Propagating Magnetic Wave Accelerator (PMWAC)for Manned Deep Space Missions

Helical Transmission Coil

Propagating Magnetic Field(from 2D MHD calculation)Magnetized Plasma Toroid

Parameter First Stage FinalSystem length 5 m 25 mPlasma mass mp : 0.2 mg D2 (same)Final plasma velocity: 3x105 m/sec (Isp = 30,000 s) 1x106 m/sAcceleration (Force): 2x1010 m/s (4 kN) (same)Thrust Power (0.2 kHz rep) 2 MW 20 MW

Propulsion Requirements for Deep SpaceMissions

• 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 formonths

Trip Time and the Specific PowerRequirement

Accelerating a mass Mss over a time=τ=implies a power P where:

One defines a characteristic velocity vc:

where=α=is the specific power.

The trip time=τtrip=to go a distance L is given roughly as:

τ≈

2

2cvssM

P

vc = ( ) /2 1 2α τ

3/1

3/2trip

ctrip

)kg/kW(

)unitsalastronomic(L2)months(vL2

α=τ≈τ

30 day

stayMars

Sun

Earth

2 1 0 1 2

2

1

0

1

2

A.U.

A.U. 0 10 20 30 40 50 60 70 80 90

3.5

3

2.5

2

1.5

1

0.5

0time in days

Isp

(104 s)

[ ] 1)months(

2)unitsalastronomic(S8)kg/kW( 3 ≈τ

=α

for Mss ~ 20 MT, Pthrust = 20 MW

Rapid Manned Mars Mission Power Requirement

Velocity and Energy Requirements for DeepSpace Missions

(αααα =1 kW/kg)Destination xtrip ~ 2 A.U. (Mars) ttrip ~ 3 months

xtrip ~ 10 A.U. (Jupiter) ttrip ~ 12 months

Characteristic vMars ~ 125 km/secVelocity vJupiter ~ 250 km/sec

Specific εMars ~ 8x109 J/kgEnergy εJupiter ~ 3x1010 J/kg

Nuclear Power is Necessary for Deep Space Travel

Propulsion System Exhaust (km/sec)Chemical 5Electric 30

FRC at RPPL 250Thermal Fusion 2000

Fuel Specific EnergyChemical 1x107 J/kgFission 5x1013 J/kgFusion 1x1015 J/kg

α=vchar2/2ttrip

ε=vchar2/2 =α ttrip

Current and Planned “Breakeven” Fusion Experiments

ITER (MFE) PHD NIF (ICF)

ICFelectron thermal conduction

ICFMTF

MFEPHDMFE

CT Classical

TokamakITER89-P

Mag. Force > Material Strength

1020 1022 1024 1026 1028 1030 1032

Density (m-3)

1012

109

106

103

100

Plas

ma

Ene

rgy

(J)

Plasma Density and Energy Regimesfor Different Fusion Concepts

⇔

Shiva Star Facility for MTF~ 10 MJ

2 Auto Batteries~10 MJ

High Voltage Energy StorageV~ 120 kV

Low Voltage StorageV~ 12 V

•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

Pulsed High Density (PHD) Fusion Basics

Field Reversed Configuration (FRC) Propulsion

External Field Coils

Center Line

Azimuthal Current

Open External Field Lines

SeparatrixClosed Field Lines

•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

Flowing Liquid Metal Heat Exchanger/ Breeder

~ 20 m

BURN CHAMBER (Rc ~ 13 mm)

5 m

1 m

Magnetic Expansion Nozzle

Accelerator Source

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

PHD Fusion Rocket

•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

Axial Position (m) 0 2.0 4.0

Shot 238

Rad

ius

(cm

)

400

Formation Accelerator ConfinementFRC mass:0.4 mg Deuterium

FRC terminal velocity:vd = 2.5x105 m/s

Average FRC acceleration:(5 - 30 µsec)

aavg = 9x109 m/s2

FRC Energy (final)

15 kJ

FRC Acceleration and Heating Expts. at UW

Thermal Conversion of FRC directed Energy

0 100 200

0.6

0.4

0.2

0

Tp

(keV)

time (µsec)

First passof FRC FRC after reflection

in downstream mirror

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 coilsEach coil in turn is switched on for one complete cycle.Phase of each coil at time of calculation is indicated by arrow

FRC Acceleration Method Employed in UW Expts.

