Brian Thesis

8/12/2019 Brian Thesis

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Density Analysis of the HIT-SI Spheromak

Brian Scott Victor

A thesis submitted in partial fulfillmentof the requirements for the degree of

Master of Science in Aeronautics and Astronautics

University of Washington

2009

Program Authorized to Offer Degree:Aeronautics and Astronautics


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University of WashingtonGraduate School

This is to certify that I have examined this copy of a masters thesis by

Brian Scott Victor

and have found that it is complete and satisfactory in all respects,and that any and all revisions required by the final

examining committee have been made.

Committee Members:

Thomas R. Jarboe

Brian A. Nelson

Date:


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In presenting this thesis in partial fulfillment of the requirements for a mastersdegree at the University of Washington, I agree that the Library shall make its copies

freely available for inspection. I further agree that extensive copying of this thesis isallowable only for scholarly purposes, consistent with fair use as prescribed in theU.S. Copyright Law. Any other reproduction for any purpose or by any means shallnot be allowed without my written permission.

Signature

Date


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TABLE OF CONTENTS

Page

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . v

Chapter 1: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 Importance of Current Drive . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 Plasma Current Drive . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.3 HIT-SI Current Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

Chapter 2: Overview of the HIT-SI Device . . . . . . . . . . . . . . . . . . 5

2.1 Steady Inductive Helicity Injection . . . . . . . . . . . . . . . . . . . 6

2.2 Current Drive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

Chapter 3: Gas Injection System . . . . . . . . . . . . . . . . . . . . . . . . 103.1 Fill Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.2 Puff Gas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

Chapter 4: HIT-SI Far Infrared (FIR) Interferometry . . . . . . . . . . . . 14

4.1 Dispersion Relation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

4.2 FIR System Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

Chapter 5: Reducing Noise Pickup in the FIR Detectors . . . . . . . . . . . 20

5.1 Improved SNR on the Scene Detector . . . . . . . . . . . . . . . . . . 20

5.2 Reference Detector Noise . . . . . . . . . . . . . . . . . . . . . . . . . 22

5.3 Software Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Chapter 6: Results of Density Analysis . . . . . . . . . . . . . . . . . . . . 23

6.1 Typical Density Profile Divided into Three Regions . . . . . . . . . . 23

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6.2 Qualitative Agreement between Plasma Current and Density Fluctua-tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

6.3 Plasma Performance in Relation to the Greenwald Limit . . . . . . . 32

Chapter 7: Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

Chapter 8: Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

8.1 Gas Pressure Measurement . . . . . . . . . . . . . . . . . . . . . . . . 36

8.2 FIR Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

8.3 Machine Operation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Appendix A: Tables of HIT-SI Density Data . . . . . . . . . . . . . . . . . . 39

Appendix B: Description of the Two Cavity FIR Laser System . . . . . . . . 43

B.1 General Overview of the Two Cavity FIR Laser System . . . . . . . . 43

B.2 Standard Operating Procedures . . . . . . . . . . . . . . . . . . . . . 44

B.3 Recent Changes to the FIR System . . . . . . . . . . . . . . . . . . . 50

Appendix C: Puff Gas Measurements . . . . . . . . . . . . . . . . . . . . . . 51

C.1 Calculating the Plenum Volume . . . . . . . . . . . . . . . . . . . . . 51C.2 The Initial Number of Particles in the Plenum . . . . . . . . . . . . . 52

C.3 Puff Plenum Pressure as a Function of Time . . . . . . . . . . . . . . 52

C.4 Operational Notes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

Appendix D: Electrical Noise Troubleshooting the FIR Signal Detection System 54

D.1 Scene Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

D.2 Reference Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Appendix E: Matlab Code . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

E.1 Density Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

E.2 Tau Based Upon Plateau Density . . . . . . . . . . . . . . . . . . . . 75

E.3 Tau Based Upon Density Decay Region . . . . . . . . . . . . . . . . . 83

E.4 j/n Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

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LIST OF FIGURES

Figure Number Page

1.1 Current drive in a z-pinch . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2 Magnetic field generation in a tokamak . . . . . . . . . . . . . . . . . 2

1.3 Formation of a spheromak using coaxial helicity injection (CHI) . . . 3

2.1 Cross section of HIT-SI. Drawing by John Rogers and Paul Sieck . . 52.2 Injector coils on HIT-SI. Drawing by John Rogers and Paul Sieck . . 6

2.3 Current drive on HIT-SI . . . . . . . . . . . . . . . . . . . . . . . . . 8

2.4 Top: injector voltage (V). Middle: injector flux (Wb). Bottom: sphero-mak current (A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

3.1 Gas injection points. Drawing by John Rogers and Paul Sieck . . . . 10

3.2 Puff gas injection system . . . . . . . . . . . . . . . . . . . . . . . . . 11

3.3 X-injector pressure transducer reading . . . . . . . . . . . . . . . . . 12

3.4 Y-injector pressure transducer reading . . . . . . . . . . . . . . . . . 12

4.1 Layout of the FIR interferometry system . . . . . . . . . . . . . . . . 16

4.2 Master laser path through the confinement region . . . . . . . . . . . 19

5.1 The 5.8 kHz noise that dominated the blue signal was reduced (redsignal) through the construction of a new scene detector . . . . . . . 21

5.2 The new enclosure houses the Schottky diode, pre-amplifier, and amplifier 21

5.3 Faraday cage further reduces electrostatic noise pickup on the scenesignal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6.1 Regions of the HIT-SI density profile . . . . . . . . . . . . . . . . . . 24

6.2 Peak density correlation to fill gas: all shots are taken with a puffpressure of 1000 Torr . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

6.3 Shot 114361: Exponential fit to the density decay region . . . . . . . 28

6.4 Plateau density dependence on fill gas pressure: all shots are takenwith a puff pressure of 1000 Torr . . . . . . . . . . . . . . . . . . . . 30

6.5 Particle confinement time based upon plateau density . . . . . . . . . 31

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6.6 Density and current for shot 114476 . . . . . . . . . . . . . . . . . . . 32

6.7 Density and current for shot 114476 . . . . . . . . . . . . . . . . . . . 32

6.8 j/n is Greatest for High Voltage Shots without Fill Gas . . . . . . . . 34

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LIST OF TABLES

Table Number Page

3.1 Average particle flow rate from 4.2 to 7.2 ms [1020 s1] . . . . . . . . 13

4.1 Machine dimensions and beam path through the confinement region . 19

A.1 Calculated Values from Density Data, HIT-SI Shots 114073 - 114075 . 39

A.2 Calculated Values from Density Data, HIT-SI Shots 114077 - 114460 . 40A.3 Calculated Values from Density Data, HIT-SI Shots 114461 - 114652 . 41

A.4 Calculated Values from Density Data, HIT-SI Shots 114659 - 114699 . 42

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ACKNOWLEDGMENTS

I would like to thank my advisor Tom Jarboe for giving me the opportunity to

work on this project, Roger Smith and Cihan Akcay for teaching me the workings

the interferometer, and George Andexler for his technical support and knowledge. I

would also like to acknowledge David Ennis, John Rogers, Brian Nelson, and Will

Hamp for their help and advice.

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Chapter 1

INTRODUCTION

1.1 Importance of Current Drive

Magnetic fields are used to confine plasmas at high enough temperatures for fusion to

occur. Due to the high temperatures reached in a reactor, contact with material walls

contaminates and degrades the plasma. In magnetic confinement devices, internal

plasma currents help to heat and confine the plasma. Plasmas Ohmically heat through

current drive in a similar way to a light bulb heating when current is driven through

the filament. Magnetic field pressure balances particle pressure to confine the plasma.

Plasma currents are typically formed in one of two ways: through electrodes or by

making the plasma the secondary of a transformer and creating a loop voltage.

1.2 Plasma Current Drive

In 1-D configurations, such as z-pinches, electrodes are used at the ends of the con-

finement volume and the voltage potential drives current through the plasma as can

be seen in Fig. 1.1. Z-pinches generate closed magnetic flux, but are susceptible to

sausage and kink instabilities [1]. Adding a magnetic field parallel to the current

helps to stabilize the configuration at the cost of creating open field lines.


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Figure 1.1: Current drive in a z-pinch [2]

2-D configurations eliminate open field lines by connecting the two ends of the

cylinder and creating a torus. Driving plasma current in a toroidal device presents

some difficulties. First of all, the toroidal nature of the device prevents the use of

electrodes. Tokamaks drive plasma current with a central solenoid, where the plasma

acts as the transformer secondary [3]. However, this has only been effective in pulsed

operation. AC operation of the central solenoid has been attempted [4], but plasma

containment has not been shown through the current direction reversal.

Figure 1.2: Magnetic field generation in a tokamak [3]


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HIT-SI is a magnetic confinement configuration known as a spheromak [5]. Sphero-

maks are advantageous over toroidal devices in that they are topologically sphericaland do not require external toroidal field coils. One method for creating a spheromak

is called Coaxial Helicity Injection (CHI). In CHI spheromaks helicity is injected as

shown in Fig. 1.3. A solenoid, inside the inner electrode, generates vacuum magnetic

field lines between the inner and outer electrodes [6]. Gas is injected and current is

driven between the inner and outer electrodes along the vacuum field lines. Toroidal

Figure 1.3: Formation of a spheromak using coaxial helicity injection (CHI) [7]


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magnetic fields encircling the inner electrode are formed from this current and, as

the magnetic field line density increases, the pressure forces the plasma into the tunacan flux conserver. The vacuum field lines form into poloidal field lines, which drive

toroidal current in the plasma. Eventually the field lines are stretched to the breaking

point and reconnection occurs. The resulting configuration is a spheromak.

1.3 HIT-SI Current Drive

As will be explained in more detail in the next chapter, HIT-SI uses Steady Inductive

Helicity Injection (SIHI) [8, 9] to inject helicity into a bow tie shaped flux conserver.Through helicity conservation and magnetic relaxation to the eigenstate of the flux

conserver, toroidal plasma current is formed. The constant influx of helicity to the

flux conserver allows for steady-state operation without the use of electrodes.


