Overview of FRC Propulsion and Materials Research

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Transcript Overview of FRC Propulsion and Materials Research

Overview of FRC Propulsion
and Materials Research
David Kirtley and George Votroubek
MSNW LLC, Redmond, WA 98052, USA
John Slough, Samuel Andreason, and Chris Pihl
Plasma Dynamics Laboratory, University of Washington
Aydin Tankut and Fumio Ohichi
Materials Science Department, University of Washington
Richard Milroy, Brian Nelson and Eric Meier
Plasma Science and Innovation Center, University of Washington
Alan Hoffman, Kenneth Miller and Daniel Lotz
Redmond Plasma Physics Laboratory, University of Washington
AFOSR Propulsion Materials Workshop
November 4, 2010
Discussion Index
1. Basic of FRC Physics
2. Summary of Propulsion Activities
3. Summary of Related DOE Activities
4. Related Materials Interests
5. Current Materials Research Program
6. Needs and Discussion
Physics of Pulsed Plasmoid
Propulsion - The FRC
R – null radius
rs – separatrix radius
rc – coil radius
xs – rs/rc
EXTERNAL
FIELD
FRC CLOSED
POLOIDAL FIELD
2
Bext
P0  n 0 kT 
2 0
Equilibrium
Relations:
rs
 
0
Radial Pressure Balance
20 P
1 2
dr

1

x s Axial Pressure Balance
2
B
2
Bext 
B vac
1  x s2


Flux conservation
Rotating Magnetic Field Formation
Synchronous electron motion
 j(r) = e ne  r
–
–
–
–
Decreases circuit requirements (100 % solid state)
Decreases radiation losses (operation on heavy gases)
Increases plasma currents and acceleration force
Minimizes wall interaction
m=1, “saddle” coils positioned
radially external to axial field
coils. Two oscillators phased at
90 produce constant amplitude
B.
The Generic RMF-Based Thruster
RMF Antenna
Trim Coil
3
J
1
2
ELF
Steady Bias
Field Coils
RMF generated plasma
current from
synchronous electrons
Fz  j  Br
Steady magnetic
field in conical
geometry
(1) Rotating Magnetic Fields (RMF) form high-density, FRC plasmoid
(2) FRC grows and accelerates driven by RMF generated currents & steady field
(3) FRC expands as ejected, converting any thermal to directed energy
Electrodeless Lorentz Force (ELF) Thruster
RMF Generation of the Field Reversed Configuration (FRC) *
Advantages
•
•
•
•
•
•
Vast Operating Range- 10-100 kW, 1000-6000 s Isp in a single thruster
Technology Scalable- 0.1-1000’s of kWs, 1018-1020 operating densities
Low Mass Thruster and PPU- 1-2 kW/kg including PPU
Efficient Ionization- Rapid, high-temperature , and magnetically isolated
COTS Electronics- Low voltage, solid-state switching
Long Life and Any Propellant- Electrodeless and magnetically isolated
Status
 Basic operation and performance demonstrated
with earlier ELF program
 Current program aims to develop from 6.1 to 6.2
and prove a steady state thruster
 Initial design and advanced antenna geometry
demonstrated
 Neutral entrainment chamber constructed and
passive operation underway
 Modeling effort contracting is underway
*Started October 2010
Fundamental Science
Neutral Entrainment *
ISSUE: Plasma formation is the primary loss mechanism for ALL
electrostatic or electromagnetic propulsion systems. It prevents
operation at lower specific impulse, lowers efficiency at all exit velocities,
and requires high mass propellants.
Solution: Entrain neutrals in an acceleration field after formation.
Benefit: Dramatic Increases in T/P across all
specific impulses and propellants, including Air.
