User's Guide for New MOSES Version 2.0
Contents
1. 10 30071 lt lt lt QOHI3W 015834510 gt gt gt vu young Jo uo 12unj se snN xnN nN Jo 0 0000670 0935 02714761 88 80 61 5350 20 andu ajdwes Av 5 JO W3180Hd 262. 00 300 t lt lt lt GOHLIW 1VH931N 015834510 JHL gt gt gt 3u8J4no uounq yo UO 30Unj se snN xnN nN 40 1264 je y 20 00005 0 duds 02718761 88 60 61 53500 203 e3ep Indu ejdues Av S HO JO 1 2 MH18OHd e ex 20 300 2 20 30072 20 30071 970 10 30071 1 1 HH HHH HHH HH HH 4 1 i l 1 i 20 300 6 HH 1 i 1 I D 1 i i 1 1 1 1 1 1 POE RARER TEARS RN AE HEH HE MAESEM 7 SE EN MAE IEA MAE AEA HME NE 0 0 1 1 j i t I l i I 1 l 1 t I 1 I 1 I 1 i i 20 300 6 1 1 HHH 1 1 1 HH HH 1 1 HH HHH 1 4 10 10071 young 30 uo 30unj e se snN xnN nN JO Jued 07
3. HE HF HF HF HF HF A HF E HF 10 3692 0 6671 10 3692 6671 01 3171 0 01 18 87 62270 610070 66t0 2 0000 00t 10 3 h 96 1 10 3 8 0 9671 21 2 11 36217 28270 640070 659722 0000 082 10 3805 0 671 10 3801 6 1 01 166970 89 2 01 3952 0 16270 610070 ce 0000 092 10 3191 0671 10 3191 0 0671 60 3212 9 2 11 3896 0 10 0 6100 0 0628712 0000 0t 10 3806 0 198 1 10 3805 1871 11 358 70 09 2 01 32617 11 0 610070 886712 0000026 10 39 lt 6 8 1 10 396 0 871 10 3121 65 2 1 LR ET0 2 70 610070 ett6 0c 0000 00 L0 3 56 0 8 71 10 3646 8L i 10 3 82 10 3648270 60 3901 11 316270 610070 6296722 0000 962 9671 96 i 172 82 0 8671 8671 91 2 120 10 3462 70 10 1 66 01 342670 01 311170 610070 9696722 000079 lt 671 6 1 19 2 62 0 10 302t 10 3021 0 01 3528 0 21 19217 610070 1291722 000096 10 267870 10 36 4 60 3181 1t 3c9 0671 0671 5972 80570 610070 1651712 0000 9 10 3815 10 361670 01 31 970 01 3901 9871 9871 66 2 ELE O 610070 6862712 0000791 L0 36 5 0 10 36 6 10 3186 01 3211 610070 1688 02 00007962 10 3286 10 3216 0 2871 2871 65 2 hef 0 8771 98171
4. 7 v w re codo Tx x We gt G ri 25 P By inserting Eq 8 into Eq 25 multiplymg by A v n d r r and integrating over and r we obtain v mv vro c C0840 3 Ma e 26 0 n oolz0 Tf one defines new coefficients m n 2 27 these coefficients have a non trivial solution only if det M B 0 28 where a Mag 29 V is the normalized tune shift E is the mit matrix and B is the matrix with elements nl E N Bo M6416 kt PRI 6 30 For a of a Gaussian distribution aud S of 13 elements of the dispersion matrix are written explicitly as 2S 2 k 1 V k m V 1 1 31 References 1 Y H Chin CERN SPS 85 2 DI MST 1985 2 Besnier D Brandt and B Zotter CERN LEP TH 84 11 1984 3 Y H Chiu CERN SPS 86 2 D MST 1986 2 Brandt J P Delahaye and A Hofman CERN LEP Note 595 1987 CERN LEP Theory Note 60 1988 6 Y Chin CERN SPS 85 9 DI MST 1985 G Besnier Nucl Instru and Methods 164 235 1974 8 B Zotter CERN SPS 81 19 DI 1981 9 M Abramowitz and 1 A Stegun Handbook of Mathematical Functions Dover New York 1965 DC OF ORSAY SAMPLE INPUT DATA FOR MOSES amp MPARM NUS 0 00792D0 ENGY 8D0 56 2 1 00
5. 0 60 340670 01 306270 2971 2971 c 14570 610070 1418781 0000022 10 316670 10 315 ms 60 320 0 01 3 610070 8982791 0000 002 6671 6671 t 2 985 0 10 3282 10 3282 0 60 3228 01 348170 610070 1649741 00007081 gt i gt t tt c 0060 10 342270 0 10 3101 01 3662 0471 0871 8671 610070 0976791 00007091 2671 e i 1072 10 3971 10 397170 60 30 t 2 Sec o 10 38917 01 3202 0 6100 0 1652 02 0000 912 10 312470 10 31265 80 366 0 21 36170 610070 2669761 00007962 10 36447 10 16 470 80 3191 0 01 301 0 171 171 tt 2 1 570 1971 I9 L t c 09 0 610070 1826761 0000 9 2 10 3601 0 10 3601 60 38 670 01 3911 1971 1971 tt 2 180 610070 0297781 00007912 10 39 10 39t 0 80 1 6170 117348170 S l 8471 EE 2 898670 610070 1891781 00007961 10 3012 70 10 30 2 80 36 1 0 01 3062 On be 9871 2 610070 24771 00007971 8 71 gE t gt 10 2 10 3812 0 60 3inl 0 3821 0 610070 Cee at 00007961 0671 0 1 10 2 10 3 9170 10 3 91 60 346170 80 19 1 EU HOL 610070 5092 02 0000 2 2 10 316 2171 10 341670 2471 10 30217 tt c 01 346170 06570 610070 61647761 0000 252 10 3691 0