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Chapter 2

OVERVIEW OF THE HIT-SI DEVICE

Figure 2.1: Cross section of HIT-SI. Drawing by John Rogers and Paul Sieck

The Helicity Injected Torus with Steady Inductive drive (HIT-SI) is a novel ap-

proach for injecting magnetic helicity to form and sustain a spheromak. Using Steady

Inductive Helicity Injection (SIHI) [8, 9], a DC plasma current is generated and formedin the bow-tie flux conserver from AC driven plasma injectors. Figure 2.1 shows the

bow-tie flux conserver, housing the spheromak confinement region, in teal and red,

and the two injectors in yellow and blue. The injectors act as 180 sections of a large

aspect ratio reversed field pinch (RFP) that connect to the spheromak confinement

volume. The confinement region is bow tie shaped to increase the MHD limit for


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the spheromak equilibrium [10].

2.1 Steady Inductive Helicity Injection

Each plasma injector has a voltage and flux coil to generate magnetic helicity. The

solenoidal-shaped flux coil (right side of Fig. 2.2) establishes flux through the sphero-

mak confinement volume, and the voltage coil (left side of Fig. 2.2) induces a current

along this flux.

Voltage Coils Flux Coils

Figure 2.2: Injector coils on HIT-SI. Drawing by John Rogers and Paul Sieck


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The helicity injection rate is given by Eq. 2.1 [5]

K= 2Vinjinj (2.1)

whereVinj is the voltage in the voltage coils and inj is the flux in the flux coils. The

voltage and flux coils on a given injector are driven in phase, generating a positive

helicity injection rate at all times

Vinj =Vmaxsin(t) (2.2)

inj = maxsin(t) (2.3)

K= 2Vmaxmaxsin2(t) (2.4)

where = 2fandfis the injector frequency, 5.8 kHz for the data in this thesis. The

injectors are driven 90 out of phase for constant helicity injection when the injectors

operate at equal voltage and fluxes.

K= 2Vmaxmax(cos2(t) + sin2(t)) = 2Vmaxmax (2.5)


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2.2 Current Drive

Figure 2.3 is a conceptual drawing of the magnetic field lines in HIT-SI. The red lines

are the field lines generated by a given flux coil. Current is driven along these field

lines to inject helicity. Through magnetic relaxation, the blue field lines form as the

magnetic helicity relaxes to its lowest energy state, known as a Taylor state [11]. This

relaxation drives the DC spheromak current.

Figure 2.3: Current drive on HIT-SI [12]

Figure 2.4 shows the injector voltage and flux signals and the resulting spheromak

current for shot 114698.


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X-injector in black. Y-injector in red.

Figure 2.4: Top: injector voltage (V). Middle: injector flux (Wb). Bottom: sphero-mak current (A)


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Chapter 3

GAS INJECTION SYSTEM

There are two methods of gas injection, one into the confinement region and one

into the midpoint of each injector. Gas injected into the confinement region, used for

pre-ionization, maintains the vacuum vessel at a constant pressure, typically around 2

mTorr. This gas is known as fill gas. Gas injected into the midpoint of each injector

fuels the plasma injectors during the course of the shot. This gas is known as puff

gas. The injection locations are shown in Fig. 3.1 below.

Figure 3.1: Gas injection points. Drawing by John Rogers and Paul Sieck

Red = Fill,Blue = Puff


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3.1 Fill Gas

The fill gas maintains the vacuum region at a constant pressure and is used for pre-

ionization. During low voltage shots,Vinj < 350 V, pre-ionization is needed for gas

breakdown. Typically a fill gas pressure of 2 mTorr is used; however, higher fill gas

pressures are possible. At higher voltages,Vinj 350 V, the voltage itself is enough

to achieve breakdown, and the fill gas is no longer needed.

3.2 Puff Gas

Puff gas fuels the plasma injectors. Without puff gas the injectors would become

starved, limiting the injector current and decreasing the helicity injection rate. The

layout of the puff gas injection system can be seen in Fig. 3.2.

Figure 3.2: Puff gas injection system

For a typical shot, the feed gas throttle is opened to fill the plenum, shown in red

in Fig. 3.2, to the main gas supply pressure, typically 1000 to 5000 Torr. Shortly

before the beginning of the shot, the solenoid valve is opened allowing He gas at 100


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psi to begin flowing. This gas, flowing through the area shown in blue in Fig. 3.2,

opens and closes the valves and is not injected into the machine. The increase inpressure opens the N/C valve and then, a short time later, closes the N/O valve.

The interval between the opening of the N/C valve and the closing of the N/O valve

is set by the control gas throttle. After the completion of the shot, the burp valve

is opened, returning the N/C valve to the closed position and the N/O valve to the

opened position. The following pressure measurements, Fig. 3.3 and Fig. 3.4, show the

pressure transducer readings for the X and Y side injectors at different puff plenum

pressures: blue is 5000 Torr, red is 3000 Torr, green is 2000 Torr, and black is 1000Torr. For information on how this measurement was taken see Appendix C.

Blue = 5000 TorrRed = 3000 TorrGreen = 2000 TorrBlack = 1000 Torr

Figure 3.3: X-injector pressure trans-ducer reading Figure 3.4: Y-injector pressure trans-ducer reading

In Fig. 3.3 and Fig. 3.4 each initial plenum pressure shows two curves: one solid

and one dashed. Time zero represents the beginning of the shot, and the end of the

shot is at eight milliseconds for all of the shots in this thesis. The solid curve is the


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reading with the N/O valve left open. The dashed curve represents the operation

of the puff gas injection system for the data taken in this thesis. The separationbetween the solid and dashed curves occurs when the N/O valve begins to close. The

premature closing of the N/O valve was limiting the injector current late in the shot

and was corrected after the data in this thesis was taken (shot 115106).

Assuming that the flow rate is proportional to the pressure transducer signal,

integrating the signal with the feed gas throttle closed and the N/O valve left open

gives a number proportional to the total number of particles in the plenum.

Pdt Nplenum (3.1)

P =KdN

dt (3.2)

where Nplenum is the total number of particles in the plenum as calculated in Ap-

pendix C, and K is the constant of proportionality to convert between the pres-

sure transducer signal and the particle flow rate. Table 3.1 lists the average par-

ticle flow rates from 4.2 to 7.2 ms for the operating pressures used in this thesis.4.2 and 7.2 ms were chosen because the density for a given shot is relatively con-

stant during this time period. This calculation was made using the MATLAB code

puff_data_integrate3.m , which can be found in Appendix E. Finally, since He is

used as the operating gas, the electron flow rate is twice that of the particle flow rate.

Table 3.1: Average particle flow rate from 4.2 to 7.2 ms [1020 s1]

Initial Puff Pressure X-Injector Y-Injector5000 Torr 17 253000 Torr 11 152000 Torr 7.2 101000 Torr 3.7 5.5


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Chapter 4

HIT-SI FAR INFRARED (FIR) INTERFEROMETRY

Interferometry measures phase shifts of a coherent light source caused by electro-

magnetic waves in the plasma. This technique provides a non-perturbative, phase-

based method of measuring the chord-averaged electron density. This is advantageous

over perturbative diagnostics, such as the Langmuir probe, which can have deleterious

effects on the plasma performance. Due to the phase-based nature of interferometry,

the measurement can be made without calibration. One disadvantage of interferom-

etry, however, is that it does not provide a local measurement.

4.1 Dispersion Relation

For a plasma with an electron cyclotron frequency, ce, negligible compared to the

frequency of the probing laser light source, ce/ 0, the index of refraction is given

as [13]

N2 = 1 2p2

(4.1)

wherep =

nee2

0me, the plasma frequency, and is the frequency of the light source.

Using a binomial series, this can be rewritten as

N= 1 1

2

2p2

+3

8

4p4

+ . . . (4.2)

For p and using the definition ofp from above, this equation can be approxi-

mated as

N= 1 1

2

nee2

0me2 (4.3)


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where ne is the electron density, e is the electronic charge, 0 is the permittivity

of free space, and me is the electron mass. The phase difference measured by theinterferometer is given by

= N 1

dl (4.4)

where is the laser wavelength. For a double-pass system, using the value of the

index of refraction from above gives

= nee

2

0me2dl (4.5)

Noting that = 2c

, writing in radians, and rearranging the above equation gives

the line-integrated density as

nedl=

20mec2

e2 (4.6)

where the right-hand side of the equation is constant except , which is the phase

change between the master and slave laser measured by the interferometer. It is

common to report data as the line-averaged density, which is defined as

ne=

nedl

L (4.7)

where L is the chord length through the plasma. The frequency of the master laser

beam is affected by changes in the electron density, while the frequency of the slave

laser beam is relatively constant through the shot. The relative change in frequency

is the source of the phase change in Eqn. 4.6.

Knowledge of the plasma density, within an order of a magnitude, is important

in selecting an appropriate laser wavelength. To balance sensitivity and accuracy

needs to be much larger thanpwhile not being too large for the signal to be drowned

out by mechanical vibrations [13]. A change in of 2 is known as a fringe. For


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HIT-SI, using ne 1019 m3, with a chord length ofL 1 m, indicates must be

greater than 20m for more than one fringe to be detected. For this reason the bestchoice of wavelength is in the far-infrared spectrum, on the order of 100 m.

4.2 FIR System Layout

A heterodyne detection system is used to measure the line-integrated density. A

schematic of the HIT-SI interferometry system can be seen in Fig. 4.1. An overview

of the interferometer is given in this section and a detailed description of the system

and its operation can be found in Appendix B.

Figure 4.1: Layout of the FIR interferometry system


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4.2.1 FIR Laser System

The FIR system consists of a CO2 laser that optically pumps two difluoromethane

lasers. The CO2 laser operates at 9.2 m and outputs about 60 W of power at this

wavelength. The two difluoromethane lasers, known as the master and slave lasers,

lase at 184.3 m. The master laser outputs approximately 70 mW of power and

the slave laser outputs approximately 30 mW. Due to the high frequency oscillations

of the plasma density, a beat frequency between the lasers of 3 to 4 MHz is used.

