A MULTI-STAGE DISTRIBUTED ENERGY PLASMA ARC RAILGUN
by
RYAN KARHI, B.S.E.E., M.S.E.E.
A DISSERTATION
IN
ELECTRICAL ENGINEERING
Submitted to the Graduate Faculty
of Texas Tech University in
Partial Fulfillment of
the Requirements for
the Degree of
DOCTORATE OF PHILOSOPHY
IN
ELECTRICAL ENGINEERING
Prof. John Mankowski
Chairperson of the Committee
Prof. Michael Giesselmann
Co-Chairperson of the Committee
Prof. Stephen Bayne
Prof. Jahan Rasty
Dr. Ian McNab
Dr. David Wetz
Ralph Ferguson
Dean of the Graduate School
September, 2010
Texas Tech University, Ryan William Karhi, November 2010
ACKNOWLEDGMENTS
First and foremost I would like to thank my family for their unconditional love
and encouragement throughout my studies. A special thanks goes to the Air Force Office
of Scientific Research (AFOSR), whom without, these projects would not be possible.
Thank you for your continued support and trust towards the Center for Pulsed Power and
Power Electronics (P3E) at Texas Tech University. I want to also thank the Institute for
Advanced Technology (IAT) at the University of Texas, especially Ian McNab and David
Wetz, for their generous donations and collaboration on the Multidisciplinary University
Research Initiative (MURI) railgun project. To my advisors, Prof. Mankowski and Prof.
Giesselmann, your guidance and support throughout this project led to its success. Thank
you for taking me under your wing and sharing your knowledge.
I also wish to
acknowledge Dr. Hemmert, who provided me with my first railgun project and an
introduction to electromagnetic launch technology. I would like to give credit to Jeff
Diehl, Patrick Kelly, and Ian El-Dana who aided in the fabrication and assembly of
numerous components. To my pulsed power colleagues, thank you for your advice and
motivation. Special thanks goes towards the technicians and machinists of the P3E lab,
Danny, Dino, Elmer, Shannon, Lee, and Joel for their valued assistance and broad
expertise.
Finally, I want to acknowledge a positive camaraderie within the P 3E
laboratory and I am grateful for the wisdom and experience gained.
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Texas Tech University, Ryan William Karhi, November 2010
TABLE OF CONTENTS
ACKNOWLEDGMENTS .................................................................................................. ii
ABSTRACT ...................................................................................................................... vii
LIST OF FIGURES ......................................................................................................... viii
INTRODUCTION .............................................................................................................. 1
1.1 Railgun Background ......................................................................................... 2
1.2 Distributed Energy Store Background .............................................................. 5
1.3 Plasma Armature Background .......................................................................... 9
1.4 Synchronous Theory........................................................................................ 12
1.5 Motivation ....................................................................................................... 14
PRELIMINARY PLASMA ARC RAILGUN EXPERIMENTS ..................................... 16
2.1 Introduction..................................................................................................... 16
2.2 Switching Schemes .......................................................................................... 17
2.3 Experimental Results ...................................................................................... 19
2.3.1 Breech-fed Railgun Data ......................................................................... 19
2.3.2 Asynchronous DES Railgun Data............................................................ 23
2.3.3 Pseudo-synchronous DES Railgun Data.................................................. 27
2.4 Conclusion ...................................................................................................... 29
PLASMA ARC SPLITTING ............................................................................................ 31
3.1 Introduction..................................................................................................... 31
3.2 Arc Splitting Theory ........................................................................................ 31
3.3 Arc Splitting Data ........................................................................................... 33
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Texas Tech University, Ryan William Karhi, November 2010
3.4 Arc Splitting Prevention .................................................................................. 38
PLASMA ARC LENGTH ................................................................................................ 40
4.1 Introduction..................................................................................................... 40
4.2 Experimental Setup ......................................................................................... 40
4.3 Experimental Results ...................................................................................... 43
4.4 Conclusion ...................................................................................................... 46
DEVELOPMENT OF A NEW SYSTEM PROTOTYPE ................................................ 48
5.1 Introduction..................................................................................................... 48
5.2 Free-Arc DES Railgun Simulation.................................................................. 49
5.2.1 Introduction .............................................................................................. 49
5.2.2 Implemented Simulation Equations ......................................................... 50
5.2.3 Simulation Parameters and Results.......................................................... 54
5.2.4 Conclusion ............................................................................................... 58
5.3 Experimental Setup ......................................................................................... 59
5.3.1 Rails and Containment Structure ............................................................. 59
5.3.2 Energy Modules ....................................................................................... 62
5.3.3 Diagnostics............................................................................................... 65
5.3.4 Plasma Injector ........................................................................................ 66
5.3.5 Control System ........................................................................................ 67
5.3.6 Support Structure and Built System......................................................... 68
5.4 Experimental Results ...................................................................................... 70
5.5 Conclusion ...................................................................................................... 73
A 40-STAGE DES PLASMA ARC RAILGUN .............................................................. 76
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Texas Tech University, Ryan William Karhi, November 2010
6.1 Introduction..................................................................................................... 76
6.2 Experimental Setup ......................................................................................... 77
6.2.1 Containment Structure and Rails ............................................................. 77
6.2.2 Energy Module Modification................................................................... 78
6.2.3 Printed Circuit Board Diagnostics ........................................................... 80
6.2.4 Data Acquisition System ......................................................................... 83
6.2.5 Built System ............................................................................................. 85
6.3 Control System ................................................................................................ 87
6.3.1 Introduction .............................................................................................. 87
6.3.2 Hardware .................................................................................................. 87
6.3.3 Software ................................................................................................... 89
6.4 Experimental Results ...................................................................................... 91
6.4.1 Asynchronous Energy Scheme ................................................................ 91
6.4.2 Synchronous Energy Scheme .................................................................. 93
6.5 Conclusion ...................................................................................................... 95
SUMMARY AND CONCLUSION ................................................................................. 97
REFERENCES ............................................................................................................... 102
APPENDIX A ................................................................................................................. 103
MULTI-STAGE DES FREE-ARC SIMULATION ........................................... 103
APPENDIX B ................................................................................................................. 112
CONTROL SYSTEM CODE ............................................................................. 112
B.1 Control Program for Stages 1-24 ............................................................. 112
B.2 Control Program for Stages 25-40 ........................................................... 121
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Texas Tech University, Ryan William Karhi, November 2010
APPENDIX C ................................................................................................................. 124
RAILGUN SYSTEM OPERATION MANUAL................................................ 124
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Texas Tech University, Ryan William Karhi, November 2010
ABSTRACT
The development process pertaining to the design, fabrication, coding, and testing
of multi-stage distributed energy plasma arc railguns are presented. In collaboration on
an Air Force Office of Scientific Research (AFOSR) funded Multidisciplinary University
Research Initiative (MURI) project, the Center for Pulsed Power and Power Electronics
(P3E) at Texas Tech University is responsible for developing and investigating a
functional scale model of a multi-stage distributed energy store (DES) railgun to analyze
its effectiveness to suppress a restrike phenomenon and increase plasma armature railgun
performance 1. The term “restrike” denotes the formation of an electrical breakdown in
the railgun bore some distance behind a traveling plasma armature. The formation of this
secondary arc reduces the driving force on the primary armature and has led to a velocity
ceiling of approximately 6 km/s on all breech-fed plasma armature railguns. Numerous
solutions have been theorized as viable methods of restrike prevention but lack
experimental verification. The primary objective of our research team within the MURI
effort is to experimentally test Dr. Jerry Parker’s theoretical restrike suppression
technique
2
that was developed at Los Alamos National Laboratory in the 1980’s. The
project tasks are organized to identify potential problematic issues and verify theoretical
concepts before implementation of a full scale system.
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Texas Tech University, Ryan William Karhi, November 2010
LIST OF FIGURES
Fig. 1.1: Schematic of Ampere’s Law ................................................................................ 3
Fig. 1.2: Railgun Force Schematic ...................................................................................... 4
Fig. 1.3: Breech-fed Energy Scheme .................................................................................. 6
Fig. 1.4: Distributed Energy Store Scheme ........................................................................ 7
Fig. 1.5. Illustration of the Electric Field Profile for a Breech-Fed Scheme and a DES
Scheme. ............................................................................................................................... 8
Fig. 1.6: Schematic of a Free-Arc Traveling Below Mach 10. ......................................... 10
Fig. 1.7: Schematic of a Free-Arc Traveling Above Mach 10.......................................... 11
Fig. 2.1. Circuit Diagrams of the 3 Types of Switching Schemes. (a) Breech-Fed (b)
Asynchronous and (c) Pseudo-Synchronous. ................................................................... 18
Fig. 2.2. Plasma Velocity Comparison. ........................................................................... 20
Fig. 2.3. Breech-Fed System Data Using the Alumina Bore Insulators. ......................... 21
Fig. 2.4. Breech-Fed System Data Using the G-10 Bore Insulators. ............................... 22
Fig. 2.5. Arc Erosion Photographs. (a) Breech Region and (b) Middle Region. ............. 23
Fig. 2.6. Asynchronous DES Railgun Data Using G-10 Bore Insulators. ....................... 24
Fig. 2.7. Asynchronous DES Railgun Data Using Alumina Bore Insulators. ................. 26
Fig. 2.8. Pseudo-Synchronous DES Railgun Data Using G-10 Bore Insulators. ............ 28
Fig. 2.9. Pseudo-Synchronous DES Railgun Data Using Alumina Bore Insulators........ 29
Fig. 3.1. Distributed Energy Current Waveforms. ........................................................... 34
Fig. 3.2. Armature B-dot Probe Signals from Shot 1....................................................... 36
Fig. 3.3. Armature B-dot Probe Signals from Shot 2....................................................... 37
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Fig. 3.4. Armature B-dot Probe Signals from Shot 3....................................................... 39
Fig. 4.1. Schematic of Photodiode Reverse Voltage Circuit11......................................... 41
Fig. 4.2. A Drawing of the DES Railgun and Optical Diagnostics. ................................ 41
Fig. 4.3. Illustration of the Fiber Line Mounting. ............................................................ 42
Fig. 4.4. A Picture of the Five Optical Fiber Couplers. ................................................... 43
Fig. 4.5. Photodiode Waveforms with Corresponding Armature Current. ...................... 44
Fig. 4.6. Arc Length Calculations vs. Pressure and Location. ......................................... 45
Fig. 4.7. Arc Velocity Calculations vs. Pressure and Location. ...................................... 46
Fig. 5.1. Schematic of a Stage in which the Plasma Arc has Passed Through2. .............. 51
Fig. 5.2. Schematic of a Stage that Contains the Plasma Arc2. ....................................... 51
Fig. 5.3. Simulated Current Waveforms for a 40-Stage System. Top: Current Waveforms
for Stages 1-20. Bottom: Current Waveforms for Stages 21-40. ...................................... 56
Fig. 5.4. Simulated Armature Current. ............................................................................ 57
Fig 5.5. Simulated Arc Velocity. ..................................................................................... 58
Fig. 5.6. Cross-Sectional View of the Railgun Prototype. ................................................ 60
Fig. 5.7. Interior View of the Containment Structure. ...................................................... 61
Fig. 5.8. Partially Disassembled Railgun View. ............................................................... 61
Fig. 5.9. CAD Drawing of the Distributed Energy Module.............................................. 63
Fig. 5.10. Variable Self-Inductance Scheme. ................................................................... 64
Fig. 5.11. Rail B-dot Probe Orientation. ........................................................................... 66
Fig. 5.13. Control System Hardware. ............................................................................... 68
Fig. 5.14. Photographs of the 7-Stage Prototype System. (a) View of Switch and Diode
side. (b) View of Capacitor Bank Side. ............................................................................ 70
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 5.16. B-dot Measurements from the Prototype System. ............................................ 72
Fig. 6.1. CAD Drawing of a 40-Stage DES Railgun. ....................................................... 76
Fig. 6.2. Photograph of the Containment Structures. ........................................................ 77
Fig. 6.3. Photograph of the Lap Joint Rail (Top-Back View, Bottom-Front View). ........ 78
Fig. 6.4. CAD Drawing of the Distributed Energy Module.............................................. 79
Fig. 6.5. Photograph of the PCB B-dot Probe and Plot of the Integrated and Calibrated
Data. .................................................................................................................................. 81
Fig. 6.6. Photograph of the PCB Rogowski Coil and Plot of the Integrated and Calibrated
Data. .................................................................................................................................. 82
Fig. 6.7. PCB Armature B-dot Probes. (a) 2-Turn Design. (b) 14-Turn Design. (c) 28Turn Design. ..................................................................................................................... 83
Fig. 6.8. National Instruments DAQ System. ................................................................... 85
Fig. 6.9. Photograph of the 40-Stage DES Railgun (Top/Side View). ............................. 86
Fig. 6.10. Photograph of the 40-stage DES Railgun (Isometric View). ........................... 86
Fig. 6.11. Control System Hardware. ............................................................................... 88
Fig. 6.12. Flow Chart of the Control Program. ................................................................. 90
Fig. 6.13. Current Waveforms from a 40-Stage asynchronous DES Railgun. ................. 92
Fig. 6.14. Armature B-dot Waveforms from a 40-Stage asynchronous DES Railgun. .... 93
Fig. 6.15. Current Waveforms from a 40-Stage Synchronous DES Railgun. .................. 94
Fig. 6.16. Armature B-dot Waveforms from a 40-Stage Synchronous DES Railgun. ..... 95
Fig. B.1. LabVIEW Control Program for Stages 1-24 with Red Zoom Box Labels. ..... 112
Fig. B.2. 3 Second Wait Function (Z1). .......................................................................... 113
Fig. B.3. Set Line Direction for Digital Input/Output Modules (Z2). ............................ 114
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Fig. B.4. Check Digital Input/Output Modules Status (Z3). ........................................... 114
Fig. B.5. Trigger Sequence for DAQ, Plasma Generation, and Stage 1 (Z4). ................ 115
Fig. B.11. LabVIEW Control Program for Stages 25-40 with Red Zoom Box Labels. . 121
Fig. B.12. 1 Second Wait Function (Z9). ........................................................................ 122
Fig. B.13. Trigger Loop to Start Reading the B-dot Probes (Z10). ................................ 123
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Texas Tech University, Ryan William Karhi, November 2010
CHAPTER Ι
INTRODUCTION
The Air Force’s interest in electromagnetic launch technology is driven by the
search for an economical means to launch large numbers of micro-satellites into orbit.
The current costly method involves burning millions of pounds of fuel and is growing
obsolete. Recent plasma railgun development alongside the development of smaller and
lighter satellites has brought new hope back to the electromagnetic launcher. Rapidly
advancing integrated circuit (IC) technology has opened the door for an inrush of micro
devices. These devices include satellites weighing a mere 20 pounds that are capable of
withstanding the large G-forces associated with fast acceleration up to the escape velocity
of approximately 11.2 km per second.
Achieving the escape velocity using a solid metal armature is an unlikely
scenario.
An extremely large magnitude of current (Mega-Amperes) is required to
accelerate the satellite launch package to velocities in excess of 10 km per second. Heat
flux generated by Mega-Ampere currents flowing through the armature for hundreds of
milliseconds to seconds will melt the solid structure and eventually transition into
plasma. Reducing this current magnitude to kilo-Amperes and slowly accelerating the
armature is a solution; however, this requires a launcher length in excess of a few
kilometers and would be difficult to maintain electrical contact due to armature erosion or
degradation as it travels down the long rail length. In addition, solid metal armatures will
gouge the rails at hypervelocities, resulting in a short rail lifetime. Therefore, a plasma
armature is presently the only solution to achieve hypervelocities using a railgun.
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Texas Tech University, Ryan William Karhi, November 2010
Challenges still exist to successfully launch any payload to a hypervelocity using
a plasma armature railgun. These obstacles include: thermal management, structural
failure, pre-injection, plasma puffing and/or blow-by, plasma bifurcation, and restrike
suppression. The latter is the most misunderstood problem to resolve in order to achieve
the hypervelocity regime. Restrike refers to secondary arcs that form behind a primary
plasma armature and prove to be detrimental to achieving the theoretical velocity of
electromagnetic launchers. Further explanation of this effect is covered in the plasma
armature background, Section 1.3. Numerous solutions have been theorized as viable
methods of restrike prevention but lack experimental verification. Our research team is
tasked to analyze a theory involving a multi-stage DES railgun system. This concept was
first proposed by Marshall3 in an asynchronous scheme and later by Parker2
synchronously. This paper will investigate the design and performance of small scale
DES railgun systems, with future motivation towards a full scale product.
1.1 Railgun Background
The laws of physics that govern the operation of a railgun are not new to the
scientific community. A power source supplies a large magnitude of current, kA to MA,
through the conductive rails and armature.
From Ampere’s law, a mathematical
consequence of the Biot-Savart law, this current produces a large magnitude magnetic
flux density. This magnetic flux circulates the rails in accordance to the right hand rule
shown in Fig. 1.1.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 1.1: Schematic of Ampere’s Law
The interaction of this current (moving charged particles) in a magnetic field leads
to an interesting effect. A Dutch theoretical physicist, Hendrik Lorentz, discovered in
1896 that electric and magnetic fields interact with charged particles4. This causes a
force called the Lorentz force and we concentrate our attention on the Lorentz magnetic
force, equation 1.1.
This equation describes the main driving force behind
electromagnetic projectile acceleration.
