Belle. Belle- KCG Seminar Feb. 7, 2002

Transkript

1 - KCG Seminar Feb. 7, 22

2 ' # & % %#$ "! #! ) # % ' "! # "( -,+ * 67 1/. 1/48 Inroducion Moivaion SVD1. was killed by he synchroron radiaion (SR) rom HER. Limiaion or he HER seering magnes Some curren values are close o he limis. ( igure) Smaller-radius IR beampipe ( 2. cm 1.5 cm 1. cm?) Larger beam currens or higher luminosiies more SR A new idea has been proposed by Hioshi Yamamoo: Fiing BPM-measured values Real beam orbi Waage disribuion in he IR Online alarm or SR or he HER seering magnes or deecor damages

3 1/. 2/48 In he HER Sraigh Secion kick angle on Jan. 28 (22) Max. allowed angle Kick range or 1<r<2cm 2 Kick Angle [mrad] QCSL QC1LE QC2LE BC1LE ZHQC2LE BH2LE BH1LE BC3LE QC3LE ZHQC3LE ZVQC3LE QC4LE BH3LE ZVQC4LE QC5LE BH4LE BH5LE QA2LE QA3LE QA4LE QA5LE QA6LE QA7LE ZVQC5LE s [m] -,+ *

4 8 -,+ * 67 1/. 3/48 Calculaion Mehod [I] Orbi Calculaion In he HER sraigh secion (see ) Using a linear approximaion ranser marices Implemened in my own program HER Sraigh Secion (~1m) e BSWTLE QA6LE QA7LE QCSL QC1LE QC2LE IP

5 R E R H H E b E Q Q q R Wn[ H Wn[ q Wn[ m Wn[ Q R H U? xwv ~ b b Q B ] ] d ` ˆ m 1/. 4/48 Transer Marices e B C N SJSJSJSKSMT e IJIJIJIKIML E F Be cd ]_â` [Z\? Y V>XW U = : SJSJSJSKSMT E OB C N B C P OB C P IJIJIJIKIML EGF BDC A <=>@? 9;: E Bo e =sr W o5p E Bo e E Bo e SKSJSJSJSKT E Bo e u =sr W op E Bo e u E Bo e =sr o W IKIJIJIJIKL F^ ]kjl U i? gh E Bo e u E Bo e u =sr o W E } Be cd ]_â` SMSKSJSJSJT ƒ IMIKIJIJIJL Es~ } Be cd ]_â` F ^ ]_y@z{ ŽE B5 ~ ^ ]kjl ŽEs~ d ` F ]ƒ z U i? gh \ -,+ *

6 -,+ * 67 1/. Check o he Transer-Marix Implemenaion [1] 5/48 x [mrad] Jus aer BSWTLE α = 1.9, β = 18.8 m, ε = 1.8E-8 m βx 2 + 2αxx + γx 2 = ε x [cm] Beam Orbis (HER) 2 βε (envelope rom he design) / 32 Consan Mean.3386E E-2 Sigma E-2 βε =.16 mm BSWTLE x [cm] -1.5 QA7LE QA6LE QA5LE QA4LE QA3LE QA2LE BH4LEBH5LE QC5LE QCSL QC1LE QC2LE ZHQC2LE QC4LE BH3LE QC3LE ZHQC3LE BH2LEBH1LE s [m] x (IP) [mm] > IP y [mrad].4.2 Jus aer BSWTLE α = -2.61, β = 17.3 m, ε = 3.6E-1 m βx 2 + 2αxx + γx 2 = ε y [cm] Beam Orbis (HER) 2 βε (envelope rom he design) / 42 Consan Mean.596E E-1 Sigma E-1 βε = µm y [cm] QA7LE QA6LE QA5LE QA4LE QA3LE QA2LE QC5LE ZVQC5LE QCSL QC1LE QC2LE BC1LE QC4LE ZVQC4LE QC3LE ZVQC3LE BC3LE s [m] y (IP) [µm]

7 -,+ * 67 1/. 6/48 Check o he Transer-Marix Implemenaion [2] Numerical comparison wih SAD on QC3LE In[61]:= TranserMarix["QC3LE","LX86E.1"] Ou[61]:= { , ,, E-16} { , , E-18,} { E-17, E-16, , } { E-18, E-17, , } Ÿ E B œ œ E B