Through trial and error this frequency range was found to limit the number of fringe

jumps encountered in measuring the density.

4.2.2 FIR Signal Detection System

There are two detectors, using quasi-optical corner cube detectors connected to Schot-

tky diodes, that are used to detect the beat frequency between the master and slave

lasers. The signal at the reference detector is used as a basis of comparison for the

beat frequency between the lasers over the duration of the shot. The reference signalis split from the main signal with a silicon mirror, which acts as a beam splitter.

This mirror, when used with the scene detectors silicon-based focusing lens, is able

to produce a large signal on the reference detector with little effect on the magnitude

of the scene detector signal.

The scene detector measures the beat frequency between the master laser, which

passes through the confinement region, and the slave laser. A Martin-Puplett config-

uration is used to achieve this [14]. The slave beam, with horizontal polarization, isreflected by the polarizing beam splitter. The beam then reflects off a rooftop mirror,

oriented 45 to the axis of polarization, rotating the polarization of the scene beam

90. The scene beam then passes through the polarizing beam splitter to the scene

detector. The master beam, with vertical polarization, passes through the polariz-

ing beam splitter. After the beam passes through the confinement region, a second


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rooftop mirror rotates the beam to horizontal polarization. When the master laser

beam is incident upon the polarizing beam splitter on its return path, it is reflectedto the scene detector.

4.2.3 Beam Path through the Spheromak Confinement Region

A cutaway of the spheromak confinement region is shown in Fig. 4.2. The data taken

in this thesis uses a beam path that reflects off the rooftop mirror above port 7,

shown by the red line in Fig. 4.2. The beam passes through a region of closed flux

as indicated by computer simulations [15]. The dimensions of the machine and beampath are shown in Table 4.1.


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Figure 4.2: Master laser path through the confinement region

Table 4.1: Machine dimensions and beam path through the confinement region

Major radius 0.5 mConfinement Volume 0.38 m3

Volume of each injector 0.025 m3

Impact parameter 0.35 mChord length 0.71 m


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Chapter 5

REDUCING NOISE PICKUP IN THE FIR DETECTORS

Using a phase-based diagnostic lessens the deleterious effect of electrical noise

pickup. However HIT-SI is a very noisy electromagnetic environment, creating noise

which can degrade the quality of the signal to the point of making the data unusable.

There are two main sources of noise in the FIR signal. One is from the injector voltage

and flux circuits and the other the RF antenna.

5.1 Improved SNR on the Scene Detector

The largest noise source in the scene signal is from the Y-side voltage coil. The noise

pickup is at the frequency of the injectors, 5.8 kHz. To improve the signal to noise

ratio a new scene enclosure was constructed. Before the new enclosure was made,

noise from the injector dominated the beat frequency. After redesigning the scene

enclosure, the noise was significantly reduced (see Fig. 5.1).

The new enclosure for the scene detector was designed to allow the pre-amplifier

and amplifier to be housed in the same enclosure as the detector (see Fig. 5.2). Byshortening the cables connecting the detector to the pre-amplifier and amplifier, the

noise amplitude was reduced by about 50%. Also a Faraday cage was constructed (see

Fig. 5.3) to house the scene enclosure, further reducing the noise by another 50%. The

bias supply was also moved from near the scene detector to inside the screen room in

order to eliminate the need for two enclosures near the machine.


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Figure 5.1: The 5.8 kHz noise that dominated the blue signal was reduced (red signal)through the construction of a new scene detector

Figure 5.2: The new enclosure housesthe Schottky diode, pre-amplifier, andamplifier

Figure 5.3: Faraday cage further re-duces electrostatic noise pickup on thescene signal


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Chapter 6

RESULTS OF DENSITY ANALYSIS

Measuring the plasma electron density gives information on fueling dynamics, the

particle confinement time, and the plasma performance in relation to the Greenwald

limit [16]. The two methods of gas injection affect the density profile differently.

Injecting fill gas causes a large initial spike in the density, while puff gas has a larger

effect on the steady-state density. Fluctuations in the density during the second half

of the shot correlate to fluctuations in the spheromak current. Comparing electron

density to spheromak current density indicates the best plasma performance occurs

at higher voltage without fill gas.

6.1 Typical Density Profile Divided into Three Regions

A typical density trace can be broken up into three regions: an initial density spike,

a density decay region, and a density plateau (see Fig. 6.1). First the fill gas pressure

is compared to the initial density spike to find information on the percent ionization.

In the second region, an exponential fit to the density decay gives the confinement

time of the fill gas. Finally, using the particle flow rate of the puff gas and the

approximately steady-state densityplateau density during the end of the shot a

second confinement time is calculated.


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6.1.1 Region 1: Initial Density Spike

Increasing the initial fill gas pressure leads to an increase in the initial density spike.

The relation between the peak density and the fill gas pressure gives information

on particle ionization. For a constant pressure in the vacuum vessel, the number of

particles in the confinement region and injectors can be found using the ideal gas law:

N=PV

kT (6.1)

where k = 1.381 1023

J/K, T = 298 K, and V = 0.43 m3

, the volume of theconfinement region and injectors. For a fill pressure of 2 mTorr, N = 2.8 1019

particles. For helium as the fill gas this is 5.6 1019 electrons.

Figure 6.2 shows the effect of increasing the fill gas pressure with the puff pressure

at 1000 Torr. The linear fit in Fig. 6.2 does not pass through zero because the puff

gas also has an effect on the peak density. For this reason it is important to look at

the slope of the linear fit at a constant puff pressure. At an injector voltage of 275 V,

an increase in fill pressure of 2 mTorr corresponds to an increase in peak density of2.81019 electrons per m3. Assuming uniform density, this corresponds to an increase

of 1.1 1019 electrons in the confinement region.

Comparing the number of particles in the confinement volume and injectors to the

average electron density, about 20% of the fill electrons are utilized during the initial

density spike.


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Figure 6.2: Peak density correlation to fill gas: all shots are taken with a puff pressureof 1000 Torr

6.1.2 Region 2: Exponential Density Decay gives Fill gas Confinement Time

To calculate a particle confinement time, the number of particles needs to be related

to the particle time rate of change. In the density decay region the number of particles

can be approximated as

N=Aet/ (6.2)

and the particle time rate of change as

dN

dt =A

et/ (6.3)

Relating these two equations gives

= N

dN/dt (6.4)


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which has units of seconds. Therefore, the coefficient in the exponential fit to the

density decay region gives the particle confinement time. This calculation is based onone chord through the machine and can be made without the assumption of uniform

density throughout the confinement region. The steps taken to make this calculation

are outlined below:

1. The density data is filtered so that an appropriate time for the peak density can

be established.

(a) The start point is 0.1 ms after the peak filtered density.

2. The end point was chosen based upon the shot characteristics. For example, for

shots with higher plateau densities the time interval between the peak density

and the plateau density is short. Therefore an end point 0.8 ms after the start

point was selected. For shots with lower plateau densities an end point up to

1.5 ms after the start point was used.

3. The plateau density, the average density between 4.2 and 7.2 ms, is subtracted

from the total density.

(a) This step is important to make the exponential fit have its zero level equal

to the plateau density.

4. For the selected range of data points, an exponential fit was made to the data

using the MATLAB code listed in Appendix E, n_initial_tau6.m. The expo-

nential fit is made to the unfiltered data.

The resulting values and the time range used can be found in Appendix A. A

typical fit of this exponential to the data is shown in Fig. 6.3, with the exponential fit

shown plotted out to 4.2 ms. Typical values forvaried between 0.5 and 1.5 ms. The

values calculated for were compared to various machine parameters, such as puff


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pressure, fill pressure, and injector voltage. Little correlation between the machine

parameters and could be found.

Figure 6.3: Shot 114361: Exponential fit to the density decay region


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6.1.3 Region 3: Confinement Time based upon Plateau Density and Puff Particle

Injection Rate

A second confinement time can be calculated by comparing the plateau density

based upon the assumption of uniform density throughout the confinement regionto

the puff particle injection rate. Similar to the previous section, the confinement time

is calculated by comparing the number of particles to the particle time rate of change.

= N

dN/dt (6.5)

In this case, N is dependent on the plateau density and dN/dt is the puff particle

injection rate. The steps taken to make this calculation are outlined below:

1. The plateau density is calculated as the average density between 4.2 and 7.2 ms.

2. Fig. 6.4 shows that the plateau density increases with increased fill gas. The

slope of the linear fit relates the increase in fill gas pressure to the increase

in plateau density. To calculate the confinement of the puff gas, the plateaudensity dependence on the fill gas is subtracted from the total plateau density.

This means that for an increase of 2 mTorr in fill gas pressure 0.4 1019 m3 is

subtracted from the plateau density for this calculation.

3. The adjusted plateau density is divided by the time dependent puff particle flow

rate between 4.2 and 7.2 ms.

4. The average value forover this time range is calculated.

(a) For details on this calculation refer to the MATLAB code,

puff_data_integrate3.m, in Appendix E.

Fig. 6.5 shows the calculated confinement times for the shots analyzed in this thesis

with an injector flux of 1 mWb and a vertical field of 1 A, where the vertical field is


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Figure 6.4: Plateau density dependence on fill gas pressure: all shots are taken witha puff pressure of 1000 Torr

a steady-state field in the axial direction. Shots taken with an initial puff pressure

of 1000 Torr tend to have the worst performance. There is a lack of data points

at 5000 Torr because the density measurement tends to have more discontinuities

fringe jumpsat higher operating pressures. In general the best confinement times

result from running the machine at higher injector voltages. This result is consistent

with other measures of plasma performance, such as spheromak current, which have

the best values at higher injector voltages.


