Table Of Content.
SLAC-R-626
Positron Production in Multiphoton Light-by-Light Scattering
ThomasK offas
StanfordL inear AcceleratorC enter
StanfordU niversity
Stanford,C A 94309
SLAC-Report-626
Preparedfo r the Departmenot f Energy
underc ontractn umberD E-AC03-76SF00515
Printedi n the United Stateso f America.A vailable from the NationalT echnicalI nformation
Service,U .S. Departmenot f Commerce5, 285P ort Royal Road,S pringfield,V A 22161.
*Ph.D.t hesisU, niversitoy f Rochester
ii
Curriculum Vitae
ThomasK offasw asb orni n IrakiionA ttikfs, Greecein 1970.H e receivedh is bacb-
PositronP roductioinn ’ . clors’ degreein Physicsfr om the Universityo f Athensi n 1993.A a an undergraduate
he workeda t the Delphie xperimenat t CEKN during the summero f 1991a nd then
MultiphotonL ightrby-LighStc attering
in the NESTORe xperimenut nderP rofessoLr . K. RcsvanIeI.n the summeor f 1993
ho startedg raduates tud& towardsh ls Ph.D. degreein the PhysicsD epartmenot f
by the Universityo f Kochcsterw, hereh ej oinedt he El44 collaborationu nderP rofessor
ThomasK offac A. C. MelissinosI‘h’. e presenth esisc ontainsth e resultso f the workd onew ithin that
collaboration.
Submittedin Partial FWillment
of the
Requiremenftos r the Degree
Doctoro f Philosophy
Supervisebdy
ProfessoAr . (3; Mcliminos
Departmenot f Physicsa nd Astronomy
The College
Arts and Sciences
tJnivcrsityo f Rochester
KochesterN, ewY ork
1998
.. .
111 iv
My highesta cknowledgmeins td ue to my advisora nd mentord uringm y gradu-
Acknowledgments’
ate studentc areer,A drian MelissinosH. e is an excellent eachera nd advisor. His
uniquep hysicali nsighti s of the kind that makesa physicistg reat..H is continuous
encouragemefnotr hard workw ase ssentiaflo r completingth is thesis.
It is hard to expressm y thanksa ndg ratitudet o all the peoplet hat helpeda nd Last but not leastI wouldl ike to thankm y parentsG eorgioas nd AmaiiaTotrh eir
workedw ith me during my graduates tudentc areer. First I would like to thank lovea nd constants upport,m y brother Mattheosf or, amongo ther things,s haring
the peoplea t the Universityo f Rochesterw, ho advisedm e during my first stepso f with me the gooda ndb ad momentso f a graduates tudents’ l ife and my Greekfr iend
graduatew ork, Pat Borolli, lbm Ha&n, Larry Kuntz and Alan Eky. David Reis of old P. Kousoulisfo r beinga friende venf rom 10,000m ilesa way.
sharedw ith me innumerableh ourso f studyingf or classeasn dw orkingi n the lab at This work wass upportedin part by the 0. S. Departmenot f Energyg rant No.
SLACa ndi n additionh is friendshipa sa sideb enefit. DEFG02-9IER40685.
At SLAGa numbero f peoplei n the El44 collaborationw erei nstrumentaflo r
thos’ uccesso f the experimenta nd the completiono f this thesis. Much of my ini-
tial worki nvolvedw orkingw ith the Universityo f Rochestepre opleb aseda t SLAC,
amongw hichT heofilosK otseroglouS, teveB oegea ndC harlieB amberw eret he more
prominent.P rofessoDr avid Meyerhofert,h e drivingf orceb ehindt he laser,s hared
with mea t leasta smallf ractiono f his vastk nowledgaeb outl asers.L ongd iscussions
with Glenn Horton-SmithK, cstya ShmakovC, liveF ielda nd Kirk McDonaldw erea
constants ourceo f inspirationa nd their ideasa nd ohvations arc rcflcctedi n this
thesis.B ut most of all I would like to thank ChristianB ula my main advisore spe-
cially duringt he mostr ecenty earsa t SLAC.M osto f the data analysisp resenteidn
this thesisis laid on the foundationsth at he first built.
