Measuring and Analyzing Transverse Emittances of Charged Particle Beams
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Measuring and Analyzing Transverse Emittances of Charged Particle Beams. Martin P. Stockli and many collogues at SNS and other Accelerator Labs. BIW’06 Fermi National Accelerator Laboratory Batavia, IL, May 1, 2006. CD-4 achieved 4-28-06 15:30. Outline:. Concepts and Definitions - PowerPoint PPT Presentation
Transcript of Measuring and Analyzing Transverse Emittances of Charged Particle Beams
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Measuring and Analyzing Transverse Emittances of Charged Particle BeamsMartin P. Stockliand many collogues at SNS and other Accelerator LabsBIW06Fermi National Accelerator LaboratoryBatavia, IL, May 1, 2006
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CD-4 achieved 4-28-06 15:30
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Outline:Concepts and DefinitionsApplicationsThe Emittance EllipseDilemmasMeasuring Emittance Distributions (Destructive)Nondestructive Measurements of the Emittance EllipseAnalysis of emittance Ellipse Analysis of Emittance DistributionsConclusions
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The EmittanceThe emittance is the 6-dimensional hypervolume in the phase space x,y,z,px,py,pz that is occupied by a number of beam particles. The coordinates are normally referenced with respect to the center, by zeroing the first moments:yxzp(x0,y0,z0)If the axial motion does not couple to the transverse motions, the hypervolume can be separated into the 2-dimensional longitudinal emittance, which describes the beam current profile as a function of time, and the transverse emittance which describes the beam current as a function of transverse position. The transverse emittance is the 4-dimensional, occupied hypervolume in the phase space x,y,px,py: If transverse motions are not coupled, the emittance can be separated into its components, which form 2-dimensional areas in {x,px} and {y,py}: with form-factor 2
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Emittance in Trace-Space:For pz invariant along the beam axis, p can be factored out, yielding the transverse emittance in the trace space x,y, x=dx/dz, and y=dy/dz. If transverse motions are not coupled, the emittance can be separated into its components, which form the 2-dimensional areas {x,x} and {y,y}: All these terms are normally called Emittance. However, rigorous authors call them either Volume Emittance or Area Emittance. Most then go on to introduce the Emittance as the semi-axis-product of an hyper-ellipsoid with the same area or volume:Confusion can be avoided by stating whether the quoted emittance value is a volume, an area, or a semi-axis-product!
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Units of Emittances in the Trace-Space Emittances have the dimension of (lengthangle)n.
Common are mmmrad, cmmrad, and mrad
However, the radian angle is a dimensionless ratio, and therefore some people use m, mm, and m (= mmmrad).For semi-axis-products it is common to write mmmrad, cmmrad, or mradThe is supposed to assure the reader that the has the has been factored out of the phase space area (Sanders, 1990).However, if the was factored out, it was factored out in the definition. The in the unit has no clear meaning. It is neither a real unit, nor a true multiplier. It is a one-of-a-kind object that has no precedent in the physics literature! It has created as much confusion as it intended to eliminate. A trend has started to omit the in the unit.Confusion can be avoided by stating whether the quoted emittance value is a volume, an area, or a semi-axis-product!Unless otherwise stated, semi-axis-products will be quoted throughout this presentation!
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Normalized Emittances As the particles are accelerated from vz1 to vz2, the trace angles narrow, causing the emittance to shrink.The emittance can be normalized by multiplying the emittance with the dimensionless particle-velocity to speed-of-light ratio:The normalized emittance stays roughly the same throughout most parts of most accelerators!vTvTvz1vz2x1x2withandwithor
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The RMS EmittanceEmittance volumes or areas that contain all particles are of limited merit because they are very large and dominated by a very few particles of questionable character. The volume of an entire Gaussian distribution is infinite. This problem can be reduced by quoting the emittance volume of a certain fraction of the beam, e.g. 90%, yielding E90% or A 90% . The problem is resolved with the rms emittance that averages over all particles with a weight given by the particles distance from the center:This is the semi-axis-product of an ellipse. For a Gaussian distribution, the ellipse contains 39% of the beam. (E90% = 4.6Erms)For a finite current , the rms-emittance is finite. There is no absolute need to threshold the data, but tresholded rms-emittances are common, e.g. E rms,90%. Unfortunately many authors fail to be specific!, with, ande.g.:,,,
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What is it all good for?According to Liouvilles theorem, emittances are conserved if the particles are subjected only to conservative forces, such as time-invariant electric and magnetic fields. Therefore the emittance allows for predicting the downstream beam transport, the beams focusability, the losses in downstream restricted beam line apertures, etc. It is invaluable for designing accelerators and beam lines! Some non-conservative forces, such as collisions, scattering, and fluctuations of electric or magnetic fields, increase the emittance. Other non-conservative forces, such as E-M radiation, decrease the emittance.The emittance is conserved under space charge as long as the forces are caused by the charged particle cloud, rather than by individual particles. Due to the nature of the beam formation in ion sources and/or the collimation in the extractor- and other apertures, emittances are normally of elliptical shape. Beams collimated by rectangular wave guides (in dipole magnets) or by straight slits can exhibit rectangular shapes. In this presentation we will focus on elliptical emittances.