6. 1 14 re Eb 4 m 25 e ta where is the exponential integral 9 and quM 15 28 Next we solve Eq 1 by Besnier s dispersion matrix method Tn this method we expand not the longitudinal distribution 9 7 but also the transverse distribution f r Using the orthogonal polynomials d r which satisfy 7 6 16 J0 where w rz is the transverse weight function defined by wir 17 with the normalizing factor K f r can be expanded as f r w r Seded 18 0 We expand also the product of 5 and f r in the same orthogonal polynomials S rs fers welts 5 d r 19 where the coefficients 6 are related to the coefficients c by b Nae 20 0 where m 21 JO 11 is called the dispersion matrix The transverse dipole moment D can now be expressed with the coefficients c by inserting Eq 18 into Eq 3 with the result D wr d r ridr 22 7 do If one uses the fact that the lowest polynomial is proportional to 7 dir 23 one finds that only the lowest coefficient in the summation remains Therefore 7 K 24 If we insert Eqs 17 20 and 24 into Eq 1 and notice that is Eq 1 be rewritten as mv gt 7 9 7 P
7. 0172 862170 070 0 0 0 0 970 610070 Lteh Gl 00007021 1271 118 90 2 918 0 6100 0 90007001 070 070 070 970 98171 HOL 668 0 LOE 640070 sein et 0000 08 0 0 171 0 086 70 19870 0 4072 640070 9gitie et 0000 09 0 0 0 Lith 0 668 0 0 4072 640070 2869701 0000 0t 9071 212 0 6 0 2072 0 0 0 coco gt 610070 088478 0000702 070 61170 610070 808079 00007951 070 2 l 0 0 06 070 0172 070 86 70 610070 062761 00007911 027 S6L 029 0 80 2 6100 0 1816781 0000796 070 4171 070 089 0 0 64870 070 10 2 0 8171 70 66 0 21870 9 so z 16670 0 2 6100 0 618 L 0000791 070 28270 610070 91267641 0000 2 1 0 271 70 288 0 60 2 0 80870 610070 0520761 00007211 0271 5147 928 0 80 2 070 29670 070 991 070 8071 070 to z 610070 066177 0000721 070 998770 610070 651 GL 00007821 2271 198 60 2 10870 70 70 0 70 610070 8168741 00007801 070 6171 070 062 070 06870 070 8072 070 9171 070 189 070 66870 070 9072 an oo eff ove ooo 8071 Suc 22670 to z 640070 66176 0000782 11 3029 0 SEIS 01 3091 0 2071 01 3 8270 91670 11 3
8. 10 300 0 8671 10 100 96 t 11 3886 0 1 2 0 3892 0 11270 610070 598 22 0000 265 10 301 2 S6 i 10 30 2 0 4671 60 34WuL 1472 11 3806 0 98270 610070 f69h 22 0000 212 10 316470 2671 10 31 lt 4 2671 60 320170 99 2 01 101170 46270 610070 88 0 22 0000 ZS 10 36847 6871 10 3 85 0 6871 01 369 70 2972 50 0 610070 6269712 0000 2 10 3126 0 6871 10 3126 4871 60 3281 85 2 01 360670 61670 610070 9802712 00007214 10 3186 1871 10 3116 0 1871 80 3016 01 32691 92570 610070 68 7 02 00007262 10 3016 0 4471 10 30 67 lt 10 3651 16 i 10 364670 1674 60 328170 8 72 01 3996 8 2 0 6100 0 2408722 0000 882 10 3682 0 S6 L 10 3682 6671 01 310970 0L c 11 30 7 70 18270 640070 zz 0000 892 10 3 tf 2671 10 3 tin 0 2671 01 3296 0 99 2 LL 322t8 0 16270 670070 8866712 000078 10 326 70 8871 10 326t 8871 60 36 1 0 19 2 11 362170 10670 610070 1694712 0000826 10 3426 4871 10 3 2670 871 60 31 t 16 2 01 380170 4170 610070 9111712 0000 802 10 3 1 6 0 08 1 10 3 t66 0871 80 3962 EE ce 01 36 t 82670 640070 5069702 0000 882 10 3 5 10 3126 0 9L i 1671 1671 L c 10 362 0 10 362 01 3469 0 11 319170 09270 AHVNIOVMI wau 6100 0 6821 22 0000 185 6 i 4671 69 2
9. 90 3862 90 18Gt 0 69 0 AMvNIOVMI wau 610070 0086761 0000712 Lek Jg 61 2 10 3h28 0 10 3h28 90 35 2 0 L0 3 9 0 10L 0 v3y 640070 8066781 00007422 10 111970 10 3129 90 32 270 10 319270 22170 AUVNIOVMI vau 6100 0 6108781 0000 02 12 1 ke te 6172 efit 1172 10 3 8270 10 3282 10 361170 10 321670 16170 AHVNIOVMI 1 34 6100 0 SG9L 1l 0000 181 9271 4171 472 51 0 zoooo AVN IOV OHO 2s 5 oe on se o 0 0 0 AdVNIOVMI 610070 1066791 00007111 0 2 i 716 0172 0 0 0 SnN XnN nN gun UOJ404UOUAS young vu SnN xnN nN auny U0J10JMOUAS young 3us44n9 to SnN xnN nN aun uoJ104uouAS Young vu uasan tt SnN xnN nN aun uoJ304uouAS y36ua young vu quausng 177 SnN xnN nN aun uoJ40JUOUAS young vu 7 sng xnN nN aun uoJ304u2uAS u36ue uoung vu auauun9 cc SNN XNN NN sun1 uoJ3104uou S u35uej young vu 18 HEHE HAH HE E HE HE HE HE HE HE HH HE HE HE HEE EE HE HE HEE HE E HE HE HE HE HH E PE HE HE HE HF E HE HEH E HE HE HE HF HEH
10. HHH 1 I 1 HH HHHH HHH HHH i HHHH HHRHH HH 1 1 1 Pt HHHH HEHHE HHRHH HHHH HEHHE HHHH 1 lt 4 00430072 1 t 1 1 1 t 1 HHH HE 1 1 HHH HHHH HHHH HH 1 t I t 1 1 1 HHHH 1 1 HHHH 1 l 1 HIHHHHH HHHH HEHEHE 1 N 1 1 HHHH HHH HHH HHHH 1 RC amp 44 00 30071 1 1 t X l 1 1 1 t 1 t ow 1 1 HHH 1 l i em l 1 ow 1 1 1 t 1 i 1 1 070 t 1 1 f 1 1 1 I 1 1 1 1 1 1 HHHH HHHH HHHH 1 1 HH HHRHH HHHH He HEH HHHH HHHHH 1 1 1 HHHH HHH HHHH H HHH HHHH 1 5 00 30071