The cross product of current density and a
magnetic field results in a magnetic force given by
⃗⃗⃗⃗
⃗
𝐹𝑚 = ⃗𝐽 × 𝐵
(1.1)
⃗ is the magnetic field vector [T].
where ⃗𝐽 is the current density vector [A/m2] and 𝐵
This force can be much stronger than the pull of Earth’s gravity and has attracted
the attention of scientists for a variety of applications. In the application of a railgun, this
force is applied to a metallic conductor or conducting plasma, known as the armature. An
equivalent form of the Lorentz magnetic force in relation to a railgun is given by
1 𝑑𝐿
𝐹𝐴 = ( ) 𝐼2 − 𝐹𝐷
2 𝑑𝑥
3
(1.2)
Texas Tech University, Ryan William Karhi, November 2010
where I is the current through the armature [A] and dL/dx is known as the inductance
gradient [L/m] which is a function of the rail geometry.
The force applied to the
armature must overcome a frictional drag FD associated with contact with the rails.
The breech-fed railgun concept and forces are shown schematically in Fig. 1.2.
The armature completes the electrical circuit between the rails and allows current to flow
provided by an energy source. The cross product of the current density through the
armature and the magnetic field rotating around the rails and coupling into the armature
produces, in accordance with the Lorentz magnetic force, a force vector parallel to the
rails and directed away from the breech end. Since the rails are also present in this
magnetic field and have current flowing through them, additional Lorentz forces acts to
push the rails away from each other. Therefore, the rails must be contained in an
enclosure to oppose these forces and retain the electrical connection between the
armature and rails.
Fig. 1.2: Railgun Force Schematic
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Texas Tech University, Ryan William Karhi, November 2010
1.2 Distributed Energy Store Background
Two main energy schemes are discussed in this dissertation and it is worthwhile
to explain their differences. One is the breech-fed energy scheme and the other is the
distributed energy store (DES) scheme. An explanation of the breech-fed energy scheme
is addressed first since it is the simpler of the two.
In a breech-fed energy scheme, Fig. 1.3, electrical energy is applied to the breech
end of the rails using a single energy source. The input current flows in a loop through
both rails and the armature. For maximum energy efficiency, all of the electrical energy
would be converted into kinetic energy to drive the armature. In reality, there are many
loss mechanisms associated with the presented configuration. However, we will focus on
the two dominate mechanisms. One is the joule heating resistive losses in the rails and
armature. Rail conductivity and geometry determine this resistance. As the armature
travels further away from the breech, the current must flow through an increasing length
of rail. The result is a larger resistance and in effect, larger power losses. The second
dominating loss mechanism is associated with the rail inductance. About half of the
input energy is converted into magnetic energy where it is stored in the rails. As the
current flows through an increasing rail length, more of the electrical input energy is
converted and stored magnetically. The combination of these loss mechanisms results in
poor energy efficiency for systems with long rail lengths.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 1.3: Breech-fed Energy Scheme
To reduce the described energy losses, Marshall3 proposed a new railgun
configuration in 1980 known as the distributed energy store (DES) scheme, Fig. 1.4. For
the breech-fed scheme, a single current loop exists that grows in length with the armature
motion, all the way down to the muzzle. The DES scheme maintains continuous rails but
creates multiple current loops that flow through reduced rail distances.
This is
accomplished by replacing the large breech-fed energy source with many smaller
independent energy sources known as distributed energy stores, which are electrically
connected to the rails at different locations along the rail length. The combination of a
single DES and the length of rail between it and the subsequent DES is known as a
“stage” within the system. Each of these stages produces short current pulses behind the
armature to maintain a Lorentz driving force. The short current pulses sourced from each
of the stages flows through a small portion of the rail length which reduces the inductive
and resistive energy losses.
Additional advantages to this energy scheme include:
improved current waveform control, reduce switch current carrying requirements, and a
reduced electric field several bore diameters behind the armature.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 1.4: Distributed Energy Store Scheme
In 1989, Parker1 theorized an additional advantage of the DES scheme. During
his research analyzing the formation of restrike arcs within plasma armature railguns, he
concluded that restrike is an electrical breakdown that requires an electric field across the
rails. His experiments also discovered that these restrike arcs developed many bore
diameters behind the primary plasma armature.
He postulated multiple solutions to
suppress restrike, including the DES scheme. The DES scheme is theorized to suppress
restrike arc formation because the electric field, Fig. 1.5, associated with the back EMF
voltage is localized to active stage regions. This reduces the probability of an electrical
breakdown in the dense ablated gas trailing behind the armature. Due to an end of
plasma armature railgun research in the 1980’s, this theory was never experimentally
tested for legitimacy.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 1.5. Illustration of the Electric Field Profile for a Breech-Fed Scheme and a DES
Scheme.
Although energy efficiency is improved in the DES scheme, electrical complexity
increases with the number of stages implemented. If energy is released by a stage ahead
of the armature, the effect is the creation of a Lorentz force opposing the desired muzzle
oriented motion. This result is detrimental to achieve the target velocity and must be
prevented at all costs. Since a number of DES railguns are examined in this paper, issues
associated with timing control are addressed by implementing control systems for
accurate and reliable railgun operation.
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Texas Tech University, Ryan William Karhi, November 2010
1.3 Plasma Armature Background
Plasma armature railguns have been the subject of active research and
development since the Rashleigh and Marshall paper5 was published in 1978. This paper
stated the theoretical possibility of accelerating plasma armatures to a significant fraction
of the speed of light with velocity limitations realized by projectile-bore interactions. A
decade later, experimental research identified the true velocity limiting factor, known as
plasma restrike. The processes contributing to the generation of these secondary arcs are
presented below. For a more in depth description refer to the following papers1,6.
The experiments in this paper accelerate a different type of armature known as a
“free-arc”. Unlike solid metal armatures, this armature is essentially a super heated gas
in a plasma state. The plasma typically has a temperature ranging from 20,000 to 30,000
Kelvin, similar to the surface temperature of the Sun. The reason it is referred to as a
free-arc is because no physical load exists for the plasma to push, with exception of the
bore fill gas. In a conventional plasma armature railgun, the plasma is accelerated
electromagnetically by the Lorentz force and contained and compressed by the magnetic
pressure. When a nonconductive payload is placed ahead of the plasma, the plasma
pressure pushes or accelerates the payload to a target velocity. For the MURI project this
payload is a 20 lb micro-satellite with a target velocity equal to the escape velocity. To
relieve the financial burden of a large energy storage facility required to accelerate a
launch package, a free-arc railgun is an adequate substitution to physically emulate inbore plasma dynamics at hypervelocities. It is imperative to understand the in-bore
physical interactions involving a free-arc to analyze the data presented in this paper.
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Texas Tech University, Ryan William Karhi, November 2010
This section will give the reader a basic understanding of the underlying free-arc
physical processes. A small amount of plasma is generated inside of the bore at the
breech end. This conductive plasma is accelerated by the Lorentz magnetic force. In our
experiments, the bore is filled with air at pressures varying from 5 to 50 Torr. In this low
pressure environment the plasma rapidly accelerates to a velocity much greater than 0.34
km/s, the speed of sound in air. This effect results in the formation of a shock front as the
radiating plasma sweeps up the air ahead of it, seen in Fig. 1.6.
Fig. 1.6: Schematic of a Free-Arc Traveling Below Mach 10.
When the plasma velocity exceeds Mach 10, the shocked gas begins to ionize and
becomes part of the moving plasma6. Therefore, two well defined regions exist inside of
the bore; the accelerating plasma arc and the unshocked gas ahead of it, displayed in Fig.
1.7.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 1.7: Schematic of a Free-Arc Traveling Above Mach 10.
Assuming no ablation, the plasma arc’s velocity can be calculated6 by
𝐿′
𝐼
1
ℎ
𝑥
√1+(𝑥 )
𝑠
𝑣𝑝 = √(𝛾+1)𝜌 ( )
0
(1.3)
where 𝐿′ =dL/dx is the inductance gradient, 𝛾 is the ratio of specific heat, 𝜌0 is the initial
gas density, I is the armature current, ℎ is the rail separation distance, 𝑥 is the distance the
shock front has moved, and 𝑥𝑠 is a scale length describing the viscous forces.
The illustration, shown in Fig. 1.7, depicts a free-arc traveling above mach 10 in a
quasi-equilibrium state after having moved a substantial distance down the rail length.
The extreme heat radiating from the plasma ablates material from the walls. This ablated
material becomes ionized which allows magnetic forces to accelerate it. A small portion
of this ionized material joins the main plasma arc while most experiences viscous
boundary forces and is swept backwards to form the plasma tail region. In this region the
ionized particles mix with neutral gas that reduces the conductivity. The weakly ionized
particles lose much of their acceleration and fall even further back into what is known as
the neutral region, where no current flows. The gas in this region is highly energetic and
both heat and momentum continue to ablate material from the walls. The high gas
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Texas Tech University, Ryan William Karhi, November 2010
density and weak ionization contribute to quench conductivity. However, the presence of
a high electric field will cause run-away ionization and the resulting Paschen breakdown
will establish a secondary arc that is known as restrike. According to Paschen’s Law,
electrical breakdown is a function of the gas composition, the pressure, and the electric
field across a constant gap distance. The electric field that causes restrike is generated by
the moving magnetic field emanating from the rails1, given by
𝐸=
𝐿′ 𝐼(𝑣𝑎 −𝑣𝑔 )
ℎ
+
𝑉𝑎
ℎ
(1.4)
where 𝐿′ =dL/dx is the inductance gradient, 𝐼 is the armature current, 𝑣𝑎 is the plasma
armature velocity, 𝑣𝑔 is the gas velocity behind the armature, 𝑉𝑎 is the armature voltage,
and ℎ is the rail separation distance. The first term in the equation is known as the back
electromotive force (EMF) voltage. This induced voltage is a consequence of changing
magnetic flux and is a function of the armature velocity. Therefore, an armature traveling
at a hypervelocity can generate a back EMF voltage large enough to exceed the
breakdown voltage across the rail gap.
1.4 Synchronous Theory
This paper will discuss two different current waveform profiles implemented on a
DES scheme. The first is known as “synchronous” and the second is “asynchronous”.
Synchronous refers to the speed of an electromagnetic wave in the LC transmission line
formed by the rails and capacitors being matched to the velocity of the armature. A
synchronous distributed energy system is theorized to prevent restrike by reducing the
breech voltage, a function of arc velocity, to a magnitude below the high voltage
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Texas Tech University, Ryan William Karhi, November 2010
breakdown threshold. The electric field associated with this breech voltage is generated
by the moving magnetic field emanating from the rails, Eq. 1.4. Examining this equation,
the armature current can be carefully chosen such that the rail current in critical sections
of the railgun can be near zero. This is accomplished by underdamping the DESs to
source negative current. An asynchronous DES scheme does not match the armature and
phase velocities and in addition, does not allow current reversal to take place on any of
the energy banks.
The two schemes are similar in that both implement the technique of distributed
energy to increase efficiency and reduce the trailing electric field. However, according to
the electric field equation, Eq. 1.4, the synchronous scheme will be more effective.
Current reversal is utilized on a synchronous scheme to effectively cancel residual
positive current remaining in regions many bore diameters behind the main plasma arc.
Elimination of this current does not fully quench the E-field, but reduces the magnitude
to prevent restrike.
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Texas Tech University, Ryan William Karhi, November 2010
1.5 Motivation
The Center for Pulsed Power and Power Electronics (P3E) at Texas Tech University
continues to develop and investigate distributed energy source (DES) schemes applicable
to hypervelocity electromagnetic launch systems. The goal is to identify potential
problematic issues and verify theoretical concepts before implementation onto a full scale
system. A distributed energy scheme is attractive for a number of reasons:
(1) Theoretically predicted to suppress restrike arc formation
(2) Proven to increase energy conversion efficiency vs. breech-fed configuration7
(3) Ability to tailor the projectile acceleration (soft launch and constant acceleration)
(4) Multiple stages reduce the switch current carrying requirements
Although Marshall3 is credited with the DES railgun concept, the theoretical analysis
and mathematical background of (1) was developed at Los Alamos National Laboratory
in the 1980’s by Parker2.
The primary objective of our research team within the
Multidisciplinary University Research Initiative (MURI) effort is to examine Parker’s
theoretical concept through basic research. Although all DES railguns have the potential
to suppress restrike, Parker’s theory2 maximizes the energy efficiency while minimizing
the current in the bore behind the armature. This is accomplished by two main principles.
The first is to operate in a “synchronous” mode where the plasma velocity is matched to
the gun’s intrinsic velocity, or phase velocity. This is accomplished by adjustment of the
pressure and current so the arc transits a stage in about the half cycle time of the DES
discharge current. The second principle involves under-damped DES current waveforms
that provide negative current to cancel out residual positive current that is trailing behind
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Texas Tech University, Ryan William Karhi, November 2010
the armature. This promotes an enhanced isolation of the electric flux in the bore behind
the armature.
The second discussed benefit (2) becomes important when launcher lengths exceed a
few meters. Since the projected satellite payload will inherently contain electronics
prone to failure by excessive acceleration forces, a launcher of considerable length
becomes a critical requirement to reduce or “soften” the acceleration loads. For
applications where railgun lengths greater that ten meters are required (as in our case),
sustaining energy store simulations show energy conversion efficiencies in excess of 60
percent can be achieved8.
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Texas Tech University, Ryan William Karhi, November 2010
CHAPTER ΙΙ
PRELIMINARY PLASMA ARC RAILGUN EXPERIMENTS
2.1 Introduction
This chapter reiterates restrike data obtained from a breech-fed railgun and brings
closure to past DES railgun experiments at Texas Tech University.
The experimental
setups and control systems are described in the thesis9; therefore, these topics will not be
discussed in this paper.
Experimental results from three preliminary railgun configurations are presented.
These include a breech-fed railgun, a 4-stage asynchronous DES railgun, and a 4-stage
pseudo-synchronous DES railgun. The latter DES railgun does not meet all of Parker’s
requirements for synchronous operation and is therefore referred to as “pseudosynchronous.”
The two DES systems are simply a first step approach to analyze
distributed energy schemes and identify possible problem areas undetected by theory and
simulations. Acquired data from the breech-fed system determined the amount of energy
and current magnitude required for restrike in the railgun bore. These conditions were
applied to the distributed energy schemes to determine if the preliminary systems could
prevent restrike before movement to a truly synchronous system.
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2.2 Switching Schemes
Three different switching schemes are employed. They are breech-fed, asynchronous,
and pseudo-synchronous. The circuit diagram for each configuration is shown in Fig.
2.1. The breech-fed scheme, shown in Fig. 2.1(a), is the most conventional switching
scheme. Each of the capacitor banks are connected to the breech side of the railgun.
Switching of each of the banks is staggered in order to generate a “trapezoidal” type
current pulse. The asynchronous switching scheme, shown in Fig. 2.1(b), employs a
distributed energy feed. Each of the capacitor banks delivers current upon arrival of the
armature at the respective feed point to the railgun. Since the SCRs only conduct current
in one direction, only positive current is fed to the railgun. The pseudo-synchronous
switching scheme, shown in Fig. 2.1(c), is similar to the asynchronous type with the only
variation in the first stage switching. An SDD303KT rectifier diode is placed in antiparallel with the thyristor to act like a triac switch and allow both positive and negative
current flow. The diode has a peak hold-off voltage of 6 kV and a non-repetitive peak
surge current of 60 kA for 8.3 ms. The magnitude of the negative current was controlled
using a carbon resistor in series with the diode.
Pseudo-synchronous switching
experiments utilizing the alumina inserts were preformed for two cases: the first without
this resistance and the second with a 120 m resistor.
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Texas Tech University, Ryan William Karhi, November 2010
(a)
(b)
(c)
Fig. 2.1. Circuit Diagrams of the 3 Types of Switching Schemes. (a) Breech-Fed (b)
Asynchronous and (c) Pseudo-Synchronous.
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Texas Tech University, Ryan William Karhi, November 2010
2.3 Experimental Results
2.3.1 Breech-fed Railgun Data
The control system was not integrated onto the breech-fed system. Rather, fixed trigger
timing was applied to the three stages sequentially at 1, 160, and 190 s. The graph in
Fig. 2.2 displays the effects of ablation on the arc’s velocity for the breech-fed system.
The experimental data is an average of two shots per pressure using alumina and G-10 as
the ablated material. As expected, experimentation using the alumina inserts resulted in
higher arc velocities. Heavy ablation with the G-10 resulted in an increase of arc mass
and therefore an arc velocity reduction. A noticeable reduction is observed at pressures
of 5-10 Torr where the effect of ablation on the arc’s velocity is more profound.
Increasing pressure slowed down the arc for both cases because there are more initial gas
molecules to be swept up and added to the plasma mass. Accompanying the two velocity
waveforms
is
a
third
velocity
waveform
calculated
from
Eq.
1.3.
This equation is a function describing the plasma velocity assuming no ablation.
Calculations made using Eq. 1.3 at each pressure correspond reasonably to experiments
using the low ablating alumina.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 2.2. Plasma Velocity Comparison.
The collected data in Fig. 2.3 used the alumina bore insulators, a chamber pressure of 5
Torr, and a charging voltage of 3 kV. The current contribution from all three stages is
shown alongside four rail B-dot probe signals. The four probes were located 18.5, 96.7,
174.8, 241.3 cm, respectively, from the breech. Each B-dot measures the derivative of
the rail current at different sections of the railgun. The raw voltage signals (not shown)
have been integrated to analyze the current through the rails at each probe location. A
Rogowski coil measured a 40 kA, approximately trapezoidal, current pulse 500 s in
width. This waveform shape maintained a constant driving force on the plasma arc for
the majority of propagation through the bore. The rail current waveforms in this figure
show no indication of restrike. The current seen at B-dot 2 appears to exceed the input
current. This effect can be attributed to calibration error and was later corrected. The
occurrence of restrike was absent from all experimental tests utilizing the alumina
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Texas Tech University, Ryan William Karhi, November 2010
insulators in the breech-fed system.