8 Ÿ -,+ * 67 1/. 7/48 Check o he Transer-Marix Implemenaion [3] Numerical comparison wih SAD on QKELE In[62]:= TranserMarix["QKELE","LC51LAE"] Ou[62]:= { , , , E-4} { E-5, , , } { , E-4, , } { , , E-5, } Ÿ E B œ œ E B Ÿ Ÿ

9 ««È ³ Å Ä Ò ä Ü Ò ä Ü Ü Ü Ò æ Ù å Ô Ý Ý Ô Ô Ô ô ô q q ë ø ø ê ö ö q q E îí ì îí ì ì ö ö 1/. 8/48 [II] Orbi Fiing ¼½»º ¹ Ǵµ ³² ± ª«Inpu parameers: ÆDÇ Ã ¾ ¾À ÂÁ ÉËÏÐ, Ê ÉËÊÍÌ Floaing parameers: Î ÐÏ ÎÊ Ê Ì áâã Û Þà ÛÐÖ ØÚæ áâã ÛßÞà ÛÐÖ ØÚÙ çéè ÒÓÑ ÐÖ ÔÍÕ Minimizaion using MINUIT 7.ï ø ëõñ 7.ñ ö 7.ñ ø ëõï 7.ï ö ëðñ ê ëðï ê E Bò îí Bó 7.ñ ø 7.ï ø -,+ *

10 ù ú ù ü ü } û 1/. 9/48 Fiing Example m (including ose uncerainies) BPM resoluion: 1 Daa on Nov. 7 (21) VERTICAL HORIZONTAL 2 2 BPM measuremens 1.5 BPM measuremens 1.5 Ÿ È Ã ÿ üþý } û ó 1 y [cm] È Ã ÿ üþý } û ò 1 x [cm] QCSL QC1LE QC2LE BC1LE BC2LE BC3LE QC3LE ZVQC3LE QC4LE ZVQC4LE -1.5 QCSL QC1LE QC2LE ZHQC2LE BH2LE BH1LE QC3LE ZHQC3LE QC4LE BH3LE QC5LE BH4LE BH5LE QA2LE QA3LE QA4LE QA5LE QA6LE QA7LE QC5LE ZVQC5LE QA2LE QA3LE QA4LE QA5LE QA6LE QA7LE -2-2 s [m] s [m] ÿ üþý mm & º Failure wih Need Some Ose Correcions! -,+ *

11 ë " 7 ò! ò ë " 7 ó! ó $ ë E ' 1/. 1/48 Ose Deiniion Quadrupole x (BPM) x (QUAD) + x (BPM) (QUAD) BPM x Desgin orbi s ò ò ë êf # ó ó &% B -,+ *

12 ? < A;? > < > > > < > :=< :;< /. 11/48 Ose Deerminaion Using BETARAW sample: one o he ollowing six ses o seering magnes ON 2 5. *4 )( / 5. *4 )( 2 3. *+, )( / 3. *+, )( 2.- *+, )( /.- *+, )( 2. *46 ( /. *46 ( 2 3. *1, ( / 3. *1, ( 2.- *1, ( /.- *1, ( m m,?@< ; m, m, m, m, 78 An oscillaion around he original orbi Six dieren orbis are obained. Orbi beore he kick HER BPMs BPM number rom IP Deviaion rom he Original Orbi [mm] -,+ *

13 ù ö Á ö J µ V Á V ù ù E NM BL È K K o o -,+ * 67 1/. 12/48 Floaing Parameers Saring and ending poins o orbis: BC DFE Ÿ Á Á Á Á BC HG Oses o BPMs and QUADs Scales o bendings: o &O ÃP RQ Å ³ IÆ EU T BS o &O I we loa all, 1 loaing parameers Large oses ( 1 cm) Muli-soluion No posiive-deinie Hessian marix Common among all he orbis Global Fi