11. 10 396 10 396 0 60 3t02 01 3611 68270 AdvN1SVMI v3 610070 6925 22 0000 192 10 366470 10 3 68 60 3181 0 01 200 66270 AvNIOVMI 6100 0 2016712 0000 hf 8871 09 2 9 c 10 3005 10 3005 60 3 1 0 01 3291 602 0 AdVNIOVMI v3 610070 1218712 0000826 10 1256 10 32 6 60 309 11 3109 61670 AdVNIOVMI Ivau 610070 8620712 0000 102 g t 871 98 2 61 1 6L i t c 10 316 10 3116 80 3 h6 11 3617 0 AHVNIOVMI Iva 6100 0 2166702 0000 182 6471 6171 10 3 6 70 10 3268 MV ShN xnN nN uojJ104uouAS ua6uo uoung vu 3u944n2 SnN XnN nN aun u0J40JUOUAS young vu sng xnN nN 9un3 uo4104uou AS young vu 2 2 tt snN xnN nN eun UOJ40JUOUAS young vu 3uauJno tt sng xnN nN gun3 uoJ10Ju2uAS young vu 34u8JJno SnN xnN nN auny 104104 20 6 wo young vu 20 3007 lt 20 30072 20410071 070 00 300 1 t 1 I t j 1 I HHH HHHH 1 1 1 i
12. 8 8600 REVFRQ 3 17D0 ALFA 7 88D 2 CHROM 0 D0 SPRD 5 0 4 amp END amp CPARM CRNT 5 0D0 STPC 0D0 NCR 100 NMODF 2 NMODE 1 KRAD 0 1PRINT TRUE amp END amp I PARM FREQ 1300 D0 RS 4D0 QV 1 00D0 amp END amp HPARM MMIN 3 MMAX 1 TAUMIN 1 TAUMAX 1 amp END amp SPARM LMTRIX FALSE LINTGL TRUE LMAP FALSE NDISP 0 5 5 1 SPRDO 0 EX 0 1 EY 0 01 5 1 00 10 ZEPS 0 0 DXMAX 0 5 ESPC 0 001 CXMAX 0 5 amp END Figure 1 A sample input data for MOSES Figure 2 Output for the test job shown in Fig l 0000670 20 00000 1 0 0000470 970 60 00000170 10 000001 0 0000170 0 0 l 00001 0 0000170 t ror z 00 vu 000078 vu 00007 000071 0000870 ZHN 0 00 1 lt lt OViddS SVH JNNL NOU1VI3S gt gt 20 000005 0 070 10 00088 70 2 004L 009878 lt lt IN3YYNO HLIM SIHVA HION 1 HONNE gt gt 000071 499 00008 0 20 000261 0 nut ou wma I I nw XVMXO 2453 XVWXa 5437 5433 x3 0dddS Sd1SN dS IN 191011 XIuiWi 1dSN NIWNYL XYWNY L NIWW XVMw 101591 avy AGOWN YON Od LS 1890 AD Sd baud 0845 LERA DYA oviad ZWOS A9N3 SNN X NI 39NVHO WNNIXVW SINAL N33Ml8 JONVLISIC WnWINIW X 30 39N3333310 WNWIXVW 2 10 30N39U3ANOO 80 NOIUJIIHO 3 30 HO NOINUJLINO HOu
13. 962 0 3168 0 0671 10 3568 0671 10 3 6670 10 3 667 10 3 lt 1 90 30 1 0 171 1471 Sh 2 11970 6410070 988 722 0000 262 1971 2971 11 2 029 0 10 311670 10 3216 90 3t 90 361170 610070 681 22 0000 215 10 3929 10 3929 10 319270 10 3804 h9 i 971 1 4 0t 9 0 610070 88 022 0000 252 10 3122 10 3122 10 3966 90 3611 610070 8269712 0000 2t 1671 1871 1572 26970 1971 1971 te z 14970 10 320870 10 3208 10 3969 10 3965 610070 9802712 0000721 10 3 99 0 671 10 398 EG ks 90 3611 0 92 c 90 36117 9970 610070 4684702 0000262 10 3668 0 6 71 10 3668 Gtt 10 3224 0 0 71 10 3229 0 71 40 3122 0 2 40 3281 0 51970 610070 2108722 9000 882 10 3016 0 10 30867 1971 10 3129 0 1472 10 3912 0 22970 610070 22 0000 895 10 398970 10 3959 9 1 10 3282 18 2 90 3162 0 29 0 610070 98166712 00007886 10 36 2 0 09 t 10 36 0971 90 3621 0 g 90 3611 8970 610070 1696712 00007826 10 191870 9671 10 3919 9471 10 396670 Ot 2 90 3641 59 0 610070 9111712 0000 802 10 321870 2471 10 32 8 26871 070 1272 10 396470 99970 610070 099 0 0000 882 10 3206 0 8 1 10 3206 81 1 10 3 0 10 3288 10 3 1 0 90 140270 61970 AdVNIOVMI TV38 610070 6821722
14. Uu 3ueJJno uounq se snN xnN nN Jo 2264 jeay 070 quds 02714761 88 10 61 53500 J0j ajdwes Av SYO JO Q 204300 20 300 2 20 300 1 0 0 00 300 l 1 1 HHH 1 I l 1 HH HH 1 1 HHHH l 1 l l OHHH HHHH HHHH HHHH HHH HEH HEHEHE 1 1 1 1 i 1 1 i HE HEHE HEE O HHHHR T HEHH REHAR H 004900 27 WH HHHH HHH HHH i i HH HHHH 1 1 1 Ge en i 1 1 l 4 RH 1 1 dx ee 1 1 HH HH 1 R t 1 1 1 HHH HHH oie OO 300 1 HHRH l l i i HH HH l 1 1 1 1 1 i 1 1 4 3 0970 1 l HHHO HHHH HHHO HH HHHH HEEE dtd Lee 1 HR HHRHH HHHH HHHH l 1 1 HHRH HHRHH l 1 l 1 1 1 I 1 i
15. the bunch length varies with the bunch current according to the user specified arrays of the bunch lengths SGMTOC i aud the bunch currents 6 1 see also the explanation of SGMTOC and CTOSGM for more details If SGMZ lt 0 the buuch length varies with the bunch current according to a user defined function The user must supply bunch length function into the source program Copy the source file into your file and edit the subroutine function FSGM X following the instruction written there Beta function at the location of the impedance Revolution frequency of a reference particle Momentum compaction factor Linear chromaticity defined by dv dp p Betatron Lune spread at one standard deviation of bunch length A parabolic amplitude dependence of tune spread is assumed namely V SPRD ZZ Sce also the Appendix When NUS 0 these variables are used NUSTOC i is the array to store the synchrotron tones at the bunch currents CTONUS i The synchrotron tune between two points CTONUS i and CTONOS i 1 is calculated by lincar interpolation When 5607 0 these variables are used CTOSG i NAMELIST FREQ RS QV NAMELIST CRNT STPC NCR NMODE NMODF KRAD LPRINT NAMELIST mA i lt 120 amp IPARM MQ m amp CPARN mA mA defautt 60 default 2 default 1 defanlt 0 Logical i default T SHP ARM SGNTOC i is the a