Thrust
Isp
Dynamic formation and acceleration of an FRC, shown with 4 field coils
*Started October 2010
ElectroMagnetic Plasmoid Thruster (EMPT)*
A 1 kW-scale FRC thruster for deep space missions
EMPT Thruster:
• 200-2000 Watt FRC thruster (3”diameter, 4” long, 0.2-2 Joule)
• Very long lifetime, throttle-able power, deep space propulsion
• Dramatically lower mass than existing EP
ELF
• In-situ operation on ambient propellants
First Demonstration of FRC formation at <1 Joule
• Plasmoid Achieved 1000-6000s Isp in Xenon, Hydrazine (simulant)
• Revolutionary step in both scale and performance
• First demonstration of steady state operation (50 plasmoids at 2 kHz)
• Demonstrated technology scaling and circuit efficiencies (10 nH stray )
*Phase II awarded November 2010
High Energy FRC Programs
•Plasma Liner Compression (PLC)
• High energy magnetic compression
• Xenon plasma ions at > 2 keV at end regions
• Pulsed High Density (PHD)
• FRC formation and collision, >10 MW plasma
• > 10 GW/m2 transient energy loading
•Foil Liner Compression (FLC)
• Metallic liner implosion
• Intense transient neutron and UV radiation pulse
•Translation Compression and Sustainment (TCSU)
• Steady State RMF-Formed FRCs at 10 MW energies
• Low density, requires low recycle/impurity rates
500 Joule Xenon RMF FRC - PLC
High speed photography of Foil
Liner Compression
1m diameter colliding FRC- PHD
RMF Translation, Compression, and
Sustainment, Experiment (TCS)
RMF
Antennas
TCS Chamber
LSX/mod
(confinement & RMF drive)
(formation & acceleration)
Study Formation & Sustainment of RMF driven FRCs.
Either form FRCs directly using RMF alone, or translate and
expand theta-pinch formed FRCs from LSX/mod.
FRC/RMF Materials Issues
Fundamentally Non-Equilibrium
Transient loading
•
•
•
•
Pulsed devices have transient wall loading of optical radiation, electric fields, and perhaps
some ions.
What are the equilibrium temperature and sputtering effects of pulsed wall loading?
Sputtering rates are non-linear, how is this affected?
Gas deposition and recycling are key to fusion plasmas.
Wall chemistry for reactive gases
•
•
FRC thrusters and fusion devices operate on chemically reactive gases.
What effects do high-temperature ion-wall interactions (even if they are very reduced)
create if the ions are Oxygen, Nitrogen, or Hydrogen? In fusion plasmas the chemical
sputtering rate can be more important than the purely kinetic energy sputtering rates.
Effects of magnetized plasma
•
•
FRC thrusters run with magnetically confined ions. This means pulsed, large magnetic
fields (300-3000 Gauss), large gyroradii (possibly greater than the device), and very large
electric fields at the wall (measured up to kV).
How does pulsed magnetic fields this change the wall interaction and lifetime picture?
Optical and Nuclear Radiation
•
•
A pulsed, high-temperature device will deliver pulsed optical radiation to the wall. This
has effects for both contamination as well as the sputtering.
What are the effects of pulsed optical radiation on a thruster wall, both in terms of thermal
loading and interaction with a neutral gas at the wall boundary.
FRC Propulsion Specific Interests
Magnetic Isolation dramatically limits plasma-wall interaction –
To what degree?
RMF – FRC Propulsion Materials Interests
1. Very long lifetimes must be demonstrated
• ELF, EMPT development programs
• Erosion of insulator. How small? Is an insulator needed?
2. RF coupling to high-temperature insulators (dissipation)
• Quartz is great, but low thermal conductivity
• BN, AlO, SiN FRC wall materials are unknown
3. Transient thermal and electromagnetic radiation loading is new for propulsion,
must be studied
Quartz Insulator
4. Fundamentally non-equilibrium
Backplate
FRC Thruster Elements
1. Wall : Quartz, SiN, Other Insulators
2. Magnet: Aluminum Flux Conservers
3. RMF: Copper Antenna
Aluminum Flux Conservers
Reflectors, and Heatsinks
Current DOE Plasma-Wall Research 1
1.
2.
3.
4.
5.
