Mission down design approach
Mission Architecture Goal
90 Transit times to and from Mars
Adequate stay time (30+ days)
Single launch (130 MT IMLEO)
No pre-‐deployed assets
DRA 5 Payload mass (63 MT)
Full propulsive MOI & EOI
Reusable spacecraft
9
210 day Round-trip
Manned Mars Mission
Fusion Equation
61 MT payload
83 MT
27 MT
FDR
8000
1 launch
134 MT
Isp (s)
6000
4000
(IMLEO)
2000
0
210 days
100
200
300
Fusion Gain
Isp = 5000 s
Power Input= 180 kW
Gain 200
Power(Jet)= 36 MW
Spacecraft Mass = 15 MT
Payload Mass = 61 MT
134 MT
15 MT
Refuel
Re-crew
For future
missions
(May 19, 2018)
DRA 5.0 (NTP), 9 launches, 848.7 MT IMLEO, 1680 da
210 day Round-trip (Mission Details)
Trans-Earth
Injection
V
12.0km/s
T
1.6days
MI
19.2
MF
15
V
16.5km/s
T
2.9days
MI
26.8
Mf
19.2
40
DeltaV (km/s)
EarthOrbitInsertion
50
30
20
10
0
0
x 10
50
100
150
Time (Days)
200
250
50
100
150
Time (Days)
200
250
4
Trans-MarsInjection
V
7.3km/s
T
7.1days
MI
133.4
Mf
115.0
MarsOrbitInsertion
V
13.2km/s
T
10.5days
MI
115.0
Mf
87.8
Mass (Kg)
15
10
5
0
0
11
Near Body Maneuvers
Maneuver
V (km/s)
T (days)
Near Body Simplified Near Body
TMI
MOI
TMI
MOI
TEI
EOI
Total
12.7
8.5
16.6
11.2
49.0
TEI
7.3
13.2
16.5
12
49.0
8.9
4.7
1.7
1.6
16.8
Simplified
7.1
10.5
2.9
1.6
22.1
TOI
12
Future Mission Studies
Mars
Single launch to Mars (Opposition Class)
Mission refinement
Long Stay Mission (>500 day) (Conjunctive Class)
Single trip on orbit assembly
Larger s/c (fuel launched separate)
Pre-deploy mission architecture
Classic DRA style with pre-curser cargo mission
Ultra-fast (30 day) transfers
Jupiter
Enter and exit gravity well
Moon mission
NEO
Sample return
Redirection?
13
1.
2.
3.
4.
Background
Mission Architecture Design
Spacecraft Design
Fusion Physics
14
Spacecraft Scaling
Mission Assumptions
Payload mass
Spacecraft mass
IMLEO
Earth Orbital Altitude
Mars park orbit
Total Mission Time
Stay Time
63
15
MT
MT
~130
MT
407
km
1
250 x 33793
210
30
sol
km
days
days
Mission
Architecture
Design
Jet Power
Specific Power
5000
36
240
6000
Isp (s)
Propulsion Requirements
Isp
8000
s
MW
W/kg
4000
2000
0
100
200
300
Fusion Gain
15
Power System Scaling
ENERGY STORAGE
Gain of 200
2.4 MJ Input Energy @ 2 kJ/kg
1.2 MT of Capacitors
50% space de-‐rating
POWER SOURCE
1.8 MT of Energy Storage
Solar panels have flown on 99% of all space mission.