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The Emittance ellipsexxxxxzbeam envelopebeam waistxxxWhile the area is constant, the emittance ellipse shape and orientation changes. It is described by:
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The Ellipse and the Twiss parameter: Divergence:
Beam radius:xxabdiverging beam: 0>0 by definition [mm/mrad]0
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The Transformation of Ellipses:The transfer matrix is normally used to calculate individual particle rays:Similarly, the ellipse equation can be written as:e.g.:withorwithWhich allows to calculate the beam envelope as:
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Real emittances:Angular spread shrinks as as beam is accelerated.Non linear forces, such as lens aberrations and space charge, often cause low-energy emittances to be S-shaped.Particles far from the central ellipse are preferentially lost in the RFQ. Ellipses are good approximations for high energy beams.SNS LEBT (65 keV)SNS MEBT (2.5 MeV)~70 mrad~15 mrad
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x (mm)
x' (mrad)
sheet1
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4-290
4.2000002861-290.0289999992
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3-260.7710000277
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4.2000002861490.224999994
4.4000000954490.1860000044
4.5999999046490.0540000014
4.8000001907490.0780000016
5490.0390000008
5.2000002861490.0590000004
0520
0.200000003520.0149999997
0.400000006520.0240000002
0.6000000238520.0199999996
0.8000000119520.0240000002
1520
1.2000000477520.0340000018
1.3999999762520.1030000001
1.6000000238520.1459999979
1.8000000715520.1509999931
2520.0930000022
2.2000000477520.0489999987
2.4000000954520.0390000008
2.6000001431520.0199999996
2.7999999523520.1070000008
3520.0199999996
3.2000000477520.063000001
3.4000000954520.0289999992
3.6000001431520.0199999996
3.7999999523520.0489999987
4520.0340000018
4.2000002861520.0240000002
4.4000000954520.063000001
4.5999999046520.0240000002
4.8000001907520.0340000018
5520.0240000002
5.2000002861520.0289999992
0550.0149999997
0.200000003550.0149999997
0.400000006550.0199999996
0.6000000238550.0149999997
0.8000000119550
1550.0289999992
1.2000000477550.0340000018
1.3999999762550.0240000002
1.6000000238550.0289999992
1.8000000715550.063000001
2550.0680000037
2.2000000477550.0240000002
2.4000000954550.0149999997
2.6000001431550.0049999999
2.7999999523550
3550
3.2000000477550
3.4000000954550
3.6000001431550
3.7999999523550
4550
4.2000002861550.0289999992
4.4000000954550.0240000002
4.5999999046550.0049999999
4.8000001907550.0049999999
5550.0149999997
5.2000002861550.0340000018
0580.0340000018
0.200000003580.0099999998
0.400000006580.0099999998
0.6000000238580
0.8000000119580
1580.0199999996
1.2000000477580.0199999996
1.3999999762580.0240000002
1.6000000238580.0049999999
1.8000000715580.0099999998
2580.0289999992
2.2000000477580.0049999999
2.4000000954580.0049999999
2.6000001431580.0049999999
2.7999999523580
3580
3.2000000477580
3.4000000954580
3.6000001431580
3.7999999523580
4580
4.2000002861580
4.4000000954580.0240000002
4.5999999046580.0049999999
4.8000001907580.0049999999
5580.0049999999
5.2000002861580.0340000018
0610.0199999996
0.200000003610.0199999996
0.400000006610.0199999996
0.6000000238610.0049999999
0.8000000119610.0240000002
1610.0099999998
1.2000000477610.0149999997
1.3999999762610.0049999999
1.6000000238610
1.8000000715610
2610
2.2000000477610
2.4000000954610
2.6000001431610.0049999999
2.7999999523610
3610
3.2000000477610
3.4000000954610.0049999999
3.6000001431610
3.7999999523610.0099999998
4610.0049999999
4.2000002861610.0049999999
4.4000000954610.0289999992
4.5999999046610.0199999996
4.8000001907610.0149999997
5610.0099999998
5.2000002861610.0149999997
0640.0199999996
0.200000003640.0099999998
0.400000006640.0240000002
0.6000000238640.0049999999
0.8000000119640.0439999998
1640.0049999999
1.2000000477640.0340000018
1.3999999762640.0240000002
1.6000000238640
1.8000000715640
2640
2.2000000477640
2.4000000954640.0049999999
2.6000001431640
2.7999999523640
3640
3.2000000477640.0099999998
3.4000000954640
3.6000001431640
3.7999999523640
4640
4.2000002861640.0149999997
4.4000000954640.0049999999
4.5999999046640.0199999996
4.8000001907640.0099999998
5640.0149999997
5.2000002861640.0240000002
0670.0099999998
0.200000003670.0240000002
0.400000006670.0049999999
0.6000000238670.0240000002
0.8000000119670.0049999999
1670.0049999999
1.2000000477670.0149999997
1.3999999762670.0199999996
1.6000000238670
1.8000000715670
2670
2.2000000477670
2.4000000954670