14 ab on k lm ^] ZY XW hg _ ` j ced s p rq wvu - xyz { Sraegy Fiing Parameers [\ BPM oses(1) QUAD oses(11) BEND scales (5or6) or 1 loaed; Ohers ixed. or 1 loaed; Ohers ixed. or 1 loaed; Ohers ixed. Global Fis or All he Combinaions Crieria Choose he bes χ 2! 13/48 ij

15 ij hg ab ` _ on k ^] [\ ZY XW } } } } } ƒ ƒ s rq p { wvu ced j lm 14/48 Crieria MINUIT convergence wih a posiive-deinie Hessian marix BPM oses QUAD oses }~ }~ 1 cm BEND rescaling acor } ~ mm 1 cm (alignmen) }~ } ~ 2% (kick angle) mm We ind a soluion Wih he smalles modiicaion Wihin he scope o he numerical approach - xyz

16 on ^] ZY ˆ Ÿ œ œ œ œ œ œ wvu j lm k ij hg ab ` _ [\ 15/48 ced BETARAW sample on Jun. 4, 21 Horizonal loaing BPM M6QC4LE M6QC4LE M6QC4LE M6QC4LE loaing QUAD QC2LE QC2LE QC2LE QC2LE loaing BEND BH12LE BH45LE ZHQC5LE Ž œ œ œ Ÿœ œ Ÿœ œ Ÿ œ [mm] BPM ose œ Ÿœ œ Ÿœ œ Ÿœ œ Ÿœ [mm] QUAD ose [%] BEND scale œ Ÿœ œ œ œ Ÿœ œ œ IP ose [mm] œ œ œ œ œ œ œ œ M5QC3 ose [mm] Ÿ œ œ œ œ Ÿ œ œ œ œ M8QA2 ose [mm] s rq p { xyz -

17 on ^] ˆ «œ œ œ wvu j lm k ij hg ab ` _ ª 16/48 ced BETARAW sample on Jun. 4, 21 Verical «««loaing BPM M2QC1LE M2QC1LE M3QC2LE loaing QUAD QA2LE QA2LE QA2LE loaing BEND ZVQC3LE ZVQC5LE ZVQC5LE œ œ Ž œ œ Ÿ œ œ Ÿ œ Ÿœ [mm] BPM ose œ œ œ œ œ œ [mm] QUAD ose Ÿ [%] BEND scale œ œ œ œ œ œ IP ose [mm] œ œ œ œ M5QC3LE ose [mm] œ œ œ œ œ Ÿ œ M8QA2LE ose [mm] s rq p { xyz -

18 on ^] ˆ œ œ œ wvu j lm k ij hg ab ` _ ª 17/48 ced BETARAW sample on Oc. 24, 21 Horizonal loaing BPM M6QC4LE M6QC4LE M6QC4LE loaing QUAD QC2LE QC2LE QC2LE loaing BEND BH12LE BH45LE Ž œ œ œ œ œ Ÿœ [mm] BPM ose œ œ œ œ œ œ [mm] QUAD ose Ÿ [%] BEND scale œ œ œ œ œ œ IP ose [mm] œ Ÿ œ œ Ÿ œ œ œ M5QC3LE ose [mm] œ œ Ÿ œ œ œ M8QA2LE ose [mm] s rq p { xyz -

19 on ^] ˆ œ œ wvu j lm k ij hg ab ` _ ª 18/48 ced BETARAW sample on Oc. 24, 21 Verical «««loaing BPM M2QC1LE M2QC1LE M2QC1LE loaing QUAD QA2LE QA2LE QA3LE loaing BEND ZVQC3LE ZVQC5LE ZVQC5LE œ œ œ Ž Ÿ œ œ Ÿ œ œ Ÿ œ œ [mm] BPM ose œ œ œ Ÿœ œ Ÿ Ÿœ [mm] QUAD ose [%] BEND scale œ Ÿœ œ Ÿœ œ Ÿœ IP ose [mm] œ œ œ œ M5QC3LE ose [mm] œ œ œ œ œ œ M8QA2LE ose [mm] s rq p { xyz -

