High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
High Brightness Electron Beam Diagnostics and their ... - CASA
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
.<br />
. . . . . .<br />
. . .<br />
.<br />
. . .<br />
. .<br />
.<br />
. . . . .<br />
. . .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. . .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
. .. . .<br />
.. .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. . . . .<br />
.<br />
. . ..<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. . . . .<br />
.<br />
.<br />
. . . .<br />
.<br />
. .<br />
. . . .<br />
. .<br />
. . . . .<br />
.<br />
.<br />
. .<br />
. . . .<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
. . .<br />
.<br />
.<br />
.<br />
. . .<br />
. .<br />
. .<br />
. . .<br />
. . .<br />
. .<br />
.<br />
.<br />
. .<br />
. .<br />
.<br />
. .<br />
. . .<br />
.<br />
.<br />
. .<br />
.<br />
. . . . . .<br />
. . .<br />
.<br />
. . .<br />
.<br />
.<br />
. . . .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
. .<br />
. . . . .<br />
.<br />
.<br />
. . . .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
. . .<br />
.<br />
. . . . .<br />
. . . . . .<br />
. . . .<br />
.<br />
.<br />
.<br />
. . .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
. . .<br />
.<br />
.<br />
. . . .<br />
. . . . .<br />
.<br />
. . .<br />
.<br />
. .<br />
.<br />
. .<br />
. . . .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. . . . .<br />
.<br />
.<br />
. . .<br />
.<br />
. . .<br />
. .<br />
. . .<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
. . .<br />
. . .<br />
. .<br />
. .. .<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
. . . . . .<br />
. . . .<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
. . .<br />
.<br />
. .<br />
. .<br />
.<br />
. . . .<br />
. . . . . . .<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
.<br />
.. .<br />
. . .<br />
.<br />
.<br />
. . .<br />
. . . .<br />
.<br />
.<br />
. . .<br />
. . . . . .<br />
. .<br />
. . . . .<br />
. . . .<br />
.<br />
. . .<br />
.<br />
. .<br />
. .<br />
. . .<br />
. . . .<br />
.<br />
.<br />
.<br />
. . .<br />
. . . . .<br />
. . .<br />
.<br />
. .<br />
. . . . .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
. . .<br />
. . . . .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
.<br />
. . .<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. . .<br />
. .<br />
. . .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
.. .<br />
.<br />
. . .<br />
.<br />
. .<br />
. . . .<br />
.<br />
.<br />
.<br />
. . . . . .<br />
. . . .<br />
.<br />
.<br />
. .<br />
. . . .<br />
. .<br />
.<br />
.<br />
. . . .<br />
.<br />
.<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. . . . .<br />
. . . . .<br />
.<br />
. .<br />
. . . .<br />
.<br />
.<br />
.<br />
. . .<br />
. .<br />
. .<br />
. . . .<br />
.<br />
. . . . . .<br />
. . . .<br />
. .<br />
. . .<br />
.<br />
.<br />
. . . .<br />
. . .<br />
.<br />
. . .<br />
.<br />
.<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
. . . .<br />
.<br />
. . .<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
. .. .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. . . .<br />
.<br />
.<br />
.<br />
. . . .<br />
. .<br />
. . .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. . .<br />
. .<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
. . . .<br />
. . .<br />
. .<br />
.<br />
. . . . .<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
. .. .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. . . .. .<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. . .<br />
. . .<br />
. . .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
. . .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
. .<br />
. . . .<br />
.<br />
. . . . . . .<br />
.<br />
. . .<br />
.<br />
. . . . . .<br />
.<br />
.<br />
. . . .<br />
. . .<br />
.. . .<br />
. . .<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
. . .<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
. .<br />
. .<br />
. . . .<br />
.<br />
.<br />
. .<br />
. . . .<br />
. . . .<br />
.<br />
.. . .<br />
.<br />
.<br />
. . .<br />
. . . . .<br />
.<br />
. .<br />
.<br />
. .<br />
. . .<br />
.<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