16. 0 2 01 3601 66570 AJVNIOVWI V33 610070 0086761 00007182 9 1 971 10 3 6470 10 3288 60 32 6 0 01 382170 89670 AHVNIOVMI 1V3 610070 8066781 0000422 10 1696 1671 10 369670 1671 60 3 21 2 01 3611 29 70 AHVNI9VMI 1v3u 610070 6108781 0000 02 10 366270 10 3662 80 3052 0 01 3850t 0 165 0 AdVNIOVMI 1v3W4 610070 5581 LL 0000 181 0671 0671 t 2 10 36 2 10 3S 2 0 1170 1 1 Zh be 19 1 11 3 970 1870 ANVNIOVMWI 1 3 610070 5911781 00007491 10 2681 0 10 358 01 3686 0t 3 1 0 0 AHVNIOVMI val 610070 1066791 00007111 20 366 70 6271 20 366t 6271 01 3985 10 2 pE i 1 1072 ANS MV MV SnN xnN nN eun 004202402045 young vu ugJJno SnN xnN nN eun uoJ304uoU S young vu 3ue44n9 SsnN xnN nN euni uoJ304u2u AS young vu snN xnN nN aun UOJ30JHOUAS uo u36ua young vu ug8aJno snN xnN nN auny uoJ304uouAS u35u9 young vw snN xnN nN aun UOJ30JMQUAS 36 21 young vu quasung SnN xnN IN aun3 UOJ30JUOUAS 2609 young vu 21 HEHEH HF HE HE HHE HF HE HE HE E DE HF HE HE HE HE HF HE HF HFH HF HF HF HF HF HF A HE E HF
17. 001 minimum distance between different solutions in the complex plane If their distance is within this value they are considered to be the same solution CXMAX default 0 5 The maximum change in real tune shift which can be accepted as a solution for the current one step larger If the change is larger than this value that solution is neglected 3 Output of MOSES The output for the test data is shown in Fig 2 We will briefly explain how to interpret this for the reader s convenience The beginning of the output is signalled by the title of the program followed by the date time and the version number of MOSES All the input variables printed with short explanations of their definitions and with their units Next follows the printout of the bunch length and the syuchrotron mc as a function of the bunch current if they vary with the current When SGMZ NUS 0 the content of the arrays SGMTOC and CTOSGM NUSTOC and CTONUS will be printed If LPRINT TRUE complex values of all coherent tune shifts normalized by the synchrotron tune are printed for each bunch current together with the bunch length and the synchrotron tune If SPRD 0 and LINTGL TRUE the betatron tunc spread is printed at the head of printout The normalized coherent tune shifts are plotted at separate pages by line printer The window of these figures are defined in NAMELIST The title of the job date tine and the tune spread are prin
18. 9971 10 3 95 9971 80 3 0 0 2 01 306270 2970 640070 6 0000 2 2 10 396 0971 10 3856 0 0971 60 324670 tt 2c 0t1 319t 91870 610070 6449781 00007212 10 3228 70 Eo 10 322 5671 80 3801 t 2 01 3921 0 16 70 610070 1650781 00007261 10 38627 10 386270 6 71 80 3822 2 01 3821 0 10870 610070 2066771 00007271 10 302 0 LE 10 35027 EE LS 01 2696 to g 11 3268 82870 610070 2889791 0000261 10 3861 8271 10 3861 0 82 1 01 3170 to z tt c 80 19260 11 3526 0 610070 1091702 0000 892 10 360470 10 3606 90 3 9 01 3661 610070 2989761 0000882 4971 8971 t c 9 0 0 71 0 71 EE g 26 70 10 3064 10 306 80 318170 11 31 870 610070 25017614 00007822 10 308 0 9671 10 3082 85 1 90 3901 t 2 11 3109 61570 610070 1128 81 0000 802 10 360 amp 10 360 60 3819 0 117392670 6100 0 S 16 4L 0000 881 1671 1671 2 6 0 10 3952 0 10 3912 60 3112 0 01 3422 6100 0 eno sb 0000 891 St i S t 1072 92470 th tt 2 01470 10 3161 10 3161 0 60 3881 0 11 2964 610070 GONG OL 00007811 10 3611 0 9271 10 3681 9271 01 3111 10 2 tb 28570 AVNIOVMI 1v3u 610070 6640702 0000192 10 396 6971 10 3961 0 69 1 90 39 9