First Wall Material Coatings and Preparation
Materials Concerns
•
Ta, SiO2, coating for surface gas loading
1. Impurities from Wall Materials
Steel and Quartz Chemistry during reversals
2. Impurities from Gaseous Wall Loading
•
Siliconization, atomic oxygen loading
3. Chemical and Kinetic Sputtering
Ti-Gettering
4. Gas Implantation – Recycling, Embrittlement
Diagnostics (SAS)
5. Neutron Activation, Embrittlement
•
Cylindrical Mirror Analyzer (CMA)
•
Energy Dispersive X-Ray Spectroscopy (XPS)
•
Plasma Chemical Vapor Deposition (PCVD, RGA)
•
Aurger Electron Spectroscopy (AES)
•
Vacuum materials handling capabilities
Diagnostics (TCS and UW)
•
He-GDC
•
Scanning Electron Microscopy (SEM)
•
Multi-point Thompson Scattering (MTS)
•
In-situ Optical First Wall Diagnostic
•
Scrape-off layer Langmuir
Current DOE Research Program 2
•
UW Experimental Efforts
• Wall Materials Selection
• First Wall Processing
• High Energy Diverter Studies
• Neutron Studies, DPA limits
•
PSI-Center Modeling Efforts
• NIMROD FRC modeling of scrape-off and wall
layer
• NIMROD modeling of diverter flow
• First wall interaction *
•
•
•
•
•
A. Tankut, G. Vlases, K.E. Miller, et al. “Wall conditioning in TCSU and its effect on plasma performance”, Journal of Fusion Materials, 2010
A. Tankut, K.E. Miller, et al. “An XPS study on the evolution of type 304 stainless steel surface during routine TCSU operation”, JFM, 2010
Aydin Tankut “Surface Analysis Studies in the Translation, Confinement, and Sustainment Upgrade (TCSU) Experiment”, Doctoral Thesis, 2009
A. Tankut, F. S. Ohuchi . “Surface Analysis Studies of TCS-U Components”, Innovative Confinement Concepts Meeting, 2008
A. Tankut, F.S. Ohuchi.” Surface Analysis Studies on the Wall Conditioning of TCSU”, APS 2008
Needs and Discussion
Fundamental Science Question: What are the average temperature and
sputtering effects of, non-equilibrium, chemically-reactive, transient
plasma-wall interaction in a highly magnetized plasma?
1. Experimental effort to demonstrate FRC lifetimes and identify erosion concerns
2. Empirical quantification of erosion, deposition, chemistry in pulsed, magnetically
confined plasmas
3. Modeling effort to determine transient plasma radiation and thermal transport
4. Modeling effort to assess optimal geometries and materials
Proposed Effort Extension
•
Leverage University of Washington DOE programs for propulsion efforts
• UW MSE, RPPL experience, diagnostics, and hardware
• UW Personnel*
• PSI-Center Modeling
1.
2.
3.
Add interface to the Neutral Entrainment experiment to utilize existing SAS Hardware
MSE post doc runs investigation (Dr. Tankut), supervised by Shumlak, Nelson
MSE diagnostic package
1. Erosion
2. Deposition
3. Surface Chemistry
4. Materials Selection
PSI-Center Boundary Condition and Geometry Group modeling effort
1. NIMROD runs for ELF
2. Implement UEDGE Tokamak code
4.
Questions to Answer
1. What and where is the erosion on a steady state ELF thruster
2. What is the erosion, deposition, and chemical interaction for NE and reactive propellants
3. What are the steady state temperature and erosion rates of non-equilibrium,
chemically-reactive pulsed plasma-wall interaction in a highly magnetized plasma?
TCSU Surface Analysis System
Equipped With:
- Analysis Chamber: X-Ray Photoelectron
Spectroscopy (XPS), Auger Electron
Spectroscopy (AES)
- Glow Discharge Test Chamber: Taelectrode, Residual Gas Analyzer (RGA)
- Sample Transfer Device
RGA
Glow Discharge Test
Chamber
Pbase: high 10-8 - low 107 Torrs
Glow Gas
Inlets
Ta
electrode
Additional (Campus) Facility
Scanning Electron Microscopy (SEM)
+
Energy Dispersive X-ray
Spectroscopy (EDS)
Sample
Transfer
Device
Pbase: low 10-8 Torrs
Electron
Energy
X-ray Analyzer
Source
Ion
Pump
Turbomolecula
r
Pump
Transportable
P-supply
Analysis
Chamber
Pbase: low 10-9
Torrs
Impurity problem in TCS
Radiated Power vs. Total Input Power
Significant fraction of the
input power was radiated
Impurities prevented the study
of FRC physics in TCS
After He-GDC
After Standard
Cleaning
GDC
After Up to
atmospheric N2
After Plasma
Summary of Plasma
the evolution of SS in TCSU
Up to N2 atm.
