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

•Upper plot of flux contours taken from numerical calculations for discharge 1647 during the acceleration of an FRC at UW. •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).