36 MW Jet Power
180 kW of Input power OR 400 kW at Mars
Gain of 200
500 W/kg to 1000 W/kg are speculated for the future
Direct energy recovery from fusion reaction possible
200
W/kg
2 MT of Solar Panels
16
Mass Budget
Spacecraft Component
Mass (MT)
Energy storage3
Solar Panels6
Switches and cables5
Spacecraft structure1
Lithium containment vessel
FRC Formation2
Propellant Feed mechanism
Liner driver coils4
Thermal Management
Magnetic Nozzle
Margin
Spacecraft Mass
Crew habitat (DRA5.0)
Lithium Compound Propellant
Total Mass
1.8
2.0
1.8
3.8
0.1
0.2
1.2
0.3
1.1
0.2
2.5
15
63
56
134
Payload mass fraction 46%
1. Fairings, support structure, communication, data handling ACS, Batteries
2. Hardware responsible for formation and injection of Fusion material (FRC)
3. Capacitors (1.8 MJ @ 1 kJ/KG), switches, power bus
4. Electromagnetic coil used to drive inductive liner
5. Pulsed power electronic components need to charge and discharge capacitor bank
6. 180 kW @ 200 W/kg
Switches and cables equal to
energy storage mass
Simple aluminum coil, but
most likely composites with
We, Be, or Cu liners
Thermal control, 10% heat
rejection @ 1 kW/kg with a
margin of 3X
FRC formation based of lab
equipment
Propellant Feed roll of film
ring formation and injection
20% Margin
17
Fusion Driven Rocket Engine
Shadow Shield
Main Compression Coils
Magnetic Nozzle
FRC Formation
Engine Truss
ShockAbsorbers
Liner/Propellant Injector
18
Spacecraft Layout
Considerations
1.6 m
10.5 m
11.3 MT
36 caps
12 /ring
4.8 m
Energy Storage Packing
Propellant spool Packing
5 m
45 m
19
FDR Spacecraft Layout
Solar Panels
Transit
Habitat
Mars Lander
Spline
Truss
Energy
Storage
Liner/Propellant
Fusion Driven Rocket
Radiators
Final Spacecraft Design
21
Future Design work
Spacecraft Component
Mass
(MT)
Spacecraft structure
Propellant tank
FRC Formation
Propellant Feed
Energy storage
Liner driver coils
Switches and cables
Solar Panels
Thermal Management
Nozzle
Margin
Spacecraft Mass
Crew habitat
3.8
0.1
0.2
1.2
1.8
0.3
1.8
2.0
1.1
0.2
2.5
15
61
Propellant
Total Mass
56
134
TRL
4
5
4
2
7
3
6
8
5
2
Mission
Dependent
X
X
X
X
Fusion
Dependent
Support
Structure
Bias magnets
X
X
X
X
X
X
X
X
X
X
Magnetic
Nozzle coils
Liner
converging
FRC formation
region
X
X
X
X
X
Liner Drive coils
For a more accurate spacecraft design and total launch mass
A more defined mission and fusion conditions are need
Liner
start
22
1.
2.
3.
4.
Background
Mission Architecture Design
Spacecraft Design
Fusion Physics
23
Approach
1. Analytical
2. Computational
1D Liner Dynamic + Circuit
3D Structural compression
(ANSYS)
Neutronics
3. Experimental Validation
24
Field Reversed Configuration (FRC)
Magnetic Field lines and Pressure Contours
r
xs
rs
rc
Be
Bvac
rc
Ls
2rs
rs
R
Ls
SOL
z
Bvac
1 x2s
Bext
Key
Equilibrium
Relations:
P0
n0kT
1
B2ext
2 0
External measurements of B yield
FRC separatrix radius rs(z), FRC length Ls
volume, position, velocity
Radial Pressure Balance
Simple cross-‐tube interferometric
measurement with rs from yields n and T
Axial Pressure Balance
1
2
Flux Conservation
x2s
With above obtain plasma energy,
Inventory, confinement times
FRC equilibrium constraints and the diagnostic measurements that together with the
equilibrium relations that are employed to determine the basic parameters of the FRC
25
equilibrium
Fusion Based on Inductively Driven Liner
Compression of the FRC
The energy within the FRC separatrix at peak compression is dominated by
plasma energy that is in pressure balance with the edge magnetic field B0, so that
one can write:
1
EL
4
2
2M
L
vL
3n0 kT0
B0
3
3 r0
3
r0
(1)
0
The zero subscript indicates values at peak compression where rs ~ r0 and
magnetic pressure balance (2n0kT0= B02 /2 0).