19. HE HF HF HEHE HE HE HF HE E HEE HE HE HE 4 E HH HE HC HE HE HE HE HF HE HE HE HE HE HF HE HF E HE HE HF HE AR HE HEF HF HF HE HE EF HE HE HE HE HE HF HE AE HE HE HF HE HE HF RRR HE HF HF HE E HE HH HF HE HE HE HE HE HE HE HEF HE HH HF DE HE HE E HF HE HE HF HF HE HE HEH HE HE HE HE HE HE HE HE HFF HF HE HF HE HF HE E E HF HF HF HF FF HF HF HF E 00000 000 09 000702 Lah OZ 000 082 tt 6L 000 0hc 182781 000 002 976791 0007091 tiet 6L 00070241 848751 000 08 69701 00070 596722 0007966 291722 000794 lt 662712 0007916 652 02 0007922 26761 000792 891781 0007961 8 9l 0007961 062761 0007911 Guc tl 00079 Ge OL 000 9 688722 000 265 610722 00072656 602712 000721 192702 00072272 812761 000 222 9007261 889791 0007241 510761 0007211 600751 000727 82676 000726 4108722 000886 566712 000 81 811712 000 805 191702 000892 601761 0007822 167 0007881 086791 0007881 168781 0007801 91 el 000 89 46476 000792 621722 0007486 016712 000 titi 920712 0007 0 09002 000 192 166781 000 nhee 98 77 41 000 18 06 9L 0007111 50 HL 0007101 806721 0007189 0206 0007124 619 22 000 08 628712 0007085 6 02 0007006 966761 0007092 118781 0007022 969771 0007081 1 lt 2791 00070 Gn 0007001 e
20. coupling Single bunch instability in an Electron Storage ring is a com puter program which computes oscillation tunes of transverse coherent motion as a function of the bunch current for a Gaussian beam and provides their graphical representation on a line printer The first version of MOSES was published in 1986 3 Since then it has been shown in several publications that the program gives good agreement with computer simulations 4 MOSES was installed to the program BBIE by Zotter and Gygi Hanney 5 and can be called from the inside of or can be used as a stand alone program The new version of MOSES presented in this note has the following two differences from the old version 1 The betatron tune may have a spread 2 The synchrotron frequency can be varied with the bunch current as the user wishes The method of calculation in the presence of betatron tune spread can be chosen to be either the author s dispersion integral method 6 or Besnier s dispersion matrix method Their outline is explained in the Appendix Details of the formalism can be found in Refs 6 8 In the former method solutions are obtained by finding zeros of the determinant of certain complex matrix This method is valid only when the zeros have non zero imaginary parts Stationary solutions cannot be calculated correctly However some users night want to guess where the tunes of stationary modes will appear even if it is rough guess MOSES provid
21. 0 0846 02714741 88 10 61 53500 Indu ajdwes A v S JO 100 20 300 2 20 300 2 20 300 070 10 300 1 t i i 1 1 1 i I i 1 1 1 t 1 l 1 1 1 1 1 1 l 1 1 t 1 1 HHH HHH I lt 20 100 6 HHRH i 1 LLLI EI 1 HHHH uL I law 1 ETT D 1 1 1 I 1 1 HH HH 1 HH 1 1 1 1 i 1 1 1 1 i 0 0 i 1 1 1 1 1 1 I He i i 1 HHH HH 1 1 1 HH 1 1 1 HE 1 1 1 o l e 1 HH 1 I x 1 20 300 S HHHH HHRHH HHHH l 1 1 1 1 1 l i 1 1 1 l 1 1 1 1 1 1 1 1 1 1 t lt
22. 0000 185 10 3296 0 99 1 10 3296 9971 10 364670 2 10 386270 82970 AuVNIOVMI Iva 610070 69Z 00007196 6971 6971 72 10 36599 0 10 1699 10 321t 0 90 380 0 65970 AHVNIOVMI 79384 6100 0 2016 12 0000 971 8971 9t c 10 396 70 10 3962 10 3966 0 90 3611 0 19 0 AvNIOVMI 610070 1418712 0000 6671 6671 t c 10 3628 0 10 3628 90 3611 0 6671 6471 62 2 0 0 96970 AHVNISVMI v34 6100 0 98620712 0000 HOE 10 3189 0 10 3188 90 38 2 0 10 3966 89970 AHVNIOVMI vay 610070 2866702 000082 L0 3506 0 10 3106 1671 1671 1272 187 1 1 V V MV snN xnN nN SUN uoJ104uoU S uoung 3uaJu4n5 ShN XnN nN gun uoJ104uouAS young vu 4ugdJno snN xnN nN gun uoJ304u2u S 36 91 young vu Juauung SnN XnN nN eun uo4304uou S u35ue young vu snN xnN nN euni UOJ 30JUOUAS wo young vu 177 snN xnN nN euni uoJ304u2uAs young vu 19 01 361147 96470 670070 69529 00007081 20 3612 271 20 3612 0 a 60 1251 1072 01 3 62 0 94870 610070 00007021 070 171 60 349 ELES 01 318670 2072 01