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Figure 6.5: Particle confinement time based upon plateau density


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6.2 Qualitative Agreement between Plasma Current and Density Fluc-

tuations

Looking at the density and current time histories of several shots, times of higher

spheromak current corresponded to increases in density. This observation is most

readily visible during the plateau density period. Figures 6.6 and 6.7 show two shots

with the same machine parameters:Vinj= 275 V, Fill = 2 mTorr, and Puff = 3000 Torr.

The density and current are shown on the same plot for each shot from 2 to 7 ms.

Each plot shows increases in density corresponding to increases in current.

Density fluctuations show qualitativeagreement to spheromak current:

Vinj = 275 V, Fill = 2 mTorr, Puff = 3000 Torr

Figure 6.6: Density and current for shot114476

Figure 6.7: Density and current for shot114476

6.3 Plasma Performance in Relation to the Greenwald Limit

An empirical relationship in plasma physics, known as the Greenwald limit [16], relates

the plasma current density, j, to the electron density, n. Plasmas operating below

j/n = 1014 Am tend to be radiation dominated, thus it is important to pursue a

parameter space with low density in relation to plasma current. By increasing j/n


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the plasma performance would improve, becoming less radiation-dominated.

The current density is calculated using the following equation

j=ItoroidalA

(6.6)

where Itoroidal is the frequency compensated spheromak current calculated using the

20 external flux loops andA = 0.2 m2 is the cross-sectional area of HIT-SI. Assuming

uniform electron density, the ratio of current density to electron density is calculated

as

jn

= Itoroidal

nA (6.7)

where nis the line-averaged density.

Figure 6.8 shows the maximum value ofj/nfor each shot. Typical plasmas tended

to achieve a peakj/non the order of 1 to 21015 Am. The four shots in the upper-

right portion of Fig. 6.8, with values of j/n approaching 51015 Am, were run with

no fill gas at Vinj = 350 V. To continue to increase j/n, the parameter space in this

regime needs to be further explored.


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Figure 6.8: j/n is Greatest for High Voltage Shots without Fill Gas


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Chapter 7

CONCLUSION

A study of the puff gas injection system was made. Knowledge of the particle

flow rate aided in the optimization of the feed and control throttle valves to achieve

symmetry in both injectors. This will also allow the injectors to be run without a

decrease in injector current from a lack of puff gas due to the N/O valve closing before

the end of the shot.

In order to reduce the noise pickup on the FIR signal, a new scene detector was

constructed and ground loops near the reference detector were removed. This im-

proved the signal to noise ratio of the scene and reference signals.

Analysis of the density profiles provided two means of calculating the particle

confinement time. An exponential fit to the density decay region showed confinement

times that varied between roughly 0.5 and 1.5 ms. The second confinement time

was found by comparing the plateau density to the puff gas injection rate at that

time. Values for this confinement time averaged 1.5 ms. Comparison of the density

profile to the toroidal plasma current showed that times of high current corresponded

to increases in density. Finally, the ratio of current density to electron density was

calculated for each shot. While all of our shots were below the Greenwald limit, shots

with no fill gas and high voltage approached values of 0 .5 1014 Am.


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Chapter 8

FUTURE WORK

8.1 Gas Pressure Measurement

Pressure increases from the puff gas system need to be measured at the midplane of

the confinement region. This will allow effects on the puff gas injection between the

pressure transducer and confinement region to be measured. Possible asymmetries in

injection rates between the injectors could also be found.

8.2 FIR Signal

To prevent losses in the FIR signal along transmission lines a line driver should be

installed. In order to accommodate the line driver the scene detector enclosure needs

to be redesigned.

8.3 Machine Operation

The control valves for the puff gas system need to be optimized for the fueling of the

injectors. To increase the ratio of current density to electron density the machine

should be operated without fill gas at higher voltages.


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BIBLIOGRAPHY

[1] U. Shumlak. AA558: Plasma theory, Spring 2008.

[2] ZaP: Z-pinch attributes. http://www.aa.washington.edu/research/ZaP/attributes.html, July 2009.

[3] R. Pitts, R. Buttery, and S. Pinches. Fusion: the way ahead. Physics World,

March 2006. http://physicsworld.com/cws/article/print/24295.

[4] B.J.D. Tubbing et al. AC plasma current operation in the JET tokamak.NuclearFusion, 32(6):967972, 1992.

[5] T.R. Jarboe. Review of spheromak research. Plasma Phys. Control. Fusion,36(6):945990, 1994.

[6] How to make a spheromak. http://ve4xm.caltech.edu/Bellan_plasma_page/howto.htm, February 2000.

[7] W.C. Turner, G.C. Goldenbaum, E.H.A. Granneman, J.H. Hammer, C.W. Hart-man, D.S. Prono, and J. Taska. Investigations of the magnetic structure and thedecay of a plasma-gun-generated compact torus. Physics of Fluids, 26(7):19651986, 1983.

[8] T.R. Jarboe. Steady inductive helicity injection and its application to a high-betaspheromak. Fusion Technology, 36(1):8591, 1999.

[9] P.E. Sieck, W.T. Hamp, V.A. Izzo, T.R. Jarboe, B.A. Nelson, R.G. ONeill, A.J.Redd, and R.J. Smith. Initial studies of steady inductive helicity injection on

the HIT-SI experiment. Plasma Science, IEEE Transactions on, 33(2):723728,2005.

[10] U. Shumlak and T.R. Jarboe. Stable high beta spheromak equilibria using con-cave flux conservers. Physics of Plasmas, 7(7):29592963, 2000.

[11] J.B. Taylor. Relaxation and magnetic reconnection in plasmas.Rev. Mod. Phys.,58(3):741763, 1986.


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Appendix A

TABLES OF HIT-SI DENSITY DATA

Appendix A lists the shots presented in this thesis. The machine parameters and

calculated values are presented in the tables that follow. All of the shots are run at

inj = 1.0 mWb and a vertical field of 1.0 A.

[1] indicates that decay tau was calculated with the end of fitting period 0.8 ms

after the density peak.

[2] indicates that decay tau was calculated with the end of fitting period 1.5 ms

after the density peak.

[3] indicates that a decay tau couldnt be calculated because of the plasma pa-

rameters.

[4] indicates that the shot contained a VCE fault.

Table A.1: Calculated Values from Density Data, HIT-SI Shots 114073 - 114075

Shot Fill(mT)

Puff(T)Vinj(V)

PeakItor(kA)

Peak j/n(1015 Am)

Plateau ne(1019 m3)

Decay (ms1)

End (ms1)

114073 2 3000 275 11.9 1.7 2.6 0.51 1.7114074 2 2000 275 7.0 1.3 1.4 0.65 1.1

114075 2 2000 275 3.8 1.2 1.0 0.70 0.6


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Shot Fill(mT)

Puff(T)Vinj(V)

PeakItor

(kA)

Peak j/n(1015 Am)

Plateau ne(1019 m3)

Decay (ms1)

End (ms1)

114077 2 2000 275 10.0 1.6 1.5 0.86 1.2114093 4 2000 275 8.0 1.3 2.7 1.3 2.1114094 4 1000 275 4.9 0.6 1.2 1.1 0.9114096 4 2000 300 8.0 1.1 2.3 1.0 1.6114104 2 1000 350 11.0 1.6 0.7 1.0 0.5114106 0 2000 350 20.1 3.6 0.9 [3] 1.0114107 0 3000 350 18.8 4.9 2.8 [3] 2.1114323 2 5000 275 11.2 1.2 4.3 0.64 1.8114356 0 3000 350 20.2 3.8 3.4 [3] 2.5

114359 0 3000 350 20.2 4.6 3.0 [3] 2.2114360 2 3000 325 18.1 1.3 3.5 1.5 2.3114361 2 3000 325 15.5 1.7 3.2 0.99 [1] 2.1114362 2 2000 325 14.1 2.3 2.0 1.1 1.7114363 2 2000 325 9.3 1.5 1.9 0.98 1.7114364 2 2000 325 16.3 2.6 2.1 0.99 1.9114373 2 2000 275 8.7 1.8 2.0 1.6 [1] 1.8114374 2 2000 275 5.6 1.4 2.0 0.79 1.7114457 2 3000 325 15.0 1.2 3.3 1.4 [2] 2.1114459 2 2000 325 16.6 2.2 2.0 [3] 1.8114460 2 2000 325 12.3 1.6 2.2 0.46 2.0


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Shot Fill(mT)

Puff(T)Vinj(V)

PeakItor

(kA)

Peak j/n(1015 Am)

Plateau ne(1019 m3)

Decay (ms1)

End (ms1)

114461 2 2000 325 13.7 2.0 1.8 0.63 1.6114465 2 3000 300 13.4 1.2 4.0 [3] 2.7114480 2 3000 300 13.7 1.6 3.3 0.75 2.2114481 2 2000 300 8.2 1.8 1.9 0.93 1.6114482 2 2000 300 11.2 1.2 2.3 0.76 2.1114483 2 2000 300 9.0 1.5 1.9 0.91 1.6114563 2 5000 350 7.0 1.0 0.0 [4] [4]114625 2 2000 325 13.9 2.4 2.1 1.1 1.8114626 2 2000 325 14.6 2.1 2.5 [3] 2.4

114627 2 2000 325 12.7 1.7 2.2 2.0 2.0114628 2 2000 325 12.5 1.8 2.1 1.1 1.9114644 2 1000 300 6.2 0.7 0.7 0.50 0.5114645 2 1000 300 7.0 0.9 0.7 [3] 0.6114646 2 1000 275 2.4 0.7 0.7 1.0 0.6114647 2 1000 275 2.4 0.4 0.8 0.93 0.8114648 4 1000 275 5.7 0.6 1.0 [3] 0.5114649 4 1000 275 6.2 0.7 1.0 1.1 0.4114650 4 1000 275 6.6 0.8 1.1 1.3 0.7114651 4 1000 300 6.9 0.8 1.2 1.2 [2] 0.8114652 4 1000 300 6.7 1.0 1.0 1.5 [2] 0.4


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Shot Fill(mT)

Puff(T)Vinj(V)

PeakItor

(kA)

Peak j/n(1015 Am)

Plateau ne(1019 m3)