Fusion energy produced in the FRC during the
compression:
Efus
1.2 10
12
4
n 0v
3
2
3
r0
D
1.1
dwell time
42
2
10 n0
4
2 r0
T0
vL
D
at peak
(2)
where n0 and T0 are the peak density and temperature, and where the liner shell
dwell time at peak compression, D, ~ 2r0/vL
26
Fusion Based on Inductively Driven Liner
Compression of the FRC (cont.)
The usual approximation for the D-‐T fusion cross section in this temperature
range:
1.1x10-‐31 T2(eV) was also assumed. Pressure balance, together with
expressions (1) and (2) yields for the fusion gain:
G
E fus
EL
1.73
ML
10 3 B0
l0
4.3x10 8M 1 L/2 E11 L /8
where l0 (= 2r0 ) is the length of the FRC at peak compression. The last expression
is obtained from adiabatic scaling laws
EL ~ B0 2 r02 l0 ~ B0 4/5 and l0 ~ r02/5 ~ B0 1/5
to express G in terms of the liner kinetic energy EL and mass ML only.
Fusion Ignition will amplify gain by large factor. It is estimated that the total fusion
gain GF ~ 5-‐10 G. For a large margin of safety, it is assumed that:
GF = 2.5G or,
GF = 1.1 10-‐7 ML1/2 EL11/8
27
Comp - 1D Liner Code
Source Free RLC Circuit
x 10
dI
dL
V=L
I
+IR
dt
dt
9
0
-1
Solved as 2 First Order equations
r=0.41 m
w=6 cm
l=0.2 mm
0.015
2
Time (s)
3
x 10
-4
0.01
0.005
Ringing
Crowbar
Diode
0
1
2
Time (s)
3
x 10
-4
0.2
0
1
2
Time (s)
3
x 10
-4
0
1
Various Current waveforms
Magnetic flux diffusion
Resistivity -‐ (T)
Latent heats
Radiative cooling
Energy conservation
Data for actual coil and
collector plate used
In Foil Liner Compression
(FLC) Test bed
Liner resistance ( )
1
0.4
0
dV
dt
0
0
0
-2000
I=C
3
2
Time (s)
x 10
-4
0.04
Phase change
Increasing
Cross-‐section
0.02
0
Latent heat
0
1
2
Time (s)
3
x 10
-4
1500
Temperature (K)
-2
Liner Parameters
changing
inductance
1
2000
Liner Radius (m)
Liner Velocity (m/s)
Liner Acceleration (m/s2)
R=3 m
L=20 nH
420 uF
40,000 V
Thickness (m)
Circuit Parameters
1000
500
0
0
1
2
Time (s)
3
x 10
28
-4
ANSYS Explicit Dynamics® Calculations
Three 0.4 m radius, 5 cm wide, 0.2 mm
thick Aluminum liners converging onto
a stationary test target.
T = 0 µs
T = 120 µs
T = 40 µs
T = 160 µs
T = 80 µs
T = 195 µs
First 3D structure compression of
metallic liner
No gross instabilities were observed
due to the structure rigidity of the
material
Forces are well beyond the plastic
deformation limit of the material,
resulting in a uniform compression
Low internal energy from the liner
compression which is different from
plasma or thick liner compression
Liner behavior agreed very well with 1D Liner Code
29
FRC Fusion at MSNW
of a High Temperature Plasma through Merging and Compression of
Supersonic Field Reversed Configuration Plasmoids
Fusion, 2011
Fusion with this technique is proven, this is not another fantasy
$5 M DOE-‐funded programs demonstrated high field compression
of FRC to fusion conditions
o
o
o
o
2.3 keV Deuterium Ions
>100 microsecond lifetimes of 1E22 plasma
>1E12 D-‐D neutrons created in this program
At only 1.2 Tesla!