20 on ^] ˆ ¾ ¾ º» wvu j lm k ij hg ab ` _ ª 19/48 ced Resuls o he Ose Correcion (Horizonal case) HORIZONTAL HORIZONTAL 2 2 BPM measuremens BPM measuremens W/ he Ose Correcion W/O he Ose Correcion ƒ½» ¹ ± ¼ ¹º» µ 1 ½ƒ ± À µ ±³² 1 x [cm] ¼ º» ±³² QCSL QC1LE QC2LE ZHQC2LE BH2LE BH1LE QCSL QC1LE QC2LE ZHQC2LE BH2LE BH1LE QC3LE ZHQC3LE QC4LE BH3LE QC5LE BH4LE BH5LE QA2LE QA3LE QA4LE QA5LE QA6LE QA7LE QC3LE ZHQC3LE QC4LE BH3LE QC5LE BH4LE BH5LE QA2LE QA3LE QA4LE QA5LE QA6LE QA7LE s [m] s [m] x [cm] s rq p { xyz -

21 on ^] ˆ ¼ ¾»» wvu j lm k ij hg ab ` _ ª 2/48 ced Resuls o he Ose Correcion (Verical case) VERTICAL VERTICAL 2 2 BPM measuremens BPM measuremens W/ he Ose Correcion W/O he Ose Correcion º Ã½» ¹ ± ¹ Â Âº µ ±³² Á 1 ½ƒ ± Ä µ ±³² Á 1 y [cm] ½» QCSL QC1LE QC2LE BC1LE BC2LE BC3LE QC3LE ZVQC3LE QC4LE ZVQC4LE QCSL QC1LE QC2LE BC1LE BC2LE BC3LE QC3LE ZVQC3LE QC4LE ZVQC4LE QC5LE ZVQC5LE QA2LE QA3LE QA4LE QA5LE QA6LE QA7LE QC5LE ZVQC5LE QA2LE QA3LE QA4LE QA5LE QA6LE QA7LE s [m] s [m] s rq p y [cm] { xyz -

22 on ^] ˆ Ì Ñ Ù Ç Ñ Í û ð ø ê ö ô à ðá î î ù wvu j lm k ij hg ab ` _ ª 21/48 ced [III] Waage Calculaion Using he ollowing analyical ormula (Phys. Rev. 75 (1949) 1912) : ÉÈ Ý ÛÞ Ü Ý ÛÚ Ù Ü Ø ÅÔ ÅÓ ÅÒÑ ÐÏÎ ÅÆ ß Ñ ËÊ ÑÖÕ ý ÿ ýþ øü õ ô&õ ó íåæ åñò ä ç ãäïî êìëí çéè åæ âfãä àá ðú φ φ ψ ψ s rq p { xyz -

23 on ˆ Ì Ø Ñ Æ Ù Î Ç Ñ Í wvu j lm k ij hg ab ` _ ^ ª 22/48 ced s φ ρ ß Ñ ÉÈ Ý Þ Ü Ý Ù Ú Ü Ô Ñ ËÊ Ñ Õ 3D-inegraion is perormed using BASES. (MC inegraion) s rq p { xyz -

24 on ˆ! wvu j lm k ij hg ab ` _ ^ ª 23/48 ced Projecion o a Plane s orbi ψ angen poin in he plane Mapping: s rq p { xyz -

25 ab ` _ ^ on k ij hg ª ˆ " ¹ s rq p { wvu ced j lm 24/48 Check o he Waage Calculaion by comparing wih he SAD calculaion Sar wih he same laice model ile (/ldaa/kekb/kcg/her/herq27.sad) For a cerain componen (e.g. QC3LE) My Calculaion SAD Waage disribuion in he plane a # cm - xyz

26 on ˆ 4 + ƒ A J 8 I O Â < O ^ $ Æ + Ç Í wvu j lm k ij hg ab ` _ ^ ª 25/48 ced Exac Calculaion using SAD R saring wih he Feynman-Heaviside ormula $ 1 3 $( $(1 2, Ê-/. Ç + $('*) $&% x τ (, r q =?>@ N 5ML 8 =K G : *H G 5 9: F 5 6 ; 59: 576 CED =B> 5 8L &P Poyning vecor: QSR ÌZY\[] X Ï +W $ ' ) $VU T R s rq p { xyz -