I would also like to thank thep coplcin the broadeEr 144/FFTB familya t SLAC,
who helpedm e during my acceleratowr ork. Jim Spencewr ast he first to introduce
me itI the field of beamo ptics. PeterI‘ &renbaumt aught mea lot about final focus-
ing configurationasn da leo sharedw ith me his cxcitcmenfto r real time accelerator
operationsI. am mostt hankful to DavidB urkef or his constanst upporta nd trusting
in my capabilitiesa ndf or helpingm et o takea dvanta8oef asm ucha sp ossibleo f the
numerouosp portunitiesfo r learninga boutr ccclcratorp hysicso ffereda t SLAC.
vi
Abstract
Wep resentt he resultso f an experimentasl tudy on e*e- pair productiond uring Contents
the colbsiono f a low emittancc4 6.6G eV electronb eamw ith terawattl aserp ulses
from a Nd:gla.slsa sera t 527n m wavelengtha nd with linearp olarization.T he exper-
iment was conducteda t the Final FocusT est Beamf acility in the StanfordL inear
1 Introctuction 1
AcceleratorC cntcr. Resultsw ith a 49.1G eV electronb eama re also included. A
1.1 PhysicaMl otivation. . . . . . . . . . . . . . . . . _ . . . . . . . . . . 1
signalo f 106f 14 positronsf or the 46.6 GeV electronb eamc asea nd of 22 f 10
1.2 ExperimentiO verview. . . . . . . . . . . _ . . . . . . . . . . . . . . 5
positronsf or the 49.1G cV casea boveb ackgroundh, asb eend etected.W e interpret
the positronse s the productso f a two-stepp rocessd uring which Iaserp hotonsa re 3 Theory 12
backscatteretdo high energyg ammap hotonst hat absorbin tbeir turn severala ser 2.1 Notationa ndU nits ............................ 13
photonsi n order to producea e+e- pair. The data comparew ell with the existing 2.2 FreeE lectronin an IntenseL aserF ield ................. 14
theoreticalm odels.T his is the first observationin the laboratoryo f inelasticI ight- 2.2.1 ClassicaAl nalysb ........................ 14
by-Iights catteringw ith only real photons.A lternatively,t he data are interpreteda s 2.2.2
coN!rErrrs vii
5.3.2 MonitorC alibration ....................... 151 3.1.2 BeamE mittance ......................... 57
5.3.3 DropoutC leanup ....... ; ................. 158 3.1.3 Measuremenotf the BeamE mittance ............. 61
3.2 FFTB Line Setup ............................. 65
162
6 46.6 GeV Date Analysts
3.3 BetaM atch ................................ 71
6.1 ClusterS earchA lgorithm. ........................ 164
4 3.3.1 Reconstructioonf the IncomingB eam ............. 71
6.2 46.6G eVP ositronS earch ......................... 168
3.3.2 Implementatioann d Verification ................ 75
6.2.1 ClusterS electionC uts ...................... 168
3.4 IPl Spotm ning ............................. 79
6.2.2 ClusterS electionC utsT hing ................. 171
3.4.1 A‘ ming Procedure ........................ 79
6.2.3 OvesIapC ut nning. I&wits .................. 175
3.4.2 Measuremenotf the IPl Spot Size ............... 80
6.2.4 PositronM omentumS pectra .................. 177
3.5 49GeVBeamSetUp ........................... 86
6.3 Estimateso f the LaserI ntensityP arameteqr .............. 179
*
6.3.1 Initial Considerations. ..................... 179 4 The Laser System 89
6.3.2 The LeastS quaresM ethod[ 56] ................. 180 4.1 LaserS ystemD escription.. ....................... 89
6.3.3 The ConstrainedF it ....................... 184 4.2 The LaserI‘ kansport Systema nd InteractionP oint .......... 102
6.3.4 Testso f the Fit Algorithm .................... 187 4.3 Law-ElectronT iming .......................... 104
6.3.5 The ProbabilityC ut ....................... 192 4.3.1 ExperimentaSl etupf or Laser-ElectroTni ming ........ 105
6.3.6 Scalingo f the Input Signal ................... 195 4.3.2 Timing Jitter andL ongT erm Drift ......... _ ..... 112
6.3.7 q E&matesa nd Verification .................. 201 4.4 Laser-ElectroSnp atiala ndT emporalO verlap ............. 123
6.3.8 Systematicsonq ................... : ..... 207
5 Detectors 129
6.4 IneRiciencCy orrectionsa ndB ackgroundL evels ............ 210
5.1 Calorimeter.s. .............................. 130
6.4.1 OverlapI ncfficicncyE stimates ................. 211
5.1.1 GeneraDl escription ....................... 130
6.4.2 ClusterS earchA lgorithmE fficiency .............. 214
5.1.2 MomentumM apa nd Acceptances. .............. 131
6.4.3 hCkgmd8 ........................... 215
5.1.3 SignalC orrcXtions. ....................... 137
7 49.1 GeV Data Analysis 218 5.2 LinearM onitors. ............................. 145