2.6000001431670
2.7999999523670
3670
3.2000000477670
3.4000000954670
3.6000001431670
3.7999999523670
4670.0199999996
4.2000002861670.0099999998
4.4000000954670.0049999999
4.5999999046670.0149999997
4.8000001907670.0049999999
5670.0289999992
5.2000002861670.0099999998
0700.0289999992
0.200000003700.0240000002
0.400000006700.0049999999
0.6000000238700.0149999997
0.8000000119700
1700.0099999998
1.2000000477700.0240000002
1.3999999762700.0149999997
1.6000000238700.0049999999
1.8000000715700
2700
2.2000000477700
2.4000000954700
2.6000001431700
2.7999999523700
3700
3.2000000477700
3.4000000954700
3.6000001431700.0049999999
3.7999999523700.0149999997
4700.0099999998
4.2000002861700.0149999997
4.4000000954700.0240000002
4.5999999046700
4.8000001907700
5700.0099999998
5.2000002861700.0099999998
Paste emittance data into columns (maximum=10,000 entries, data starts in row 1):A - x data in mmB - x' data in mradsC - I (current) in arbitrary units
analyze emittance
sheet1
0.004999999900.04899999870.15600000320.26399999860.21999999880.12200000140.10700000080.09300000220.08799999950.09300000220.07800000160.02899999920.01999999960.00999999980.03900000080.01999999960.02400000020.0149999997000.004999999900.019999999600.01499999970.014999999700.00499999990.00999999980.014999999700.01499999970.03400000180.01999999960.01999999960.00999999980.0289999992
0.02899999920.01999999960.03900000080.16099999850.28299999240.20999999340.16099999850.12700000410.11200000350.10300000010.10700000080.11200000350.02400000020.02400000020.00499999990.01999999960.01499999970.02400000020.00999999980.01999999960.00999999980.00999999980.02400000020.004999999900.00499999990000.01999999960.01499999970.01499999970.01499999970.00999999980.01999999960.00999999980.02400000020.0240000002
0.02400000020.02400000020.03900000080.12700000410.2489999980.21999999880.1759999990.13699999450.12200000140.10300000010.12700000410.15099999310.10700000080.01499999970.014999999700.00999999980.02899999920.02899999920.02899999920.04899999870.00999999980.02400000020.01999999960.00999999980.01999999960.01499999970.00499999990.00499999990.03400000180.00499999990.02400000020.01999999960.00999999980.01999999960.02400000020.00499999990.0049999999
0.02899999920.03400000180.02400000020.09799999740.2489999980.21999999880.20999999340.13699999450.10700000080.12200000140.14599999790.15600000320.1759999990.063000001000.03400000180.01999999960.07299999890.14200000460.11699999870.10700000080.12700000410.10300000010.13199999930.14200000460.06800000370.00499999990.00999999980.028999999200.01999999960.014999999700.00499999990.00499999990.02400000020.0149999997
0.004999999900.02400000020.10700000080.23899999260.20499999820.18099999430.13699999450.13199999930.13699999450.13699999450.16599999370.18099999430.15099999310.05400000140.01999999960.01999999960.11699999870.23399999740.34200000760.44400000570.49799999590.4490000010.39100000260.48300001030.527000010.61500000950.20499999820.05900000040.00999999980.02400000020.0240000002000.02400000020.04399999980.00499999990
0000.12200000140.22900000210.20499999820.16599999370.14200000460.13699999450.12200000140.13699999450.14599999790.21500000360.21999999880.05900000040.04899999870.12700000410.33199998740.62000000480.99099999671.26499998571.20099997521.19099998471.25499999521.38199996951.65499997141.51900005341.02499997620.30799999830.10300000010.028999999200.02899999920.01999999960.00999999980.00499999990.00499999990.0099999998
0000.05400000140.20499999820.1759999990.13699999450.12700000410.13199999930.16099999850.14200000460.15099999310.21500000360.29300001260.18099999430.08799999950.33199998740.97699999811.71399998662.32899999622.95900011063.27600002293.21300005913.09100008012.87599992752.71000003812.58299994472.03600001341.24000000950.52200001480.12200000140.03400000180.03400000180.01999999960.01499999970.03400000180.01499999970.0240000002
0000.07299999890.24400000270.16099999850.14200000460.13199999930.12200000140.18099999430.18999999760.1759999990.25900000330.30300000310.30799999830.25900000330.87900000812.29500007633.62299990654.62400007254.52099990844.13600015643.5060000423.25699996952.98799991612.85199999812.52900004392.33899998661.76300001140.85900002720.37099999190.10300000010.02400000020.02400000020.00499999990.02400000020.01999999960.0149999997
0000.07299999890.26399999860.24400000270.16599999370.15600000320.16099999850.1759999990.18600000440.2000000030.23899999260.34200000760.46900001170.59100002051.99199998383.58400011065.18100023275.2639999394.16499996192.99799990651.76300001141.47899997231.37699997431.44000005721.59200000761.78699994091.59700000290.93699997660.37599998710.14599999790.02899999920.00499999990000.0049999999