If the current magnitude was incrementally
increased, eventually restrike would be observed.
Fig. 2.3. Breech-Fed System Data Using the Alumina Bore Insulators.
An example of restrike is shown in Fig. 2.4 for the breech-fed system. This particular
shot used G-10 bore insulators, a chamber pressure of 10 Torr, and a charging voltage of
3.5 kV.
Collected data from a number of shots (not shown) indicated repeated
development of restrike arcs using the G-10 bore insulators. By observing the rail
currents seen at rail B-dots 4-7, it is apparent that the rail current at these locations does
not match the sourced current magnitudes from the capacitor banks. A portion of the
current must therefore be flowing elsewhere, demonstrating a classical example of
restrike. The data suggest that a secondary arc formed sometime after 130 s.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 2.4. Breech-Fed System Data Using the G-10 Bore Insulators.
Figures 2.5(a) and (b) show different erosion patterns on the copper rails after
approximately 15 shots. Figure 2.5(a) is a picture taken at the breech end of the rails.
The plasma arc formation appears to be a highly dynamic process. The “chicken scratch”
erosion traces produced by the plasma are streamer-like with no defined structure. As the
plasma travels a distance of many bore diameters, the magnetic pressures within the bore
confine the plasma to the center of the rails. Figure 2.5(b) shows the rail erosion at a
location between the breech and the muzzle. Here, the erosion trace is only present at the
center of the rail surface, suggesting a narrow arc profile. Light sanding refinished the
surface and allowed the rails to be used repeatedly.
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Texas Tech University, Ryan William Karhi, November 2010
(a)
(b)
Fig. 2.5. Arc Erosion Photographs. (a) Breech Region and (b) Middle Region.
2.3.2 Asynchronous DES Railgun Data
The experimental results obtained from a 15 kJ, 4-stage asynchronous DES plasma arc
railgun are presented. The railgun was divided into four equal distant stage lengths
measuring 58 cm. Replication of the breech-fed system current waveform was achieved
to close approximation. This allows for direct comparison of ablation and restrike data
between the two systems. Experimental results using the two in-bore materials, alumina
and G-10, are discussed.
The collected data in Fig. 2.6 used the G-10 bore insulators, a chamber pressure of 10
Torr, and a charging voltage of 2.7 kV. The current distribution from all four stages is
shown alongside five rail B-dot probe signals. The five probes were located 18.5, 96.7,
135.7, 194.3, 322.6 cm, respectively, from the breech. To analyze a distributed system
properly, the current contribution from all stages prior to the probe location must be
compared to the probe’s signal. The stage 1 probe analysis shows no observable restrike.
The probe’s signal shows the current rise up to the full current magnitude and then
follows the current waveform throughout 450 s.
From 450 to 500 s, the probe
indicates a negative 6 kA magnitude flowing toward the breech. This current is sourced
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Texas Tech University, Ryan William Karhi, November 2010
from the energy released in stage 4 and is the time when a secondary arc arrives at the
probe.
Fig. 2.6. Asynchronous DES Railgun Data Using G-10 Bore Insulators.
A clear indication of current flowing toward the breech is observed in the remaining
three stages. In stage 2 probe analysis, the negative current waveform (observed between
250-500 s) mirrors the waveform produced from the last two stages with a reduced
magnitude. This indicates that not all of the current released by stages 2, 3, and 4 is
flowing toward the primary arc.
The plasma arc has an approximate length of 5-15 bore diameters neglecting ablation
and increases linearly throughout its bore travel6. Calculation of the upper limit of this
approximation results in a plasma arc 25.5 cm in length, nearly half the stage length. The
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Texas Tech University, Ryan William Karhi, November 2010
upper limit is appropriate with the high ablating G-10 bore insulators. Analysis of the
control system trigger timing indicates stage firing when the head of the arc has traveled
less than half the length of the respective stage. Since the full arc length is not ahead of
the input current location, a portion of the distributed current will be diverted to the
trailing plasma tail. This tail region is composed of highly ionized ablated material swept
back from viscous boundary forces. Compared to the arc head, this plasma region lacks
the density required for stability and is vulnerable to bifurcation from the arc head by
magnetic pressure gradients sourced from a distributed current feed. These presented
data confirm the discovery of a new type of secondary arc formation within a plasma arc
railgun, referred to as “plasma arc splitting.” By definition of the Lorentz force, the
portion of the plasma in front of the input current location continues to accelerate toward
the muzzle while the portion behind is accelerated toward the breech. In these data, this
process is observed when the second stage is triggered. Since the arc traveling toward the
muzzle is now significantly reduced in length, plasma arc splitting will not occur when
the last two stages fire. The rate at which the plasma tail grows during this time interval
is reduced as a consequence of the high arc velocity ablating less material. A velocity
calculation using Eq. 1.3 with the current magnitude flowing toward the breech suggests
that the secondary arc arrives at the stage 1 probe at 450 s (in agreement with the data
presented in Fig. 2.6) if it starts from the second stage position. Chapter III describes this
plasma arc splitting process in greater detail.
The collected data in Fig. 2.7 used the alumina bore insulators, a chamber pressure of
10 Torr, and a charging voltage of 2.7 kV.
The four probes were located 18.5, 96.7,
135.7, 322.6 cm, respectively, from the breech. The total rail current magnitude has
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Texas Tech University, Ryan William Karhi, November 2010
increased and the pulse width has decreased in direct comparison to the data presented in
Fig. 2.6. These effects are realized by an increase of the arc velocity due to the low
ablation characteristic of the Alumina. In other words, the increased velocity caused the
latter stages to trigger earlier due to the active control system.
With comparable energy to the breech-fed system using the alumina bore insulators,
Fig. 2.3, secondary arc formation by restrike should not occur. Analysis of the data
proves the existence of a secondary arc within the bore which can be associated with
plasma arc splitting. In these data sets, the stage 1 probe analysis shows no current
diversion or negative current. Current diversion is first observed in the stage 3 probe
signal.
Fig. 2.7. Asynchronous DES Railgun Data Using Alumina Bore Insulators.
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Texas Tech University, Ryan William Karhi, November 2010
The low ablating alumina and higher arc velocity allow the full arc length to pass the
second stage input current location before it is triggered. Therefore, plasma arc splitting
does not occur at the second stage. When the arc arrives at the third stage, the arc length
has increased and its velocity has been reduced. The velocity reduction is attributed to
the growing arc mass while it sweeps up ablated material from the bore walls and the fill
gas ahead of it. Thus, the probability of plasma arc splitting increases and occurs when
stage 3 fires. The secondary arc is accelerated past the stage 2 probe but lacks the
velocity required to reach the stage 1 probe before the system energy has expired.
2.3.3 Pseudo-synchronous DES Railgun Data
The experimental results obtained from the 15 kJ, 4-stage pseudo-synchronous DES
plasma arc railgun are presented. The stage lengths remain identical to the asynchronous
energy scheme, 58 cm. Equal stage lengths were chosen for analysis of the constant
energy model2. Both alumina and G-10 were experimentally tested and the results are
compared to the previous systems.
The collected data in Fig. 2.8 used the G-10 bore insulators, a chamber pressure of 10
Torr, and a charging voltage of 2.5 kV on the first stage and 2.9 kV on the last three
stages. This allowed for a more constant total rail current waveform. The five probes
were located 18.5, 96.7, 135.7, 194.3, 322.6 cm, respectively, from the breech.
A
resistance of 120 m placed in series with the diode, Fig. 2.1(c), limited the stage 1
negative current flow to a maximum 11 kA.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 2.8. Pseudo-Synchronous DES Railgun Data Using G-10 Bore Insulators.
Once again, plasma arc splitting is observed when stage 2 is fired. No conclusion
can be made pertaining to the pseudo-synchronous energy scheme’s ability to suppress
restrike. Since the secondary arc that formed by the bifurcation is accelerated towards
the breech, the breech voltage attributed to back EMF is reduced. This voltage reduction
prevents a restrike arc formation.
The collected data in Fig. 2.9 used the alumina bore insulators, a chamber pressure of
10 Torr, and a charging voltage of 2.5 kV on the first stage and 2.9 kV on the last three
stages. The four probes were located 18.5, 96.7, 135.7, 322.6 cm, respectively, from the
breech. No series resistance is added to the diode, allowing a negative current flow of 24
kA.
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Texas Tech University, Ryan William Karhi, November 2010
Neither plasma arc splitting nor restrike is observed in these data sets. All of the
integrated probe signals follow their respective current waveforms. The stage 2 probe
analysis shows a discrepancy between the probe signal and the expected current;
however, this is most likely due to a calibration error. Velocity calculations using Eq. 1.3
provide reassurance that no current is being diverted from the primary arc.
Fig. 2.9. Pseudo-Synchronous DES Railgun Data Using Alumina Bore Insulators.
2.4 Conclusion
Three different energy schemes were built, tested, and analyzed for secondary arc
formation. Two types of secondary arcs were observed, restrike and plasma arc splitting.
The latter proved dominate in the distributed energy schemes. The suppression of such
arcs is essential to maintain acceleration on the payload. All three systems used a plasma
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Texas Tech University, Ryan William Karhi, November 2010
arc which allowed for velocities up to 11 km/s with 15 kJ of energy. The arc length is
believed to be in excess of 20 bore diameters, especially when the G-10 bore insulators
are implemented. An accurate calculation of the arc length was not possible with data
obtained from the rail B-dot probes. Further investigation of the arc length is discussed
in Chapter IV.
Similar energy and current waveforms provided direct comparison between the
schemes when analyzing ablation effects and analysis of secondary arc formation. Rail
B-dot probes measured the rail current at different locations along the rail to provide a
means to detect these secondary arcs and provide in-bore velocity measurements. A real
time feedback control system was integrated into the distributed systems for a precise
release of energy upon the armature’s arrival to a later stage.
The breech-fed system did not require a feedback control system; instead, it used fixed
trigger timing. Restrike was detected using the G-10 bore insulators after a period of 130
s with an average current magnitude of 40 kA.
Experimentation under similar
conditions using the alumina bore insulators showed no indication of restrike and an arc
velocity matching closely to a calculated velocity (assuming no ablation). This provides
evidence to suggest ablation as one contributing factor to restrike.
The asynchronous and pseudo-synchronous DES railguns both experienced plasma arc
splitting which prevented an accurate restrike prevention analysis. Interestingly, the
pseudo-synchronous shot using the alumina bore insulators did suppress both types of
secondary arc formation. Plasma arc splitting must be prevented to provide an accurate
assessment of restrike suppression by distributed energy railguns.
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Texas Tech University, Ryan William Karhi, November 2010
CHAPTER ΙΙΙ
PLASMA ARC SPLITTING
3.1 Introduction
Analysis of rail B-dot data presented in Chapter II revealed current diversion
away from the primary arc. The cause of this effect was initially believed to be restrike,
where a secondary arc forms near the breech and draws current from active distributed
stages. However, the conditions required for such a restrike event to occur were not met
using the alumina bore insulators. To improve the analysis and determine the cause of
this current diversion, alternative diagnostics (armature B-dot probes) were implemented
to provide real-time measurement of the location, velocity, and direction of secondary
plasma arcs.
The experiments using this railgun diagnostic provided evidence to
discredit the restrike phenomenon as the cause of the observed current diversion. These
presented data confirm the discovery of a new type of secondary arc formation within a
free-arc railgun, referred to as “plasma arc splitting.” This chapter investigates the
splitting methodology and provides a viable method of prevention.
3.2 Arc Splitting Theory
Plasma arc splitting occurs at the distributed energy input locations along a freearc DES railgun bore and is believed to be a product of opposing magnetic pressures
perturbing the plasma arc.
According to basic railgun theory, magnetic pressure
magnitudes are dominated by the current and exist on both the rails and the armature, or
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Texas Tech University, Ryan William Karhi, November 2010
in our case, a plasma arc. The magnetic pressure on the arc is equal to the Lorentz force
acting on the arc per area,
𝑃𝑎𝑟𝑐 =
1 ′ 2
𝐿𝐼
2
ℎ𝑤
(3.1)
where 𝐿′ is the inductance gradient [H/m], I is the current through the arc [A], h is the
rail separation distance [m], and w is the bore width [m]. Additional variables that may
contribute to the splitting process include the plasma’s ion density and electron density.
For traditional breech-fed railguns, this arc magnetic pressure is always confined
to the rear or downstream region of the arc. For the distributed energy railgun, this is not
always the case. Let’s examine a situation where a distributed feed is triggered to release
its energy into the tail of a long plasma arc. When the energy is released, some of the
current will flow into the primary current carrying region of the arc, now ahead of the
feed location, while some will flow through the ionized plasma tail.
This ionized
material provides a low resistance path which will eventually lead to a breakdown
formation across the rails. Since current conduction is now located both ahead of and
directly at the feed location, the opposing magnetic pressures will perturb the plasma and
split the primary arc into two separate current carrying bodies. This effectively generates
a secondary arc within the railgun bore. According to the Lorentz force, the arc ahead of
the distributed feed will continue to be accelerated toward the muzzle and the arc behind
the feed will be accelerated toward the breech.
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Texas Tech University, Ryan William Karhi, November 2010
3.3 Arc Splitting Data
The rail B-dot probes used in past experiments10 detects the flow of current
through a rail at a specific rail location. This diagnostic proved useful in the detection of
diverting current, but the measurement of the number of current carrying arcs, their
positions in the bore, and their propagation directions yields too complex to extract from
the rail probe data. To overcome this problem, armature B-dot probes are employed.
The armature B-dot probe functions to detect the changing magnetic field of current
carrying arcs in the railgun bore. This allows for the detection of multiple arcs, if
present, and their propagation direction.
Four independent armature B-dot probes were integrated into the system. The
four probes were located 30.5, 47.0, 63.5, 78.7 cm respectively from the breech. Data
collected from the four armature B-dot probes are analyzed for three separate railgun
shots to investigate the dynamic arcs behaviors. All of the experimental shots presented
utilize a 2-stage asynchronous plasma arc DES railgun. The first stage has 1660 F of
capacitance and a 1 H power conditioning inductor.
The second stage, which is
distributed, utilizes three series RLC circuits comprised of an 830 F capacitor and a 2
H inductor. These three circuits have independent switches which are closed by a hard
coded timing scheme to produce relatively constant current. The distributed feed is
located 58 cm from the railgun breech. The charging voltage is 2.7 kV with an air
background gas pressure of 10 Torr. The first and second shot contain a 1 s delay of the
second stage trigger upon arrival of the armature, while the third shot has a delay of 25
s. The current waveforms of each stage are displayed in Fig. 3.1. These waveforms are
integrated Rogowski coil data collected from the first experimental shot discussed. The
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Texas Tech University, Ryan William Karhi, November 2010
second shot produced nearly identical current waveforms, due to similar initial
conditions; however, the waveforms of the third and final experiment varied slightly
because of a longer delay of the second stage trigger.
Fig. 3.1. Distributed Energy Current Waveforms.
These collected data in Fig. 3.2 shows the armature B-dot voltage signals from the
first discussed shot. No calibration procedure was performed on the sensors. A post
processed offset along the voltage axis allows for a clear view of their magnitudes
throughout the presented time interval. The main armature arrives at the first probe at 70
s, indicated by a positive voltage spike. Arrival to the second, third, and fourth probe is
clearly evident by the first positive voltage spike in each observable trace. By measuring
the time between the maximums of these preliminary spikes, the velocity from the breech
to the first probe is 4 km/s, 7 km/s from the first to second and second to third, and 8
km/s from the third to fourth probe. It is important to note that the location of the second
stage distributed energy feed resides between the second and third probes, 58 cm from
the breech. The second stage is triggered at 110 s upon the arc arrival to the distributed
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Texas Tech University, Ryan William Karhi, November 2010
feed location. Beginning 37 s after this release of energy, the second probe detects time
varying magnetic fields emanating from an unknown source. These oscillations are
observed until the first stage shuts off at 214 s, indicated by a positive spike in voltage.
A corresponding spike occurs in the first probe signal but is absent from the last two. A
pair of negative voltage spikes at 243 s and 268 s is also visible along the first two
probe signals.
These data suggest that a secondary arc is formed by the plasma arc splitting
phenomenon.
The magnetic pressure created by the second stage sourced current is
imparted on the plasma and believed to cause perturbations which lead to its division into
two separate current carrying arcs. At this time, nearly all of the current released from
the breech is diverted to the secondary arc because it is the path of least resistance and
inductance. This breech current produces a Lorentz force that should drive the secondary
arc toward the muzzle. However, a second Lorentz force is acting in opposition that
restricts its movement. This additional Lorentz force is a product of current flow to the
secondary arc sourced by the distributed feed.
Because current flowing from the
distributed feed is shared between both arcs, the primary arc continues acceleration
toward the muzzle as indicated by the third and fourth armature B-dot signals. The
opposing magnetic pressures on the secondary arc confine it to remain between the
distributed current feed and the position of the first B-dot probe. This event is identified
in these data of the second B-dot probe from 147 s to 183 s, which corresponds to the
unknown source of voltage oscillations discussed earlier. The breech current continues to
decay over time and stops flowing at 214 s. This is indicated by the pair of positive
voltage spikes (induced voltage by an opening switch) observed in the first and second
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Texas Tech University, Ryan William Karhi, November 2010
probe signals. Since these spikes only appear on the first two probe signals, the position
of the secondary arc has to be between the second and third probe locations. After this
time the secondary arc has a magnetic pressure component solely in the breech direction.
The arc now moves past the second probe position at 243 s and past the first probe at
268 s, indicated by negative voltage spikes because the magnetic flux enters from the
opposite face of the B-dot loop.
Fig. 3.2. Armature B-dot Probe Signals from Shot 1.