7.1 Selectiono f the Data Sample.. ..................... 219 5.2.1 GeneraDl escription ....................... 145
7.2 49.1G eVP ositronS tarch ........................ 221 5.2.2 LinearM onitorC alibration ................... 147
7.2.1 ClusterS electionC utsA‘ ming ................. 221 5.3 NonlinearM onitors ............................ 150
7.2.2 OvwlapC ut Tuning. R.esults. ................. 223 5.3.1 NonlinearM onitorD escription ................. 15U
CONTENTS ix CONTENTS X
7.3 Estimateso f the LaserI ntensityP arameteqr .............. 225 A.7.2 LowI nteractionY ields ...................... 287
7.3.1 ConstrainedF it Setup ...................... 225 A.7.3 CPUI ntensiveP rocesses .................... 287
7.3.2 Sealingo f the Input Signal ................... 227 A.7.4 Optimizationo f SecondarCy omptonS cattering. ....... 288
7.3.3 Recoveroyf Lost DataP ointsw ith ECAL ........... 229 A.7.5 Optimizingt he Breit-WheelePr air Production ........ 290
7.3.4 q Estimatesa nd Verification .................. 233 h.7.6 Effecto f Optimizations ..................... 291
7.3.5 Studyo f Systematics.. ..................... 237 A.8 SavingR esults. .............................. 294
7.3.6 EfficiencyE stimates ....................... 240
B Event Selection 299
8 Conclusions 245 B.1 BeamR elatedC uts . . . . . . . , . . . . . . . . . . . . . . . . . . . . 300
8.1 MultiphotonB reit-WheelePr air ProductionR esults. . . . . . . . . . 245 8.2 TheShazamC ut . . . . _ . . . . . . . . . . . . . . . . . . . - . . . . 393
8.2 SpontaneouVsa cuumB reakdownR esults. . . . . . . . , . . . . . . _ 254
C Nonlinear Compton Scattering Results 306
References 258 C.l ExperimentaSl etup. . . . . . _ . . . . . . . . . . . . . . . . . . . . 307
Appendices C.2 Data Analysisa nd Results. . . . . _ . . . . . . . . . . . . . . . . . . 308
A Simulation Code Description 264
A.1 Introduction .. _ ............................. 264
A.2 BasicF ormulas .............................. 267
A.2.1 GeneraHl eiatians ........................ 267
A.2.2 NonlinearC omptonS cattering ................. 268
A.2.3 MultiphotonP air Production .................. 269
A-2.4 MultiphotonI‘ lKdent Pair Production ............. 270
A.3 Space-TimeIn tegration. ......................... 272
A.4 SecondaryP rocesses. .......................... 276
A.5 ProgramF low ............................... 279
A.6 SecondO rderC orrections ................. : ...... 281
A.61 EffectiveC r-osbinAgn gle ..................... 281
A.6.2 EffectiveB eamD ensity ..................... 283
A.7 SpeedO ptimizations ........................... 284
A.7.1 VariableS tep Sizei n z ’ ntrd t .................. 285
xi
LIST OF TABLES xii
7.1 Results4 9.1G eV Data. .......................... 224
7.2 ConstrainedF it ConvergencSet udy4 9.1G eV Data. .......... 230
7.3 List of Systemsticosn (q), 49.1G eVD ata. ............... 239
7.4 List of Correctionds ue to OverlapI nefficiency4,9 .1G eV Data .... 242
List of Tables 7.5 ClusterS earchA lgorithmI nefficiency4,9 .1G eV Data.. ........ 243
8.1 List of Systematicosn PowerL aw Fit. ................. 247
8.2 List of Systematicosn PowerL aw Fit. ................. 251
3.1 ElectronB eamB unchL engths. ..................... 55
8.3 List of Systematicosn ExponentiaFl it, 46.6G cV Data. ........ 255
3.2 &Match QuadrupolSe trengths,. .................... 76
3.3 /Y-MatchQ uadrupoleS trengths. .................... 77
3.4 QuacbupolSet rengthsfo r IPl Focusing4 6.6G eVE lectronB eam. .. 81
3.5 IPl beamS izes4 6.6G eVD ata. ...................... 83
4.1 Laser-ElectroRne lativeT iming. ..................... 112
5.1 SpectrometeMr agnetP ositionsa nd Dimensions... ......... 132
5.2 SpectrometeMr agnetF ieldM easurement.. ............. 133
5.3 Soft BendF ield Strengths.. ...................... 136
5.4 NonlineaMr onitor CalibrationR un Summary.. ....... 1 ... 152
5.5 NonlineaMr onitor CalibrationX V. Settings. ............. 157
6.1 Results4 6.6G eVD ata. ......................... 176
6.2 MomentumS pectraC ompatibility. ................... 179
6.3 Residualuss ingt he differentm onitore rrors. .............. 189
6.4 ConstrainedF it ConvergenScetu dy4 6.6G eV Data. .......... 201
6.5 Run Chamcteristicfso r t) Verification.. ................ 203
6.6 List of Systematicosn (7i). ........................ 209
6.7 List of &m&.ions duet o OverlapI ne&iency. ............. 213
6.8 ClusterS earchA lgorithmI neiiicicncy... ................ 215
.. .
