1. PRIMARY PROPULSION FOR PILOTED
DEEP SPACE EXPLORATION
Michael R. LaPointe, Ph.D.
Horizon Technologies Development Group
Cleveland, OH 44135
Phone: (216) 476-1170
E-mail: HorizonTDG@aol.com
Presented at the NIAC Fellows Meeting
NIAC Headquarters, Atlanta, GA
November 9, 1999

2. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
PRIMARY PROPULSION FOR PILOTED
DEEP SPACE EXPLORATION
MOTIVATION
Characteristic Velocity Increments for
Planetary Transfer Missions*
Earth orbit to:
Mars orbit and return: 1.4´104 m/s
Venus orbit and return: 1.6´104 m/s
Jupiter orbit and return: 6.4´104 m/s
Saturn orbit and return: 1.1´105 m/s
Rocket Equation:
M
M
f = e - D V /
Ue
0
Increase delivered payload:
· Match propellant exhaust
velocity, Ue, to mission DV
· High Isp for planetary and deep
space exploration missions
· Variable Isp to optimize mission
profiles, reduce propellant mass
*Impulsive, minimum propellant semiellipse trajectories

3. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
CURRENT PROPULSION SYSTEMS
CHEMICAL:
ELECTRIC:
NUCLEAR:
· HIGH THRUST
· REQUIRED FOR LAUNCH SYSTEMS
· LOW EXHAUST VELOCITY (< 5000 m/s)
· INEFFICIENT FOR DEEP-SPACE (Ue << DV)
· LOW THRUST (mN – N)
· HIGH EXHAUST VELOCITY
- MPD: 5´104 m/s
- ION: 105 m/s
· EFFICIENT IN-SPACE PROPULSION
· LOW ACCELERATION, LONG TRIP TIMES
· HIGH THRUST
· MODERATE EXHAUST VELOCITY (<104 m/s)
· ENABLING FOR NEAR-TERM MISSIONS
· Ue << DV FOR DEEP SPACE MISSIONS

4. HORIZON TECHNOLOGIES
IDEAL DEEP-SPACE PROPULSION SYSTEM:
DEVELOPMENT GROUP
LONG LIFE, MODERATE THRUST, HIGH Isp
SYSTEM PROPERTY: REQUIREMENT:
HIGH Isp PLASMA PROPELLANT
(HIGH KINETIC TEMPERATURE)
MODEST THRUST 100 N – 1000 N
(REDUCED TRIP TIMES)
LONG LIFE ELECTRODELESS
(MITIGATE PLASMA EROSION)
CANDIDATE SYSTEM: COLLISIONAL THETA-PINCH

5. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
THETA-PINCH SYSTEM
· EVALUATED DURING EARLY
YEARS OF FUSION PROGRAM
· PULSED AXIAL MAGNETIC FIELD
COMPRESSES AND RADIALLY
CONFINES IONIZED PLASMA
· WITHOUT MIRRORS, PLASMA
ESCAPES ALONG AXIAL FIELD
LINES
PLASMAS AND CONTROLLED FUSION,
ROSE AND CLARK, 1961
MODIFY THETA-PINCH GEOMETRY TO PROVIDE
DIRECTED, HIGH ENERGY PLASMA EXHAUST

6. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
BASIC CONCEPT
· USE MAGNETIC MIRROR TO BLOCK UPSTREAM END OF
THETA PINCH (MIRROR RATIO > 5)
· PULSE INJECT NEUTRAL PROPELLANT GAS
· PREIONIZE OUTER SURFACE AREA OF GAS FILL
(PREIONIZATION PULSE IN DISCHARGE COIL)
· ADIABATICALLY COMPRESS AND HEAT PREIONIZED
PROPELLANT TO REQUIRED DENSITY, TEMPERATURE
· ALLOW DOWNSTREAM EXHAUST TO PRODUCE THRUST
· FIX REPETITION-RATE TO PRODUCE DESIRED THRUST

7. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
APPROACH
PHASE I:
· SIMPLE THEORY TO DETERMINE VIABILITY
· ANALYTIC MODEL TO ESTIMATE POTENTIAL
THRUSTER PERFORMANCE
PHASE II:
· 2-D CODE DEVELOPMENT FOR DETAILED
PHYSICAL MODELING
· EXPERIMENTAL EVALUATION

8. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
SIMPLE THEORY
· IDEAL EXHAUST VELOCITY RELATED TO TEMPERATURE:
Ue
RT
M
g
g
gI i SP =
-
=
2
1
h
( )
Ue = exhaust velocity hi = ideal cycle efficiency
T = propellant temperature g = adiabatic index
M = propellant molecular weight g = 9.8 m/s2
R = gas constant Isp = specific impulse (s)
HIGH TEMPERATURES, LOW MOLECULAR WEIGHTS

9. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
SPECIFIC IMPULSE vs. PLASMA TEMPERATURE
1 eV = 11605 K

10. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
SIMPLE THEORY
· PLASMA HEATED BY ADIABATIC COMPRESSION:
T
T
r
r
f
0
0 f
4
3
=
æ
è çç
ö
ø ÷÷
where:
T0 = initial plasma temperature r0 = initial plasma radius
Tf = final plasma temperature rf = final plasma radius
· NO IRREVERSIBLE SHOCK HEATING OF THE PLASMA

11. HORIZON TECHNOLOGIES
PLASMA COMPRESSION RATIO vs. SPECIFIC IMPULSE
DEVELOPMENT GROUP
Hydrogen
Propellant,
T0 = 0.1-eV

12. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
SIMPLE THEORY
· IDEAL GAS EQUATION OF STATE:
P = rRT = ånkT
where r = mass density, n = number density, k = Boltzmann’s constant
· ADIABATIC COMPRESSION LAW:
P
P
r
r
f
0
5
3
0
0 f f
10
3
=
æ
è çç
ö
ø ÷÷
=
æ
è çç
ö
ø ÷÷
r
r
provides compressed plasma pressure in terms of compression ratio

13. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
SIMPLE THEORY
· PLASMA PRESSURE BALANCED BY MAGNETIC FIELD:
P
B
2
= 0 = R T
0 2 m
r
· NEGLECT RADIAL DIFFUSION ACROSS MAGNETIC FIELD
· MIRROR RATIO RM ³ 5 AT UPSTREAM END OF CHAMBER
P
R
M
LOST R
M
= -
æ -
è ç
ö
1
ø ÷
1 £
10%
1
2
· PLASMA FREELY ESCAPES FROM OPEN END OF CHAMBER

14. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
SIMPLE THEORY
· TIME FOR PLASMA TO ESCAPE FROM CHAMBER LENGTH L:
t P
L
U
e
»
· MASS OF PLASMA LOST FROM SYSTEM IN TIME tP:
Dm = r ( pr 2 )
L 0 0
· IMPULSE-BIT PROVIDED BY PULSED PLASMA EXHAUST:
I N s m U BIT E ( - ) = D ´
· AVERAGE THRUST = IBIT ´ f (Hz) £ IBIT/tP

15. HORIZON TECHNOLOGIES
MAGNETIC FIELD STRENGTH vs. INITIAL NUMBER DENSITY
DEVELOPMENT GROUP
HYDROGEN PROPELLANT, Isp = 5000 s

16. HORIZON TECHNOLOGIES
THRUST (100% DUTY CYCLE) vs. INITIAL NUMBER DENSITY
DEVELOPMENT GROUP
HYDROGEN PROPELLANT, Isp = 5000 s

17. HORIZON TECHNOLOGIES
MAGNETIC FIELD STRENGTH vs. INITIAL NUMBER DENSITY
DEVELOPMENT GROUP
HYDROGEN PROPELLANT, Isp = 10,000 s

18. HORIZON TECHNOLOGIES
THRUST (100% DUTY CYCLE) vs. INITIAL NUMBER DENSITY
DEVELOPMENT GROUP
HYDROGEN PROPELLANT, Isp = 10,000 s

19. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
RESULTS FROM SIMPLE THEORY
· USEFUL THRUST OVER RANGE OF Isp
· REASONABLE MAGNETIC FIELD STRENGTHS
· REASONABLE PLASMA NUMBER DENSITIES, TEMPERATURES
· ELECTRODELESS DEVICE MITIGATES EROSION FOR LONG LIFE
THETA-PINCH PLASMA THRUSTER APPEARS VIABLE

20. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
ANALYTIC THETA-PINCH MODEL
· TIME DEPENDENT NUMERICAL SIMULATION
- Stover, Computer Simulation of Plasma Behavior in Open-Ended
Theta Linear Machines, Dept. of Energy DOE/ET/53018-6, 1981.
· INCORPORATES ADDITIONAL PLASMA PHYSICS
- Time Dependent Plasma End Loss
- Bremsstrahlung Radiation Losses
· COMPARE WITH EXPERIMENTAL THETA-PINCH DATA
- Scylla I-C Collisional Theta-Pinch
· EVALUATE THETA-PINCH THRUSTER PERFORMANCE

21. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
THETA-PINCH MODEL
DURING COMPRESSION:
N
P
kT
= 0
(p 2 )
r L 0
0
0
P t
P
2
r
r t
( )
0
( ) 0
10
3
=
æ
è ç
ö
ø ÷
T t
= 0
p 2
P t
kn t
( )
( )
( )
=
INITIAL PARTICLE NUMBER:
RADIAL PRESSURE BALANCE: P t
B t
( )
( )
= 0
0 2m
n t
N
r t L
( )
( )
ADIABATIC COMPRESSION:
PLASMA NUMBER DENSITY:
PLASMA TEMPERATURE:

22. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
THETA-PINCH MODEL
AFTER COMPRESSION:
¶
N
¶ t
t
N
c
= -
i L M
t c C
kT
=
æ
è ç
ö
ø ÷
2 2
1
2
¶
¶
e
2
¶
¶
¶
¶ t
E
t
N
t
P
A
t
E
th
= - - -
CHANGE IN PARTICLE NUMBER:
RADIAL PRESSURE BALANCE: P t
B t
( )
( )
= 0
0 2m
n t
N t
r t L
( )
( )
( )
=
p 2
PARTICLE CONFINEMENT TIME:
PLASMA NUMBER DENSITY:
PLASMA TEMPERATURE:
e = (5/2)T, E = internal ion energy, tth = thermal conduction time, A = plasma column area, c » 2.5

23. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
THETA-PINCH MODEL
COMPARISON WITH SCYLLA I-C EXPERIMENT*
CHAMBER RADIUS: 0.018 m
CHAMBER LENGTH: 1.0 m
INITIAL PRESSURE: 100 mTorr
INITIAL TEMPERATURE: 1-eV
EST. CONFINEMENT TIME: 14-ms
*McKenna, K. F. and York, T. M., “Plasma End Loss Studies in Scylla I-C”, Phys. Fluids, 20,
pp 1556-1570, 1979.

24. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
APPLIED MAGNETIC FIELD

25. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
NUMBER DENSITY PREDICTIONS

26. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
ION TEMPERATURE PREDICTIONS

27. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
USING SCYLLA I-C AS A THRUSTER…
NUMBER DENSITY
TEMPERATURE

28. HORIZON TECHNOLOGIES
… IS NOT A GOOD IDEA
DEVELOPMENT GROUP
EXHAUST VELOCITY
INTEGRATED IMPULSE-BIT
· EXHAUST VELOCITY IS HIGH, BUT
TOTAL PROPELLANT MASS IS TOO
LOW TO PROVIDE USEFUL THRUST

29. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
IMPROVE THRUSTER PERFORMANCE
· CHAMBER RADIUS: 1 m
· CHAMBER LENGTH: 10 m
· INITIAL PRESSURE: 1 Torr
· INITIAL TEMPERATURE: 1-eV
· USE SAME DRIVING FIELD AS SCYLLA I-C

30. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
TEMPERATURE
vs.
TIME
NUMBER
DENBSITY
vs.
TIME

31. HORIZON TECHNOLOGIES
· LARGER CHAMBER, HIGHER INITIAL PRESSURE INCREASES IMPULSE
· CAN TAILOR AXIAL MAGNETIC FIELD TO IMPROVE COMPRESSION
DEVELOPMENT GROUP
EXHAUST VELOCITY
IMPULSE-BIT

32. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
PROGRAM STATUS
· ANALYTIC MODEL PREDICTS THAT USEFUL THRUST, Isp CAN BE
OBTAINED FROM A THETA-PINCH THRUSTER
· DETAILED THRUSTER PHYSICS REQUIRES 2-D MODEL
DEVELOPMENT (UNDERWAY)
POTENTIAL ISSUES
· MHD INSTABILITIES MIGHT ARISE THAT LIMIT COMPRESSION
TIMES IN LONG THRUSTER CHAMBERS
· NEED TO ESTABLISH OPTIMUM DRIVING FIELD CONFIGURATION
FOR EFFICIENT THRUSTER OPERATION

33. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
PROGRAM PLANS
· DEVELOPMENT OF ROBUST 2-D NUMERICAL MODEL TO
BETTER SIMULATE THETA-PINCH THRUSTER PHYSICS
· USE CODE TO IDENTIFY OPTIMUM THRUSTER GEOMETRY
FOR DEEP SPACE MISSION APPLICATIONS
· USE DYNAMIC SIMILARITY TO DEFINE SMALL-SCALE
THETA-PINCH THRUSTER EXPERIMENT
· EXPERIMENTALLY EVALUATE SCALED THETA-PINCH
THRUSTER PERFORMANCE

34. HORIZON TECHNOLOGIES
DEVELOPMENT GROUP
ACKNOWLEDGEMENTS
SUPPORT FOR THIS PHASE I RESEARCH PROGRAM HAS BEEN PROVIDED BY THE
NASA INSTITUTE FOR ADVANCED CONCEPTS, DR. ROBERT CASSANOVA, DIRECTOR.