Decay (ms1)

End (ms1)

114659 4 1000 275 6.0 0.8 0.9 1.4 0.2114660 4 1000 275 5.9 0.7 1.1 1.2 0.6114661 6 1000 275 5.1 0.6 1.4 2.4 [2] 0.3114662 6 1000 275 6.4 0.8 1.5 1.3 0.6114663 8 1000 275 7.5 0.7 1.6 1.3 0.0114664 8 1000 275 5.5 0.8 1.9 1.2 [2] 0.6114669 4 1000 325 9.6 1.2 1.5 1.2 1.5114671 6 1000 325 8.0 0.8 1.5 1.2 0.7114673 2 1000 325 8.8 0.9 0.7 1.2 0.6

114674 2 1000 325 7.3 1.1 0.6 0.86 0.4114675 2 2000 350 15.5 1.7 2.2 [3] 2.0114676 2 2000 350 16.5 2.1 1.9 1.0 1.6114687 2 3000 275 12.2 1.3 3.2 0.99 2.1114689 2 3000 300 13.0 1.3 3.2 0.56 2.1114690 2 3000 325 14.7 1.5 3.3 1.1 2.1114691 2 3000 325 15.7 1.6 3.3 0.83 2.1114692 2 3000 350 14.3 1.3 3.0 [3] 1.9114696 4 2000 325 9.6 1.2 2.6 [3] 2.0114698 2 2000 350 18.1 2.2 2.6 [3] 2.4114699 2 2000 350 14.5 1.5 2.5 0.68 2.3


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Appendix B

DESCRIPTION OF THE TWO CAVITY FIR LASERSYSTEM

Note: this description of the system is taken from Appendix D in R.G.

ONeals dissertation [17] with changes applicable to the current system in

bold.

The two cavity FIR laser system is made primarily of equipment donated from

Lawrence Livermore National Laboratory, and was renovated for use on the HIT-SI

experiment. This appendix gives a general overview of the system and a standard

operating procedure for running the system.

B.1 General Overview of the Two Cavity FIR Laser System

The FIR system consists of a 100 Watt CW rated carbon dioxide pump laser, and

two difluoromethane FIR lasers. The CO2 pump laser is tuned to the 9R32 transition

( 9.2m) with a diffraction grating. The power output measured by calorimeter on

this line is approximately 55 - 65 Watts continuous in practice. The beam is focused

using a 2 m radius concave spherical mirror. Before the beam converges, it is split

by a ZnSe partial reflector. One beam is directed into the master FIR cavity, and

the other into the slave cavity. The optical path is laid out such that the CO2 beamcomes to a waist as it enters the input coupler of the FIR cavities. The FIR input

couplers are 2 diameter mirrors with a 3 mm hole in them for the beam to enter. To

maintain vacuum, the beam is passed through a ZnSe Brewster window, (uncoated

ZnSe glass tilted at its Brewster angle). The CO2 beam expands from its waist at

the entrance hole to fill the FIR cavity. The FIR output couplers are gold-coated


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silicon wafers and a quartz window for vacuum. The output couplers are mounted

on PZT stacks so that the cavity length can be precisely adjusted. The FIR cavitiesare filled with 55 mTorrof difluoromethane gas, and lase at 184.3m. By tuning

the PZT stacks, a frequency difference of 3 - 4 MHz can be maintained between

the two cavities. The FIR cavities output 30 100 mWatts of FIR light each.

The master beam polarization is rotated by a quartz half-wave plate, so that it is

perpendicular to the slave beam. The beams are combined and made collinear at a

free standing polarizing wire grid. The beams are coupled to a quartz tube which acts

as a waveguide and guided towards the Martin-Puplett interferometer. The beamsare detected with quasi-optical corner cube detectors which have a point contacted

whisker antenna connected to a forward biased low capacitance Schottky-diode. The

intermediate frequency is amplified and digitized.

B.2 Standard Operating Procedures

This subsection describes how to turn the system on, set it up for interferometry, and

shut it down.

B.2.1 Turning on the Data Acquisition

1. Ensure that the reference and scene Schottky detectors are in SHORT or OFF

position.

2. Never jolt/jostle/elctrostatically shock/smack. This could kill the diode. They

are fragile, and very sensitive to electrostatic discharge.

3. Never change the state of bias supplies or amplifiers the detectors are connected

to unless the detector is in the OFF or SHORT position.

4. Turn on the CAMAC crate in the blue rack in the screen room.


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5. Turn on the scene detector preamplifier power supply. It is a small blue box on

a shelf in the northeast corner of the screen room.

6. Turn on the reference detector preamplifier power supply. It is an aluminum

paneled supplyto the left of the scene detector preamplifier power sup-

ply.

7. Turn the reference Bias supply to internal (the middle state of the 3 state

switch). It is located near the reference detector.

8. Turn the oscilloscope on.

9. Turn the reference detector to ON. You should see the reference signal on the

oscilloscope go from clean to noisy.

10. Turn the scene detector bias supply to internal. It is located near the scene

detector preamplifier power supply.

11. Turn the scene detector ON, and then close up the aluminum electrostatic shield

and copper Faraday cage.

12. Check that the scene signal is showing noise on the oscilloscope.

B.2.2 FIR Lasers Start Up

Wear CO2 Safety Goggles When Working Around the Laser!

1. Turn on the Neslab water chiller. It is best to turn this on 30 minutes before

starting the rest of the system so the water cools.

2. Turn on the three PZT bias supplies in the orange rack.


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3. Place one of the kiln bricks in front of the CO2laser, about 1 to 2 feet away from

the output coupler. This will block the beam and allow for the beam strengthand mode to be visualized as a glowing yellow hot spot on the brick.

4. Close the sliding acrylic panels to enclose the business end of the CO2 laser.

5. Start the dry air flow from the yellow air bottle next to the screen room. Verify

that there is pressure in the tank.

6. Open the green Nupro valve under the south-west corner of the laser table wideopen.

7. Adjust the black flow meter valve next to the Nupro until the CO 2 baratron

gauge reads about 5.0 Torr.

8. Flip the blue Spellman HV supply (at the bottom of the orange rack) to on.

9. Position yourself next to the orange rack so that you can see the cathode (outputend electrode) on the CO2 laser.

10. Push the red HV button on the Spellman, and immediately look at the cathode:

If the discharge glows up around the sides of the cathode, push the black

RESET button immediately. Wait 10 seconds, and try again.

If the discharge goes out the pumpout tube, push the black RESET button

immediately. Wait 10 seconds, and try again.

If the discharge does anything else abnormal, push the black RESET but-

ton immediately. Figure out what went wrong, and fix it.

The discharge SHOULD go from JUST the bottom tip of the cathode,

through the laser tube to the anode. It should be white or faint pink. It


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250 mVoltspeak to peak on the scene, and 800 mVoltson the reference are

typical. Its hard to describe a concise procedure for this, but here are sometricks.

First, tune the CO2 laser diffraction grating to maximize/clean the signal.

Nudge/Prod the FIR output couplers with your hand to see if moving them

improves anything. If it does, make the appropriate adjustments on the

knobs. Dont touch the PZT stacks, you can get a jolt.

Sometimes, a wide, sweeping scan of the FIR output coupler knobs isrequired to find a good mode. If you do this, first be sure the CO2 is at

good power, make note of where the FIR knob is before moving it, and

move only one FIR knob at a time.

If the signal is strong and sinusoidal, but not at a good frequency, adjust

the PZT bias on either the slave or master to change the frequency.

If the signal has sidebands, or is not sinusoidal, check which FIR cavity is

making the bad signal by sticking your hand in one beam or the other at

the FIR output coupler and seeing which one interrupts the undesirable

signal. Tune that one. Dont stick your hand into the beam at the FIR

input coupler.

If there is no visible signal, make only minor adjustments, nudging and

prodding the output couplers, and CO2 diffraction grating. If that doesnt

work, there is probably something wrong, like a detector/amplifier is off,

there is no difluoromethane gas in the cavity, the beam is obstructed,

the pump laser is on the wrong line, or something. Dont make large

adjustments to the FIR knobs when there is no signal. Instead, look around

for something that is obviously wrong.

If you suspect the pump laser is on the wrong line, put the kiln brick in the


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pump beam, tune the CO2 until the beam is strong, and remove the brick

again while watching the FIR convectron pressure. If it is the right line,the pump beam will raise the FIR pressure by 5 mTorr within about

two seconds of removing the brick. If it is the wrong line, the pressure will

not change, or will change by 1 to 2 mTorr slowly, over five to ten seconds.

If it is the wrong line, put the brick in and adjust the wavelength knob

in one direction until you find another series of powerful lines. ( 1 2

full turns). Try the pressure test again. If you really get lost, there is a

spectrometer that can be set up. The laser doesnt normally go off of the9R32 line unless youve been adjusting the wavelength knob.

A good intermediate frequency will appear as a clean sinusoidal signal on

both the scene and reference detectors. If you obstruct either the slave or

the master beam at the FIR output couplers, the signal will completely

disappear on both detectors. If the signal does not disappear when an FIR

laser is obstructed, the signal is not a proper intermediate frequency, and

there is a problem in the unobstructed cavity.

B.2.3 FIR System Shut Down

1. Switch the scene and reference detectors to OFF or SHORT position.

2. Switch off the scene and reference detector bias supplies.

3. Turn off the amplifier power supplies.

4. Push the black RESET button on the Spellman HV supply.

5. Wait a few seconds, and then turn off the Spellman HV supply.

6. Open the FIR cavity pumpout valve, and let the FIR lasers pump down.


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7. Turn the green Nupro valve under the south-west corner of the table to closed.

8. Close the yellow dry air bottle.

9. Turn the Neslab chiller off.

10. Turn off the oscilloscope.

11. Turn off the three bias supplies in the orange rack.

12. Check with the operator before turning the CAMAC crate off.

B.3 Recent Changes to the FIR System

The layout of the cooling system was changed to allow higher water pressure to flow.