0000.09799999740.34200000760.31700000170.24400000270.21500000360.18099999430.1759999990.23899999260.25400000810.30799999830.40500000120.57599997521.49899995333.34500002865.08799982075.74700021744.77099990842.94400000571.65499997141.0060000420.76200002430.68800002340.69300001860.81499999761.08399999141.3179999590.87900000810.41499999170.15099999310.0630000010.00999999980000
0000.09799999740.37599998710.38100001220.27799999710.24400000270.20999999340.1759999990.21999999880.25400000810.33700001240.47900000210.82999998332.39299988754.8829998976.15700006485.48299980163.72600007061.8070000411.02999997140.65399998430.55199998620.49300000070.47900000210.54699999090.71299999950.99099999670.91799998280.31200000640.09300000220.06800000370.02899999920000
0000.11200000350.44400000570.44400000570.37599998710.28799998760.24400000270.21999999880.20999999340.28799998760.40999999640.58600002530.94700002673.64299988756.30399990086.34800004964.45300006872.289999961900.66900002960.527000010.49799999590.45399999620.43500000240.48800000550.570999980.72799998520.71799999480.16599999370.04899999870.02400000020.00499999990000
0000.09799999740.44400000570.52200001480.40500000120.33700001240.28799998760.29300001260.27799999710.28799998760.48300001030.82499998811.32799994954.3756.86499977115.82499980932.85199999811.13800001140.70800000430.54199999570.5030000210.43000000720.42500001190.45399999620.43900001050.49300000070.54699999090.679000020.43900001050.03900000080.01499999970.004999999900.004999999900
0000.13199999930.45399999620.570999980.45899999140.38600000740.34700000290.32699999210.32199999690.35600000620.59600001571.21099996572.05599999435.21000003816.34800004965.21999979022.2360000610.77600002290.54699999090.4490000010.4000000060.37599998710.38100001220.41999998690.40500000120.4490000010.46399998660.6010000110.32699999210.01999999960.00499999990.00499999990.0049999999000
000.00499999990.14200000460.48300001030.67400002480.54699999090.45899999140.4000000060.39100000260.4000000060.53200000520.92299997812.37299990653.05699992185.57600021365.64900016784.63399982452.03600001340.63499999050.45399999620.37599998710.32199999690.34200000760.35199999810.34700000290.35600000620.36100000140.38600000740.52200001480.4000000060.1070000008000000
000.03400000180.16099999850.4000000060.77100002770.67400002480.54699999090.50800001620.48300001030.54199999570.76200002431.40600001813.59899997714.09200000765.5079998974.90700006483.47699999811.87999999520.58600002530.39100000260.30300000310.27300000190.27300000190.28799998760.33199998740.32199999690.32199999690.36100000140.45899999140.38600000740.0199999996000000
00.01499999970.07299999890.14599999790.43000000720.87400001290.86900001760.81999999280.73699998860.75199997430.92799997331.42100000382.73399996764.99499988565.28299999245.1030001643.73000001912.26600003241.11300003530.49799999590.32699999210.24400000270.19499999280.25400000810.27300000190.25400000810.24400000270.28299999240.28799998760.38100001220.4000000060.0630000010000.009999999800
000.05900000040.20499999820.78600001341.23000001911.34300005441.25999999051.36199998861.47000002861.84599995612.85199999813.97000002865.05900001535.3610000613.93600010872.71000003811.32299995420.58600002530.38600000740.28299999240.18600000440.1759999990.14599999790.20499999820.21500000360.19499999280.18600000440.21999999880.35600000620.29800000790.0289999992000.0049999999000
00.01999999960.02400000020.12200000140.43000000720.98100000621.72399997712.15799999242.45600008962.75900006293.29099988943.74000000954.10599994663.753.68199992182.55900001531.58700001240.76200002430.2249999940.24400000270.20999999340.16099999850.16099999850.13199999930.16599999370.18099999430.18099999430.15600000320.21500000360.32699999210.2489999980.0199999996000000.0049999999
0.0099999998000.00499999990.18999999760.85900002721.8070000412.53900003433.06200003623.05200004583.04200005532.98300004012.45099997521.74800002571.68900001051.12300002570.75199997430.298000007900.10300000010.19499999280.17100000380.10300000010.13199999930.13699999450.14200000460.16099999850.19499999280.2249999940.31700000170.29300001260.0489999987000.0099999998000.0149999997
00.00999999980000.13699999451.05999994281.97300004962.08500003811.82599997521.25999999051.10399997230.98600000140.79100000860.77100002770.48300001030.33199998740.14200000460.05400000140.03400000180.16599999370.17100000380.12200000140.09799999740.11200000350.12700000410.14599999790.20999999340.233999997400.20999999340.0340000018000.004999999900.01999999960.0099999998