x111 LIST OF FIGURiZS xiv
3.6 BeamBllipseinaBeamI’kansportLiie. ................ 60
3.7 Historyo f EmittanceM easuremenints S ector2 8. ........... 63
3.8 SLC Line Wire. ....... _ .................... - . 64
3.9 BSY Line. ................................. 65
3.10 FFTB LineO ptics. ............................ 66
List of Figures
3.11 DumpLine. ................................ 67
3.12 X-ScanQ uadQ 5. ......................... _ ... 71
1.1 ExperimentaSl etupO verview. . . , . . . . . . . . . . . . . . . . . . 4 3.13 Y-ScanQuadQ.5.. ........................... 72
1.2 FFTB DumpL ine. ............................ 5 3.14 V-ScanQuadQ5.. ............................ 74
1.3 LaserS ystemO verview. ......................... 6 3.15 X-WaistS cana t the FFTB FocalP oint. ................ 77
1.4 El44 Calorimeter. ............................ 8 3.16 Y-WaistS cana t the FFTB FocalP oint. ................ 78
1.5 CCD7 Detector. ............................. 9 3.17 SpotS izeM easuremeant the FFTB FocalP oint. ......... _ . 79
1.6 El44 T‘ riggerL ogic. ........................... 10 3.18 Simulationo f the FFTB Line Optics. .................. 82
1.7 El44 DataA cquisition. ......................... 11 3.19 IPl VerticalW ire Calibration.. ................. _ _ .. 83
3.20 IPlo; 46.6GeVD ata. ............. _ ............ 84
2.1 NonlineaCr omptonS catteringD iagram.. ................. 31
3.21 IPl cr, 46.6G cV Data. .......................... 85
2.2 KinematicE dgesf or Backscattere7ds’ . ................. 32
3.22 IPl vz 49.1G eV Data. .......................... 86
2.3 NonlineaCr omptonS catteringS pectra.. ............... 35
3.23 IPI a, 49.1G eV Data. ................ _ ....... _ . 87
2.4 Multiphoton& e&Wheeler Diagram.. ................. 37
2.5 EnergyT hresholdsfo r Pair Production.. ............... 39 4.1 LaserS ystemS etup. ........................... 90
2.6 Ordero f MultiphotonB reit-WheelePr rocess... ........... 40 4.2 Resonancbek equencoyf the ModelocheCr rystal ............ 91
2.7 MultiphotonB reit-WheeleCr rossS ection. ............... 42 4.3 Optimal ModelockeTre mperature.. .................. 92
2.8 The CorrectionR mction g(r)). ...................... 49 4.4 OscillatorP uiseB audwidthM easurement... ............. 93
4.5 Oscilktor PulseC W Autocorreiatokre . ............... 93
3.1 The StanfordL inear Collider( SLC). .................. 52
4.6 BegenP ulseT rain. ............................ -95
3.2 FFTB LineL ocation. ........................... 53
4.7 Simulationo f the SlabF lashlampCs urrent. .............. 96
3.3 North DumpingR ing CompressoVro ltage.. .............. 54
4.8 SlabG ain. ................................. 97
3.4 North BTL CompressoCr alibration. .................. 55
4.9 LaserE nergya t the IP. .......................... 99
3.5 The BeamE llipse. ............................ 59
4.10 GreenL aserP ulseW idth. . . . . . . . . . . . . . . . . . . . . . . 100
LIST OF FIGURES xv LIST OF FIGURES xvi
4.11 LaserS potS izea t the IP. ........................ 101 5.7 BremsstrahlunSgp ectrum. ....................... 147
4.12 InteractionP oint Box. .......................... 103 5.8 Error Estimatein the LinearM onitors. ................. 150
4.13 Overviewo f the TimingS ystem. .................... 105 5.9 N2 MonitorE rror andA cceptance.. .................. I53