Currently the cooling system has four parallel paths that originate from the Neslab

chiller: one for the CO2 laser chamber, one for each of the FIR laser chambers, and

one for the laser input and output couplers.

The focusing lens for the scene detector was changed to match the diameter of

the waveguides. A lens made out of HRFZ-SI was purchased in order to achieve a

focal length of one inch with 1.5 inch diameter lens. The lens was purchased from

TYDEX, J.S.Co. Information on this lens can be found at www.tydex.ru


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9. For the X-side: Vplenum = 9.7 107 m3

For the Y-side: Vplenum = 8.9 107

m3

C.2 The Initial Number of Particles in the Plenum

The number of particles in the plenum can be found using the ideal gas law:

N=PVplenumkT

(C.2)

wherek = 1.381 1023 J/K and T = 298 K. For an initial pressure of 5000 Torr:

N= 1.6 1020 particles for the X-side

N= 1.4 1020 particles for the Y-side

For helium there are two electrons per particle.

C.3 Puff Plenum Pressure as a Function of Time

1. Hook up the power supply (PCB Piezotronics Model 482A06) to the pressure

transducer (PCB 61 A01)

2. Connect to a digitizer. The data in this thesis was taken using digitizer

\HIT_612_ZZ2:INPUT1.

3. For X-side measurements point the node \PRESS_XINJ:RAWto the correct digi-

tizer input.

4. For Y-side measurements point the node \PRESS_YINJ:RAWto the correct digi-

tizer input.

5. The measurements taken in this thesis are found in shots 114778 to 114805.


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C.4 Operational Notes

Since the flow rate measurements described above were taken, the setting of the

control gas throttle valve was changed so that the N/O valve closes 20 ms after the

beginning of the shot. The pressure transducer measurements for these new settings

are found in shots 115101 to 115105. The feed gas throttle valve has been changed

to ensure that the measured gas pressure at the pressure transducer remains nearly

constant through the duration of the shot. It should also be noted that all of the data

reported in this thesis uses Helium as the operating gas.


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Appendix D

ELECTRICAL NOISE TROUBLESHOOTING THE FIRSIGNAL DETECTION SYSTEM

D.1 Scene Signal

The following are some helpful tips if electrical noise pick up becomes a problem with

the scene signal.

1. If anything is moved inside of the scene detector enclosure it is important to

keep the components electrically isolated from each other and from the walls of

the enclosure.

(a) The pre-amplifier and amplifier should be positioned so that they are sep-

arated by Kapton tape.

(b) Check that none of the connections make a loop to the wall or to the

Schottky diode.

2. The scene enclosure also needs to be isolated from the Faraday cage.

(a) The scene detector should rest on nonconductive material.

(b) Also, the shielding surrounding the output from the scene detector needs

to be isolated from the hole in the back of the Faraday cage.

D.2 Reference Signal

The following are some helpful tips if electrical noise pick up becomes a problem with

the reference signal.


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1. The most common source of noise in the reference signal is from ground loops.

(a) If there is new noise on the signal the most likely cause is that an oscillo-

scope was hooked up without a cheater.

(b) If that doesnt eliminate the noise check that the other electrical equipment

on the laser table are grounded properly.

(c) Also check that the pre-amplifier isnt touching the laser table.


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Appendix E

MATLAB CODE

E.1 Density Calculation

There are several versions of the density calculation code. Included in the folder is a

readme file that explains the difference between the different codes. Most notably, itis important to calculate the frequency, for filtering purposes, using the stronger of

the reference and scene signals. This program is adapted from the program written

by Griff ONeal [17]. This file is located on the HITSI server at

U:\bvictor\Matlab\den_calc\density_calc_sig7.m

c le ar a l l ; c lo se a l l;

% l oa d t h e i nf o rm at i on from t h e t r e e

load s : \Matlab\ d e n c a l c \ f i r i n i . d at ;

[ a , s t a t u s ] = m ds op en ( l a n da u . h i t : : h i t s i , 0 ) ;

c u r r e n t s h o t = m ds v al u e ( $ s h o t ) ;

disp( [ c u r r e n t s h ot : i n t 2 s t r ( c u r r e n t s h o t ) ] ) ;

shot = f i r i n i (1 );

m dscl ose ;

s h ot i n = input( [ What s h o t ? D e f a u l t : [ i n t 2 s t r ( s h o t ) ] ] ) ;

i f ( s h o t i n ) ;s ho t = s h o t i n ;

end ;

[ a , s t a t u s ] = m ds op en ( l a n da u . h i t : : h i t s i , s h o t ) ;

N c h o r d s = 1 ; %f i r i n i ( 2 ) ;


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c h o r d n u m 1 = 7 ; % f i r i n i ( 3 ) ;% c h o r d n um 1 i n = i n p u t ( [ What c h or d ? D e f a u l t i s

% [ i n t 2 s t r ( c hord num1 ) ] ] ) ;% i f ( c h o r d n u m1 i n )% chord num1 = ch or d n um1 i n ;% end ;

disp( [ A n a l y z in g S h ot : i n t 2 s t r ( sho t ) ] ) ;

%%

% s e t s r e f t o t he v al ue o f \f i r r e fr e f = m ds va lu e ( r e f = \ f i r r e f );

% s e t s s i g t o t he v al ue o f \f i r d e t

s i g = m ds va lu e ( s i g = \ f i r d e t ) ;

% t t = m d s va l u e ( d i m o f ( \ f i r r e f ) ) ;

% us e t h i s f o r t he ti me c a l c u l a ti o n t o e ns ur e c on st an t d t t mi n = m ds v al u e ( m i nv a l ( d i m o f ( r e f ) ) ) ;

tm ax = m dsval ue( m axval ( di m of ( r e f )) ) ;

d t = m ds va lu e ( s a m p l i n g i n t e r v a l ( r e f ) ) ;

tt = tmin : dt : tmax;t t = t t ;

%%

% machine parameters

% r a di u s o f t h e p la sma R e f f = 0 . 5 0 ; % [m]

% im pa ct p a ra me t er s o f t h e v a r i o u s c h or d s % add l i n k t o f i l e o f p i c tu r e o f t he c ho rd s

% c h a nn e l 1 i mp ac t p ar a me te r s [m] ( f o r c h or d s 1 10)

i m pa c t l o w er = [ . 1 6 5 5 , . 1 6 5 5 , . 1 6 5 5 , . 2 1 3 7 , . 2 6 1 , . 3 0 6 7 , . 3 5 0 7 , . . .. 3 9 28 , . 4 32 6 , . 4 7 ] ;

% % c h a nn e l 2 i mp ac t p ar a me te r s [m] ( f o r c h or d s 1 10)% i m pa c t u p p er = [ . 2 0 2 , . 2 0 2 , . 2 0 2 , . 2 5 , . 2 9 7 , . 3 4 2 , . 3 8 9 , . . .% . 4 26 8 , . 4 6 5 9 , . 50 1 4 ] ;

% % t he i mp ac t p ar am et er f o r t h e c u r r e nt s h o t i m pact1 = i m pac t l ower ( chord num1 ) ; % . 3 5 0 7 ;


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% th e c ho rd l e n gt h f o r t he c ur r en t s ho t c h o r d l e n g t h 1 = 2 sqrt ( R e f f 2 i m pact1 2 );

m dscl ose ;

%%

% al lo ws t he p l o ts t o b e tu rne d o f f

S h o w P l o t s = 0 ;Show = input ( E nt er y t o s ee a l l o f t he p l o ts . , s ) ;i f( strcmp (Show , y ))

S h o w P l o t s = 1 ;end

% a l l o ws an a u t oc o r r ec t i o n a l go r it h m t o b e u se d % 1 = on , 0 = o f f A u t o C o r r e c t = 0 ;

%%

% cr op t h e n umber o f d at a p o in t s , e l i m i na t i n g p o i nt s b e f o r e and a f t e r s h ot % o r i g in a l s t a r t t ime = 0 .0 02 6 s , e nd t i me = 0 . 0 18 s t s = 0. 0005; % new s t a r t t im e t e = 0 . 0 1 2 4 ; % new e nd t i m e [ aa , Is ] = min(( ttt s ) . 2 ) ; % fi n d t he p oi nt n ea r es t t he s t a r t t im e [ bb , Ie ] = min(( ttt e ) . 2 ) ; % f in d t he p oi nt n ea r es t t he end t ime t = t t ( I s : I e ) ; % c ro p t h e t im e t m = 1 0 0 0 t ; % g iv e s t he ti me i n m i l li s e co n d s p o i nt s = length ( t ) ; % l e n gt h o f t he v e ct o r c r e f = r e f ( I s : I e ) ; % c ro p r e f s i g n a l c s i g = s i g ( I s : I e ) ; % cr op s ce ne s i g n a l

%%

% v a lu e s us ed f o r f r e q c a l c u l a t i on s S a m p l e r a t e = round ( 1 / d t ) ; % av e n umber o f p t s p er s e c F n y q u i st = S a m p l e r a t e / 2 ; % N y q ui s t f r e q ue n c y

disp( [ S a m p le r a t e = i n t 2 s t r ( S a m p le r a t e / 1 e3 ) . . .

KS/ s e c ; Time S t ep = i n t 2 s t r ( dt 1 e 6 ) m i c r o s e c ] ) ;

%%% th e n ex t t wo s e c t io n s c a l c u l a t e t he f re qu en cy o f t he r e f and s ce ne % s i g na l s f or f i l t e r i n g p ur po se s . I t i s b e st t o c a l cu l a te t he f re qu en cy % f rom w h ic h ev e r s i g n a l h as a l a r g e r m ag ni tu de %%

% c a lc u l at e t he f re qu en cy o f t he r e f s i g na l


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r e f p o i n t s = round ( . 0 0 0 2 / dt ) ;

% re mo vi ng a 0 t h o rd er dc o f f s e t b a s e r e f = c r e f ( 1 : r e f p o i n t s ) sum( c r e f ( 1 : r e f p o i n t s ) ) . . .

