Anderson Travia INTERACTION CROSS SECTIONS NEEDED FOR SIMULATION

119 Pages·2009·1.18 MB·English

AndersonTravia INTERACTION CROSS SECTIONSNEEDED FOR
SIMULATION OFSECONDARY ELECTRON EMISSION SPECTRA FROM THIN
METALFOILSAFTER FAST PROTON IMPACT (Underthedirection ofDr.
MichaelDingfelder)DepartmentofPhysics,June2009
MonteCarlo simulationsofsecondaryelectron emissionfrom thinmetalfoilsafter
fast protonimpactrequirereliableinteractioncrosssectionswiththetarget under
consideration. Totaland energy differentialinelasticcrosssectionshavebeen derived
foraluminum,copper, and goldthin-metalfoilswithintheplane-wavefirst Born
approximation(PWFBA) thatfactorizes thedoublecross sectionintothegeneralized
oscillatorstrengthandkinematicfactors. Thegeneralized oscillatorstrengthorBethe
surface ofthemediumisobtainedbyusingasemi-empiricalopticaloscillatorstrength
distributionpublishedintheliteratureand an extensionalgorithmbasedon the
delta-oscillatormodel. Energy differential,total,and stoppingcross sectionsarethen
obtainedby simpleintegrations. Comparisonswithothercalculationsand
experimentalvaluesfromtheliteratureshowthatourmodeloffers agoodagreement
intheenergy rangeconsidered. Asa final step,thecrosssectionsand atransport
modelforcopperhavebeen implementedintotheMonteCarlo track structurecode
PARTRAC where simulationsofsecondary electronemissionspectrafromcopperfoil
havebeen performed.