0.02400000020.01499999970.01999999960.00499999990.028999999200.01499999970.66900002961.22599995140.93699997660.43900001050.36599999670.36100000140.33700001240.29800000790.13199999930.08299999680.06800000370.02400000020.01999999960.06800000370.16599999370.14200000460.10700000080.12700000410.14599999790.17100000380.21999999880.2489999980.29300001260.2249999940.02400000020.028999999200.00499999990.01499999970.00999999980.0149999997
0.00999999980.00499999990.01999999960.00499999990.00499999990.01499999970.02400000020.01999999960.26399999860.26399999860.2000000030.09799999740.09300000220.12200000140.09300000220.0630000010.0630000010.02899999920.03900000080.02400000020.05900000040.11699999870.14599999790.12200000140.10700000080.12700000410.14200000460.23399999740.24400000270.27799999710.18600000440.0630000010.02400000020.02400000020.02899999920.00499999990.00499999990.0240000002
0.03400000180.024000000200.028999999200.02400000020.01999999960.00499999990.01999999960.03900000080.04399999980.04399999980.03900000080.01999999960.04399999980.01499999970.01499999970.04399999980.04899999870.03400000180.01999999960.0630000010.10300000010.09300000220.07800000160.10300000010.11200000350.2249999940.26899999380.16599999370.05400000140.02400000020.00499999990.00499999990.01999999960.01999999960.01499999970
0.01499999970.009999999800.01499999970.03400000180.00499999990.00499999990.00999999980.02400000020.01999999960.02400000020.00499999990.05900000040.03900000080.02400000020.00499999990.009999999800.01999999960.01999999960.01499999970.03900000080.08299999680.07800000160.07299999890.09799999740.10700000080.21500000360.27300000190.1759999990.07800000160.03400000180.00499999990.00499999990.01499999970.00999999980.00499999990
0.00999999980.02400000020.00499999990.00999999980.014999999700.024000000200.00999999980.024000000200.00999999980.004999999900.01999999960.00499999990.03900000080.00999999980.02400000020.01499999970.04399999980.03400000180.0630000010.07299999890.05900000040.09300000220.08299999680.15600000320.27799999710.09799999740.03900000080.02400000020.01499999970.00499999990.00999999980.01499999970.02899999920.0099999998
00.00499999990.02400000020.00499999990.01499999970.014999999700.01499999970.02400000020.02899999920.028999999200.01499999970.01999999960.01499999970.00999999980.03400000180.00999999980.02400000020.02400000020.03900000080.03900000080.01999999960.05900000040.03900000080.05400000140.04899999870.10300000010.26399999860.11200000350.05900000040.02899999920.03400000180.03400000180.01499999970.02400000020.00999999980.0099999998
-41.00
-38.00
-35.00
-32.00
-29.00
-26.00
-23.00
-20.00
-17.00
-14.00
-11.00
-8.00
-5.00
-2.00
1.00
4.00
7.00
10.00
13.00
16.00
19.00
22.00
25.00
28.00
31.00
34.00
37.00
40.00
43.00
46.00
49.00
52.00
55.00
58.00
61.00
64.00
67.00
70.00
x (mm)
x' (mrad)
sheet2
0.004999999900.04899999870.15600000320.26399999860.21999999880.12200000140.10700000080.09300000220.08799999950.09300000220.07800000160.02899999920.01999999960.00999999980.03900000080.01999999960.02400000020.0149999997000.004999999900.019999999600.01499999970.014999999700.00499999990.00999999980.014999999700.01499999970.03400000180.01999999960.01999999960.00999999980.02899999920000000000
0.02899999920.01999999960.03900000080.16099999850.28299999240.20999999340.16099999850.12700000410.11200000350.10300000010.10700000080.11200000350.02400000020.02400000020.00499999990.01999999960.01499999970.02400000020.00999999980.01999999960.00999999980.00999999980.02400000020.004999999900.00499999990000.01999999960.01499999970.01499999970.01499999970.00999999980.01999999960.00999999980.02400000020.02400000020.2000000030.2000000030.2000000030.2000000030.2000000030.2000000030.2000000030.2000000030.2000000030.200000003
0.02400000020.02400000020.03900000080.12700000410.2489999980.21999999880.1759999990.13699999450.12200000140.10300000010.12700000410.15099999310.10700000080.01499999970.014999999700.00999999980.02899999920.02899999920.02899999920.04899999870.00999999980.02400000020.01999999960.00999999980.01999999960.01499999970.00499999990.00499999990.03400000180.00499999990.02400000020.01999999960.00999999980.01999999960.02400000020.00499999990.00499999990.4000000060.4000000060.4000000060.4000000060.4000000060.4000000060.4000000060.4000000060.4000000060.400000006
0.02899999920.03400000180.02400000020.09799999740.2489999980.21999999880.20999999340.13699999450.10700000080.12200000140.14599999790.15600000320.1759999990.063000001000.03400000180.01999999960.07299999890.14200000460.11699999870.10700000080.12700000410.10300000010.13199999930.14200000460.06800000370.00499999990.00999999980.028999999200.01999999960.014999999700.00499999990.00499999990.02400000020.01499999970.60000002380.60000002380.60000002380.60000002380.60000002380.60000002380.60000002380.60000002380.60000002380.6000000238
