Propagating Magnetic Wave Accelerator (PMWAC) for Manned Deep Space Missions Propagating Magnetic Field Magnetized Plasma Toroid
(from 2D MHD calculation)
Helical Transmission Coil
Parameter System length Plasma mass mp : Final plasma velocity: Acceleration (Force): Thrust Power (0.2 kHz rep)
First Stage
Final
5m 0.2 mg D2 3x105 m/sec (Isp = 30,000 s) 2x1010 m/s (4 kN) 2 MW
25 m (same) 1x106 m/s (same) 20 MW
Propulsion Requirements for Deep Space Missions • High Specific Power - α=(kWthrust/kgspaceship) α > 1 kW/kg • High (and variable) exhaust velocities vex max vex ~ 104 km/s (Isp = vex/g ~ 106 s) • Continuous power with near zero maintenance for months
Trip Time and the Specific Power Requirement Accelerating a mass Mss over a time=τ=implies a power P where: M ss v c2 P≈ 2τ
One defines a characteristic velocity vc: v c = ( 2 α τ ) 1/ 2
where=α=is the specific power. The trip time=τtrip=to go a distance L is given roughly as: L τ trip ≈ 2 vc
τ trip ( months )
=
2 L (astronomic al units ) 2 / 3 α ( kW / kg )1 / 3
Rapid Manned Mars Mission Power Requirement 3.5
2
3 1
2.5 Isp
2 (104 s) 1.5
Sun
A.U. 0 Earth
1
1
y da y 30 sta
Mars
0.5
2
0 2
1
0
1
2
0
10
20
A.U. α ( kW / kg) = 8
[S (astronomical units)]2 τ( months)
3
30 40 50 60 time in days
≈ 1
for Mss ~ 20 MT, Pthrust = 20 MW
70
80
90
Velocity and Energy Requirements for Deep Space Missions (α α =1 kW/kg)
Destination
xtrip ~ 2 A.U. (Mars) xtrip ~ 10 A.U. (Jupiter)
Characteristic Velocity
vMars ~ 125 km/sec vJupiter ~ 250 km/sec
Specific Energy
εMars ~ 8x109 J/kg εJupiter ~ 3x1010 J/kg α=vchar2/2ttrip ε=vchar2/2 =α ttrip
ttrip ~ 3 months ttrip ~ 12 months
Propulsion System Exhaust (km/sec) Chemical Electric FRC at RPPL Thermal Fusion
5 30 250 2000
Fuel
Specific Energy
Chemical
1x10 J/kg
Fission
5x10 J/kg
Fusion
1x10 J/kg
7
13 15
Nuclear Power is Necessary for Deep Space Travel
Current and Planned “Breakeven” Fusion Experiments
ITER (MFE)
PHD
NIF (ICF)
Plasma Density and Energy Regimes for Different Fusion Concepts 1012
Plasma Energy (J)
Mag. Force > Material Strength 109
MFE
ICF electron thermal conduction
PHD MFE ICF
MTF 106 CT Classical 103 Tokamak ITER89-P 100 1020
1022
1024
1026
Density (m-3)
1028
1030
1032
High Voltage Energy Storage
Low Voltage Storage
V~ 120 kV
V~ 12 V
⇔
Shiva Star Facility for MTF ~ 10 MJ
2 Auto Batteries ~10 MJ
Pulsed High Density (PHD) Fusion Basics •Fusion reaction rate R: R = nDnT <σ DT v> At Tp = 10 keV, <σ DT v> ≅ 10-22 m3/sec
•For space-based fusion: G ~ 3 (thermal electrical) nτburn ~ 1x1020 m-3 sec
To maintain burn: τE ~ τburn •Lawson Criterion: ~ nτE ~ 1x1020 m-3 sec •Plasma pressure < Magnet Yield Limit (2x104 Atm): (Tp = 10 keV)
nfus = 1x1024 m-3
and
τE = 100 µsec
Field Reversed Configuration (FRC) Propulsion Closed Field Lines
Azimuthal Current
Separatrix Center Line Open External Field Lines External Field Coils
•Propellant (plasma) is magnetically insulated from thruster wall •No plasma detachment problem -plasma (FRC) contained separate a magnetic envelope •Plasma is thermally isolated from thruster walls -fully ionized plasma is vacuum isolated •Both thrust and Isp can be varied easily over a wide range -change of gas fill pressure is all that is required •Thrust and Isp are decoupled from plasma thermal energy -with vdir >> vth theoretical efficiency can approach unity •Enables a direct, simple method to achieve fusion propulsion with minimum investment
PHD Fusion Rocket Magnetic Expansion Nozzle
BURN CHAMBER (Rc ~ 13 mm)
Accelerator
Source 1m
5m
~ 20 m
Flowing Liquid Metal Heat Exchanger/ Breeder
From past FRC experiments: τE ~ τN = 1.3x10-12 xs rp2 n1/2 (xs = rp/Rc) with n = nfus, rp =1 cm (Rc = 1.3 cm) with lp/rp= 5 Ep= 50 kJ rep rate = 200 Hz 17 MW directed thrust power •FRC formed at low energy (~5 kJ) and relatively low density (~1021 m-3) •FRC accelerated and compressed by low energy propagating magnetic field (< 0.4 T). •FRC is decelerated, compressed, and heated as it enters high field burn chamber •FRC expands and cools converting thermal and magnetic energy into directed thrust
FRC Acceleration and Heating Expts. at UW
FRC terminal velocity: vd = 2.5x105 m/s Average FRC acceleration: (5 - 30 µsec)
Formation
Accelerator
Confinement
40 0
Radius (cm)
FRC mass: 0.4 mg Deuterium
Shot 238
aavg = 9x109 m/s2 0
FRC Energy (final)
4.0
Axial Position (m)
15 kJ
Thermal Conversion of FRC directed Energy
2.0
0.6
Tp
0.4 First pass of FRC
(keV) 0.2 0
0
FRC after reflection in downstream mirror 100 time (µsec)
200
FRC Acceleration Method Employed in UW Expts.