INTERACTION CROSS SECTIONS NEEDEDFOR SIMULATIONOF
SECONDARY ELECTRON EMISSION SPECTRA FROM THIN METALFOILS
AFTER FAST PROTON IMPACT
A THESIS
PRESENTED TO
THE FACULTYOF THEDEPARTMENT OFPHYSICS
EAST CAROLINA UNIVERSITY
In Partial Fulfillment
oftheRequirementsfortheDegree
MasterofSciencein AppliedPhysics
by
AndersonTravia
June, 2009
INTERACTION CROSS SECTIONS NEEDEDFOR SIMULATIONOF
SECONDARY ELECTRON EMISSION SPECTRA FROM THIN METALFOILS
AFTER FAST PROTON IMPACT
by
AndersonTravia
APPROVED BY:
DIRECTOR OFTHESIS:
____________________________________
MichaelDingfelder, Ph. D.
COMMITTEEMEMBER:
____________________________________
Larry H.Toburen, Ph. D.
COMMITTEEMEMBER:
____________________________________
JeffersonL. Shinpaugh,Ph. D.
COMMITTEEMEMBER:
____________________________________
David W.Pravica, Ph. D.
INTERIM CHAIR OFTHE DEPARTMENTOFPHYSICS:
____________________________________
James M.Joyce, Ph. D.
DEAN OFGRADUATE SCHOOL:
_____________________________________
PaulJ. Gemperline,Ph. D.
Acknowledgements
Iwouldliketo thanktheDepartmentofPhysicsofEastCarolinaUniversityandin
special Dr. MichaelDingfelderand Dr. Larry H. Toburenforprovidingthemeansfor
theconclusionofthisproject. Needless tosay, withouttheirgenerosityand assistance
theconclusionofthisstudywouldbejustimpossible. Thank youverymuch foryour
lectures, comments,suggestions,and supervision. IalsowouldliketothankDr.
Jefferson L.Shinpaughand Dr. DavidW. Pravicafortakingtheirtimetoread this
work andforprovidingtheiralsoextremelyimportantcriticism. Finally,Iwouldlike
tothank mywifeforsupportingmethroughthistoughjourney.
Table of Contents
ListofFigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .vii
1 Introduction 1
1.1 Initialfacts andobservations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Motivationandobjectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Theory 5
2.1 Basic principles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Cross-sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.2 FromMaxwell’sequationstodifferentialcross-sections . . . . . . . . . . 8
2.2 Theelectricfieldduetoaninducedchargeddensity . . . . . . . . . . . . . . . . . .11
2.3 Modelingthecurrentchargedensity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
2.3.1 Thepointradiator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .15
2.3.2 Scatteringpowerfortheoscillatingfreeelectron . . . . . . . . . . . . . . .16
2.3.3 Thescatteringcross-sectionofasinglefreeelectron . . . . . . . . . . . . 19
2.3.4 Scatteringbyboundelectrons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.5 Scatteringbymany-electronatoms . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4 Theatomicscatteringfactorandtheoscillatorstrength . . . . . . . . . . . . . . . 27
2.5 BethetheoryandtheGOSofamaterial . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 GOSHartree-Fock approximationfor singleatomiccollision . . . . . . . . . . 32
2.7 DICS incondensed-phase-modelingtheenergy-lossfunction . . . . . . . . . 35
2.7.1 Thekeyquantity-energy-lossfunction . . . . . . . . . . . . . . . . . . . . . .35
2.7.2 Linkwiththedifferentialcrosssectionand GOS . . . . . . . . . . . . . . 37
2.8 MonteCarlosimulationofradiationtransport . . . . . . . . . . . . . . . . . . . . . .39
2.8.1 Trackingofachargedparticle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.8.2 Theprobabilitydistributionfunctionand samplingmethods . . . . . . 40
2.8.3 Randomtrackgeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .42
2.8.4 Anexampleusingahypotheticalmean-free-path PDF .. . . . . . . . . .43
3 Procedures 45
3.1 ConsistencytestfortheOOS-sum-ruletest . . . . . . . . . . . . . . . . . . . . . . .45
3.1.1 AluminumOOS .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.1.2 CopperOOS .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .49
3.1.3 GoldOOS .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.2 Limitsofintegration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .51
3.3 Shellseparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.3.1 Aluminumedge-energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .58
3.3.2 Copperedge-energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.3.3 Goldedge-energies . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . .58
3.4 Angulardistributionofprimaryandsecondary particles. . . . . . . . . . . . . . .66
3.4.1 Angulardistributionofprimaryprotons. . . . . . . . . . . . . . . . . . . . . . 66
3.4.2 Angulardistributionofprimaryelectrons . . . . . . . . . . . . . . . . . . . . 68
3.4.3 Angulardistributionofelectrons inducedbyelectron impact . . . . . . 69
3.4.4 Angulardistributionofelectronsinducedby protonimpact . . . . . . . 70
3.4.5 DeterminationofA(w)andB(w) . . . . . . . . . . . . . . . . . . . . . . . . . . .70
3.4.6 Aluminum,copper,andgoldBethecoefficients . . . . . . . . . . . . . . . . 73
4 Results 79
4.1 Electronimpactinaluminum,copper,andgoldthinfoils . . . . . . . . . . . . . .80
4.1.1 AluminumDIMFP,IMFP,andSTP .. . . . . . . . . . . . . . . . . . . . . . . 80
4.1.2 CopperDIMFP,IMFP,andSTP .. . . . . . . . . . . . . . . . . . . . . . . . . . 83
4.1.3 GoldDIMFP,IMFP,andSTP .. . . . . . . . . . . . . . . . . . . . . . . . . . . .86
4.2 Protonimpactinaluminum,copper,andgoldthinfoils . . . . . . . . . . . . . . . 89
4.2.1 AluminumDIMFP,IMFP,andmassSTP .. . . . . . . . . . . . . . . . . . . .89
4.2.2 CopperDIMFP, IMFP,andmassSTP .. . . . . . . . . . . . . . . . . . . . . .92
4.2.3 GoldDIMFP,IMFP,andmassSTP .. . . . . . . . . . . . . . . . . . . . . . . .95
4.3 Electronyieldsfrom0.1microncopperfoilafter6MeVprotonimpact . . . .98
4.3.1 Forwardelectronyield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.3.2 Backward electronyield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
5 ConclusionandRemarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102