0.004999999900.02400000020.10700000080.23899999260.20499999820.18099999430.13699999450.13199999930.13699999450.13699999450.16599999370.18099999430.15099999310.05400000140.01999999960.01999999960.11699999870.23399999740.34200000760.44400000570.49799999590.4490000010.39100000260.48300001030.527000010.61500000950.20499999820.05900000040.00999999980.02400000020.0240000002000.02400000020.04399999980.004999999900.80000001190.80000001190.80000001190.80000001190.80000001190.80000001190.80000001190.80000001190.80000001190.8000000119
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-41.00
-38.00
-35.00
-32.00
-29.00
-26.00
-23.00
-20.00
-17.00
-14.00
-11.00
-8.00
-5.00
-2.00
1.00
4.00
7.00
10.00
13.00
16.00
19.00
22.00
25.00
28.00
31.00
34.00
37.00
40.00
43.00
46.00
49.00
52.00
55.00
58.00
61.00
64.00
67.00
70.00
x (mm)
x' (mrad)
x-x' 3D plot
Sheet3
-107.3600845337-119.3164138794
-92.3213729858-129.8165130615
-83.0932006836-134.5061035156
-75.4854812622-137.5751953125
-68.7594985962-139.7625732422
-62.6146888733-141.3687896729
-56.8930206299-142.5518493652
-51.4990196228-143.4072265625
-46.3697395325-143.9978790283
-41.4610023499-144.3680114746
-36.740398407-144.5500030518
-32.1833190918-144.5684661865
-27.7705059052-144.4426574707
-23.4866008759-144.1879425049
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-11.2934436798-142.7652587891
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-3.6289083958-141.3525543213
0.0832200348-140.5260772705
3.7217950821-139.6260223389
7.2909564972-138.6565856934
10.7943534851-137.6213684082
14.2352142334-136.5236053467
17.6164131165-135.3661956787
20.9405155182-134.1516723633
24.2098255157-132.8823699951
27.4264068604-131.560333252
30.5921192169-130.1874389648
33.708656311-128.7653656006
36.7775306702-127.2956314087
39.8001365662-125.779624939
42.7777175903-124.2185897827
45.7114143372-122.6136856079
48.6022567749-120.9659118652
51.4511795044-119.2762298584
54.2590332031-117.5454711914
57.0265846252-115.7744140625
59.754524231-113.9637451172
62.4434890747-112.1140975952
65.0940246582-110.2260284424
67.7066421509-108.3000335693
70.2817687988-106.3365478516
72.81980896-104.335975647
75.3210830688-102.2986450195
77.7858963013-100.2248458862
80.2144775391-98.1148223877
82.6070175171-95.96875
84.9636764526-93.7868041992
87.2845535278-91.5690689087
89.5697097778-89.315612793
91.8191680908-87.0264587402
94.0328979492-84.7015762329
96.2108383179-82.3409118652
98.3528747559-79.9443359375
100.4588623047-77.5117111206
102.5285873413-75.0428314209
104.5618209839-72.5374526978
106.5582580566-69.9952774048
108.5175552368-67.4159698486
110.4393310547-64.7991333008
112.3231277466-62.1443214417
114.1684417725-59.4510192871
115.9747009277-56.7186737061
117.7412872314-53.9466438293
119.4674835205-51.1342315674
121.1525192261-48.2806625366
122.795539856-45.3850708008
124.3955917358-42.4465141296
125.9516296387-39.4639511108
127.4625244141-36.4362258911
128.9269866943-33.3620834351
130.3436431885-30.2401218414
131.7109222412-27.0687961578
133.0271453857-23.8464069366
134.290435791-20.5710697174
135.4986724854-17.2406921387
136.6495361328-13.8529443741
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144.222457885723.9602890015
144.46339416528.2579631805
144.573867797932.6861038208
144.538162231437.2604484558
144.3364410442.0007743835
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141.212158203163.2795143127
139.550384521569.479888916
137.283264160276.2856292725
134.08369445884.0237884521
129.111694335993.5344009399
x (mm)
x' (mrad)
Data filter ellipse
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Filter ellipse size (mm mrad)
rms emittance of enclosed distribution (pi mm mrad)
RMS emittance of enclosed distribution
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Filter ellipse size (mm mrad)
Fraction of current enclosed
Enclosed current fraction versus filter ellipse size
0
0
0
0
0
0
0
0
0
0
0
0
0
Filter ellipse size (mm mrad)
1-Fraction of current enclosed
Enclosed current versus filter ellipse size
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Fraction of Beam
Beam emittance (pi mm mrad)
Intensity - emittance plot
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Percent from max
Beam emittance (pi mm mrad)
Intensity - emittance plot
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Fraction of Beam
Beam emittance (pi mm mrad)
Intensity - emittance plot
0
0
0
0
0
0
0
0
0
0
0
0
0
0