23. 10070 2092 02 00007272 10 310670 10 3106 90 36 17 90 386270 610070 2151 61 0000 252 ht th b 2272 898970 6 1 6 1 02 2 20170 10 3858 70 10 3898 90 3641 gt 90 3862 0 610070 12761 0000 2 2 n l RE ke 91L 0 10 3912 0 10 3902 90 2120 90 3t 610070 64 9781 00007212 6271 6271 9172 16770 10 3861 0 10 3865 90 3 1170 40 3202 6100 0 2660781 0000261 9271 6i 1 HE a 19170 610070 2066711 00007271 70 1271 6071 EL 0 0 0 0 19 0 70 0 0 640070 2889791 00007261 6271 696 LE 070 0 0 0 0 272 90 39t 2 9819 0 90 3852 0 620070 1091702 0000892 ERS ec c 16970 10 3 6870 10 32468 90 3611 90 364170 670070 2989761 00007882 8 71 GE AS 02 2 80770 10 32718 0 10 3218 90 3621 90 3852 0 610070 2501761 0000 822 EE te 98172 61770 10 32117 90 30 470 90 3212 6100 0 8426781 0000 802 10 311470 8271 OIE 8271 10 361 9172 40 ff 0 86770 640070 6516741 0000881 98271 tt e 06 70 610070 tS 2 1L 0000 89 1271 1071 2172 19170 60070 GOhG 91 0000 6271 496 tiz 0 0 0 0 0 0 90 3611 272 90 386670 08970 AHVNIOVMI Wwau 610070 6650702 000071892 ch t l e 10 3068 0 10 3068
24. 34227 6470 610070 00007004 60 199270 0 t 60 36 27 071 11 3621 50670 04 360 70 2072 640070 98t2u l 0000 08 60 38 1 816 60 3 617 816 01 382 0 15670 070 072 610070 8142721 0000709 60 3161 1071 11 3e96 992 01 39 2 8260 0 0 0 2 610070 2469701 000070 01 3 26 1 60 3622 0 119 01 3191 64970 070 0 e 6100 0 0881 8 0000702 01 220 0 6100 0 8080791 00007961 0 320 0 20 3202 0 60 3611 01 3181 1271 1271 2072 09470 610070 062761 00007911 60 312170 60 36 0 01 391270 01 2 1270 1171 1171 h8f 0 2072 610070 1912 0000796 2071 2071 11670 2072 01 32 27 60 392170 01 3504 60 382170 610070 EL 00007 91 68 69 81670 0 2 60 3712 0 60 180270 01 322 070 610070 4696711 0000796 2071 1541 686 0 0 c 60 316170 60 161970 01 3 0 0 6100 0 1428701 0000 92 60 3691 60 360170 01 3 2170 070 6071 LLG 199 0 t0 2 610070 66187 0000791 01 310870 6100 0 9126761 00007251 60 3169 60 3102 0 01 312670 01 31217 E 6171 6171 2072 49470 610070 0670741 00007211 60 2 lt 6 60 318 0 OL ahhth 0 01 3064 0171 0171 681 0 2072 610070 HOLL RL 0000 26 0071 0071 41570 t 0 2 60 3612 0 60 3518 01 3202 0
25. 591 0 00 2 610070 0 6279 000078 107 AHVNI9VMI IOVI ANVNTOVI 0 0 061 0 AdVNISVNI 610070 2666761 000074821 070 1271 0970 6 8 070 60 2 0 0 11870 610070 2504781 00007401 070 98171 070 1217 070 fc8 0 070 10 2 610070 9t69 l 0000748 6171 909 199 0 90 2 oooco 9 0 0 9 W AHVNIOVMI 6100 0 0804721 0000 19 1171 0 1 26870 to z 6100 0 H6CO tL 0000 tt 0 1071 0 OLE 0 1 6 0 0 20 2 12 610070 861076 0000712 070 SnN xXnN nN euni UOJ 30JUOUAS ua6ue Young vu 3u94J4n2 snN xnN nN eun uo4304uouAS young vu t SnN XnN nN Sun3 UOJ 30JUOUAS Young vu snw xnN nN aun uoJ304uouAS wo u36ug1 young ri vu SNN XNN NN eun3 uoJ41304u9U S young vu snN xnN nN euni uoJ304uouAS young vu 77 SnN xnN nN eun UOJ30JYOUAS uo u36ue young vu Qv3uds 3Nnl 1 138 HF HE HF HF HC HE HE HE HE HE HE HF HF HE HE HE HE HF E HF HE HF HF HE E HF HF HF HF HE HE HE E E HE FEF E EEE EEE EHEER gt gt gt N34809 SA snN xng nN SINIYA 3013 lt lt lt eH 90 3
26. 611 92 2 90 36110 14970 610070 2468702 0000 082 10 3606 0 9871 10 36067 9 71 90 361 1 90 38 2 0 99 0 610070 1866 61 000047092 10 128870 COTE 10 32288 90 3611 s 1272 90 3852 0 96970 610070 9264764 0000042 10 3208 0 9671 10 3208 9 1 90 3t 82 0 6 2 90 3 S2 0 01770 610070 1448781 00007022 10 382970 1671 10 3 297 LE t 10 319270 4172 90 1286170 2770 610070 8982781 00007002 10 3621 0 1271 10 3680 Go ls 10 3126 Si 2 10 326 70 04270 610070 1469771 000070814 070 8271 070 l t 0 0 0 0 1910 610070 096791 00007091 070 9271 070 6071 070 rA 90 3822 0 10 3966 0 2 2 51970 6100 0 6GE 02 0000 9 2 10 3106 0 10 3106 90 36417 90 371470 610070 2668761 0000942 Gn l 6 71 98970 10 3128 0 10 3128 90 3621 90 2182 0 6100 0 1426761 0000 9562 S l 6671 81 2 51 70 0871 0871 1272 66970 10 392270 10 3924 st 90 299 0 90 3211 0 610070 0291781 00007912 10 2 9670 10 3 96 90 306270 90 3 6217 0671 OE Ee 91 2 82270 610070 1491781 0000961 8271 2271 1 2 cht 0 10 3012 10 3182 0 60 38 0 10 3 lt 617 610070 0826771 00007971 8271 1171 09 70 620070 EE9 9L 00007941 9271 1071 1174 0 0 0 0 0 0 52 2 61970 90 3611 90 386 0 6
27. 70 610070 8800751 0000727 60 31 60 382170 01 3 62 070 610070 911971 0000 25 60 394270 60 300170 01 3 9 0 0 0 998 898 26470 0 2 2071 9217 00970 t0 2 6100 0 9126 6 0000 2 01 191670 60 361 0 60 3161 0 0 L69 0 SiS S0 1 t0 2 6100 0 066177 0000721 01 392 1 6100 0 166 741 000082 60 3119 0 60 16627 01 3881 11 291270 610070 168711 0000 90 60 31 5 0 60 3851 0 01 3082 0 01 2266 0 6100 0 9806751 0000789 01 3921 70 60 30 0 11 211270 070 640070 9L er 0000 89 01 328 70 60 1 417 01 3259 0 0 610070 th9t Lb 0000 81 01 321870 01 3 98 01 3 19 0 0 0 610070 66476 0000782 60 3108 0 01 362 01 3198 0 070 610070 016279 000078 90470 L 1 4171 20 2 691 0 1 1071 1071 f6h 0 e0 2 196 196 26 0 gorg th8 118 09670 0 c 0 1 19 0 0 Z 6h 4071 Onl 0 0 z 01 35927 26470 AdVNIOVMI 1939 610070 25667614 00007421 6171 6171 2072 60 319270 60 30 8 60 3621 01 302 Hho AdVNIOVMI 1v3W 610070 2407711 00007101 6071 4071 66470 60 3902 0 60 312 0 01 3 81 01 3518 20 2 AdVNIOVMI V33 610070 8169781 0000 18 60 181170 60 314670 01 3692 0 216 216 0 65 0 070 0 c AdVNIOVMI 1934 610070 0806721 000074