4.14 The SLAC Main DriveL ine. ....................... 106 5.10 N3 Monitor Error and Acceptance.. .................. 154
4.15 PowerS pectrumo f the LaserR eferencaet 119MHzH F. ........ 108 5.11 N2,N3M onitor Acceptances... .................... 155
4.16 Timing StabilizerB lockD iagram.. ................... 109 5.12 NonlinearM onitorP ositions.. ...................... 136
4.17 Setupo f the Timing System.. ..................... 110 5.13 DropoutE ventsi n the NonlinearM onitors.. .............. 159
4.18 Schematic of the RingingC avity. .................... 111 5.14 RelativeE ventT ime DelayD istribution. ................ 160
4.19 TypicalT iming Scan.. .......................... 113 5.15 CleanedN onlinearM onitorS ignals.. .................. 161
4.20 PowerS pectrumo f the LaserO scillatorP ulseH‘ -am.. ......... 114
6.1 PositronD ata CollectionS etup. ..................... 162
4.21 Timing Jitter Measurement... .................... 115
6.2 ClusterS electionS trategy.. ....................... 165
4.22 PhaseN oiseM easuremenSte tup. .................... 116
6.3 ClusterP ositionW eights.. ....................... 167
4.23 Calibrationo f the PhaseN oiseS etup.. ................. 117
6.4 ClusterS electionC uts. .......................... 168
4.24 PhaseN oiseM easuremen.t.. ..................... 118
6.5 Exampleo f ClusterS electionC uts. ................... 169
4.25 Measuremenotf the LongT ermD rift. .................. 119
6.6 Tuningo f SingleC lusterS electionR ange... .............. 172
4.26 Timing Drift w/ andw /o StabilizingF eedback.. ........... 120
6.7 Tuningo f Clusterx -PositionS electionR ange. ............. 173
4.27 Effecto f 360 Hz Noisein the oscillatorS tability. ........... 121
6.8 DataC lustersS electionR anges. .................... 174
4.28 Timing Drift Measuremenwth enS tabilizingF eedbaciks off. ..... 122 .
6.9 I‘Iming of N=l OverlapC ut. ....................... 175
4.29 IP FlagS chematic.. ........................... 123
6.10 46.6G eV PositronM omentumS pectrum... .. : ........... 178
4.30 Geometryo f XT-Scar. .......................... 125
6.11 ConstraintF unctionf or 46.6G eV Data. ................ 186
4.31 Signalo f a Lineara nda NonlinearM onitord uringa n XT-Scan. . , . 126
6.12 Fimt Test of ConstrainedF it Algorithm. ................ 188
4.32 Zp-ScanP lots. ............................... 127
6.13 SeconBd‘ zt of ConstrainedF it Algorithm. ............... 190
5.1 Electron-PositroCn ahxirnetera. . . . . . . . . . . . . . . . . . 130 6.14 Third T&t of ConstrainedF it Algorithm.. ............... 191
5.2 MagneticF ieldsf or the First 3 PernrauenBte ndM agnets. . . . 134 e.15 Simulatiouo f N3 Taila. ........................... 193
5.3 MagneticF ieldsf or the Last 4 PermanenBt endM agnets. . . . 135 6.16 ProbabilityC ut. .............................. 195
5.4 Exampleo f CoherenNt oiseS ubtraction.. . . . . _ . _ _ . . . . 143 6.17 2-DS cauo f the Nl and 1v2S ignalS calingF a’ ctors. .......... 196
5.5 Resultsfr om CohereuNt oiseS ubtraction. . . . . . . . . . . , . . 144 6.18 46.6G eV OverlapP lots. ......................... 198
5.6 TypicalE l44 LinearM onitor. . . . . . . . . . . . . . . . . . . 146 6.19 Iv2 Error Scaling. ............................ 200
LIST OF FIGURES Ll!ZTO F FIGURES Xvii:
6.20 Comparisoonf Fit and Laserv . . : ................... 202 8.2 PositronE nergyS pectraa fterq Cut, 46.6G eV Data. . . . . . . . . . 241