The collected data in Fig. 3.3 shows the armature B-dot voltage signals from the
second discussed shot. Initial conditions are identical to the first shot, but the results are
slightly different. Once again, a secondary arc is believed to develop as a direct result of
plasma arc splitting due to the distributed feed. Similar voltage oscillations are observed
from 156 s to 176 s at the time the when the current magnitude sourced from the
second stage equals and surpasses the first stage current magnitude. The first observable
difference is an absent voltage spike at 215 s on the second probe signal. This implies
that the secondary arc is located in a region between the first and second probe at the time
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Texas Tech University, Ryan William Karhi, November 2010
the first stage turns off. Further evidence to support this statement is seen by a missing
negative voltage spike in the second probe signal after the breech-fed current falls to
zero. As the secondary arc is accelerated toward the breech a strong negative voltage
spike at 250 s signifies its propagation past the first probe location.
Fig. 3.3. Armature B-dot Probe Signals from Shot 2.
The conclusion after examining these data of the first two shots leads our team to
believe that plasma arc splitting is a real phenomenon. If multiple secondary arcs are
formed behind the distributed feed through plasma perturbations, the opposing magnetic
pressures from the breech current and distributed feed current most likely cause the arcs
to collapse together into a single entity. Although no restrike was observed with the DES
railgun system of Chapter II, a new form of secondary arc formation has been discovered
which threatens plasma armature performance.
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Texas Tech University, Ryan William Karhi, November 2010
3.4 Arc Splitting Prevention
Plasma arc splitting develops from the flow of current into the ionized tail or
body of the plasma arc. This can be prevented by waiting until the full length of the arc
is ahead of the distributed feed location before the release of energy. This allows the
arc’s magnetic pressure to exist only at the tail end region. The triggering delay time in
the control system was lengthened to 25 s, allowing adequate time for the arc length to
pass the distributed feed position. All other initial conditions remain identical to the first
two shots.
The collected data in Fig. 3.4 shows the armature B-dot voltage signals from the
third shot. There is no observable secondary arc detection from any of the B-dot probe
signals. The primary arc movement is detected by each sensor and is traveling towards
the muzzle. It is also evident that a small positive voltage spike appears in all four
waveforms at 220 s. As discussed in the first two shots this is an induced voltage
caused by turn off of the first stage switch. Because this effect is now seen in all four
probe waveforms, the current sourced from the breech is flowing past each probe location
and through the primary arc. Thus, plasma arc splitting can be prevented by maintaining
the arc magnetic pressure to the back of the plasma arc.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 3.4. Armature B-dot Probe Signals from Shot 3.
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Texas Tech University, Ryan William Karhi, November 2010
CHAPTER ΙV
PLASMA ARC LENGTH
4.1 Introduction
Since secondary arc formation from plasma arc splitting can be suppressed by
precise timing of the release of distributed energy, insight into the length of the arc is
critical. Optical diagnostics were originally integrated into the railgun in effort to analyze
plasma density and composition by the use of spectroscopy (not discussed in this
dissertation). A simple replacement of the spectrograph with photodiodes provided an
accurate arc length measurement device. It is possible to extract the arc length from data
obtained by B-dot probes, but luminosity profiling does not require complex post
processing techniques. These experiments utilize the same 2-stage asynchronous plasma
arc DES railgun discussed in Chapter III.
4.2 Experimental Setup
The optical diagnostics selected are Hamamatsu S1336-18BK photodiodes. The
photodiodes have a spectral response range of 320 nm to 1100 nm and a rise time of 0.1
s. To improve the frequency response and linearity, a reverse voltage of 4.5 V was
applied across the diode. A schematic diagram of the circuit is shown below in Fig. 4.1.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 4.1. Schematic of Photodiode Reverse Voltage Circuit11.
The values of R and C in the schematic are 10 kand 0.1 F, as recommended
by Hamamatsu. Five of these photodiodes are utilized to provide light detection at five
different in-bore locations, Fig. 4.2. The photodiodes cannot be directly exposed to the
bore due to the intense heat radiated by the plasma arc. Instead, optical fibers coupled the
light signals to the detectors at a safe distance away.
Fig. 4.2. A Drawing of the DES Railgun and Optical Diagnostics.
The optical fiber selected was available in-house and is manufactured by
Fiberguide Industries, item# SFS200/220 N. It is made of pure fused silica for efficient
light coupling and high quality transmission. In order to expose the optical fiber to the
inside of the bore, 1.0 mm holes were drilled into the middle of the alumina tiles. The
hole diameter was kept to a minimum because it encourages plasma leakage. Additional
holes, 1.3 cm in diameter, are drilled into the adjacent G-10 support structure to allow for
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Texas Tech University, Ryan William Karhi, November 2010
internal access to the alumina tile holes. The actual optical fiber mounting location along
the length of the gun is not accurate in Fig. 4.3, but the picture shows an exposed bore to
illustrate how the fibers are oriented. The optical fibers are drawn in blue and the black
boxes represent the coupling of two fiber lines.
Fig. 4.3. Illustration of the Fiber Line Mounting.
The coupling fasteners of the five optical fibers are shown in Fig. 4.4. They are
spaced 7.6 cm apart and are symmetrically positioned at the distributed feed location with
the third fiber located directly at the distributed feed point. This allowed plasma length
data to be collected before, after, and directly at the secondary stage. Foreshadowing
thermal damage to the exposed fiber tips, optical couplers were used to provide a 5 cm
replaceable fiber lead extending into the alumina.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 4.4. A Picture of the Five Optical Fiber Couplers.
4.3 Experimental Results
As previously mentioned, these experiments utilize the same 2-stage
asynchronous plasma arc DES railgun discussed in Chapter III. The charging voltage
remained at 2.7 kV; however, the in-bore background gas pressure was varied from 5 to
30 Torr. The five induced voltage signals from the photodiodes are displayed in Fig. 4.5
for a bore pressure of 20 Torr.
The plasma arc current waveform is plotted on a
secondary y-axis for correlation. Traditional techniques to calibrate the sensors were
abandoned due to fiber polish degradation during repeated experimental testing.
Therefore, a comparison of the arc current magnitude to light intensity is neglected with a
focus on the waveform shape and pulse width. All of the photodiode waveforms more or
less exhibit a similar shape. There is an exponential rise of voltage on the leading pulse
edge followed by a linear transition extending to the point of maximum amplitude. As
expected, there appears to be a larger current density through the arc head than through
the body. The brief exponential rise indicates a short, compact plasma arc head and the
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Texas Tech University, Ryan William Karhi, November 2010
linear region is indicative of a long plasma body. The long body is unique to the freerunning arc since it is only bound by viscous drag and the in-bore gas pressure, not a
solid projectile. Current distribution is difficult to determine in the body region. Highly
ionized ablation products present in this region due to viscous drag continue to emit
radiation. Thus, the voltage induced luminosity is not directly correlated with a current
carrying region. The falling edges of the waveforms appear to decay exponentially, with
the longest fall time observed on the fourth photodiode waveform. This delayed decay is
associated with a long tail region.
Fig. 4.5. Photodiode Waveforms with Corresponding Armature Current.
The plasma arc length is measured from the photodiode data and presented in Fig.
4.6. The length is calculated by multiplying the photodiode waveform pulse width with a
calculated arc velocity derived from the rise times. A length calculation is provided for
each fiber location for varying gas pressures between 5 and 30 Torr. A monotonically
increasing function of arc length for both position and pressure would be expected from a
breech-fed energy scheme. While the distributed energy scheme proves to agree with the
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Texas Tech University, Ryan William Karhi, November 2010
latter, the arc length traces are not monotonic in relation to position. A trend in shape
does exist however and will be explained with a focus on a single curve.
Analyzing the 5 Torr trace, the arc length is initially 17.7 cm as it moves past the
first fiber location. This length is reduced to 8.9 cm at the second fiber position. As
discussed in Chapter III, the opposing magnetic pressures sourced from the distributed
feed can perturb the plasma. These perturbations allow the plasma to expand from 13.5 –
19.5 cm as it propagates past the third and fourth fiber locations. Interestingly, when the
arc reaches the fifth fiber location, the length is reduced once again to a value of 9.4 cm.
This can be explained by a return of the magnetic pressure to the tail end of the plasma
arc. These experiments found the arc length to be as long as 37 cm (30 Torr air pressure)
and conversely as short as 8 cm (5 Torr air pressure). These data shed insight into the
complex and highly dynamic interactions of multiple magnetic pressure vectors acting
near the distributed feed. The arc length calculations presented were beneficial to the
suppression of plasma arc splitting during future experiments.
Fig. 4.6. Arc Length Calculations vs. Pressure and Location.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 4.7 is a plot of the calculated arc velocity as a function of position for various
pressures. A decrease in velocity is observed on all of the traces at the second fiber
location. This further supports the hypothesis that an opposing Lorentz force is acting on
the plasma sourced from the distributed feed.
Velocity calculations from the third
through fifth fiber locations indicate slight increases and decreases of velocity. It is
postulated that this could be a direct consequence of either a variable plasma mass or
variable magnetic pressure. The perturbations could alter the plasma mass through
bifurcation while a variable magnetic pressure corresponds to a changing driving force.
The derivatives of these velocities (accelerations) could have a significant impact on the
payload.
Fig. 4.7. Arc Velocity Calculations vs. Pressure and Location.
4.4 Conclusion
This chapter described an experiment to measure the plasma arc length in effort to
determine the appropriate firing times of distributed energy modules to prevent plasma
arc splitting. The arc length was measured using five equally spaced optical diagnostics
(photodiodes) positioned before, after, and directly at a distributed current feed. Optical
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Texas Tech University, Ryan William Karhi, November 2010
fibers exposed to the bore coupled the light signals to the photodiode detectors to prevent
thermal damage radiating from the plasma. The same 2-stage asynchronous plasma arc
DES railgun discussed in Chapter III was implemented in these experiments. The light
intensity profiles indicated a short, compact plasma arc head and long plasma body and
tail region. The plasma length was calculated for each fiber location for varying air
pressures between 5 and 30 Torr. As expected, the arc length increased with rising air
pressure because the higher pressures provided more available fill gas molecules
vulnerable to ionization by the plasma. These experiments found the arc length to be as
long as 37 cm (30 Torr air pressure) and conversely as short as 8 cm (5 Torr air pressure).
Further, the investigation found the arc length to be dynamic near the distributed current
feed. This result was not foreshadowed and is believed to be a product of gradient
magnetic pressures perturbing the plasma arc. In addition, these perturbations affected
the arc velocity which could impart significant changes of acceleration on the payload.
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Texas Tech University, Ryan William Karhi, November 2010
CHAPTER V
DEVELOPMENT OF A NEW SYSTEM PROTOTYPE
5.1 Introduction
The knowledge acquired from experiments described in Chapters II-IV is utilized to
design and test a fully synchronous DES railgun. Since a large stage number is required
to achieve synchronous operation, our team decided to build a DES railgun with 40
stages. This number was selected based on a theoretical synchronous system2 described
by Parker. The complexity of a DES railgun increases with stage number, so after
completion of the full system design, it was agreed to first build a prototype that mimics
the design and operation of the first few stages.
This chapter will discuss the
development of a synchronous DES railgun simulation, as well as the design,
construction, and testing of a 7-stage DES railgun prototype. The objectives of the
prototype are to design, built, and test:
a) A 7-stage DES railgun with successful
arc propagation towards the
muzzle.
b) A containment structure capable of maintaining low pressures (mTorr range).
c) A bore compression technique to suppress plasma leakage.
d) A flange to couple multiple containment structures together while maintaining
vacuum and bore compression.
e) Compact distributed energy modules capable of sourcing the necessary energy.
f) Precision diagnostics including B-dot probes and Rogowski coils.
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Texas Tech University, Ryan William Karhi, November 2010
5.2 Free-Arc DES Railgun Simulation
5.2.1 Introduction
The overall Texas Tech objective is to characterize a fully synchronous
distributed energy railgun. To this point only a 4-stage pseudo-synchronous DES railgun
has been built and tested. Although not fully synchronous, discoveries made with the
initial system highlighted critical design issues advantageous for the new system in
development. A necessary phase of the design called for a computer simulation to
characterize component values and ultimately determine economic feasibility.
Both
simulation results and practical system components are discussed. The simulation is
designed to achieve an arc velocity greater than 8 km/s with 40 stages contributing to
provide 50 kA of nearly constant current.
The circuit equations implemented are
characterized by a lumped circuit element model2. These design equations are coded and
calculated using the MATLAB® environment. Complex plasma armature dynamics are
neglected due to their irrelevance for the design information sought. The energy stored
within each stage and its length will remain constant; however, variations of these
constants are analyzed for optimization of a realistic design. Values obtained from the
simulation allow for the selection of realizable system components such as: capacitors,
switches, and power conditioning devices.
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Texas Tech University, Ryan William Karhi, November 2010
5.2.2 Implemented Simulation Equations
The code was developed in accordance to derived circuit equations for a distributed
energy model2. The code implements the derivation of two loop equations from a
lumped circuit element model describing the capacitive energy store stages. The first
loop equation characterizes the electrical system for the case when the arc has passed
through a respective stage. The simulation equation yields
𝑖
𝑖
𝑘=1
𝑘=1
𝑞𝑖
𝑞𝑖+1
− 𝑅𝑖 𝑞̇ 𝑖 − 𝐿𝑖 𝑞̈ 𝑖 −𝑟𝑖 𝑆𝑖 ∑ 𝑞̇ 𝑘 − 𝐿′ 𝑆𝑖 ∑ 𝑞̈ 𝑘 +
𝐶𝑖
𝐶𝑖+1
+𝑅𝑖+1 𝑞̇ 𝑖+1 + 𝐿𝑖+1 𝑞̈ 𝑖+1 = 0, 1 ≤ 𝑖 ≤ (𝑁 − 1),
(5.1)
where i represents the stage number, 𝑞𝑖 in coulombs is the charge on capacitor 𝐶𝑖 [C], 𝑅𝑖
is the stage resistance [], 𝐿𝑖 is the stage inductance [H], 𝑟𝑖 is the stage rail resistance
[/m], 𝑆𝑖 is the stage length [m], and 𝐿′ =dL/dx is the inductance gradient [H/m]. A
thorough derivation is presented2, including dimensionless variables and equations. The
schematic from which equation (5.1) was derived is shown in Fig. 5.1.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 5.1. Schematic of a Stage in which the Plasma Arc has Passed Through2.
The second loop equation characterizes the electrical system for the case when the arc
is contained within a respective stage. Here, N refers to the stage number and the second
order differential equation used in the simulation yields
𝑞𝑁
𝐶𝑁
′ ∗ 𝑁
– 𝑅𝑁 𝑞̇ 𝑁 − 𝐿𝑁 𝑞̈ 𝑁 − (𝑟𝑥 ∗ − 𝐿′ 𝑥̇ ) ∑𝑁
𝑘=1 𝑞̇ 𝑘 − 𝐿 𝑥 ∑𝑘=1 𝑞̈ 𝑘 = 0,
(5.2)
where 𝑥̇ is the arc velocity [m/s], and 𝑥 ∗ is the arc distance from the beginning of stage N
in meters. The schematic from which Eq. 5.2 was derived is shown in Fig. 5.2 below.
Fig. 5.2. Schematic of a Stage that Contains the Plasma Arc2.
If the arc is at a distance 𝑥 from the railgun breech, the relationship between 𝑥 and 𝑥 ∗
can be described as
𝑥 ∗ = 𝑥 − ∑𝑁−1
𝑖=1 𝑆𝑖 .
(3)
The second order differential equations of (5.1) and (5.2) are solved using a
MATLAB® routine ode45 with syntax of
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Texas Tech University, Ryan William Karhi, November 2010
[t,Y] = ode45(odefun, tspan, y0, options)
where odefun is a function that evaluates the right side of the differential equations, tspan
is a vector specifying the interval of integration, y0 is a vector of initial conditions, and
options is a function to adjust the integration parameters which was useful for the 𝑞̈
calculation or equivalently the dI/dt calculation. The algorithm used for the ode45
routine is based on an explicit Runge-Kutta formula known as the Dormand-Prince pair12.
The terms presented in equations (5.1)-(5.3) are all straight forward with the exception
of the arc velocity term. The simulation uses a derived plasma velocity equation (1.3)
which assumes no in-bore wall ablation and has the form
𝑣𝑝 = √(𝛾∗
𝐿′
𝐼
( )
+1)𝜌0 ℎ
1
𝑥
,
(4)
√1+(𝑥 )
𝑠
where 𝐿′ =dL/dx is the inductance gradient [H/m], 𝛾 ∗ is the ratio of specific heat [unit
less], 𝜌0 is the initial gas density [kg/m3], I is the armature current [A], ℎ is the rail
separation distance [m], 𝑥 is the distance the shock front has moved [m], and 𝑥𝑠 is a scale
length as a consequence of viscous forces [m]. The equation for the scale length is
characterized by
1
ℎ
4
𝐶𝑓
𝑥𝑠 = (𝛾 ∗ + ) ( ),
(5)
where 𝐶𝑓 is the drag coefficient [unitless].
The location of the shock front, the ratio of specific heat, the scale length, and the drag
coefficient are all difficult to determine by neglecting complex physics. The values used
in the simulation were determined using experimental data with comparable parameters10.
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Texas Tech University, Ryan William Karhi, November 2010
For strong ionizing shocks, the ratio of specific heat has a strong dependence on the
degree of dissociation and ionization6. A common value of 1.2 under this condition is
used in the simulation. The scale length is calculated by setting the drag coefficient to a
constant value of 0.0049, which was calculated from the comparable experiment. By
analyzing Eq. 5.4 it can be observed that the arc velocity is now a function of only two
temporal variables, the current through the arc and the shock front distance. Since the
current is a user defined variable, the remaining dependent variable to be determined is
the location of the shock front. This is not an intuitive calculation and drastically affects
the arc velocity in the simulation. An attempt was made to approximate the shock front
movement by setting it equal to the arc movement. Since the current is essentially
constant, this produced a linear decrease of the velocity as the arc traveled down the rails.