27 on ˆ e d : : wvu j lm k ij hg ab ` ` _ ª 26/48 ced Example o My Calculaion on QC3LE cm acb a Y [mm] Waage [W/mm 2 ] X [mm] X [mm] Y [mm] : coordinae sysem " s rq p { xyz -

28 ij hg ab ` ` _ on k ª ˆ p ù øs p o î ø øs o î s rq p { wvu ced j lm 27/48 x w å vu s lmn k j hgi x w å vu s nrq lmn k j hgi Y = 12 mm AND Z = -8 mm Y = 12 mm AND Z = -8 mm Waage [W/mm 2 ] T. Abe SAD Waage [W/mm 2 ] T. Abe SAD 4.7 W X [mm] X [mm].85 W (T.Abe) (T.Abe) 4. W (SAD) Waage [W/mm 2 ] X = -17 mm AND Z = -8 mm T. Abe SAD Waage [W/mm 2 ] X = -17 mm AND Z = -8 mm T. Abe SAD.75 W (SAD) Y [mm] Y [mm] - xyz

29 ab ` ` _ on k ij hg ª ˆ y ~ } s rq p { wvu ced j lm 28/48 Conclusions on he Waage Calculaion My geomery calculaion is successul. Good agreemens on disribuions Small dierences on!{z disribuions: higher han SAD resuls or z kev. - xyz

30 on ˆ ƒ ± ~ O Ä ½ Â O» O ƒ ƒ» O ƒ ƒ» Ž j lm k ij hg ab ` ` _ ª 29/48 ced HER SR ( ::) Z = 8 cm ma À ½¹ 2 kev ½ƒ 6 ZVQC4 1 Y [mm] ƒ ˆ BH12LE Magne Waage HER mask LER mask ƒ ½» BC1LE QC1LE BC1LE ZHQC5 I ½ƒ ½» BH1LE -1 I ½ƒ BH2LE I ½ƒ O ¾ º» ZVQC4-2 I ½ƒ O ¾ º» ZHQC5 I ½ƒ QC1LE I ½ƒ QC2LE X [mm] / -

31 ³ ¹º µ ¾ Ã À Ä Ë Ê º É Ìº Æ Ï Ê º Í Æ Ï Ê º Í Æ Ð Ê º Æ Ñ Ê º Æ Ò Ø ²± «ª ` _ Ÿ œ 3/48 HER SR ( ::) Z = cm ma 2 kev»½¼ ZVQC4 1 Y [mm] º Å Â Á BH12LE Magne Waage HER mask LER mask ºÇÆ BC1LE QC1LE BC1LE ZHQC5 È?É ºÇÆ BH1LE -1 Ë Ê º BH2LE Î É ZVQC4-2 Î É ZHQC5 É QC1LE É QC2LE X [mm] ÔÓÕ Ö / -

32 Û ç ç Ý æ Ý É Ü Ü Á éè Á éè ïþ Ü Ò òø ²± «ª Ú Ù Ÿ œ 31/48 Error Esimaion ose uncerainies are esimaed. Errors on he BPM resoluions Using he daa on Nov. 7 (21) a 1:PM ãëìí à ß Ã*Þ ãäå áâ ¾ à ß Ã*Þ I êâ ê à ß ñã*þð. Ý/î so ha ÔÓÕ Ö ö óô/õ -

33 Ú Ù Ÿú ùø Ò ö òø «ª ²± 32/48 The values a he aserisks are used. One-σ Conour One-σ Conour X ini [mm] Y ini [mm] X IP [mm] Y IP [mm] ÔÓÕ Ö óô/õ

34 ùø Ÿú Ù Ú «ª ²± 33/48 Posiion Errors or Ä û üý þ ÿ ¾ ê û ã ç ß û ß ã ç ß û ß Ä ýü þ ÿ ¾ ê ã ç ß û ß ã ç ß û ß Ò ÔÓÕ Ö òø óô/õ ö

35 û À Ì Í Ò òø ²± «ª Ú Ù ú ùø 34/48 1 E γ > 1keV & Waage > 1E-16W mm ºÇÆ <Xmask > [mm] QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE 1 E γ > 1keV & Waage > 1E-16W.5 mm ºÇÆ À -.5 <Ymask > [mm] QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE -1 ö ÔÓÕ Ö óô/õ