FRC programs at similar size demonstrated >3 ms lifetime
30
Experimental
IDL Unity Gain Validation Experiment at MSNW
Picture of the FDR validation experiment
construction now underway.
CAD rendering of the Foil
Liner Compression (FLC)
test facility at MSNW
31
Experimental Results
400
s
40 cm radius, 6 cm wide, 0.4 mm thick Aluminum liners
400
s
0.6
420
s
410
s
¼ Power
Aluminum Liner
Testing for code
Validation
420
s
20 kV | 840 F |16 mil
440
s
450
s
460
s
470
s
460
s
470
s
0.3
0.2
0
0
440
s
450
s
0.4
0.1
430
s
10
Magnetic Field in Gap (T)
430
s
ANYSIS Max R
Exp. R(30349)
Exp. R(30331)
Exp. R(30351)
ANSYS Min R
1D Code R
0.5
Liner Radius (m)
410
s
1
2
3
Time (s)
4
5
6
x 10
-4
1D Code B
Exp. B(30351)
8
6
4
2
0
0
1
2
3
Time (s)
4
6
5
x 10
-4
32
Summary
Mission Architecture Goal
Mission Assumptions
90 Transit times to and from Mars
Single launch to Mars (130 MT IMLEO)
No pre-‐deployed assets
Payload mass
Spacecraft mass
63 MT Payload mass
Full propulsive MOI
Full propulsive EOI
Reusable spacecraft
63
15
MT
MT
IMLEO
130
MT
Earth Orbital Altitude
Mars park orbit
Total Mission Time
Stay Time
407
1
210
30
km
sol
days
days
Halfway through Phase 2 NIAC
Mission architecture
Spacecraft Design
Fusion Physics
Analytical
Computational
Experimental
Propulsion Requirements
Isp
Jet Power
Specific Power
Gain
5000
36
240
200
s
MW
W/kg
33
BACK-UP SLIDES
34
Estimated Total Equivalent Doses
Current technology
Mars sortie mission
(30 days stay)
(210 days)
NTP/NEP
(150 days)
Long stay at Mars
base (525 days)
Fusion Driven
Rocket
(30 days)
Solid bars
calculation for spacecraft with a minimum shield (5 g/cm2 Al)
Dashed bars
calculations for a thick shield (20 g/cm2 Al)
The career limit is 400 mSv for a 25 year old for a 3% risk of fatal cancer
There is still great uncertainty as to what the actual risk is for long term
low level exposure
35
Lindl-‐Widner Diagram with Magnetic Field
Confinement Of the Fusion Alphas
FDR
The BR form of the L-‐W diagram. Ignition curves for different product BR.
When the BR parameter exceeds the threshold value, the dT/dt > 0 region extends t
36
infinitely small R and ignition becomes possible at any R.
Anticipated Parameters from
FDR Validation Experiment
FRC adiabatic
scaling laws
In experiment, FRC
radial and axial
compressions would
occur simultaneously
Initial FRC size, temp
density and energy
FRC lifetime
>> dwell ~ 4 s
Final field
similar to
that achieved
in several
flux
compression
expts.
Sub MJ FRC
Requires only
33% bank eff.
Final FRC parameters yield a fusion gain G = 1.6 (ML=0.18 kg Al)
37
Material Constraints with Inductively
Accelerated Liners
The material properties relating to this resistive heating (electrical
conductivity, melting point, heat capacity, etc.) can be characterized by a
parameter gM
0
tm 2
I dt
gM A
2
I -‐ current flowing through the material cross-‐sectional area
A = w , where w is the liner
liner thickness.
The driving force is simply the magnetic pressure (B2/2µ0) applied over the
surface area of the metal facing the coil when in close proximity to the
driving coil.
The
reasonably approximated as B = µ0I/w.