For transmission line:

For shell capacitor (per unit length):

Inductance (per unit length):

From these eqs. Solving for Rc

and finally for the phase velocity:

CP

Power Supply Switch

C

L

Dielectric ShellOuter conductor

Inner helical conductor

CLZ

CL12

pv 2 ==

VS0cR2

Cεκεπ

=

2n2cR0L πµ=

2B2cSV2

cRεκ

=

n2c

2/1

S3cR

V2Pv

π

�

��

�

�

εκ=

s/mnR

10x35.1v 5.1c

5

P =

εS = 5x106 V/mκ = 2500*ε0V = ± 25 kV

BaTiO3

1 cm

vP = 106 m/s B = 0.5 T for Rc = 5.5 cm n = 10 turns/m

Propagating Magnetic Wave Accelerator

213456

16

V0

1

17

16

X4sw

IL1

17

17

∆

10

11

VLoad

24

RG10K

1 2L164n

2

9

C1100n

2 3

L264n

3

13

C2100n

3 4

L364n

4

14

C3100n

4 5

L464n

5

15

C4100n

5 6

L564n

6

18

C5100n

6 7

L664n

7

19

C6100n

7 8

L764n

8

20

C7100n

8 21

L864n

21

129 13

R2.0001

13 14

R3.0001

14 15

R4.0001

15 18

R5.0001

18 19

R6.0001

19 20

R7.0001

20 12

R8.0001

10

11

RLoad1

1111

1010

2517

CS1u

1010

1111

1 1

∆

1

25

VSource

1 1

25

25

6

V6IL10

21 22

L964n

22

23

C9100n

12 23

R9.0001

R1.0001

24 9

22 10

L1064n

10

11

C10100n

1123R10.0001

C8100n

10 101010

11 111111

ILoad

25 24

LS200n

24

2424 24

IR1

K12L1

K13L1

K14L1

K23L2

K24L2

K25L2

K34L3

K35L3

K36L3

K45L4

K46L4

K47L4

K56L5

K57L5

K58L5

K67L6

K68L6

K69L6

K78L7

K79L7

K710L7

K89L8

K810L8

K910L9

IL6

3

30

20

10

0

-10-1 0 1 2 3 4 -1 0 1 2 3 4

Vacuum load Dissipative load (plasma)

1 6 10 1 6 10

1 6 10

40

I(kA)

Time (µsec) Time (µsec)

PMWAC SPICE Calculation for Constant Z

R(m)

0.2

0

0.2

Z (m)6 5 4 3 2 1 0

Time(µsec)

5

10

15

17.5

20

Resistive 2D MHD Calculation of FRC withPropagating Magnetic Field (0.4 T)

6.0

4.0

2.0

0

vFRC

(105 m/s)

0 5 10 15 20

Time (µsec)

T(keV)

1.2

0.8

0.4

0

Ti

Te

Vaccel = 30 kV, MFRC =

Time(µsec)

5

10

15

20

25

30

R(m)

Z(m)

0.2

0

0.26 5 4 3 2 10

0 5 10 15 20 25 30

vFRC

(105 m/s)

4.0

3.0

2.0

1.0

0

MFRC = 0.2 mg

T (µsec)

a = 1.2x109 g

V = ± 3.5 kV ⇔ Bacc = 0.2 T

PMWAC Can Also Be Employed to Provide High Isp, High Thrust Electrical propulsion

Gas feed

Capacitor

SS Switch Coil straps

Strip-linefeedplates

Magnetic field

Magnetized plasma

Inductive Magnetized Plasma Accelerator SourceDeveloped with NASA STTR funding at MSNW

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).