28. 9 60 301270 60 3165 0 01 3 22 1071 8 69670 070 0 2 AgVNIOVWI 1v34 610070 660 900071 60 3611 60 396170 01 3989 hO L 1 9 929 0 0 0 0 2 AHVNIOVWI vay 610070 861076 0000 hz 070 60 3282 01 3 92 0 24870 070 0 2 AdVNIOVMI Iva 610070 88967 000074 0 00000 amp 0 502 071 77 snN xnN nN aun3 uoJ304uouAS uo ua6ue young vu 3uaaJno snN xnN nN aun uabua young vu ueJJno snN xnN nN 74 eun uoJ304u2u S wo young vu 3uo44n5 SnN xnN nN aun UO 30JMQOUAS young vu 3u844n5 t7 snN xnN nN eun uOo430Ju2uAS u35uai young vu 3uaJano 777 SnN xnN nN oun UOJ30JMOUAS wo u36ue young vu uasang 177 SnN xnN nN aun uoJ304uoU S young vu avaudS 1 NOH1V1 d BEBE HE I PE HE HE HEHE ME HE at HFF HF HEHE HF HF HF HF FFE EF HFH gt gt gt LNIYYNO SA SnN XnN nN SINIYA N3913 KLLH t 2 0 90 3981 01 3401 610070 2468702 0000082 10 3 265 10 3126 0 471 Bei on Gnt O 80 3 4 7 01 3221 610070 1846761 00007092 8971 8971 c 1670 10 298 0 10 398 10 30217 01 342270 610070 926761 00007082 10 3828 0
29. E HE E E HE HE HEHEHE DE HE HE HE HE HE HE DE HE HE HE HE HE E HE HE HE HE 0 3512 0 10 368 10 369670 20 361 21 1 2471 iu 2 10970 610070 66t0 c 0000004 6971 6971 t 2z 919 0 10 312570 10 31 87 10 34227 90 309170 640070 6 9 0000 086 10 31886 0 10 3186 10 308 0 90 30 1 0 9971 9971 92970 640070 9fh 00007096 10 389 0 10 2589 90 321 90 3102 0 610070 0628712 0000 0t 10 3212 0 10 32717 90 36417 90 3611 0 640070 1886712 0000 02 4471 4671 62 2 64970 2971 2971 6 2 1 9 0 8671 96 1 2672 14970 10 318870 10 3118 10 3966 0 90 3611 0 610070 ett6 02 0000 002 10 3889 0 10 3888 0471 08 1 10 3212 0 10 321 10 39665 90 361170 14 1 9t 2 60970 610070 629622 0000 962 10 3161 0 10 3961 90 3211 90 310 0 89 8971 2 2 819 0 610070 9696722 00007976 10 140970 10 3509 10 3802 0 90 394170 6971 59 1 SE 829 0 610070 1291722 000079656 10 3260770 10 350 90 3 22 90 3h22 0 610070 16 7142 00007 95 2 10 3428270 10 3282 10 3964 10 396 610070 6862712 00007916 671 HE 1 8272 19970 1971 1971 2 65970 8671 9671 LE lt 04970 10 3668 0 10 3698 10 3966 0 90 2621 0 610070 168 07 0000
30. EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH CERN LEP TIURS 05 User s Guide for New MOSES Version 2 0 MOde coupling Single bunch instability in an Electron Storage ring Y H Chin Geneva Switzerland April 26 1988 Abstract MOSES is a computer program which computes complex coherent betatron tune shifts as a function of the bunch current for a Gaussian beam and provides their graphical representation a line printer The new version of MOSES presented in this note is different im two respects from the old one 1 the betatron tune may have a spread 2 the synchrotron tuuc can be varied as a function of current as the user wishes The method of calculation in the presence of betatron tune spread can be chosen to be cither the author s dispersion integral method or Besnier s dispersion matrix method The outline of these methods is explained in the Appendix MOSES is available as source code in both the CERN IBM VM CMS and the MVS Wylbur System 1 Introduction bunched beam in storage ring interacts with its environment clectromagnetically by exciting wake fields These fields kick the beam and the oscillation frequency of coherent particle motion may be changed When the frequencies of two different transverse coherent motions coincide one of those motions will become unstable with a growth compara ble to the synchrotron frequency This is called a transverse mode coupling instability 1 2 MOSES MOde