/ length ( c r e f ( 1 : r e f p o i n t s ) ) ;% m u lt i pl y s u c ce s s i ve p o in t s c r o s s p o i n t s = b a s e r e f ( 1 : length ( b a s e r e f ) 1). . . .

b a s e r e f ( 2 : length ( b a s e r e f ) ) ;% c re a te v e ct o r w it h 1 s a t c r o ss i n gs and 0 e l se w he r e c r o s s p o i n t s = ( c r o s s p o i n t s . / ( abs ( c r o s s p o i n t s ) ) 1 ) / (2 );

% t o t a l z er o c r os s in g s z c t r e f = sum( c r o s s p o i n t s ) ;

% f r e q u e n c y r e f f r e q = ( z c t r e f / 2) /( length ( b a s e r e f ) dt ) ;

disp( [ R e f e r e n c e F re qu en cy = i n t 2 s t r ( r e f f r e q / 1 0 00 ) kHz ] ) ;

%%

% c a l c u l at e t he f re qu en cy o f t he s ce ne s i g n a l % lo ok in g a t f i r s t . 2 ms t o a vo id i n je c t or f r eq p ic k up

% r e f er e n c e d e t e c t o r s i g p o i n t s = round ( . 0 0 0 2 / dt ) ;

% re mo vi ng a 0 t h o rd er dc o f f s e t % fr om b e g i nn i n g p o i n t s b a s e s i g = c s i g ( 1 : s i g p o i n t s ) sum( c s i g ( 1 : s i g p o i n t s ) ) / . . .

length ( c r e f ( 1 : s i g p o i n t s ) ) ;% m u lt i pl y s u c ce s s i ve p o in t s c r o s s p o i n t s s i g = b a se s i g ( 1 : length ( b a s e s i g ) 1). . . .

b a s e s i g ( 2 : length ( b a s e s i g ) ) ;% c re a te v e ct o r w it h 1 s a t c r o ss i n gs and 0 e l se w he r e c r o s s p o i n t s s i g = ( c r o s s p o i n t s s i g . / ( abs ( c r o s s p o i n t s s i g ) ) 1)/( 2) ;

% t o t a l z er o c r os s in g s z c t s i g = sum( c r o s s p o i n t s s i g ) ;

% f r e q u e n c y s i g f r e q = ( z c t s i g / 2) /( s i g p o i n t s dt ) ;

disp( [ Scene F requency = i n t 2 s t r ( s i g f r e q / 1 0 00 ) kHz ] ) ;

% se t t i ng t he r e f f r eq t o t h e s i g f r eq b ec aus e t h e s i g f r eq i s more % a cc ur at e f o r f i l t e r i n g p ur po se s r e f f r e q = s i g f r e q ;

%%%%

% f i l t e r t h e s i g n a l s


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%%

% r e f e r e n c e f i l t e r % h a l f b an dw i dt h ( Hz )h b w r e f = min( 1 8 0 0 0 0 , . 2 r e f f r e q ) ;

% o r d e r o f t h e f i l t e r / 2 n r e f = 1 ;

% n o r ma l i z in g w . r . t . t h e N y qu i s t f r e q l o w f r e q r e f = ( r e f f r e q hbwref )/ Fnyqui st ;h i g h f r e q r e f = ( r e f f r e q + h b wr ef ) / F n yq u is t ;Wn ref = [ l o w f r e q r e f , h i g h f r e q r e f ] ;% f i l t e r i n g w it h t he b u t t er f i l t e r [ b r e f , a r e f ] = b u t t e r ( n r e f , W n r ef ) ;

% u s i ng t h e s e v a r i a b l e s t o f i l t e r t h e c ro pp ed r e f s i g n a l f i l r e f = f i l t f i l t ( b r e f , a r e f , c r e f ) ;

% p l ot t he r e f s i g na l ( raw a nd f i l t e r e d )i f( ShowPlots ) ;

f i g u r e( 1 ) ;c l f;grid;t i t l e ( [ S ho t i n t 2 s t r ( s h o t ) : R e f e r e n c e S i g n a l ] , F o n t Si z e , 1 4 ) ;hold on ;plot ( t m , c r e f , r , t m , f i l r e f , b ) ;h1 = legend ( Raw , F i l t e r e d ) ;se t ( h 1 , I n t e r p r e t e r , n o ne ) ;xlabel ( Time [ m s] , FontSi ze , 12 , FontWeight , bol d ) ;ylabel ( S i g n a l S t r e n g t h [ V ] , F o n t S i z e , 1 2 , F o nt We ig ht , b o l d ) ;f i g u r e ( gcf) ;

end ;

%%

% scene f i l t e r % h a l f b an dw i dt h ( Hz )hbwdet = min( . 7 e6 , s i g f r e q .3 e6 ) ;%o r d e r o f t h e f i l t e r / 2 n s i g = 3 ;

% n o r ma l i z in g w . r . t . t h e N y qu i s t f r e q l o w f r e q s i g = ( s i g f r e q hbwdet)/ Fnyq uist ;

h i g h f r e q s i g = ( s i g f r e q + h bwdet ) / F n yq u is t ;Wn sig = [ l o w f r e q s i g , h i g h f r e q s i g ] ;% f i l t e r i n g w it h t he b u t t er f i l t e r [ b s i g , a s i g ] = b u t t er ( n s i g , Wn s ig ) ;

% u s i ng t h e s e v a r i a b l e s t o f i l t e r t h e c ro pp ed s ce ne s i g n a l f i l s i g = f i l t f i l t ( b s i g , a s i g , c s i g ) ;

% p l o t t he s ce ne s i g n a l ( raw a nd f i l t e r e d )i f( ShowPlots ) ;

f i g u r e( 2 ) ;


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c l f;grid;

t i t l e ( [ S ho t i n t 2 s t r ( s h o t ) : S c en e S i g n a l ] , F o n t Si z e , 1 4 ) ;hold on ;plot ( t m , c s i g , r , t m , f i l s i g , b ) ;h2 = legend ( Raw , F i l t e r e d ) ;s et ( h2 , I n t e r p r e t e r , n on e ) ;xlabel ( Time [ m s] , FontSi ze , 12 , FontWei ght , bol d ) ;ylabel ( S i g n a l S t r e n g t h [ V ] , F o n t S i z e , 1 2 , F o nt We ig ht , b o l d ) ;f i g u r e ( gcf) ;

end ;

%%%%

% c a l c u l a t e and p l o t t he f f t s

%%

% r e f er e nc e s i g n a l

% u nf i l t e re d r e f s i g na l r e f f f t d u m = abs (f f t ( c r e f ) ) ;N r e f f f t d u m = length ( r e f f f t d u m ) ;r e f f f t = r e f f f t d u m ( 1 : round( N r e f f f t d u m / 2 ) ) ;N r e f f f t = length ( r e f f f t ) ;p l o t r e f f f t = 10 log10 ( r e f f f t /max( r e f f f t ) ) ;

% f i l t e r e d r e f s i g n a l f i l r e f f f t d u m = abs (f f t( f i l r e f ) ) ;N f i l r e f f f t d u m = length ( f i l r e f f f t d u m ) ;f i l r e f f f t = f i l r e f f f t d u m ( 1 : round( N f i l r e f f f t d u m / 2 ) ) ;N f i l r e f f f t = length ( f i l r e f f f t ) ;p l o t f i l r e f f f t = 10 log10 ( f i l r e f f f t /max( f i l r e f f f t ) ) ;

% f r e q ue n c y b a se f r e q b a s e r e f = ( 0 : N r e f f f t 1) F n y qu i st / ( N r e f f f t 1 ) ;

i f( ShowPl ots ) ;f i g u r e( 3 ) ;

c l f;hold on ;t i t l e ( [ S ho t i n t 2 s t r ( s h o t ) : R e f e r e n c e FFT ] , F o n t Si z e , 1 4 ) ;plot ( f r e q b a s e r e f /1 e6 , p l o t r e f f f t , r ) ;plot ( f r e q b a s e r e f / 1 e 6 , p l o t f i l r e f f f t , b ) ;h3 = legend ( Raw , F i l t e r e d ) ;s et ( h3 , I n t e r p r e t e r , n on e ) ;xlabel ( Frequency [ MHz] , FontSi ze , 12 , FontWeight , bol d ) ;f i g u r e ( gcf) ;

end ;


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%%

% sc en e s i g n a l

% u n f i l t e r e d s ce ne s i g n a l s i g f f t d u m = abs (f f t ( c s i g ) ) ;N s i g f f t d u m = length ( s i g f f t d u m ) ;s i g f f t = s i g f f t d u m ( 1 : round( N s i g f f t d u m / 2 ) ) ;N s i g f f t = length ( s i g f f t ) ;p l o t s i g f f t = 10 log10 ( s i g f f t /max( s i g f f t ) ) ;

% f i l t e r e d s ce ne s i g na l f i l s i g f f t d u m = abs (f f t( f i l s i g ) ) ;N f i l s i g f f t d u m = length ( f i l s i g f f t d u m ) ;

f i l s i g f f t = f i l s i g f f t d u m ( 1 : round( N f i l s i g f f t d u m / 2 ) ) ;N f i l s i g f f t = length ( f i l s i g f f t ) ;p l o t f i l s i g f f t = 10 log10 ( f i l s i g f f t /max( f i l s i g f f t ) ) ;

% f r e q ue n c y b a se f r e q b a s e s i g = ( 0 : N s i g f f t 1 )F n y qu i st / ( N s i g f f t 1 ) ;

i f( ShowPlots ) ;f i g u r e( 4 ) ;c l f;hold on ;t i t l e ( [ S ho t i n t 2 s t r ( s h o t ) : S c e ne FFT ] , F o n t S i z e , 1 4 ) ;plot ( f r e q b a s e s i g /1 e6 , p l o t s i g f f t , r ) ;plot ( f r e q b a s e s i g / 1 e6 , p l o t f i l s i g f f t , b ) ;h3 = legend ( Raw , F i l t e r e d ) ;se t ( h 3 , I n t e r p r e t e r , n o ne ) ;xlabel ( Frequency [ MHz] , FontSi ze , 12 , FontWei ght , bol d ) ;f i g u r e ( gcf) ;

end ;