The velocity measurement of a past experiment10 confirms a velocity reduction with arc
distance, but to a lesser degree than what Eq. 5.4 predicts. An advanced code6 also had
difficulty matching theory to experimental data and concluded that there must be a linear
dependence on the drag coefficient for the hypervelocity regime.
Taking this into
consideration, a compromise was made by making the shock front distance constant
while maintaining a constant drag coefficient. Therefore, the time varying velocity is
solely proportional to the arc current. When the shock front distance is set to the rail
length, reasonable values of velocity are obtained by comparison to experimental
measurements found in literature10.
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Texas Tech University, Ryan William Karhi, November 2010
5.2.3 Simulation Parameters and Results
This section describes the selected parameters and results for the simulation using a
“constant energy” model. A “constant energy” model refers to equal stage lengths,
constant efficiency, and constant electrical energy stored in each stage which allows each
stage to deliver an equal amount of energy to the arc2. The specified model was selected
because of its simplicity and practicality to build and maintain a real world system. With
the exception of the first stage, the latter 39 stages share a constant amount of stored
energy to be released upon the plasma arc’s arrival to a respective stage. The first stage
requires more energy than latter stages to rapidly accelerate the arc to a velocity near the
target velocity. This velocity is then maintained by the following stages.
The first stage contains the following parameter values:




Capacitance: 830 F
Voltage: 1500 V
Resistance: 5 m
Inductance: 1 H
Stages 2-40 that follow the “constant energy” model contain the following parameter
values:




Capacitance: 750 F
Voltage: 750 V
Resistance: 5 m
Inductance: 1.5 H
The simulated railgun contains 40 stages with each stage measuring 15.24 cm
providing a total rail length of 6 meters. The rails are assumed to be copper with a
resistance of 100 /m and are spaced 10 mm apart. An inductance gradient of 0.45
H/m was calculated13 with respect to rectangular copper rails of dimension 0.64 cm x
3.18 cm. The physical interactions of gas molecules and atomic physics are neglected;
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Texas Tech University, Ryan William Karhi, November 2010
however, the initial gas density is needed for the velocity calculation. Rapid acceleration
of the arc requires a low pressure environment with the given current magnitude. Air at a
pressure of 10 Torr was used to solve for the initial gas density. The negative current
associated with each stage was additionally attenuated with a resistance of 100 mfor
pulse shaping
The current waveforms simulated for all 40 energy stages are shown in Fig. 5.3. A
time step of 1 s was used for a total duration of 1 ms. The current magnitude of the first
stage is nearly three times the current magnitude of all remaining stages. As previously
stated, this is done to hastily accelerate the arc. By observation of the figure, the current
magnitudes of stages 2-40 are not equivalent as would be expected by following a
“constant energy” model. This is believed to be associated with the varying arc velocity,
which is proportional to the current in the computer simulation. The current released by a
stage flows through both the rails and through the arc. The rail resistance is therefore a
time varying parameter that depends on the arc velocity. In other words, as the arc
velocity increases, the arc distance increases between time steps, and the rail resistance is
a function of this distance which obviously affects the current flow. An additional
frequency dependant parameter can alter the rail resistance and is known as the skin
depth or penetration depth of current into the rail, but is not addressed in the present
simulation. 
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 5.3. Simulated Current Waveforms for a 40-Stage System. Top: Current Waveforms
for Stages 1-20. Bottom: Current Waveforms for Stages 21-40.
The total current contribution by all of the stages is displayed in Fig. 5.4. An
average value of 50 kA flows through the arc which meets the criterion of the simulation.
After an abrupt jump in magnitude attributed by the first stage, the current slowly rises,
nearly becomes constant, and then sharply decreases at the arrival to the railgun muzzle.
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Texas Tech University, Ryan William Karhi, November 2010
Negative current observed to flow after 0.6 ms is an effect of the release of energy
contained within the remaining stages.
Fig. 5.4. Simulated Armature Current.
A plot of the arc velocity is displayed in Fig. 5.5. The velocity waveform is
virtually identical to the total current waveform, which is expected because of the
velocity equation used in this computer simulation. The initial spike in velocity peaking
at 10 km/s corresponds to just over 40 kA of current. This velocity compares reasonably
well to an experimental velocity measurement from an analogous system10.
The
maximum plasma arc velocity is approximately 13 km/s, exceeding the minimum
velocity requirement by 5 km/s.
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Texas Tech University, Ryan William Karhi, November 2010
Fig 5.5. Simulated Arc Velocity.
5.2.4 Conclusion
A computer simulation of a 40-stage synchronous plasma arc DES railgun was
discussed. The simulation provides insight into the actual design and development of
both systems discussed in Chapters V and VI. The simulation results are in agreement
with the physical system requirements. The average current contribution was simulated
to be 50 kA providing a maximum arc velocity of 13 km/s. Values used in the simulation
for capacitors, switches, and power conditioning devices prove to be both realistic and
within the project budget. The experimental results will obviously not exactly match the
computer simulation so component values and parameters will require slight adjustments
for optimization.
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Texas Tech University, Ryan William Karhi, November 2010
5.3 Experimental Setup
This section will discuss the design and construction of a 7-stage DES railgun
prototype. The rationale of the prototype is to test all of the components designed for the
40-stage railgun.
5.3.1 Rails and Containment Structure
The assembled prototype is 1.2 m long with a 1.0 cm x 1.0 cm square bore cross
section. A cross-sectional view of the railgun is shown by a 2D computer-aided design
(CAD) assembly in Fig. 5.6. The railgun core utilizes rails made of UNS C11000 ETP
copper with a shoulder machined at both edges to seat the bore insulators and set the railto-rail spacing. On the back sides of the rails, 1/4’’-28 holes provide an electrical
connection for brass all-thread distributed current feeds. The distance between the first
and second feed points is 20 cm and each additional feed is spaced 15.24 cm apart. The
containment structure is machined from 10.16 cm x 10.16 cm G-10 blocks and serves to
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 5.6. Cross-Sectional View of the Railgun Prototype.
compress the core, resist the rail repulsive force, and maintain a low pressure air
environment. O-ring seals are encircled by a bolt pattern at each end to couple
flanges/faceplates to the structure. While the bottom of the containment remains solid, an
opening machined on the top aids the assembly process and provides a potential in-bore
window option to view the plasma armature. The latter is executed by replacing opaque
components with ones possessing translucent properties. During assembly, the railgun
core is seated at the bottom of a U-shaped channel cut along the length of the casing.
One side-wall of this channel is 90 degrees with respect to the channel floor while the
other has a 3 degree taper. This taper allows for the placement of shims, Fig. 5.7, to
compress the core horizontally. Vertical compression is achieved by positioning a 3.8 cm
x 3.2 cm G-10 block on top of the core and fastening top and bottom 15.24 cm x 1.9 cm
G-10 lids with an array of 3/4’’-10 fiberglass all-thread rods.
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Texas Tech University, Ryan William Karhi, November 2010
Fig. 5.7. Interior View of the Containment Structure.
A custom oval shaped o-ring, Fig. 5.8, seals the opening on the upper containment in
order to maintain vacuum. Additional locations vulnerable to vacuum leakage remain at
all of the distributed current feed access points. To prevent such leaks, NPT Nylon tube
fittings equipped with o-ring seals are mounted to the containment exterior.
Fig. 5.8. Partially Disassembled Railgun View.
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Texas Tech University, Ryan William Karhi, November 2010
The vacuum line and plasma injector are mounted at two access ports located on the
bottom of the containment. Plasma injection occurs in the breech region, 5 cm in front of
the breech current feed. This creates a small volume of magnetic pressure behind the
armature, encouraging muzzle oriented propagation. The same tube fitting implemented
for the distributed current feeds is used to seal around the plasma source. Vacuum is
drawn at the railgun muzzle to distance the bulky fittings and pressure sensors from
electrical components.
A G-10 flange, Fig. 5.7, couples two 61 cm containment structures together. The
7.62 cm long flange contains a 6.35 cm diameter thru hole which houses the railgun core.
Due to the rectangular geometry of the core, compression is maintained with semicircular
G-10 shims tapped in place on each side. It would be preferable to have the containment
machined from a single piece of G-10; however, a flange system is necessary for
expansion to a 6 meter long system.
5.3.2 Energy Modules
Six distributed energy modules are used to supply current to the rails and drive the
armature. With exception of the first stage, all of the distributed energy modules are
identical. This section will describe their design and components in detail.
A single distributed energy module of the prototype system is shown in Fig. 5.9.
The capacitors have a voltage rating of 1000 VDC and are manufactured by Electronic
Concepts (PN# UL30BL0150). Five of these 150 F film dielectric capacitors are wired
in parallel to comprise a 750 F capacitor bank. The diode and thyristor selected are both
solid state devices manufactured by ABB Semiconductors. The diode (PN#
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Texas Tech University, Ryan William Karhi, November 2010
5SDD11D2800) has a blocking voltage of 3000 V and a non-repetitive peak surge current
of 15 kA. This diode is placed in anti-parallel with the thyristor switch to act like a triac
switch and allow both positive and negative current flow.
Fig. 5.9. CAD Drawing of the Distributed Energy Module.
The resistor is a high power carbon disk and is connected in series with the diode
to attenuate the negative current amplitude as full reversal is undesirable. A computer
simulation of the system was used to determine an optimum value of 100 m should be
used; however, 0.5  resistors were used for the prototype due to availability. The
thyristor selected is manufactured by ABB Semiconductor (PN# 5STP10D1601) and has
a blocking voltage of 1600 V, a continuous 1 Hz dI/dt rating of 1000 A/s, and a peak
non-repetitive surge current of 16 kA at 125 degrees Celsius with a 8.3 ms pulse. To
close the switch a 10 s, 15 volt pulse is applied across the gate and cathode. This gate
signal is generated using a custom pulser board designed and built at Texas Tech
University. The aluminum bus bars direct the released stored energy to the railgun rails
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Texas Tech University, Ryan William Karhi, November 2010
and are designed to provide low resistance and high power dissipation. To achieve the
desired discharge waveform, power conditioning is performed by 1.5 H of selfinductance. A variable self-inductance scheme, Fig. 5.10, was developed to manipulate
stage inductance during the preliminary testing phase. The loop area can be
independently altered for each stage or be dependently altered over the entire system.
Attention must also be paid to mutual inductance between stages. A calculated value on
the order of tens of nano-Henries will not profoundly affect adjacent stages.
Fig. 5.10. Variable Self-Inductance Scheme.
Since multiple distributed energy stages are active during operation, the first stage of
the railgun requires a larger current magnitude to equal their current summation. Hence,
the first stage contains a high voltage 830 F oil filled capacitor rated to 12 kV. The
switch selected is an ABB Semiconductor (PN# 5STP34N5200) thyristor. This switch is
capable of a non-repetitive peak surge current of 60 kA for 8.3 ms and a blocking voltage
of 5.7 kV. A diode (PN# SDD303KT) is placed in anti-parallel for the same purpose
discussed for the distributed energy modules. The diode has a 6 kV blocking voltage and
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Texas Tech University, Ryan William Karhi, November 2010
is capable of conducting a non-repetitive peak surge current of 60 kA for 8.3 ms. A 0.5
 carbon resistor in series with this diode limits the negative current magnitude.
5.3.3 Diagnostics
The prototype contains seven, rail B-dot probes mounted on the containment
exterior. These probes measure the local rail current at their respective location for
current diversion analysis and velocity measurements. Six of these probes are located
between stages and an additional probe is positioned at the muzzle. The seven rail B-dot
probes were located 11.4, 29.2, 42.5, 55.2, 69.2, 87.6, and 105.4 cm, respectively, from
the location of the first stage’s feed location. Each probe contains 20 turns of 18-gauge
magnet wire. They are positioned at a 45 degree angle from the rails, Fig. 5.11, with the
loop area perpendicular to the rail orientation to maximize coupling of the magnetic flux.
Shielded air-core Rogowski coils are used to measure the output current waveforms
produced by all of the energy modules. Both types of sensors are built in-house and are
all appropriately calibrated.
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Fig. 5.11. Rail B-dot Probe Orientation.
5.3.4 Plasma Injector
A plasma injector at the breech reliably supplies plasma for each experimental
test. Plasma injection occurs in the breech region, 5 cm in front of the breech current
feed. This creates a small volume of magnetic pressure behind the plasma, encouraging
muzzle oriented propagation. The plasma injector is powered by a 5-stage solid-state
Marx generator that is charged using an external 200 VDC power supply. The Marx is
triggered by a TTL trigger pulse and provides an output pulse of 1 kV with a 10 s pulse
width. This signal is input into a 1:40 ratio pulse transformer to supply a pulse with a 40
kV magnitude to the electrodes. The injector is mounted into the G-10 containment
structure and has a coaxial electrode configuration. The plasma is generated by an
electrical breakdown across a tungsten rod cathode and stainless steel tube anode. A
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Texas Tech University, Ryan William Karhi, November 2010
hollow ceramic tube provides insulation between the anode and cathode. The plasma
generation system is displayed in Fig. 5.12.
Fig. 5.12. Plasma Generation System.
5.3.5 Control System
The control system implemented on the prototype is a hard-coded digital pulse
timing sequence determined by experimental trial and error. The trigger timing found for
each stage is 1, 45, 65, 85, 105, 135, 165 s, respectively. A feedback control system
utilizing sensors along the railgun will simplify this process and is implemented on more
complex systems discussed later.
A representation of the control system hardware is shown in Fig. 5.13. The brain
of the system consists is a National Instruments CompactRIO programmable automation
controller (PAC) that utilizes Field Programmable Gate Array (FPGA) technology to
provide real-time processing. The LabVIEW 2009 software package is used to develop
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control code which is compiled into a bit-file and downloaded into the CompactRIOs’
512 MB flash memory where it is stored and is activated after the boot cycle.
Fig. 5.13. Control System Hardware.
To initiate the release of current from an energy module, an 8-channel NI 9401 TTL
digital output module provides a 10 s, 5 V pulse to a fiber optic board on the respected
stage channel. Gate driver boards receive the light signals and convert them to 10 s, 15
V analog pulses to trigger the stage’s corresponding SCR gate and release the stored
energy in the capacitor banks.
5.3.6 Support Structure and Built System
A support structure is necessary in order to mount the railgun and provide a platform
for the energy modules to rest on. Commercially available steel tripods have been
selected that provide a stable foundation and variable height adjustment.
Besides
supporting the railgun weight, the support structure must also absorb recoil forces on the
railgun. The recoil force of a railgun is equal to the Lorentz force and acts on the current
feeds. In comparison to Mega-Ampere laboratory launchers that accelerate payloads,
only tens of kilo-Amperes are required to accelerate our plasma arc to hypervelocities.
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This reduced current requirement drastically decreases the Lorentz force, so hard
mounting a support structure to the floor is unnecessary.
The built 7-stage DES railgun prototype is shown below in Fig. 5.14. The photograph,
Fig. 5.14(a), shows an side view of the system where the switches, diodes, and rail B-dot
probes are located. In Fig. 5.14(b), an isometric view displays the capacitors, Rogowski
coils, and vacuum pump connection. Two tripods support the railgun and switches while
a table is used to support the capacitors.
(a)
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(b)
Fig. 5.14. Photographs of the 7-Stage Prototype System. (a) View of Switch and Diode
side. (b) View of Capacitor Bank Side.
5.4 Experimental Results
The experimental results obtained from a 7-stage DES railgun prototype are
presented. The current waveforms for all seven stages, along with a summed armature
current waveform, are displayed in Fig. 5.15. During the shot, the containment structure
was evacuated to roughly 10 Torr. The first stage was charged to 1800 volts and sourced
approximately 30 kA for 120 s. The last six stages were charged to 500 volts and each
output approximately 10 kA with a 100 s pulse width. The trigger timing for each stage
was hard-coded into a digital pulse generator at 1, 45, 65, 85, 105, 135, 165 s
respectively.
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Fig. 5.15. Current Waveforms for the Prototype System.
The maximum armature current is close to 38 kA which accelerated the plasma to an
average velocity of ~ 6.7 km/s. This velocity is reached within 10’s of s of arc
formation and was calculated using the rail B-dot data shown in Fig. 5.16. The seven rail
B-dot probes were located 11.4, 29.2, 42.5, 55.2, 69.2, 87.6, and 105.4 cm respectively,
from the location of the first stage’s feed location. Analysis of the B-dot traces in Fig.
5.16 reveals no indication that plasma arc splitting has occurred at any of the feed
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Fig. 5.16. B-dot Measurements from the Prototype System.
locations. In addition, these data show no presence of restrike arcs within the railgun
bore. Further analysis of the sensor outputs from the first three stages is presented in Fig.
5.17. The probe signals are integrated and multiplied by a calibration constant to produce
local rail current waveforms. The current contribution from the first three stages is
shown alongside three rail B-dot probe signals. Current diversion to secondary arcs is
not present as long as the sourced rail current waveform matches the local rail current
waveform. The probes signals show the rail current rise up to the full sourced current
magnitude and then match the sourced current waveforms shapes over the remaining
duration. This indicated an absence of current diversion.
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Fig. 5.17. Current Distribution Analysis Data.
5.5 Conclusion
This chapter discussed the development of a prototype system to test all of the
components designed for a 40-stage DES plasma arc railgun. The prototype resembles
the first 7 stages of the overall design and proves to be feasible and functioning correctly.