He+
N2 O2
H+
e
H2Oe
-
-
CxHy, H2O
Fe-O , Cr-O
O
O H
Fe0, Cr0,
Ni0
Bulk: Fe0,
Cr0, Ni0
Fe0, Cr0,
Ni0
Fe
Fe
Fe
Fe
O
C
Fe0, Cr0,
Ni0
O
O
O
C
0
0
500
800 600 400 200 0
Fe2p3
0
710
700
720
715
710
705
700
500
0
0
Fe2p3
0
0
720
500
Fe2p3
Fe2p3
0
0
0
0
720
715
710
705
700
720
715
710
705
700
A. Preliminary Ti-gettering tests:
- Basic understanding of processing parameters; SEM/EDS system was used.
- Morphology was similar for Ti-film deposited on SS and quartz.
- Increasing the substrate temperature from RT to 100oC did not result in an observable change in
morphology or deposition rate.
- Reducing the filament current b y ~15% reduced the deposition rate significantly.
ON SS
ON Quartz
High temp
(100oC)
Ti
O
Low current (~15%
lower)
C
Fe O
O
C
Ti/SS
T: RT, I: 16.5A, D: 60
min.
Ti
CO
Si
Ni
C
Ti/SiO2
T: RT, I: 16.5A, D: 60
min.
Ti/SS
T: 100oC, I: 16.5A, D: 60
min.
Ti/SiO2
T: RT, I: 14.2A, D: 60 min.
Surface analysis: Ti-gettering in TCSU (Phase I):
e-
Reduction of Fe by Ti on Ti-coated sample surface
hν
e-
Pre Ti-gettering
+16 Plasma shots
1st Ti-gettering
54% Fe0
38% Fe0
30% Fe0
710
Binding Energy (eV)
Fe-O was reduced by
Ti:
-∆GoTiO2 > -∆GoFe2O3
700
720
720
700
710
Binding Energy (eV)
24%
Fe2O3 + 3/2Ti =
3/2TiO2
0 2Fe +500
1000
∆G (kcal)
-400
-600
-800
Ti0
20%
469
H+
Ti0
0
Temperature (K)
700
H+
-200
-1000
710
Binding Energy (eV)
Intensity (au)
Intensity (au)
0
Intensity (au)
0
0
Plasma shots lead to oxidation of Ti
and reduction of Fe:
- Volatiles from SS were trapped in Ti
0
459
449 469 Binding 459
Binding
Energy (eV)
Energy (eV)
H2O
Ti film
H+
Intensity (au)
720
Intensity (au)
XPS on Ti-coated surface (SS1)
H2O
Fe-O , Cr-O
0
449
Bulk: Fe0, Cr0,
0
Bulk:
Fe0, Cr0, Ni0
Ni
3. Ti-gettering - Summary
- Preliminary Tests: Deposition rate can be controlled by filament current
- Ti-gettering in TCSU:
1st Ti-gettering: Improved vacuum, pumping H-species, reduced
Fe-O
Plasma shots: Inhibited release of H2O
- Plasma Performance:
Drastic reduction in impurity radiation (Ti on N and S bellows)
Drastic reduction in H-recycling
FRC Generation Employing a
Rotating Magnetic Field (RMF)
RMF in R- plane generated by two sets of axial conductors
(Helmholtz-like pair) placed orthogonal to each other.
Oscillating currents, phased 90 apart creates a rotating field of
constant magnitude
RF Antenna Configuration for RMF
FRC (ce >> ei) {Helicon (ce < ei)}
Field Reversed
Configuration (FRC)
Rotating Magnetic
Field B
I0sin(t)
rs rw
Separatrix
L ~ 5rs
Synchronous electron motion
 j(r) = e ne  r
3B
Ba
Ba
rw
rw
t=0
--3B
Ba
t>0
I0cos(t)
m=1, “saddle” antenna coils are positioned
radially external to the axial field coils. Two
oscillators phased at 90 produce a constant
amplitude rotating field B.
Initial axial magnetic field Ba is
reversed by synchronous J current
driven by RMF
2.
3.
4.
5.
6.
4
2
Coil Voltage [Volts]
1.