..<br />
.<br />
.<br />
. . .<br />
.<br />
. . .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. . . .<br />
. .<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
. .<br />
. .<br />
.<br />
. . .<br />
.<br />
.<br />
. . .<br />
. . . .<br />
. .<br />
. . .<br />
. .<br />
.<br />
.<br />
. . .<br />
. . . .<br />
. .<br />
. . . . . .<br />
. .<br />
.<br />
. . . . .<br />
. . . . .<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. . .<br />
. . . .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
. . . .<br />
. . .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
. . .<br />
.<br />
. .<br />
. .<br />
.<br />
. .<br />
. . .<br />
.<br />
. . . . . . .<br />
.<br />
.<br />
. . .<br />
. . .<br />
. . . .<br />
. .<br />
.<br />
. .<br />
. .<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
. .<br />
. . . .<br />
. . .<br />
. .<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. . . . . . . .<br />
. .<br />
.<br />
.<br />
. .<br />
. . .<br />
. . .<br />
. .<br />
. .<br />
. .<br />
. . . .<br />
.<br />
. . . . .<br />
.<br />
. . . .<br />
.<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. . . . . .<br />
. . .<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
. . . .<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
. . .<br />
.<br />
.<br />
.<br />
. . .<br />
. .<br />
. .<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. . .<br />
.<br />
. . .<br />
. . . . .<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
.<br />
. . . . . . . . .<br />
. .<br />
. .<br />
.<br />
. . .<br />
. . .<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
. . .<br />
. .<br />
. . . . . .<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
. .<br />
.<br />
.<br />
. .<br />
. . .<br />
.<br />
.<br />
. .<br />
. . . . ..<br />
.<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
. . . . .<br />
. . . . . . . . . . .<br />
. . .<br />
.<br />
. .<br />
. .<br />
. . .<br />
. . . . . .<br />
.<br />
. . .<br />
. .<br />
.<br />
. . .<br />
.<br />
. . . . . .<br />
. .<br />
.<br />
.<br />
.<br />
. . .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. . . .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
. . .<br />
.<br />
.<br />
. . . .<br />
.<br />
. . . .<br />
. .<br />
.<br />
. .<br />
.<br />
. . . .<br />
. .<br />
. .<br />
. . .<br />
. . .<br />
.<br />
.<br />
. . .<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
. . . .<br />
.<br />
..<br />
.<br />
.<br />
.<br />
. .<br />
. .<br />
.. .<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
. .<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
. . ..<br />
.<br />
.<br />
.<br />
.<br />
. .<br />
.<br />
.<br />
..<br />
.<br />
.<br />
.<br />
.<br />
. . . . .<br />
.<br />
.<br />
. .<br />
.<br />
. .<br />
.<br />
.<br />
1.0<br />
.<br />
. .<br />
0.5<br />
. 10%<br />
. .<br />
.<br />
.<br />
...<br />
..<br />
.<br />
.<br />
..<br />
.<br />
90%<br />
0.0<br />
.<br />
contours)usingthesimulatedbeampatternontheopticaltransitionradiationpresentedgure4.19<br />
90%<br />
50%<br />
-0.5<br />
wherehx0Biistheaveragedivergenceofthebeamcomputedfromthebeamlet:x0B=PiPjwi;jx0j Figure4.20:Comparisonoftheexpectedphase-space,generatedviaparticleretracing(eachgrey dotsrepresentamacroparticle),withtheretrievedphase-space(representedwithbacklineiso-<br />
10%<br />
Fromallthepreviouscalculationsitisthenstraightforwardtocomputetheemittance<strong>and</strong>Twiss parameters:<br />
-1.0<br />
-8 -6 -4<br />
hx2i'Pix2iPjwi;j PiPjwi;j.<br />
-2 0 2 4 6 8<br />
x<br />
PiPjwi;j<br />
(mm)<br />
hxx0i'PixiPjx0jwi;j hx02i=PiPjx02 PiPjwi;j jwi;j<br />
thenumberofsampleinpositiondoesnotexceed5<strong>and</strong>thereforesomenedetailonthedistributioncouldbemissed.Indeeditispossibletomovethebeamonthemultislitmaskbymeansoftrace-spacedistributioniso-contourcanbededucedfromthebeamletprolesincethislattercorrespondstosampleofthedistributioninposition(2(xi;x0)).Unfortunatelyundernormaloperation Aswealreadypointedoutitisalsointerestingtohaveaccesstothetrace-spacedistribution.The (4.60)<br />
upstreammagneticsteerers,<strong>and</strong>foreachsettingofthismagnetrecordthebeamlets'projection.In suchacaseitispossibletollthetrace-spacecompletely;ofcoursethisrelyonaperfectstability<br />
x (mrad)