A computer simulation was programmed to characterize component values and ultimately
determine economic feasibility. Values obtained from the simulation allowed for the
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selection of realizable system components such as: capacitors, switches, and power
conditioning devices.
The objectives of the prototype were to design, built, and test:
a) A 7-stage DES railgun with successful
arc propagation towards the
muzzle.
b) A containment structure capable of maintaining low pressures (mTorr range).
c) A bore compression technique to suppress plasma leakage.
d) A flange to couple multiple containment structures together while maintaining
vacuum and bore compression.
e) Compact distributed energy modules capable of sourcing the necessary energy.
f) Precision diagnostics including B-dot probes and Rogowski coils.
The B-dot probes waveforms, Fig. 5.16, confirm that the arc is accelerating towards the
railgun muzzle as all 7 stages discharge. A containment structure was designed and built
using G-10 with numerous o-ring seals to achieve mTorr pressures with air as the fill gas.
Plasma leakage was reduced by applying a mechanical horizontal and vertical
compression to the railgun core. The flange design proved to maintain vacuum and bore
compression. Energy modules were designed utilizing compact film dielectric capacitors
and a variable self-inductance scheme. When charged to 500 volts, the modules output
approximately 10 kA with a 100 s pulse width. These values agreed with the simulation
results.
Finally, B-dot probes containing 20 turns and shielded air-core Rogowski coils
were built in-house and calibrated for current and velocity measurements. All of the
objectives were successfully completed for the prototype system.
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The experimental results presented, show an armature current close to 38 kA. This
current magnitude accelerated the plasma to an average velocity of ~ 6.7 km/s. Analysis
of the B-dot traces revealed no indication that plasma arc splitting has occurred at any of
the feed locations. In addition, these data show no presence of restrike arcs within the
railgun bore.
In conclusion, the design and experimental data fulfilled all of the
prototype system goals and hence allowed for transition to the full 40-stage DES railgun.
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CHAPTER VI
A 40-STAGE DES PLASMA ARC RAILGUN
6.1 Introduction
The designed system components for the 40-stage DES plasma arc railgun were
demonstrated successfully on the 7-stage prototype. This allows for confident expansion
to the 40-stage system. A CAD drawing of the proposed 40-stage system is displayed in
Fig. 6.1. The assembled railgun is 7.4 meters in length. Although the large stage number
adds complexity, it will demonstrate the full potential of a DES railgun to confine the
electric flux in effort to examine theoretical restrike suppression. This chapter will
discuss the system construction and experimental results of two tested energy schemes to
examine restrike suppression on a multi-stage DES railgun.
Fig. 6.1. CAD Drawing of a 40-Stage DES Railgun.
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6.2 Experimental Setup
6.2.1 Containment Structure and Rails
The containment structures resemble the design used for the prototype with an
increased length by 53.3 cm. The G-10 containment structures measure 10.16 cm x 10.16
cm x 114.3 cm. A photograph of the machined containments and additional components
(nylon tube fittings, o-rings, hardware) is shown in Fig. 6.2.
Fig. 6.2. Photograph of the Containment Structures.
The rails, Fig. 6.3, are machined from UNS C11000 ETP copper with a shoulder
machined at both ends to seat the bore insulators and set the rail-to-rail spacing. On the
back sides of the rails, 1/4’’-28 holes provide an electrical connection for the brass allthread distributed current feeds. The current feed spacing, or stage length, is 15.24 cm.
The rail design is similar to those used in the prototype; however, a lap joint is
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incorporated on each end to build a six meter rail length. A bolt pattern on each end
fastens six 122 cm long rails together. 
Fig. 6.3. Photograph of the Lap Joint Rail (Top-Back View, Bottom-Front View).
6.2.2 Energy Module Modification
A single distributed energy module of the prototype system is shown in Fig. 6.4.
Modifications to the switch were necessary due to repeated failure for experiments
exceeding 20 distributed stages. These switches were selected based on results obtained
from a circuit simulation and financial constraints.
The simulation determined the
following switch requirements: blocking voltage of 800 V, dI/dt rating of 333 A/s, 10 –
15 kA with a 100 s pulse width. The thyristor selected is manufactured by ABB
Semiconductor (PN# 5STP10D1601) and has a blocking voltage of 1600 V, a continuous
1 Hz dI/dt rating of 1000 A/s, and a peak non-repetitive surge current of 16 kA at 125
degrees Celsius with a 8.3 ms pulse.
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Fig. 6.4. CAD Drawing of the Distributed Energy Module.
Experimental testing verified that the switches could handle a maximum current of 15
kA for the 100 s pulse width; however, the relationship between the arc velocity and
module output current was overlooked. The velocity of the arc determines the distance it
will travel down the rail length. This distance corresponds to a variable resistive load on
the energy module. At high velocities, the arc travels further which results in a “high”
rail resistance and hence a “low” output current. As the velocity is reduced, the rail
resistance seen by the energy module also decreases and the output current is increased.
During preliminary testing (20<stage number<40), the arc did not always trigger a stage
upon its arrival. The cause for this has been corrected and is explained in the next
section. This trigger failure led to a reduction of armature current and consequently, arc
velocity. Stage currents up to 25 kA were measured, exceeding the peak current carrying
ability of the switch which led to thermal failure. Part of this problem was resolved by
placing an additional switch in parallel to share the output current through two switches.
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Assuming equal current sharing, the modified energy modules would be able to withstand
magnitudes up to 30 kA for pulsed conditions.
6.2.3 Printed Circuit Board Diagnostics
The operation of the 40-stage DES railgun demands an extensive diagnostic
count. The firing sequence is controlled by a real-time feedback control system which
utilizes armature B-dot probes to detect arc arrival into a given stage. As a result, 39 of
these probes are required with one probe at each distributed current feed location. An
additional 20 rail B-dot probes, one between every other stage, monitor localized rail
current as a means of restrike detection. The requirement to monitor all of the energy
module current waveforms heightens the diagnostic count by 40. A decision was made to
manufacture all of the diagnostics (rail B-dot probes, armature B-dot probes, and
Rogowski coils) implemented on this 40-stage system on printed circuit boards (PCB) to
maintain sensor-to-sensor consistency, provide a compact package, and reduce labor
hours. Both PCB B-dot probes and PCB Rogowski coils described are designed and
manufactured in collaboration with Dr. Wetz at the IAT.
A preliminary test of both sensors was conducted and compared to previously
used diagnostics. The PCB B-dot, Fig. 6.5, is a two-turn design with a 2.54 cm loop
diameter. Observed in the raw data (not shown), one volt was induced for a ~10 kA rail
current. The probe is designed to output a low voltage in accordance with the maximum
input voltage ratings of the control system and data acquisition system. A comparison is
made between the output waveforms produced by a previously used rail B-dot (discussed
in Chapter VI) and a PCB rail B-dot, shown in Fig. 6.5. These raw data are integrated
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and calibrated to compare waveform shapes of the local rail current at one location. A
discrepancy between the two diagnostics is visible after 150 s. Since the two probes
were not located in exactly the same location (one +45 degrees from the positive rail and
the other -45 degrees), the d/dt is slightly different.
Fig. 6.5. Photograph of the PCB B-dot Probe and Plot of the Integrated and Calibrated
Data.
The PCB Rogowski coil, Figure 6.6, contains 15 turns and is printed on a 2-layer
board to include the inner coil conductor. These raw data are integrated and calibrated to
compare waveform shapes of the source current.
The Rogowski coil used in past
experiments (discussed in Chapter VI) output 50 volts while just half a volt was induced
on the PCB Rogowski coil. A high correlation exists between the two waveform shapes
over the pulse width. Results can be improved by adding shielding to the PCB probe.
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Fig. 6.6. Photograph of the PCB Rogowski Coil and Plot of the Integrated and Calibrated
Data.
The PCB B-dot, shown again in Fig. 6.7(a), has two turns and is designed to
output 5 volts for a d/dt produced by an 8 km/s arc velocity. A low output voltage is
desired to comply with the maximum input voltage ratings of the control system and data
acquisition system. This probe’s induced output voltage proved sufficient to trigger the
first 20 stages of the DES railgun but fell short thereafter. Beyond the 20th stage, the flux
coupling reduced and the induced voltage magnitude fell short of the 2.3 volts required
for triggering the TTL digital input modules within the active control system. This flux
reduction is believed to be a product of the growing arc length that smears out the current
density flowing through the arc body. This trend increases until the arc’s magnetic flux
fails to couple into the B-dot loop. To resolve this issue and induce more voltage, two
approaches were examined.
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(a)
(b)
(c)
Fig. 6.7. PCB Armature B-dot Probes. (a) 2-Turn Design. (b) 14-Turn Design. (c) 28Turn Design.
The first approach would be to move the probe closer to the plasma arc and the
second approach would be to increase the number of turns on the probe. The latter was
selected because the containment design would not allow the probes to be moved closer
to the railgun bore. A new probe design, Fig. 6.7(b), was implemented that consisted of
14 turns. These new probes provided enough signal amplification to trigger 10 additional
stages but lacked signal strength to trigger the last ten. To induce enough voltage to
trigger stages 31-40, two of the 14-turn PCB probes were electrically connected in series,
Fig. 6.7(c), doubling the turn ratio to twenty eight. This magnetic flux reduction problem
would not be encountered with a solid armature embodying a fixed length.
6.2.4 Data Acquisition System
Progression to the 40-stage system requires 79 signals to be recorded for each
experimental test. A large scale data acquisition (DAQ) system is therefore required.
The hardware, Fig. 6.8, and software selected for the task are designed and manufactured
by National Instruments. 
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The selected DAQ system is a stand-alone device equipped with a controller (PN#
PXI-8106) that contains:




2.16 Intel GHz Core 2 Duo T7400 dual-core processor
250 GB SATA hard drive
1 GB DDR2 RAM
Windows XP
Only analog input modules are required since both the B-dots and the Rogowski
coils output analog signal waveforms. The purchased DAQ system contains 10, 8channel analog input modules (PN# PXI-6133) capable of simultaneous sampling at a
maximum 2.5 MS/s using an onboard sample clock. The appropriate sampling rate was
determined from past B-dot and Rogowski coil experimental data. Four input voltage
ranges can be set from ±1.25 to ±10 V (±10 V was set for our system). The analog input
modules have a 14 bit resolution which allows them to detect voltage differences of 0.5
mV. Provided with 16 MS of onboard memory, the device can collect 0.8 seconds of
data while sampling all eight channels at 2.5 MS/s. This fell well within our data
collection time interval because the 40-stage railgun current pulse width is expected to be
approximately 1 ms. In addition, the modules contain two 24 bit counter/timers and eight
hardware-timed digital I/O lines. Additional over voltage/current protection was added to
protect the sensitive inputs.
External circuitry consisting of fast-acting fuses and
transient voltage suppressors (TVS) clamped the input voltage to ±10 V and limited the
current to 62 mA.
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Fig. 6.8. National Instruments DAQ System.
6.2.5 Built System
A photograph of the assembled 7.4 meter long 40-stage DES railgun system is
shown below in Fig. 6.9.
The top/side view shows the railgun, distributed energy
modules, support structure, diagnostics, gate driver board boxes, fiber optic and electric
cabling, and the vacuum connection and dry scroll pump. The capacitor banks, PCB
Rogowski coils, and rail B-dot probes can be viewed in Fig. 6.10. Steel tripods have
proven to be an adequate support platform for the gun to rest on. The overall design and
construction mimics the 7-stage prototype, but has been expanded to a length of 7.4
meters to allow for the connection of the additional distributed stages.

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Fig. 6.9. Photograph of the 40-Stage DES Railgun (Top/Side View).
Fig. 6.10. Photograph of the 40-stage DES Railgun (Isometric View).
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6.3 Control System
6.3.1 Introduction
The six distributed stages on the 7-stage prototype were triggered using a hardcoded
timing sequence determined by experimental trial and error.
This proved to be an
adequate technique for a system with a low stage number but became tedious when the
complexity heightened as the number of stages grew. To overcome this problem, a realtime feedback control system was integrated into the system for a precise release of
energy upon the armature’s arrival to a distributed stage.
A control system is not
essential for the operation of a DES railgun; however, it simplifies the timing control of
latter stages without the need for a complicated simulation to predict switch timing. This
became especially evident when dynamic variables such as bore pressure, ablation, and
current magnitude affected the arc velocity from shot to shot. The probability of firing a
stage prematurely is heightened without the implementation of a control system, which
can result in velocity reduction.
Additional flexibility of the trigger timing is
accomplished by a user defined time delay after the armature arrival.
6.3.2 Hardware
The control system functions to determine the armature real-time position and make
decisions accordingly. A partial representation of the real-time feedback control system
hardware is shown in Fig. 6.11. The brain of the system consists of two (only one
shown) National Instruments CompactRIO PACs that utilize FPGA technology to
provide real-time processing. The LabVIEW 2009 software package is used to develop
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control code which is compiled into a bit-file and downloaded into the CompactRIOs’
512 MB flash memory where it is stored and is activated after the boot cycle.
Fig. 6.11. Control System Hardware.
Thirty nine armature B-dot probes measure armature position and supply the real-time
feedback signals. These probes are incrementally located at each distributed current feed.
The induced armature B-dot voltage signals resemble a single cycle of a sine wave. A
positive voltage is induced as the armature approaches the probe and the polarity flips as
the armature moves away from the probe. The armature detection occurs on the rising
edge of the feedback signal which indicates its arrival to the probe location. The B-dot
voltage signals are sent to the CompactRIOs where five, 8-channel NI 9401 TTL digital
input modules measure the induced voltages. The AND gates within the digital input
module provide a faster detection method vs. measurement using analog input modules.
This device functions as a switch because of its digital nature, which can interpret the
signals in two ways. When the signal amplitudes are below 2.3 V, the TTL device
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remains in a “low” state or open by representation of a switch. Signal amplitude above
2.3 V corresponds to a “high” state or closed by representation of a switch. The induced
voltage within the B-dot probes typically exceeds 5 volts due to the d/dt and probe
design. Input signals in excess of 5 volts can damage the module’s channels; therefore,
external ±10 V transient voltage suppressors were integrated to clamp the circuit voltage
and are used for protection.
A LabVIEW 2009 program determines the appropriate switch timing for each energy
module. To initiate the release of current from an energy module, five, 8-channel NI
9401 TTL digital output modules provide a 10 s, 5 V pulse to a fiber optic board on the
respected stage channel. Gate driver boards receive the light signals and convert them to
10 s, 15 V analog pulses to trigger the stage’s corresponding SCR gate and release the
stored energy in the capacitor banks.
6.3.3 Software
The control code discussed in this section is developed using the LabVIEW 2009
software package and then compiled into a bit-file and finally downloaded into the
CompactRIOs’ 512 MB flash memory where it is stored and is activated after the boot
cycle. A flow chart of the control program is displayed in Fig. 6.12 below. The program
begins with an event sequence (not shown) that starts by waiting 1 second to allow time
for the CompactRIO to complete its boot configurations.
The next event sets line
directions and checks the status of the digital input/output modules. After these tasks are
completed a Boolean TRUE is assigned to two local variables that control triggering of
the DAQ system and plasma gun. These local variables are read by a pulse generating
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program to output two 10 s, 5 V digital pulses required to initiate the DAQ and fire the
plasma source. The following event waits 1 s to allow time for the plasma to disperse in
the breech region. As the plasma expands, a Boolean TRUE is assigned to a local
variable that controls the first stage firing. Once again this local variable is read by a
pulse generating program which outputs a signal to fire the first energy module, causing a
high voltage breakdown across the rail gap and initiating the Lorentz driving force to
accelerate the arc.
Fig. 6.12. Flow Chart of the Control Program.
As the plasma travels through the bore, the distributed stage firing sequence
begins with an event to read the armature B-dot sensor located at the second stage current
feed.
This event continues to loop until a 2.3 V threshold voltage is obtained or
exceeded. A user defined time delay is then executed to control the fire timing of the
second stage. This distributed stage firing sequence procedure is continued to detect the
armature position and trigger the remaining stages.
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6.4 Experimental Results
Two different energy schemes were experimentally tested and the results are
discussed in this section. The first energy scheme is referred to as “asynchronous” and
allows only positive current to be discharged by the capacitor banks.
This is
accomplished by opening the current loop containing an anti-parallel diode which is
electrical connected in parallel with the thyristor. The second energy scheme is referred
to as “synchronous” and allows negative current to flow through the system. An antiparallel diode connected in parallel with the thyristor allows the capacitor bank to ring
and produces under-damped waveforms. This energy scheme provides negative current
to cancel out residual positive current that is trailing behind the armature. The result is an
enhanced isolation of the electric flux in the bore behind the armature.
6.4.1 Asynchronous Energy Scheme
The current waveforms for a 40-stage asynchronous DES plasma arc railgun shot, along
with a summed armature current waveform, are displayed in Fig. 6.13. During the shot,
the containment structure was evacuated to roughly 14 mTorr. The first stage was
charged to 1000 volts and sourced a maximum 31 kA for a pulse width of 150 µs. Stages
2 through 40 were charged to 650 volts and each output 10-15 kA with a 100 µs pulse
width. The triggering of stages 2 through 40 were controlled by the active feedback
control system.
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Fig. 6.13. Current Waveforms from a 40-Stage asynchronous DES Railgun.
An attempt was made to produce a square pulse armature current waveform. The
waveform produced loosely resembles a square wave with a pulse width of 550 s. The
maximum armature current is ~ 83 kA seen at 500 µs. The plasma accelerated to a
maximum velocity of ~ 19.1 km/s from 400 µs to 416 µs. The average measured velocity
was ~13.8 km/s calculated using the armature B-dot data shown in Fig. 6.14. Analysis of
these B-dot traces reveals no indication that arc splitting has occurred at any of the feed
locations or that a restrike arc was formed.