Steady State Operation
RF-capacitor circuit is charged through pulsed-charging or steady DC
current
Bias fields are steady or fed through similar pulsed-inductive network
Gas flow is steady or synchronously chopped for high-throttled flow, no
puff
RMF discharge is timed to power flow and neutral density distribution
Thermal/Ionization energy is added to plasmoid through current drive
(Ohmic)
Kinetic energy is transferred to plasmoid through inductive transfer
(reactive)
x 10
Vacuum
Nitrogen
1.5
1
0.5
0
0
0.05
0.1
Time [ms]
0.15
0.2
(a) Instantaneous RMF coil voltage with floating, resonant ring-up in Nitrogen. (b) Instantaneous coil current for a pulsed-discharge in Xenon.
Downstream FRC Characteristics
18
10
x 10
0.12
Ion Saturation Current [A]
Electron Density [m-3]
10 cm
90 cm
8
6
4
2
0
0
0.05
0.1
Time [ms]
0.15
0.2
Downstream plasma density on centerline for a 2700 s Isp, 32 Joule Xenon
discharge.
10 cm
50 cm
0.1
0.08
0.06
0.04
0.02
0
0
0.1
0.2
0.3
0.4
0.5
Time [ms]
Downstream ion saturation current on a double Langmuir probe for a
low velocity 38 Joule xenon FRC. Shown are the fast-moving, leading
edge jet and the slower, bulk FRC.
General Scaling Laws
• Increasing neutral fill leads to
larger, slower plasmoids
• Decreasing neutral fill leads to
hotter, faster plasmoids
• Below 1E19 m-3 current drive suffers
Increasing ← Neutral Fill → Decreasing
•
•
and both thrust and velocity decrease
5-10 Joule FRCs yield 20-30 km/s
25-50 Joule FRCs yield 30-50 km/s
.A typical plot of Impulse and plasmoid velocity versus puff timing for a resonant
amplifier-driven ELF. 60 psig nitrogen discharge.
Increasing ← Neutral Fill → Decreasing
Density and velocity for a high-power, 15-35 Joule Pulsed Discharge
FRC at various fill pressures. Xenon, 10 psi.
Increasing ← Neutral Fill → Decreasing
Thrust impulse and velocity for a low-power,5-10 Joule Pulsed Discharge FRC.
Nitrogen, 50 psig.
Task 1: ELF Thruster
Program Plan
Technology
Development
Year 1 - Initial thruster design
Develop a thruster prototype that can demonstrate several pulse operation in a
representative testing environment.
•
•
•
•
•
•
•
Full thruster design using existing hardware and infrastructure
• Operate in a pseudo-steady state mode with extended operation
Investigate chamber effects
Validate performance goals and identify thruster design issues
Multiple Discharge, single gas puff Testing
Investigate chamber effects
Initial testing at AFRL to validate MSNW LLC results
High-Q power processing and circuit design
Year 2 - Demonstration thruster and electronics package
Develop a nose-to-tail thruster and electronics package for wide testing
•
•
•
•
Implement upgrades from Year 1 into a complete thruster package
Complete in-situ performance validation effort
Full thruster testing at AFRL
Validation testing at MSNW, UM
Key Results to Date
First Demonstration of Non-Inductive Formation, Acceleration, and
Ejection of FRC Plasmoids
• Plasmoid Achieved 1000-6000s Isp in Air, Xenon, Monopropellant
Isp Measurement- Langmuir, B-probes track FRC acceleration, ejection
• Produced > 1 mN-s /pulse (Air propellant)
Direct Thrust Measurement- via ballistic impulse pendulum developed at MSNW,
calibrated at NASA GRC
• Average Power 50 kW, 5-50 J discharges
Nitrogen and Air Results
• Initial testing of multiple FRC discharges
• No noticeable erosion or thruster damage
Xenon Results
• Demonstrated Kinetic >>Thermal Energy (impulse and magnetic pressure
balance)
Hydrazine (Simulant), Nitrous Oxide Results
• Demonstrated ionization and electromagnetic acceleration of a monopropellant
Fundamental Science
Task 2: Neutral Entrainment
ISSUE: Plasma formation is the primary loss mechanism for ALL
electrostatic or electromagnetic propulsion systems. It prevents
operation at lower specific impulse, lowers efficiency at all exit velocities,
and requires high mass propellants.
Solution: Entrain neutrals in an acceleration field after formation.
Benefit: Specific impulse can be tailored to
the mission, while the thruster operated
at its maximum efficiency, even on light
propellants.