Bupstream Bdc Bdown 0
â&#x20AC;˘Upper plot of flux contours taken from numerical calculations for discharge 1647 during the acceleration of an FRC at UW. â&#x20AC;˘Bottom plot illustrates phasing of the accelerator coils Each coil in turn is switched on for one complete cycle. Phase of each coil at time of calculation is indicated by arrow
Propagating Magnetic Wave Accelerator Power Supply
For transmission line: v 2p
=
1 LC
=
Z2
L C
Switch L CP
C
For shell capacitor (per unit length): 2 π R c ε0 κ εS
C =
Inner helical conductor
V
Inductance (per unit length): L = µ0 π R c2 n 2
Dielectric Shell
Outer conductor
From these eqs. Solving for Rc =
Rc
2 V κ εS c2 B2
and finally for the phase velocity: vP
1/ 2 é ù 2 V c = ê 2π n ê R3 κ ε ë c S
BaTiO3 1 cm
εS = V/m κ = 2500*ε0 V = ± 25 kV 5x106
vP
1.35x105 = m/s 1.5 Rc n
vP = 106 m/s B = 0.5 T for Rc = 5.5 cm n = 10 turns/m
PMWAC SPICE Calculation for Constant Z 1 1
1
17
CS 1u
17
VSource 24
25 25
L1 64n
24
LS 200n 24
R1 .0001
L2 64n 2
L3 64n 3
C1 100n 9
5
C2 100n
C3 100n
13
R2 .0001
RG 10K
L5 64n
L4 64n 4
14
R3 .0001
C4 100n 15
R4 .0001
L6 64n 7
C5 100n
8
C6 100n
18
R5 .0001
L8 64n
L7 64n
6
19
R6 .0001
L9 64n 21
C7 100n
10 10
10
C9 100n
12
R8 .0001
IL10
22
C8 100n
20
R7 .0001
L10 64n
C10 100n
23
11
R9 .0001
R10 .0001
K79 L7
K710 L7
K89 L8
K810 L8
ILoad
11 11
10
10
RLoad 1 11
∆
∆
16
1
10
IL6
IL1
X4 sw
6
V6
VLoad
11
IR1
V0 K12 L1
K13 L1
K14 L1
K45 L4
K23 L2
K24 L2
K25 L2
K34 L3
K35 L3
K46 L4
K47 L4
K56 L5
K57 L5
K58 L5
K67 L6
K68 L6
K36 L3
1
6
K910 L9
K69 L6
Dissipative load (plasma)
Vacuum load 40
K78 L7
1
10
6
10
30
I 20 (kA) 10 6 1 2 5 4 3
0 -10 -1
3
0
1
2
Time (µsec)
3
4
-1
0
1
2
Time (µsec)
3
4
Resistive 2D MHD Calculation of FRC with Propagating Magnetic Field (0.4 T) Vaccel = 30 kV,
Time (µsec)
MFRC =
5
6.0 4.0
vFRC (105 m/s)
10
2.0
0 1.2
Ti
15
Te
0.8 T (keV) 0.4
17.5
0 0
5
10
Time (µsec)
15
20
0.2
R (m)
0
20
0.2
6
5
4
3
Z (m)
2
1
0
PMWAC Can Also Be Employed to Provide High Isp, High Thrust Electrical propulsion Time (µsec) 5
V = ± 3.5 kV ⇔ Bacc = 0.2 T 4.0
10
MFRC = 0.2 mg 3.0
a = 1.2x109 g
vFRC
15
2.0
(105
m/s) 20
1.0 0
0.2
0
5
10
15
T (µsec)
20
25
30
R (m)
25
0 0.2
6 0
5
4
3
Z (m)
2
1
30
Inductive Magnetized Plasma Accelerator Source Developed with NASA STTR funding at MSNW Capacitor Gas feed
SS Switch
Magnetic field
Magnetized plasma
Strip-line feedplates
Coil straps
PMWAC Development Program Phase 1: •Determine Accelerator Requirements and Parameters •Design Proto-Accelerator for Electrical Validation •Construct Accelerator and Measure Electrical Performance •Develop Full Electrical Model with Plasma Interaction
Phase II: •Design and Construct Full-scale Accelerator •Install Accelerator and Demonstrate FRC Acceleration to Fusion Velocities (~106 m/s).