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Fig. 6.14. Armature B-dot Waveforms from a 40-Stage asynchronous DES Railgun.
6.4.2 Synchronous Energy Scheme
The current waveforms for a 40-stage synchronous DES plasma arc railgun shot, along
with a summed armature current waveform, are displayed in Fig. 6.15. During the shot,
the containment structure was evacuated to roughly 12 mTorr. The first stage was
charged to 1000 volts and sourced a maximum 31 kA for a pulse width of 150 µs. Stages
2 through 40 were charged to 825 volts and each output 12-21 kA with a 100 µs pulse
width. As in the asynchronous test, triggering was done with the active feedback control
system.
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Fig. 6.15. Current Waveforms from a 40-Stage Synchronous DES Railgun.
The maximum armature current, shown in Fig. 6.15, is close to 85 kA which accelerated
the plasma to a peak velocity of ~19.3 km/s. The average measured velocity was ~12.6
km/s calculated using the armature B-dot data shown in Fig. 6.16. Analysis of the B-dot
traces reveals no indication that arc splitting has occurred at any of the feed locations or
that a restrike arc was formed.
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Fig. 6.16. Armature B-dot Waveforms from a 40-Stage Synchronous DES Railgun.
6.5 Conclusion
The development process pertaining to the design, fabrication, and testing of a 40-stage
DES plasma arc railgun was discussed.
Investigation of this type of system will
determine the effectiveness of a distributed energy scheme to suppress the plasma restrike
phenomenon.
Experimentation with the 40-stage system discovered a loss of probe signal as the arc
traveled down the bore. This flux reduction is believed to be a product of the growing arc
length that smears out the current density flowing through the arc body. To resolve this
issue and induce more voltage, additional turns were added to the B-dot sensor. Before
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this new sensor was implemented, the loss of the probes’ signals caused the arc velocity
to dramatically decrease and led to thermal damage to the thyristor switches. This was
caused by exceeding the peak current carrying ability of the switch. As a result of these
switches failures, a relationship between the arc velocity and module output current was
identified. The problem was resolved by placing an additional switch in parallel to share
the output current through two switches.
A real-time feedback control system was integrated into the system for a precise release
of energy upon the armature’s arrival to a distributed stage. The control system functions
to determine the armature real-time position and make decisions accordingly. A control
system is not essential for the operation of a DES railgun; however, it simplified the
timing control of latter stages without the need for a complicated simulation to predict
switch timing.
Initial testing of a 40-stage system has been completed. Two energy schemes were
examined.
Both accelerated the arc down the full rail length and achieved
hypervelocities. Analysis of the B-dot traces reveals no indication that arc splitting has
occurred at any of the feed locations or that a restrike arc was formed. Continued
analysis of these data is necessary before any conclusions can be made about the
effectiveness of a distributed energy scheme to suppress the plasma restrike phenomenon.
In the future, researchers at TTU plan to use this railgun to test a breech-fed configuration
with equivalent energy in attempt to create restrike arcs. This breech-fed experiment is
essential to determine the restrike prevention theory of DES railguns.
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CHAPTER VII
SUMMARY AND CONCLUSION
After proving the DES principle with solid armatures9, the design of a plasma source
commenced to transition toward plasma arc experiments. This technique allowed for
more realistic armature velocities (>6 km/s) without the requirement for a large stored
energy facility. The higher velocity is owing to the fact that instead of pushing a “heavy”
solid armature we will be pushing a “light” plasma arc.
Movement to a DES plasma arc launcher called for the design and construction of a
completely new system.
In order to operate in a hypervelocity regime, system
modifications included:
a) A vacuum chamber containment structure (1 to 10 Torr)
b) A plasma source to create/form the armature
c) Increased rail and stage lengths
d) Energy sources that produce a larger current magnitude with a shortened pulse
width
e) A real-time feedback control system
As a result, a 15 kJ, 4-stage DES plasma arc railgun was developed. A 4-stage
system allowed three different switching or energy schemes to be examined: breech-fed,
pseudo-asynchronous, and pseudo-synchronous. To intentionally create restrike arcs for
analysis, highly ablating G-10 bore insulators were utilized. Although classical restrike
was observed for the breech-fed configuration, both asynchronous and pseudo97
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synchronous schemes suppressed the phenomenon. However, analysis of these data
collected from the latter energy schemes revealed an unusual current diversion away from
the primary arc with dissimilar characteristics observed from restrike.
Upon further examination, alternative diagnostics provided supporting evidence that
the restrike phenomenon was not responsible for this current diversion.
Instead of
restrike, the current diversion was attributed to a secondary arc formation by plasma arc
splitting at the distributed current injection locations. This problem was resolved by
waiting until the full length of the armature was ahead of the distributed feed location
before the release of energy, maintaining magnetic pressure behind the plasma body.
Knowledge of the plasma armature length was determined to be an important parameter
to correctly time the triggering of distributed stages. An objective to accurately calculate
the length was hence put forth. Optical diagnostics were integrated into a 2-stage DES
system at five different locations along the railgun bore for the analysis. These data
revealed a luminosity gradient along the length of the plasma armature body, suggesting a
hot, dense, compact head followed by a cooler, less dense body/tail region.
As
expected, the armature length grew when the background pressure was increased. When
conditions for arc splitting were applied, the length was found to fluctuate near the
distributed current feed location. This fluctuation is theorized to be a perturbation of the
plasma by gradient magnetic pressures located near the distributed feeds.
The final objective was to design a 40-stage synchronous DES plasma arc
railgun. A computer simulation was developed to determine the necessary component
values for each stage. The code neglects complex plasma physics and was developed in
accordance to derived circuit equations2 for a distributed energy model. Values obtained
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Texas Tech University, Ryan William Karhi, November 2010
from the simulation allowed for the selection of realizable system components such as:
capacitors, switches, and power conditioning devices. This led to the development of a
prototype system to test all of the components designed for the 40-stage system. The
prototype resembled the first 7 stages of the overall design. All of the objectives were
successfully completed for the prototype system. The B-dot probes waveforms, Fig.
5.16, confirmed that the arc is accelerating towards the railgun muzzle as all 7 stages
discharge. A containment structure was designed and built using G-10 with numerous oring seals to achieve mTorr pressures with air as the fill gas. Plasma leakage was reduced
by applying a mechanical horizontal and vertical compression to the railgun core. The
flange design proved to maintain vacuum and bore compression. Energy modules were
designed utilizing compact film dielectric capacitors and a variable self-inductance
scheme. When charged to 500 volts, the modules output approximately 10 kA with a 100
s pulse width. These values agreed with the simulation results.
Finally, B-dot probes
containing 20 turns and shielded air-core Rogowski coils were built in-house and
calibrated for use as current and velocity measurements.
The experimental results
showed an armature current close to 38 kA and an average arc velocity of ~ 6.7 km/s.
Analysis of the B-dot traces revealed no indication that plasma arc splitting has occurred
at any of the feed locations. In addition, these data show no presence of restrike arcs
within the railgun bore. In conclusion, the design and experimental data fulfilled all of
the prototype system goals and hence allowed for transition to the full 40-stage DES
railgun.
The development process pertaining to the design, fabrication, and testing of a 40-stage
DES plasma arc railgun was discussed.
Investigation of this type of system will
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determine the effectiveness of a distributed energy scheme to suppress the plasma restrike
phenomenon.
Experimentation with the 40-stage system discovered a loss of probe signal as the arc
traveled down the bore. This flux reduction is believed to be a product of the growing arc
length that smears out the current density flowing through the arc body. To resolve this
issue and induce more voltage, additional turns were added to the B-dot sensor. Before
this new sensor was implemented, the loss of the probes’ signals caused the arc velocity
to dramatically decrease and led to thermal damage to the thyristor switches. This was
caused by exceeding the peak current carrying ability of the switch. As a result of these
switches failures, a relationship between the arc velocity and module output current was
identified. The problem was resolved by placing an additional switch in parallel to share
the output current through two switches.
A real-time feedback control system was integrated into the system for a precise release
of energy upon the armature’s arrival to a distributed stage. The control system functions
to determine the armature real-time position and make decisions accordingly. A control
system is not essential for the operation of a DES railgun; however, it simplified the
timing control of latter stages without the need for a complicated simulation to predict
switch timing.
Initial testing of a 40-stage system was completed.
examined.
Two energy schemes were
Both accelerated the arc down the full rail length and achieved
hypervelocities. Analysis of the B-dot traces reveals no indication that arc splitting has
occurred at any of the feed locations or that a restrike arc was formed. Continued
analysis of these data is necessary before any conclusions can be made about the
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effectiveness of a distributed energy scheme to suppress the plasma restrike phenomenon.
In the future, researchers at TTU plan to use this railgun to test a breech-fed configuration
with equivalent energy in attempt to create restrike arcs. This breech-fed experiment is
essential to determine the restrike prevention theory of DES railguns.
The future of the plasma railgun relies on the distributed energy scheme to reduce
the trailing E-field, suppress secondary arc formation, and allow the powerful Lorentz
magnetic force to demonstrate its full potential. This would open the door to a variety of
exciting applications such as cheap space access, particle accelerators for further
characterization of quarks and other sub-atomic particles, the possibility of developing
new elements, advancing the physics of fusion, and extremely powerful weapons.
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REFERENCES
[1]: J. V. Parker, “Why Plasma Armature Railguns Don’t Work (And What Can Be Done
About It),” IEEE Transactions on Magnetics, vol. 25, pp. 418 – 424, January 1989.
[2]: J. V. Parker, “Electromagnetic Projectile Acceleration Utilizing Distributed Energy
Sources,” Journal of Applied Physics, vol. 53, pp. 6710 – 6723, October 1982.
[3]: R. A. Marshall and W. F. Weldon, “Analysis of Performance of Railgun Accelerators
Powered by Distributed Energy Stores,” 14th Pulse Power Modulator Symposium,
Orlando, Florida, June 3-5, 1980.
[4]: U. S. Inan and A. S. Inan, Electromagnetic Waves, New Jersey: Prentice Hall, 2000,
p. 417.
[5]: S. C. Rashleigh, R. A. Marshall, “Electromagnetic Acceleration of Macroparticles to
High Velocity,” Journal of Applied Physics, vol. 49, p. 2540, 1978.
[6]: J.V. Parker, W. Condit, and Y. Thio, “Investigation of Plasma Armature Dynamics,”
AFATL report, Part 2, pp.6, December 1990.
[7]: C. H. Haight and M. M. Tower, “Distributed Energy Store (DES) Railgun
Development,” Proc. of 3rd EML Symposium, pp. 81-84, Austin, Texas, April 1986.
[8]: J. P. Barber and A. Challita, “Monthly Progress Letter,” IAP Research, Inc., Dayton,
Ohio, LTVAD P.O. P-350272, April 1984.
[9]: R. Karhi, “Instrumentation and Control of Electromagnetic Launchers,” Master’s
Thesis, Texas Tech University, Lubbock, Texas, 2007.
[10]: R. Karhi, J. Mankowski, J. Dickens, M. Kristiansen, and D. Wetz, “Secondary Arc
Formation within a Distributed Energy Railgun,” IEEE Transactions on Plasma Science,
vol. 36, Issue 5, pp. 2738-2746, October 2008.
[11]: Hamamatsu Photonics, “Photodiode Technical Information,” Technical notes.
[12]: MATLAB® Help file.
[13]: J. F. Kerrisk, “Current Distribution and Inductance Calculations for Railgun
Conductors,” LA-9092-MS, November 1981.
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APPENDIX A
MULTI-STAGE DES FREE-ARC SIMULATION
function DES_FreeArc
% Multi-stage DES free-arc simulation.
% John Mankowski and Ryan Karhi, 4/12/10
clear all; close all;
% Initial conditions and first stage parameters ----------------------points = 1000;
% set number of point per iteration
Nstages = 40;
% number of stages.
L = zeros(Nstages,1);
Q0 = zeros(Nstages,1);
C = zeros(Nstages,1);
R = zeros(Nstages,1);
C(1) = .00083;
R(1) = .001;
Q0(1) = 2.5;
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
%
L(1) = 2.5*10^-6;
Lrail = 0.451*10^-6;
press = 5;
rho_0 = 1.204;
rho = rho_0*(press/760);
h = 0.01;
gamma_star = 1.2;
Cf = 0.0049;
x_const = 6.096;
S = 0.1524;
tfinal = .001;
pad L column vector with zeros.
pad Q0 column vector with zeros.
pad C column vector with zeros.
pad R column vector with zeros.
capacitor value in stage one [F].
resistor value in stage one [ohm].
initial charge on capacitor in
stage one [C].
inductor value in stage one [H].
inductance gradient of the railgun [H/m].
pressure in the bore [torr].
density of air at atmosphere [kg/m^3].
density of air in the bore [kg/m^3].
rail separation [m].
specific heat ratio [unitless].
drag coefficient [unitless].
Shock front distance [m].
distance between stages [m].
estimated final time [s].
x_s = (gamma_star+(1/4))*(h/Cf); % scale length related to viscous
% forces.
tt = zeros(points*Nstages,1);
%
position = zeros(points*Nstages,1);%
%
ir = zeros(points*Nstages,Nstages);%
%
pad tt column vector with zeros.
pad position column vector with
zeros.
pad rail current matrix with
zeros.
tstart = 0;
% initialize start time.
y0 = [Q0(1); 0; 0];
% load vector of initial conditions for
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% y,where y=[q;q';x]
% =[charge;current;position].
% --------------------------------------------------------------------% Latter stage parameters --------------------------------------------Rrail = 0.0001;
% rail resistance per meter [ohm/m].
for a = 2:Nstages;
L(a) = 1.5*10^-6;
Q0(a) = .525;
C(a) = .00075;
R(a) = 0.005;
%
%
%
%
inductunce value in latter stages [H].
capacitance value of latter stages [C].
initial charge on latter stages [F].
resistance value in latter stages [Ohm].
end
% --------------------------------------------------------------------% Calculate I,dI/dt,velocity -----------------------------------------for N = 1:Nstages-1;
tspan = linspace(tstart,tfinal,points); % creates linear space
%of time.
options = odeset('Mass',@Lprime);
%
%
%
%
%
A built-in MATLAB
mass matrix
is used to calculate the
variable inductance.
produces: f(t,y)=LP*y'
[t y] = ode45(@f,tspan,y0,options);
%
%
%
%
%
solve the ODE with ode45.
f is the function.
tspan is the time span.
y0 is the initial
conditions.
% ---------------------------------------------------------------------
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% Detects armature arrival to the next stage and sets the trigger
% timing for each stage ----------------------------------------------k = 0;
% initialize variable.
for j = 1:points;
if y(j,2*N+1) <= S*N;
k = k+1;
% if arc position is <= next stage.
% number of data points behind
% next stage.
end
end
a = t(k);
% time to trigger next stage.
% --------------------------------------------------------------------% Calculate derivatives for the new stage ----------------------------tspan = linspace(tstart,a,points);
%
%
%
%
%
%
%
creates linear space
of time.
tstart is arrival
time to the previous
stage and a is the
arrival time to the
next stage.
options = odeset('Mass',@Lprime);
%
%
%
%
%
A built-in MATLAB
mass matrix
is used to calculate the
variable inductance.
produces: f(t,y)=LP*y'
[t y] = ode45(@f,tspan,y0,options);
%
%
%
%
%
solve the ODE with ode45.
f is the function.
tspan is the time span.
y0 is the
initial conditions.
% ---------------------------------------------------------------------
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% Transfer stage data into one large array ---------------------------for j = 1:points;
tt(points*(N-1)+j)=t(j);
position(points*(N-1)+j)=y(j,2*N+1);
%
%
%
%
%
%
load stage time
data into master
time vector.
load stage position
data into master
position vector.
for c = 1:N;
ir(points*(N-1)+j,c)=-y(j,2*c);
% load stage current
% data into master
% current vector.
end
end
% --------------------------------------------------------------------% Reset initial conditions for next stage ----------------------------tstart = a;
y0 = zeros(2*N+3,1);
% tstart = next stage trigger time.
% pad y0 column vector with zeros.
y0(2*N+3) = y(points,2*N+1);%
%
y0(2*N+1) = Q0(N+1);
%
%
load the last position data point as
the next stage's initial condition.
load the next stage's charge as an
initial condition.
for b = 1:2*N;
y0(b) = y(points,b);
% set the last data point calculated
% as the next stage's initial
% conditions.
end
% --------------------------------------------------------------------end
% ---------------------------------------------------------------------
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% Calculate I,dI/dt,velocity for last stage --------------------------N=Nstages;
% equate N to the last stage #.
tspan = linspace(tstart,tfinal,points);% creates linear space of time.
% tstart is arrival time to the
% next to last stage.
options = odeset('Mass',@Lprime);
%
%
%
%
A built-in MATLAB mass matrix
is used to calculate the
variable inductance.
produces: f(t,y)=LP*y'
[t y] = ode45(@f,tspan,y0,options);
%
%
%
%
solve the ODE with ode45.
f is the function.
tspan is the time span.
y0 is the initial conditions.
% --------------------------------------------------------------------% Transfer stage data into one large array ---------------------------for j = 1:points;
tt(points*(N-1)+j)=t(j);
%
%
position(points*(N-1)+j)=y(j,2*N+1);%
%
for c = 1:N;
load
into
load
into
last stage time data
master time vector.
last stage position data
master position vector.
ir(points*(N-1)+j,c)=-y(j,2*c); % load last stage current data
% into master current matrix.
end
end
% ---------------------------------------------------------------------
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% Solve for velocity, acceleration, and armature current -------------V = diff(position)./diff(tt);
V(points*N) = V(points*N-1);
%
%
%
%
%
%
calculate velocity.
copy the second to last data
point and paste into the last
data point to match the
velocity vector length
to the time vector length.
accel = diff(V)./diff(tt);
accel(points*N) = accel(points*N-1);
%
%
%
%
%
%
calculate acceleration.
copy the second to last data
point and paste into the last
data point to match the
acceleration vector length
to the time vector length.
armature_current = sum(ir,2);
%
%
%
%
adds up stage current to
calculate armature current.