•
Basic Idea: An FRC will ‘injest’ large
quantities of neutral gas through charge
exchange collisions, not ionization. If
you accelerate an FRC while providing
upstream neutral gas, Isp can be
specified and mass/thrust added with
very high efficiency [1].
[1] Matsuzawa, Y., et. al, “Effects of background neutral particles on a field-reversed
configuration plasma in the translation process”. Phys. Plasmas 15, (2008).
Thrust
Isp
Dynamic formation and acceleration of an FRC, shown with 4 field coils
Task 2: Neutral Entrainment Program
Year 1 - Feasibility
Initial feasibility, interaction, and systems-level study
• Neutral interaction modeling
• Manifold and neutral flow design
• Dynamic neutral interaction SEL implementation
• AFRL numerical support
• Neutral interaction experimental effort
• Neutral entrainment chamber construction (ELF chamber mod)
• FRC-Neutral drag and ingestion investigations
• Neutral flow testing and puff valve modification
• Neutral beam diagnostics investigations
Year 2 - Neutral Entrainment Demonstration
Demonstrate and quantify neutral entrainment
• Neutral low modeling
• AFRL numerical support
• Neutral entrainment experimental investigation
• Dynamic acceleration system design
• Couple neutral injection and dynamic acceleration
We have developed an advanced thruster concept
that works and has wide-reaching payoffs
• The ELF thruster is a major improvement over traditional electric
propulsion, for most power levels and missions
• Neutral entrainment could make it revolutionary – dramatically
extending the specific impulse, thrust-to-power, and power
ranges.
• Direct innovative application to hypersonic vehicles, air-breathing
space propulsion, in-situ propellant utilization, high-altitude
recon, propellant sharing (multi mode), and ???.
Fundamental Questions:
Are there unforeseen technology development challenges to a pulsed inductive thruster?
What are the power, specific impulse, geometry and density limits of neutral entrainment?
Single Shot Electrodeless Lorentz Force Thruster
Operation Successfully Demonstrated at MSNW
Slough / Kirtley (MSNW), Milroy (University of Washington)
•Field Reverse Configuration used to create Plasmoids in fusion community, combined with Rotating
Magnetic Fields promise a breakthrough in high power (1 kW and up) space propulsion
J
Rotating Magnetic Field
generated plasma
current from
synchronous electrons
Fz  j  Br
RMF Antenna
Steady magnetic
field in conical
geometry
Steady Field Coil
Input Power = 50 J (25-50 kW steady state)
Propellant = Air, Argon, Xenon, Nitrous Oxide
Measured Thrust impulse = 1mN-s per plasmoid ejection
Measured Specific Impulse = 1,000-6,000 s depending mass flow rate
Measured Peak Efficiency = ~50% (Xenon), theoretical = 87%
•Full Scale tests and optimization will be conducted at AFRL/RZSS
(Haas, Brown ), modeling and Simulation AFRL RZSA / RZSS
(Cambier)
Dynamic Behavior with Rotating
B - Thruster Configuration
a)
Br
FjxB
zc
b)
Br
FjxB
Br(vac)
zc
c)
Br
FjxB
zc
d)
Br
FjxB
zc
Helicon Thruster: With no significant diamagnetic
current and negligible magnetic gradient, thruster
relies on electrothermal heating and nozzle
expansion at exit. Two fluid effects (double layer)
enhance Isp, and efficiency . Concerns are efficiency,
plasma detachment from thruster fields and beam
spread.
High Power Helicon Thruster: Larger RF field
amplitude at lower frequency leads to a much larger
high density, high  plasma. Plasma is lost from
stationary plasma through axial JBr as well as
electro-thermal expansion. Detachment and beam
spread problems greatly reduced.
Electrodeless Lorentz Force (ELF) Thruster: An
even larger, lower frequency rotating field imposes
synchronous  motion of all electrons. The resultant
field producing a completely isolated, magnetized
plasmoid (FRC). The strong axial JBr force rapidly
drives the plasmoid out of the thruster. FRC
expansion during ejection converts remnant thermal
energy into directed energy. No detachment issues.
Magnetically Accelerated Plasmoid Propulsion:
With the FRC formed in ELF, further thrust or Isp can
be obtained with peristaltic sequencing of axial array
of flux coils. Large JBr force can be maintained
throughout FRC passage enabling neutral gas
entrainment significantly increasing thruster
efficiency at optimal Isp.