One
4
vm(m/s) 2.5x10
vm(m/s) 1.6x104
Al
(mm) Aluminum 6061
Li
(mm) Lithium
38
ANSYS Maxwell® Calculations
of the 3D Electromagnetic Fields
B (T)
R
8
4
0
Solution for a 0.4 m radius coil driving a 6 cm wide, 0.2 mm thick Al liner.
The circuit was based on the capacitor bank currently available at the UW
Plasma Dynamics Laboratory.
The spatial forces on the liner at various times and radii are calculated and
used as input into the dynamic calculation similar to the one shown above.
Mutual interaction between coils and liners will also be investigated.
39
Theoretical Validation of Key
FDR Elements (peer reviewed papers)
Importance of 3D compression
Superiority of high
FRC target
Magnetic field limits thermal and
particle loss - even with (cold)
wall confinement and
>1
Ignition possible with magnetized
plasma where R <<1 but BR >
60 T-cm.
Magnetic field well within range
of larger FRCs.
Fusion Based on the Inductively-Driven Lithium Liner
Compression of an FRC Plasmoid
John Slough, David Kirtley, Anthony Pancotti, Christopher Pihl,
George Votroubek
(Submitted to Journal of Fusion Energy 2012)
Method for producing 3D liner
implosions with stand-off
Generation of FRC plasma target
with sufficient magnetization and
confinement for ignition
Method for efficient conversion of
plasma, radiation, and fusion
energy in a manner that protects
and magnetically isolates reactor
40
Theoretical Validation of Key
FDR Elements (peer reviewed papers)
Demonstrated inductively
driven liner compression
of Bz fields > 1 Mbar
Demonstrated the stable formation,
merging and magnetic compression of
the FRC
FRC lifetime better than previous scaling
Demonstrated successful FRC liner
compression with a xenon plasma liner
Hope to publish in the near future!
Experimental demonstration of fusion gain
with inductively driven metal liners
41
Magneto-‐Inertial Fusion
Best of Both Worlds
MFE
109
Plasma
P
Exceeds
Yield Str
ICF
electron t
hermal
conductio
n
ength
ICF
(ITER)
FDR)
(
(NIF)
Plasma Energy (J)
Stored Energy (J)
1012
Solid stars signify fusion gain conditions w Ti = Te = 10 keV
106
Tokamak
ITER89-‐P
103 20
10
FRC Scali
ng
1022
ITER MFE Issues:
Enormous magnetic energy requires
Cryogenic Magnets
Low power densities leads to large scale,
capital and development costs
Devastating transient instabilities defy
solution
1024
1026
1028
1030
Plasma Density (m-‐3)
NIF ICF Issues:
Enormous storage energy (~400 MJ) due to
very low driver efficiency
Even with stand-‐off , reactor wall and is
bombarded by primary fusion products
Intricate and minute target with sub-‐nsec
timing make for challenging technologies
42
1
1D Liner Code: Maxwell® Data
Data for actual coil and
collector plate used
In Foil Liner Compression
(FLC) Test bed
Total Inductance of coil with
liner at various locations. Liner
inductance was determined
theoretically
Coil Inductance (H)
3
x 10
-6
2
1
0
Description
Value
Circuit resistance
0.002
Magnet resistance
0.001
Circuit inductance
20e-‐9 H
Density of liner (Al)
2710 kg/m^
3
Width of liner
0.06 m
Radius of coil
0.41 m
Initial radius of liner
0.403325 m
Voltage
40,000 V
Capacitance
420 u F
Liner thickness
0.2 mm
r=0.41 m
w=6 cm
l=0.2 mm
Average Magnet field in the gap
between coil and liner divided
by the current in the coil for
various liner locations
Accurate definition of resistivity of
Aluminum based on NIST data.