%%%%

% f in d t he z er o c r os s in g s o f t h e f i l t e r e d s i g na l s

%%

% r ef er en ce f i l t e r e d s i gn a l

% mu l ti pl y s u cc e ss i ve p oi nt s o f t he f i l t e r e d s i g na l r e f f i l z e r o s = f i l r e f ( 1: po in ts 1 ) . f i l r e f ( 2: p oi nt s ) ;

% c re a te v e ct o r w it h 1 s a t c r o ss i n gs and 0 e l se w he r e r e f f i l z e r o s = ( r e f f i l z e r o s . / abs ( r e f f i l z e r o s ) 1)/( 2) ;


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s i g f i l z e r o s = f i l s i g ( 1: po in ts 1 ) . f i l s i g ( 2: p oi nt s ) ;

% c re a te v e ct o r w it h 1 s a t c r o ss i n gs and 0 e l se w he r e s i g f i l z e r o s = ( s i g f i l z e r o s ./ abs ( s i g f i l z e r o s ) 1)/( 2) ;

% f i nd t he l o c a t io n s o f t he c r os s in g p o in t s k s i g = find ( s i g f i l z e r o s ) ;

% fi nd t he t o t a l number o f z er o c r os s in g s o f f i l t e r e d s i g na l z c t s i g f i l = sum( s i g f i l z e r o s ) ;

%%

% c a l c u l at i o n s us ed t o f i nd t he c hang e i n ph as e o f t he s ce ne s i g n a l

% t h i s f i n ds t he t ime t h at t he z er o c r os s i ng a c t u a l l y o cc ur s b y % i n t e r p o l at i n g b etw ee n t he p oi nt b e fo r e and a f t e r t he z er o c r o ss i ng tde t (1 : z c t s i g f i l ) = t ( k si g ) dt f i l s i g ( k si g ). / ( f i l s i g ( k si g +1) . . .

f i l s i g ( k s ig ) ) ;

% c re a t es a v e ct o r t he s i z e o f t he number o f z er o c r o ss i n gs % ea ch z er o c r os s i ng i n cr e as e s t he v a lu e by p i % z c1 = pi , z c2 = 2 p i , z c3 = 3 p i% t h i s a l l o w s t h e z e ro c r o s s i n g s t o b e c h an ge d t o a measurement i n r a di a ns p h as e s i g = cumsum( pi one s ( s i z e ( t d e t ) ) ) ;

% t h i s c a l c u l a ti o n u se s t he s ame t b as e as f rom t he r e f s i g n a l c a l c u l a ti o n

% i n t e r p ol a t e s t he p r og r es s io n o f t he p lo t , u si ng t he z er o c r o ss i ng s a s t h e % de f in in g p oi nt s o f t he p l o t % p h re f i s t he phase v al ue a t each p oi nt o f t ba se p h s i g = interp1 ( t de t , p h a s e s i g , t b a se ) ;

% t he v al ue o f t he s ce ne s i g n a l c ompared t o i t s f i r s t v a lu e v a l p h s i g = p h s i g p h s i g ( 1 ) ;

%%

% t he p ha se c ha ng e b et we en t h e s ce ne and r e f s i g n a l s d e lt a p h i = v a l p h r e f v a l p h s i g ;

%%%%

% l oo k f or bad s po ts i n t h e r e f s i g na l % pl a ce s where t he av e a m pl it ud e o f t he s i g n a l i s l e s s t ha n 0 . 3 t im es t he % o v e r a l l a ve a mp li tu de % t he sum o f t h e s q ua re s o f a l l p oi nt s o f t h e f i l t e r e d r e f s i gn a l r e f s t r e n g t h = sum( f i l r e f . 2 )/ po in ts ;


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% d e f i ne s t h e w indow o ve r w hi ch t o a ve ra ge t h e s i g n a l s t r e n g t h % number o f p o i n ts i n 50 p e r i od s

b a d s p o t w i n d o w = round ( 1 /( s i g f r e q d t ) ) ;

%i n i t i a l i z e t he v ec to r b a d s p o t r e f = zeros ( 1 , p o i n t s ) ;

% l oo k in g o ve r a g iv en i n t e r v a l % t h i s a lg or it hm c a l c u l a t e s t he a ve ra ge s i g n a l s t r en g t h o ve r a g iv en % i n t e r v a l and c r e at e s a v e ct o r marking t he l o c at i o n o f t he bad s p ot s f or k = 1 : round( b a d s p o t w in d ow / 2 ) : p o i n t s b a d s p o t w i n d o w 1 ;

l o c a l s t r e n g t h r e f = sum( f i l r e f ( k : k + b a d s p o t w i n d o w ) . 2 ) . . ./bad spot wi ndow ;

i f ( l o c a l s t r e n g t h r e f < . 3 r e f s t r e n g t h ) ;b a d s p o t r e f ( k : k + b ad s p ot w i nd ow 1 ) = . . .

o n e s ( 1 , b a d s p o t w i n d ow ) ;end ;

end ;

% i n t e r p o l at e t he bad s p ot s o nto t he t ime r a te i n t e r p b s r = interp1 ( t , b a d s p o t r e f , t b as e ) ;

%%

% l o ok f o r b ad s p ot s i n t h e s ce ne s i g n a l % pl a ce s where t he av e a m pl it ud e o f t he s i g n a l i s l e s s t ha n 0 . 3 t im es t he % o v e r a l l a ve a mp li tu de % t he sum o f t h e s q ua re s o f a l l p oi nt s o f t h e f i l t e r e d r e f s i g na l s i g s t r e n g t h = sum( f i l s i g . 2 )/ po in ts ;

%i n i t i a l i z e t he v ec to r b a d s p o t s i g = zeros ( 1 , p o i n t s ) ;

% l oo k in g o ve r a g iv en i n t e r v a l % t h i s a lg or it hm c a l c u l a t e s t he a ve ra ge s i g n a l s t r en g t h o ve r a g iv en % i n t e r v a l and c r e at e s a v e ct o r marking t he l o c at i o n o f t he bad s p ot s f or k = 1 : round( b a d s p o t w in d ow / 2 ) : p o i n t s b a d s p o t w i n d o w 1 ;

l o c a l s t r e n g t h s i g = sum( f i l s i g ( k : k + b a d s p o t w i n d o w ) . 2 ) . . ./bad spot wi ndow ;

i f ( l o c a l s t r e n g t h s i g < . 0 4 s i g s t r e n g t h ) ;

b a d s p o t s i g ( k : k + b ad s p ot w i nd ow 1 ) = . . .o n e s ( 1 , b a d s p o t w i n d ow ) ;end ;

end ;

% i n t e r p o l at e t he bad s p ot s o nto t he t ime r a te i n t e r p b s s = interp1 ( t , b a d s p o t s i g , t b as e ) ;

%%%%


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i f( ShowPlots ) ;

f i g u r e( 2 2 ) ;plot ( t d e t ( 1 : end 1)1 e3 , 1 . / ( 2 ( t d e t ( 2 : end) t d e t ( 1 : end1)))/1e6 ) ;t i t l e ( [ S ho t i n t 2 s t r ( shot ) . . .

: F re qu en cy o f e ac h h a l f p e r i o d ( S c e n e ) ] , F o n t Si z e , 1 4 ) ;xlabel ( Time [ m s] , FontSi ze , 12 , FontWeight , bol d ) ;ylabel ( Frequency [ MHz] , FontSi ze , 12 , FontWei ght , bol d ) ;f i g u r e ( gcf) ;

f i g u r e( 2 3 ) ;plot ( t r e f ( 1 : end 1)1 e3 , 1 . / ( 2 ( t r e f ( 2 : end) t r e f ( 1 : end1)))/1e6 ) ;t i t l e ( [ S ho t i n t 2 s t r ( shot ) . . .

: F re qu en cy o f e ac h h a l f p e r i o d ( R e f ) ] , F o n t Si z e , 1 4 ) ;xlabel ( Time [ m s] , FontSi ze , 12 , FontWeight , bol d ) ;

ylabel ( Frequency [ MHz] , FontSi ze , 12 , FontWei ght , bol d ) ;f i g u r e ( gcf) ;

end

%%%%

% p lo t o f b ot h f i l t e r e d s i g na l s and t he phase d i f fe r e nc e

m r e f = max( f i l r e f ) ;

m s i g = max( f i l s i g ) ;

f i g u r e( 5 ) ;c l f;t i t l e ( [ S hot i n t 2 s t r ( s h ot ) : F i l t e r e d S i g n a l s ] , F o nt S iz e , 1 4 ) ;hold on ;plot (t m , pi f i l r e f /m ref , b , t m , pi f i l s i g /m sig , r ) ;plot ( tbas e 1e3 , mod ( d e l t a p h i , 2pi ) + pi , k ) ;h5 = legend ( R e f e r e n c e , S c e ne , P h a se C ha ng e ) ;se t ( h5 , I n t e r p r e t e r , n o ne ) ;xlabel ( Time [ m s] , FontSi ze , 12 , FontWeight , bol d ) ;grid;f i g u r e ( gcf) ;

%%%%

% d e ns i t y c a l c u l a ti o n

% d ef i ne v a r i a b l e s

% s pe ed o f l i g h t [m/ s ] c = 3 e 8 ;


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% e l e c t r o n mass [ k g ] m e = 9 . 1 0 9 3 8 2 e31 ;

% m ag ni tu de o f e l e c t r o n c h ar g e [ C] q e = 1 . 6 0 2 1 7 6 5 e19 ;

% p e r m i t t i v i y o f f r e e s pa ce [ C2 N 1 m2]e 0 = 8 . 8 5 4 1 8 7 8 e12 ;

% a common qu an ti ty c o n s t a n t = q e 2 /( 4pi 2 e0m e ) ;

% w a v e le n g th o f d i f l uo r o me t

Brian Thesis

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