6.21 v VerificationR, un Group1 . ....................... 204 8.3 PositronR atep er n = 1 ComptonS cattersD ependencoen r]. . . . . . 241
6.22 v VerificationR, un Group2 . ....................... 205 8.4 Dependencoef the Positron Rate per Shot on 9,49.1 GeV Data. . . - W
6.23 q VerificationR, un Group3 . ....................... 205 8.5 PositronR atep er n = 1 ComptonS cattersu s.9 ,49.1G eVD ata. . . 2%
6.24 Stability of 9 with N=I Overlap. .......... ., ......... 206 8.6 NormalizePd ositronR atef or Both 46.6G eV and 49.1G eV Data. . . 2%
6.25 Stabilityo f r) with NormalizedN =l 7s’ . ................ 207 8.7 PositronY ield per LaserS hotu s.l /T, 46.6G eV Data. . . . . . . . . 254
6.26 N2 LinearC ontaminationS canP lot. .................. 208 8.8 PositronY ield per LsserS hot~ 3.l /T, 46.6G eV and4 9.1G eV Data. 25f
6.27 IPl X-Position,4 6.6G eV Data. ..................... 211
A.1 MultiphotonI‘k ident Pair Production.. ................ 271
6.28 XT-ScanS imulation4, 6.6G eV Data. .................. 212
A.2 Definitiono f CoordinateS ystems.. .................. 27?
6.29 Dependencoef the PositronR atep er Shoto n q, ............ 216
A.3 IntegrationG rid in Space.. ....................... 274
7.1 49.1C eV Data Selection... ....................... 220 A.4 Definitiono f Time Range. ........................ 276
7.2 nming of SingleC lusterS electionR ange4, 9.1G eV Data. ...... 221 A.5 IntegrationG rid for SecondarPy rocesse.s... ............ 27?
7.3 I‘ktning of Cluster x-PositionS electionR ange4, 9.1 GcV Data. .... 222 A.6 TimeS tepf or SecondarPy rocesses.... ................ 278
7.4 f‘ining of N=l OvcriapC ut, 49.1G eVD ata.. .... _ ........ 224 A.7 SimulationP rogram Plow. ........................ 2%
7.5 49.1G eVP ositronM omentumS pectrum... .............. 225 A.8 Effective Crossing Angle.. ........................ 281
7.6 Constrainth nction for 49.1G eV Data. ................ 226 A.9 EffectiveB eamD ensityE valuation.. .................. 28Z
7.7 2-D Scano f the Nl and N2 SignalS calingF actors4, 9.1G eVD ata. . 228 A.10V ariableS tepS ize. ............................ 28e
7.8 SimulatedE CAL Ratew r). ....................... 231 A.11O ptimizationo f thew ’ IntegrationR ange. ............... 28s
7.9 q ValueC omparison4,9 .1G eV Data. .................. 232 A.12S peedO ptimizationE ffects. ....................... 293
7.10 Comparisoonf Fit and Laser1 , 49.1G eV Data. ............ 234 A.13E nergyS pectraU pdatingP rocedure.. ................. 297
7.11 q Verification4, 9.1G eV Data. ...................... 235
B.l BeamC ut Bxample. ........................... 301
7.12 Stabilityo f q with K=l Overlap,4 9.1G eV Data. ........... 236
B.2 ReamC ut Efficiency.. .......................... 302
7.13 Stability of 7 with NormalizedN =I rs’ , 49.1C eV Data. ....... 237
Il.3 The ShazAmC ut. ............................. 304
7.14 IPl X-Position,4 9.1G cV Data. ..................... 240
7.15 XT-ScanS imulation4, 9.1G eV Data. .................. 241 C.l NonlineaCr omptonS catteringS etup.. . . . . . . . . . . . . . . . . . 307
7.16 Dependencoef the PositronR atep er Shoto n q, 49.1G cV Data. ... 244 C.2 NonlineaCr omptonS catteringL, inearlyP olarizedG len Lasct, 46.6
GcV Electron Beam. . . . . . . _ . . . . . . . . . . . . , . . . . . . . 310
8.1 PositronR atep er LaserS hot m. 1). . . . . . . . . . . . . . . . . . . . 246