Filter ellipse size (mm mrad)
External current density
External current density versus filter ellipse size
9.68782329564.806043148
11.25173568732.9507362843
12.27216339111.6389143467
13.06104087830.5586423278
13.7111034393-0.3828147948
14.2652482986-1.2283535004
14.7475547791-2.0020546913
15.1731653214-2.7190599442
15.5523462296-3.3896348476
15.8924407959-4.0211248398
16.1989250183-4.6190037727
16.4760074615-5.1874818802
16.7270126343-5.7298803329
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17.1610012054-6.746658802
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17.5171527863-7.6855998039
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18.4443511963-11.5267429352
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18.3558254242-14.3521623611
18.3025035858-14.5902357101
18.2417469025-14.8208723068
18.1736660004-15.0441865921
18.0983657837-15.2602806091
18.0159358978-15.4692459106
17.9264583588-15.6711626053
17.8300037384-15.866101265
17.7266311646-16.0541229248
17.6163921356-16.2352809906
17.4993343353-16.4096164703
17.3754863739-16.5771636963
17.2448787689-16.7379512787
17.1075286865-16.8919944763
16.9634437561-17.0393047333
16.8126296997-17.1798839569
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16.4907722473-17.4408149719
16.3196926117-17.561132431
16.1418113708-17.6746444702
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15.7654695511-17.8810920715
15.5669050217-17.9739227295
15.361328125-18.0597400665
15.1486616135-18.1384677887
14.92882061-18.2100200653
14.7017068863-18.2743015289
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14.2252197266-18.3806037903
13.9755916595-18.4223690033
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12.3080511093-18.5031967163
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11.6823453903-18.4602813721
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10.3118267059-18.2553405762
9.9419794083-18.1768875122
9.5602254868-18.0865287781
9.1659431458-17.9836406708
8.758430481-17.8675231934
8.3368902206-17.7373771667
7.9004125595-17.5922927856
7.4479494095-17.431224823
6.9782862663-17.2529563904
6.4900035858-17.0560684204
5.9814243317-16.8388824463
5.450545311-16.5993976593
4.8949379921-16.3351860046
4.3116154671-16.043258667
3.6968307495-15.7198677063
3.0457737446-15.3602056503
2.3520932198-14.9579200745
1.6070957184-14.50431633
0.7983109355-13.9869260788
-0.0933241472-13.3866863251
-1.0997651815-12.6716394424
-2.2830405235-11.7797584534
-3.8024992943-10.5516939163
x (mm)
x' (mrad)
RMS data ellipse
0
0
0
0
0
0
0
0
0
0
0
0
0
0
ln(1/1-f)
Beam emittance (pi mm mrad)
Intensity - emittance plot
a=-1.2699999809-4.462135791800-0.1289970279-0.19220781336.79699993136.796999931300.2000000030.4000000060.60000002380.800000011911.20000004771.39999997621.60000002381.800000071522.20000004772.40000009542.60000014312.799999952333.20000004773.40000009543.60000014313.799999952344.20000028614.40000009544.59999990464.800000190755.20000028618.20000076298.40000057228.60000038158.800000190799.20000076299.40000057229.60000038159.80000019071010.200000762910.400000572210.600000381510.80000019071111.200000762911.400000572211.600000381511.80000019071212.200000762912.400000572212.600000381512.80000019071313.200000762913.400000572213.600000381513.80000019071414.200000762914.400000572214.600000381514.800000190715
b=0.0500000007-4.372793197600-0.1289970279-3.19220781336.54300022136.5430002213-41.000.00499999990.02899999920.02400000020.02899999920.0049999999000000000000000.009999999800.02400000020.00999999980.03400000180.01499999970.0099999998000000000000000000000000000000000000
g=52.2579994202-4.283450603500-0.12899702792.80779218675.98099994665.9809999466-38.0000.01999999960.02400000020.03400000180000000000000.014999999700.019999999600.00999999980.01499999970.00499999990.02400000020.00999999980.02400000020.004999999900000000000000000000000000000000000
e=400-4.194108009300-0.1289970279-6.19220781335.65399980555.6539998055-35.000.04899999870.03900000080.03900000080.02400000020.02400000020000000000.00499999990.03400000180.07299999890.05900000040.0240000002000.01999999960.0199999996000.00499999990.024000000200000000000000000000000000000000000
-4.104765415200-0.1289970279-9.19220733645.06300020225.0630002022-32.000.15600000320.16099999850.12700000410.09799999740.10700000080.12200000140.05400000140.07299999890.07299999890.09799999740.09799999740.11200000350.09799999740.13199999930.14200000460.16099999850.14599999790.20499999820.12200000140.004999999900.00499999990.00499999990.02899999920.01499999970.00999999980.004999999900000000000000000000000000000000000