2 indicates a summation of
ir's rows.
% --------------------------------------------------------------------% Plot waveforms -----------------------------------------------------figure(1);
plot(tt*1000,accel);
% plot acceleration waveform.
title('Arc Acceleration');
xlabel('Time [msec]'); ylabel('Acceleration [m/sec/sec]');
figure(2);
plot(tt*1000,position);
% plot position vs. time.
title('Arc Position');
xlabel('Time [msec]'); ylabel('Position [m]');
figure(3);
plot(tt*1000,armature_current/1000); % plot armature current.
title('Armature Current');
xlabel('Time [msec]'); ylabel('Projectile current [kA]');
figure(4);
plot(tt*1000,V);
% plot velocity waveform.
title('Arc Velocity');
xlabel('Time [msec]'); ylabel('Velocity [m/sec]');
figure(5);
for z = 1:Nstages;
hold all;
plot(tt*1000, ir(:,z)/1000);
% changes trace color.
% plot individual current
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% waveforms.
end
title('Current Waveforms');
xlabel('Time [msec]'); ylabel('Current [kA]');
axis([0 1 -20 80]);
hold off
% --------------------------------------------------------------------% Derivative function ------------------------------------------------function dydt = f(t,y)
% dy/dt = [qi'';V';x'']
% = [dI/dt;dV/dt;acceleration]
dydt = zeros(2*N+1,1);
% pad dy/dt column vector with zeros.
% Apply capacitor bank resistance ------------------------------------for d = 1:N;
if -y(2*d) < 0
% Applies to stages 2-N
R(d) = .1;
% Resistance for negative current
else
R(d) = .0001;
% Resistance for positive current
end
end
% --------------------------------------------------------------------% Calculate derivatives
----------------------------------------------
isum = 0;
for i = 1:N;
isum = isum+y(2*i);
dydt(2*i-1,1) = y(2*i);
% current summer routine
% store current values in
% dy/dt to calculate dI/dt
dydt(2*N+1,1) = ((sqrt(Lrail/((gamma_star+1)*rho)))...
*(abs(isum)/h)*(1/(sqrt(1+(x_const/x_s)))));
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Texas Tech University, Ryan William Karhi, November 2010
%
%
%
%
The equation above is Jerry Parker's velocity derivation for
a free-arc under ablation-free operation and assuming
dm_a/dt = 0. I replaced the variable, x, in the original
equation to a constant, x_const, for simplification.
if i < N
%
%
%
%
%
%
The equation below is part of Jerry Parker's derivation of
the lumped element circuit equation for each stage which the
armature has passed entirely through. The terms containing
inductance(that are present in the origional equation)
have been removed here, but are added back in with
excecution of the function LP.
dydt(2*i,1) = -y(2*i-1)/C(i)-R(i)*y(2*i)-Rrail*S*isum...
+y(2*i+1)/C(i+1)+R(i+1)*y(2*i+2);
else
dydt(2*N,1) = -y(2*N-1)/C(N)-R(N)*y(2*N)-Rrail*(y(2*N+1)...
-(N-1)*S)*isum-Lrail*dydt(2*N+1,1)*isum;
%
%
%
%
%
The equation above is part of Jerry Parker's derivation of
the lumped element circuit equation for the stage containing
the armature. The terms containing inductance(that are
present in the origional equation) have been removed here,
but are added back in with excecution of the function LP.
end
end
% --------------------------------------------------------------------end
% --------------------------------------------------------------------% Variable inductance function ---------------------------------------function LP = Lprime(t,y)
LP = zeros(2*N+1,2*N+1); % pad LP matrix with zeros
LP(2*N,2*N) = L(N)+Lrail*(y(2*N+1)-(N-1)*S);
% The above equation calculates the inductance gradient
% for the stage containing the armature ( L'*(x^*)) and
% adds the capacitor bank inductance L(N).
for i = 0:N;
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LP(2*i+1,2*i+1)=1;% set alternating terms in diaganol with ones
if i < N-1
LP(2*i+2,2*i+2) = L(i+1)+Lrail*S;
% The above equation adds up the capacitor bank
% inductance (L(i+1)) and the rail inductance (L'*S) for
% each stage behind the armature.
LP(2*i+2,2*i+4) = -L(i+2);
% The above equation adds the next stage's
% capacitor bank inductance (L(i+2)).
for e = 1:N-1
LP(2*N,2*e) = Lrail*(y(2*N+1)-(N-1)*S);
% The above equation calculates the inductance
% gradient for the stage containing
% the armature. L'*(x^*)
end
end
if i < N-2
for l = 1:N-2
for m = 1:l
LP(2*l+2,2*m) = Lrail*S;
% The above equation calculates the rail
% inductance of a single stage. L'*S
end
end
end
end
end
% --------------------------------------------------------------------end
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APPENDIX B
CONTROL SYSTEM CODE
B.1 Control Program for Stages 1-24
The LabVIEW program, Fig. B.1, is compiled into a bit-file and downloaded into
the CompactRIO’s 512 MB flash memory where it is stored and activated on each boot
cycle.
The program begins by simultaneously running 26 sub-routines.
This is
accomplished by the parallel processing capability of the FPGA. The first sub-routine
Fig. B.1. LabVIEW Control Program for Stages 1-24 with Red Zoom Box Labels.
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(containing Z1-Z6) initializes digital input/output modules, triggers devices (DAQ,
plasma generation, etc.), and waits to receive B-dot signals from the DES railgun. The
sequence of operations for each DES stage is identical; therefore, the program flow for a
single DES stage will be discussed in detail. The graphical user interface (GUI) is
difficult to read in Fig. B.1, so portions of the code are that are discussed are highlighted
and labeled using red boxes and red label text.
Upon entering the first sub-routine (containing Z1-Z6) a sequence of eight event
frames are initialized inside a while loop. This loop continues execution until stage 24 is
triggered. The first of the eight frames is a wait function which is configured for time
intervals in milliseconds, shown in Fig. B.2. The wait function is set to three seconds to
Fig. B.2. 3 Second Wait Function (Z1).
allow time for the CompactRIO to complete its own boot cycle and the boot cycle of an
additional CompactRIO that is a part of the full control system. The second frame sets
the line directions for the digital input/output modules, shown in Fig. B.3. The line
direction must be specified since the channels of the NI 9401 TTL digital modules can be
configured as inputs or outputs. The third frame checks the status of each digital module,
displayed in Fig. B.4, to ensure a “ready” state. Boolean case structures receive values
from the while loop iteration counter to limit this status check to execute on the first
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Fig. B.3. Set Line Direction for Digital Input/Output Modules (Z2).
Fig. B.4. Check Digital Input/Output Modules Status (Z3).
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iteration only. Frames 4-7 are shown in Fig. B.5. The fourth frame assigns Boolean
TRUE values to two local variables, Mod7/DO0 and Mod7/DO1. Mod7 refers to the
Fig. B.5. Trigger Sequence for DAQ, Plasma Generation, and Stage 1 (Z4).
seventh module connected to the CompactRIO chassis which is an 8-channel, 24V,
digital output module (NI 9474). These local variables are read by control variables
contained within a pulse generating sub-routine (Z8) to output a 10 s pulse, shown in
Fig. B.6. Channel 0 outputs a trigger signal to the DAQ system and Channel 1 outputs a
trigger signal to generate the plasma in the railgun bore. The pulse generating sub-
Fig. B.6. Pulse Generating Sub-Routine for Module7 with TRUE Input (Z8).
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routine contains two event frames inside of a while loop. In the first frame, control
variables write Boolean values to three digital channels (0-2) of module7. The local
variables, Mod7/DO0 and Mod7/DO1, in Z4 are linked to these controls which have
FALSE default Boolean values.
In the given example, values of TRUE are written to
channels 0-1 while a FALSE is written to channel 2. Channels 0-1 are now in a digital
high state, where 24V is seen across their outputs. In the second frame, the control
variable values are placed into an array and compared using an OR gate. Continuing with
our example, a value of TRUE is output from the OR gate and sent to a Boolean case
structure. When a value of TRUE is input to this case structure, an event frame sequence
waits 10 s, writes a FALSE to all three digital channels, and resets the control variables
to a value of FALSE. These actions produce a 10 s trigger pulse. If a value of FALSE
is input to the case structure, no action is taken, Fig. B.7, and the while loop starts a new
Fig. B.7. Pulse Generating Sub-Routine for Module7 with FALSE Input (Z8).
iteration. Returning to Z4, the fifth frame contains a wait function with microsecond time
intervals. This frame waits 1 s to allow time for the plasma to diffuse inside of the
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railgun bore.
The sixth frame assigns a Boolean TRUE to a local variable named
MOD1/DIO0. This initializes the fire sequence to release the stored energy within the
first stage, create a current path through the plasma, and accelerate the arc. The local
variable MOD1/DIO0 is linked to a control variable within a different pulse generating
sub-routine (Z7), displayed in Fig. B.8. The figure shows two pulse generating subroutines for Module 1 (one for channel 0 and the other for channel 1). With exception of
the channel number, the two sub-routines have identical program flow and are both
shown to view two cases of a Boolean case structure. Modules 1-6 are 8-channel TTL
digital input/output modules (NI 9401). Modules 1, 3, 5 are configured as outputs that
provide trigger signals to fire the energy stores. While, Modules 2, 4, 6 are configured as
inputs that read voltage signals produced by B-dot probes to determine the appropriate
fire times of the energy stores. The pulse generating sub-routine (Z7) is embedded within
Fig. B.8. Pulse Generating Sub-Routine for Module1 (Z7).
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a while loop. The control variable Mod1/DIO0 writes Boolean values to channel 0 and a
Boolean case structure. In the given example, values of TRUE are written to channel 0
and the case structure. Channel 0 is now in a digital high state, where 5V is seen across
its output. When a value of TRUE is input to the case structure, an event frame sequence
waits 10 s, writes a FALSE to the digital channel, resets the control variable to a value
of FALSE, and stops the while loop execution. These actions produce a 10 s trigger
pulse. If a value of FALSE is input to the case structure, no action is taken and the while
loop starts a new iteration. We now return to the seventh frame within the first discussed
sub-routine (containing Z1-Z6) shown in Fig. B.5. This frame waits 20 s to prevent a
false trigger on one of the distributed energy stores. During this time interval, the plasma
arc formation and initial acceleration produce electromagnetic interference (EMI). This
EMI couples into B-dot probes of close proximity to the breech and can produce a false
trigger on one or multiple stages.
The eighth and final frame contains plasma arc
detection routines for the first 23 distributed energy stores. This routine, displayed in
Fig. B.9, initializes a read function of individual B-dot probe voltages.
The figure
shows conditions for different Boolean inputs to the case structures. In the first arc
detection routine, shown at the top of Fig. B.9, a while loop containing the detection
program is executed. The voltage signal produced by the 2nd stage B-dot probe is read
and Boolean output values are sent to a Boolean case structure. When the input voltage
to the channel is below 2.3 V, a value of FALSE is input to the case structure and the
while loop begins a new iteration to continue reading the B-dot voltage signal. This
action begins a chain reaction, sending a Boolean FALSE to the case structure containing
the arc detection routine of the 3rd stage, and the 4th stage, and the 5th stage, ect. The
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program is coded in this fashion to read one B-dot probe signal at a time in order to
prevent the catastrophic event of all the stages firing at the same time. If the induced
voltage on the B-dot probe exceeds 2.3 V (indicating the arrival of the plasma arc), an
event frame sequence is initialized. The first frame of this sequence sends a Boolean
TRUE to the next arc detection routine to begin reading the 3rd B-dot probe signal.
Following that frame, a user defined wait function is executed to delay the trigger signal
Fig. B.9. Plasma Arc Detection Routine (Z5).
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Texas Tech University, Ryan William Karhi, November 2010
and allow time for the full arc length to be ahead of the current feed location before it is
fired. In this example, a 10 s wait is programmed. The user defined wait can vary from
shot to shot and is determined by the initial conditions. The delay is a function of the arc
velocity and length which are established by the current magnitude through the arc and
background gas pressure. The third frame sends a Boolean TRUE to the local variable
Mod1/DIO1 to generate the trigger pulse required to fire the 2nd stage. This pulse
generating sub-routine was discussed above and can be viewed in Fig. B.8. The fourth
frame halts the while loop to prevent multiple triggering of the stage’s switch. When the
arc arrives at stage 20, the plasma arc detection routine, shown in Fig. B.10, contains a
local variable to send a trigger signal to the second CompactRIO in the control system.
This action initiates the control program for stages 25-40 to begin reading the B-dot
probe voltage signal located at the 25th stage. Initializing this read prior to the arc arrival
allows the program to read multiple data points before the arc is detected.
Fig. B.10. Trigger Signal for the Second cRIO (Z6).
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B.2 Control Program for Stages 25-40
The LabVIEW program, Fig. B.11, controls the firing sequence for stages 25-40. Similar
to the control program for stages 1-24, it is stored into a second CompactRIO’s 512 MB
flash memory where it is activated on each boot cycle.
The program flow and
architecture are analogous to the program described in Appendix B.1; therefore, only the
non-correlating portions of code will be highlighted and discussed.
Fig. B.11. LabVIEW Control Program for Stages 25-40 with Red Zoom Box Labels.
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In the first frame of the first sub-routine (containing Z9-Z10), a one second wait
function, shown in Fig. B.12, is executed. This allows enough time for the CompactRIO
to complete its boot cycle. In contrast, the control program for stages 1-24 has a three
second delay. A shorter delay is implemented here to ensure the code controlling these
latter stages it ready before the firing sequence is started. The other difference between
Fig. B.12. 1 Second Wait Function (Z9).
the two control programs is found in the fourth frame of the first sub-routine, shown in
Fig. B.13. A while loop is configured to continuously read a digital input channel
(Mod5/DI0) until a Boolean value of TRUE is read.
This value is obtained from
Mod7/DO2 discussed above and displayed in Fig. B.10. Once a value of TRUE is read,
the next frame of the sub-routine is executed and starts to read the B-dot probe signals.
Module 5 is a 32-channel, 24V, digital input module (NI 9425). Modules 1-4 are 8channel TTL digital input/output modules (NI 9401). Modules 1 and 3 are configured as
outputs that provide trigger signals to fire the energy stores. While, Modules 2 and 4 are
configured as inputs that read voltage signals produced by B-dot probes to determine the
appropriate fire times of the energy stores.
All remaining sub-routines and pulse
generating function are programmed similar to the control program for stages 1-24.
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Fig. B.13. Trigger Loop to Start Reading the B-dot Probes (Z10).
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APPENDIX C
RAILGUN SYSTEM OPERATION MANUAL
1.
2.
3.
4.
5.
Notify appropriate personnel about the experiment.
Wear safety goggle/glasses.
Turn on warning light.
Evacuate all unauthorized personnel from lab space.
Provide utility power to devices (120V 60Hz):










HV power supply (12 kV, 180mA)
DC power supplies (two Sorensen XHR 600-1.7 wired in series)
DC power supply (Sorensen XHR 300-3.5)
Ross HV relay switches ( used for electrical isolation and dump)
Dry scroll vacuum pump (Varian TriScroll 300 series)
Capacitive pressure sensors LED display (Terranova model 908A)
Two NI CompactRIOs (cRIO-9004)
Five fiber optic boards (designed and built in-house)
NI DAQ system (PXI-8106)
40 gate driver boards (designed and built in-house)
6. Open the isolation valve, close the release valve, and turn the vacuum pump on.
The pump remains running during experimentation. Set the desired pressure
using the bleed valve.
7. Open the resistive dump circuit switch.
8. Charge the Marx generator capacitors to 250V using the Sorensen XHR-300 DC
power supply.
9. Turn off the Sorensen XHR 300 DC power supply.
10. Charge the DES stages to the desired voltage using the two Sorensen XHR 600
DC power supplies wired in series.
11. Turn off the two Sorensen XHR 600 DC power supplies.
12. Charge stage-1 HV capacitor to the desired voltage using the HV power supply.
13. Turn off the HV power supply.
14. Open the Ross relay switch that isolates the HV power supply.
15. Check again to ensure all unauthorized personnel have exited the lab space.
16. Enter the screen room and close the door.
17. Run the DAQ system program that waits for a trigger signal.
18. Using a LOUD voice, yell “FIRING!!”
19. Turn on the NI CompactRIOs to initialize the control program stored in the Flash
memory which begins the firing sequence.
20. After the system fires, turn off the NI CompactRIOs.
21. Exit the screen room.
22. Close the resistive dump circuit switch.
23. Monitor the capacitor bank voltage gauges until zero volts are displayed.
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24. Use a resistive “chicken stick” on all capacitors to ensure no remaining energy is
stored in the capacitor banks.
25. Turn off warning light.
26. Notify appropriate personnel the area is safe.
27. Enter screen room and save all collected data.
Fig. C.1. DES Railgun System Layout and Components.
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In presenting this dissertation in partial fulfillment of the requirements for a
doctorate’s degree at Texas Tech University or Texas Tech University Health Sciences
Center, I agree that the Library and my major department shall make it freely available
for research purposes. Permission to copy this dissertation for scholarly purposes may be
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copying or publication of this dissertation for financial gain shall not be allowed without
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