36 ²± «ª Ù Ú ùø ú òø 35/48 Horizonal Posiion Sysemaics (1) X QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö ö óô/õ

37 ²± «ª Ù Ú ùø ú òø 36/48 Horizonal Posiion Sysemaics (2) X QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö ö óô/õ

38 ²± «ª Ù Ú ùø ú òø 37/48 Verical Posiion Sysemaics (1) Y QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö ö óô/õ

39 ²± «ª Ù Ú ùø ú òø 38/48 Verical Posiion Sysemaics (2) Y QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö ö óô/õ

40 ²± «ª Ù Ú ùø ú òø 39/48 QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE Waage [W] Waage Errors on Eγ > 1keV & Waage > 1E-16W W/W Ò ÔÓÕ Ö ö óô/õ

41 ²± «ª Ù Ú ùø ú òø 4/48 QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE Waage [W] Waage Errors on Eγ > 1keV & Waage > 1E-16W W/W Ò ÔÓÕ Ö ö óô/õ

42 ²± «ª Ù Ú ùø ú òø 41/48 Waage Sysemaics (1) W / W +1% 1% QC1LE +1% 1% QC2LE +1% BC1LE 1% +1% 1% +1% 1% +1% 1% +1% 1% ZHQC2 BC3LE BH1LE BH2LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö ö óô/õ

43 ²± «ª Ù Ú ùø ú òø 42/48 Waage Sysemaics (2) W / W +1% 1% QC3LE +1% 1% ZVQC3 +1% BH3LE 1% +1% 1% +1% 1% +1% 1% +1% 1% ZVQC4 ZHQC5 BH4LE BH5LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö ö óô/õ

44 ²± «ª Ù Ú ùø ú òø 43/48 QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE Waage Errors on 1.5 Eγ > 1keV & Waage > 4E-2W Waage [W] W/W ö óô/õ Ò ÔÓÕ Ö -

45 ²± «ª Ù Ú ùø ú òø 44/48 QC1LE QC2LE BC1LE ZHQC2 BC3LE BH1LE BH2LE QC3LE ZVQC3 BH3LE ZVQC4 ZHQC5 BH4LE BH5LE Waage Errors on 1.5 Eγ > 1keV & Waage > 4E-2W Waage [W] W/W ö óô/õ Ò ÔÓÕ Ö -

46 ²± «ª Ù Ú ùø ú òø 45/48 Waage Sysemaics (1) ( kev) W / W +1% 1% QC1LE +1% 1% QC2LE +1% BC1LE 1% +1% 1% +1% 1% +1% 1% +1% 1% ZHQC2 BC3LE BH1LE BH2LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö - ö óô/õ

47 ²± «ª Ù Ú ùø ú òø 46/48 Waage Sysemaics (2) ( kev) W / W +1% 1% QC3LE +1% 1% ZVQC3 +1% BH3LE 1% +1% 1% +1% 1% +1% 1% +1% 1% ZVQC4 ZHQC5 BH4LE BH5LE IP consr. 2nd wih Q 1s wih Q 3rd χ 2 2nd χ 2 Ò ÔÓÕ Ö - ö óô/õ

48 Ú Ù ú ùø ¾ Å Í º º º ¾ Î Ì Ò ö òø «ª ²± 47/48 Summary Mehods o he real orbi and waage calculaions have been esablished. Waage disribuions in he IR My program has been checked comparing wih he SAD resuls boh on he orbi and waage calculaions. Error esimaions have been also done: : or or» ¼»½¼ mm kev, kev ÔÓÕ Ö - óô/õ

49 Ú Ù ú ùø Ã Í Ò ö òø «ª ²± 48/48 Fuure Works For online monioring Calculaion speed: Inpu parameers (BPM, sec (i & MC-inegraions) ) are already available rom he NSM. OK Beam size Transormaion o he corresponding radiaion dose Inerace o EGS4 o be implemened no ye Improvemen o he ose deerminaion algorihm Based on he curren mehod To reduce he waage errors More undersanding on he real orbi calculaion is needed. ÔÓÕ Ö óô/õ