-4.01542282100-0.12899702795.80779218674.95599985124.9559998512-29.000.26399999860.28299999240.2489999980.2489999980.23899999260.22900000210.20499999820.24400000270.26399999860.34200000760.37599998710.44400000570.44400000570.45399999620.48300001030.4000000060.43000000720.78600001340.43000000720.189999997600.02899999920.004999999900.03400000180.01499999970.014999999700000000000000000000000000000000000
-3.926079988500-0.328997016-3.19220781334.55100011834.5510001183-26.000.21999999880.20999999340.21999999880.21999999880.20499999820.20499999820.1759999990.16099999850.24400000270.31700000170.38100001220.44400000570.52200001480.570999980.67400002480.77100002770.87400001291.23000001910.98100000620.85900002720.136999994500.01499999970.02400000020.004999999900.014999999700000000000000000000000000000000000
-3.836737155900-0.1289970279-12.19220733644.49700021744.4970002174-23.000.12200000140.16099999850.1759999990.20999999340.18099999430.16599999370.13699999450.14200000460.16599999370.24400000270.27799999710.37599998710.40500000120.45899999140.54699999090.67400002480.86900001761.34300005441.72399997711.8070000411.05999994280.01499999970.02400000020.01999999960.00499999990.0240000002000000000000000000000000000000000000
-3.7473943233000.0710029602-0.19220781334.36000013354.3600001335-20.000.10700000080.12700000410.13699999450.13699999450.13699999450.14200000460.12700000410.13199999930.15600000320.21500000360.24400000270.28799998760.33700001240.38600000740.45899999140.54699999090.81999999281.25999999052.15799999242.53900003431.97300004960.66900002960.01999999960.00499999990.009999999800.014999999700000000000000000000000000000000000
-3.658051490800-0.328997016-0.19220781334.34600019454.3460001945-17.000.09300000220.11200000350.12200000140.10700000080.13199999930.13699999450.13199999930.12200000140.16099999850.18099999430.20999999340.24400000270.28799998760.34700000290.4000000060.50800001620.73699998861.36199998862.45600008963.06200003622.08500003811.22599995140.26399999860.01999999960.02400000020.00999999980.024000000200000000000000000000000000000000000
-3.568708658200-0.12899702798.80779266364.30200004584.3020000458-14.000.08799999950.10300000010.10300000010.12200000140.13699999450.12200000140.16099999850.18099999430.1759999990.1759999990.1759999990.21999999880.29300001260.32699999210.39100000260.48300001030.75199997431.47000002862.75900006293.05200004581.82599997520.93699997660.26399999860.03900000080.01999999960.02400000020.028999999200000000000000000000000000000000000
-3.479365825700-0.328997016-6.19220781334.2719998364.271999836-11.000.09300000220.10700000080.12700000410.14599999790.13699999450.13699999450.14200000460.18999999760.18600000440.23899999260.21999999880.20999999340.27799999710.32199999690.4000000060.54199999570.92799997331.84599995613.29099988943.04200005531.25999999050.43900001050.2000000030.04399999980.024000000200.028999999200000000000000000000000000000000000
-3.390022993100-0.1289970279-15.19220733644.1110000614.111000061-8.000.07800000160.11200000350.15099999310.15600000320.16599999370.14599999790.15099999310.1759999990.2000000030.25400000810.25400000810.28799998760.28799998760.35600000620.53200000520.76200002431.42100000382.85199999813.74000000952.98300004011.10399997230.36599999670.09799999740.04399999980.00499999990.0099999998000000000000000000000000000000000000
-3.3006801605000.07100296022.80779218673.94000005723.9400000572-5.000.02899999920.02400000020.10700000080.1759999990.18099999430.21500000360.21500000360.25900000330.23899999260.30799999830.33700001240.40999999640.48300001030.59600001570.92299997811.40600001812.73399996763.97000002864.10599994662.45099997520.98600000140.36100000140.09300000220.03900000080.05900000040.00499999990.014999999700000000000000000000000000000000000
-3.21133732800-0.1289970279-18.19220733643.82800006873.8280000687-2.000.01999999960.02400000020.01499999970.0630000010.15099999310.21999999880.29300001260.30300000310.34200000760.40500000120.47900000210.58600002530.82499998811.21099996572.37299990653.59899997714.99499988565.05900001533.751.74800002570.79100000860.33700001240.12200000140.01999999960.039000000800.019999999600000000000000000000000000000000000
-3.121994495400-0.3289970162.80779218673.81800007823.81800007821.000.00999999980.00499999990.014999999700.05400000140.05900000040.18099999430.30799999830.46900001170.57599997520.82999998330.94700002671.32799994952.05599999433.05699992184.09200000765.28299999245.3610000613.68199992181.68900001050.77100002770.29800000790.09300000220.04399999980.02400000020.01999999960.014999999700000000000000000000000000000000000
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