Data only went to 2000 K. Data
was linear extrapolated out to
vaporization temperature
1.5
x 10
0.1
0.2
0.3
Liner Radius (m)
0.4
0.5
0.4
0.5
-5
B(I,R) =
1
Bavg
Ic
0.5
Resistivity (Ohms/m)
Physical Parameters
Magnetic Field as funciton of R and I
0
0
0
0.1
0.2
0.3
Liner Radius (m)
6
x 10
-7
Solid-‐liquid
transition
4
2
0
0
500
1000
1500
2000
Temperature (K)
2500
3000
43
1D Liner Code
Conservation of Energy
R = Rc +Rm +RKE +RT
Resistance of the coil
equivalent resistance
value to remove the
energy from the circuit
equal to the kinetic
energy gained by the
liner
Resistance of the circuit
3.5
x 10
5
equivalent
resistance value
need to remove
energy equal to
ohmic dissipation
(heating) of the liner
EKE
3
ETherm
Energy (J)
2.5
Energy recovery
All thermal losses
drive current
inner field current
Pressure balance of inner
and outer fields
Ecap
2
Ecoil
Eresist
1.5
Ecirc
1
Etotal
0.5
Einner field
0
Ecap
-0.5
0
1
Time (s)
2
x 10
-4
44
Research Plan
Technology Roadmap for the Fusion Driven Rocket
2015
180 W/kg
2020
2025
300 W/kg
600 W/kg
2030
1000 W/kg
Solar Power
1 kJ/kg
Energy Storage
2 kJ/kg
Gain of 200
Spaceflight
Charging
Rep Rate > 0.01 Hz
Shielding
Gain of 40
Thermal
RL= 1 m
EL= 3.5 MJ
Rep Rate > 0.1 Hz
Thruster with Nozzle
Li Liner
FRC Formation
Al Liner
Magnetics
Gain > 5
Propellant
Gain < 1
Chamber/Nozzle
RL= 0.4 m
EL= 0.5 kJ
ML = 0.18 kg
D-D Operation
Single Pulse
FDR ENGINE
(Complete System)
TRL
Phase I
Phase II
NIAC
$10 M/year
Game Changing
Technology Development
RL = 0.4 m
EL= 2 MJ
ML = 0.38 kg
D-T Operation
Rep Rate > 0.01 Hz
Milestones
ConceptValidationExperiments
SubscaleGroundDemonstration
Full-ScaleGroundPrototype
In-SpaceDemonstrationMission
MannedMarsMission
$50 M/year
Manned Mars Spaceflight Program
Technology
Demonstration
Mission
NASA Mars Flight Program
Analytical Model (Fusion Side)
From action
Integral constraint
where RL= 1.2 m,
w = 0.15m
Min. ML required to
trap fusion products:
0.28 kg
Energy loss in
ionization of liner (~75
MJ/kg)
Eout = fusion energy+ E in
EL = linerkineticenergy
Ein = EL + EFRC EL
ML = mass of liner
vL = velocity of Liner
C = EL /Ecap = 0.5
T
For known
Liner Mass
a
Specific Impulse
is determined
Drop off in Isp at low
gains is due to
ionization losses
= thrust efficiency = 0.9
Ek = kinetic (Jet)energy
Isp = specific impulse
Isp links fusion conditions with mission equations
46
Analytical Model
(Mission side)
Rocket Equations
e
MR
MR
7 Equations
7 Unknowns
V
Ispg0
Mi
Mf
Ms
Ein
ML f T
PSEP
cap
Ein
SEP
Mf
Mi
Finalmass
Initialmass
MP
Propellant mass
cap
MPL MS
MPL MS MP
MP
MassRatio
Ms Structural mass
f Frequency
Mf
Mi
MR
0.1MPL
SEP
PSEP
Specific mass of capacitors
Specific mass of solar panels
Solar panel power
Isp from fusion conditions
Delta V requirement as a function of
trip time: Solution to Lambert
Problem
PSEP
f
It is assumed that initially FDR employs solar panels for house keeping power
Eventually it would be derived directly from nozzle flux compression