31. STPS and SPRDO parameters When LNAP TRUE the absolute value of Lhe determinant of the inatrix A defined in the Appendix is plotted on line printer as a function of real tune shift in a interval MMIN MMAX with increment 0 05 between points The subroutine MAP in CERN GENLIB is also used for plotting See also remarks in Sec 4 Number of higher transverse radial modes for expansion of the dipole particle distribution Used 6 only when LMTRIX TRUE NSTPS default 1 Number of steps for changing the tune spread Must be less than 10 on VM and 6 on MVS If the starting tune spread SPRDO is not zero NSTPS has to be larger than two The tune spread at each step is SPRDxi NSTPS i 1 to NSTPS when SPRDO 0 SPRDO SPRD SPRDO x i 1 NSTPS 1 i 1 to NSTPS when SPRDO gt 0 SPRDO defawt 0 Starting betatron tune spread EX default 0 1 Initial search step for the real part of the tune shifts Search is done in both directions EX and EX EY dcfault 0 01 Initial scarch step for the part of the tune shifts FEPS default 1 D 10 Criterion for convergence of the function value ZEPS default 0 Criterion for convergence of the solution When zero this criterion will be ignored DXMAX default 0 5 The maximum difference of the real tune shift im which the iuitial estimate of solutions is taken from the results for one current step smaller See also remarks in Sec 4 ESPC default 0
32. elatively large and they will always remain slightly unstable in order to suppress a strongly unstable mode In this method the number of cigensolutions will be quite large It will be helpful to split the picture for the real parts of the coherent tune shift by using the NSPL parameter Acknowledgement The author would like to thank B Zotter for proposing the problem and for helpful dis cussions and P M Gygi Hanney for her support with the CERN IBM VM CMS System He also would like to thank E Keil and the LEP TH Group for its hospitality Appendix The dispersion integral and Besnier s dispersion ma trix methods In this appendix we outline the two methods used for calculation in the presence of betatron tune spread The definition of notations follows those in Ref 1 The equation which we want to solve has the form of an integral equation for particle distribution fv mw werfen E 0 where f r and gm r ave the perturbed transverse and longitudinal distributions a function of the phase space amplitudes r and respectively and v is the coherent tune to be determined We assume that the betatron tune v is a function of r only and can be expressed as Vro Sors 2 The explicit formi of the kernel Gr r r can be derived from 2 22 of Ref 1 The transverse dipole moment D is given by Des f r ridr 3 The other notations are as follows v is the
33. es such guess hy assuming that a stationary solution may be approximated roughly by the purely real value which gives a local minimum to the absolute value of the determinant and by searching such a point with a minimization program Sometimes the program fails to find local minima for large tune spreads mainly because they are not well defined or do not exist On the contrary solutions in the latter method are obtained as eigenvalues of the complex matrix as in the absence of tune spread and hence are determined without uncertainty But this requires a rather large matrix size 100 x 100 for accurate solutions and therefore is very time consuming actually solutions converge to those obtained with the dispersion integral method in the limit of infinile matrix size A combined use of the two methods is therefore recommended We discuss this problem again in Sec 4 There are some new variables related to the above differences There is no change in the old variables so the user can still nse input data for the old version These old variables are already explained in Ref 3 However for the convenience of the reader T shall try to make this note serve as a full user s guide by explaining all input variables even if many of them may have been described in Ref 3 The output of MOSES contains in addition to the printout of all input parameters complex values of the coherent tune shifts of a specified number of modes and their graphical
34. ils to find stationary solutions this might be due to the nature of the problem The parameter DXMAX is related to the initial estimate of solutions There are two ways to set he initial estimate from the result for a smaller tune spread at the same current or from the result for a smaller current at the same tune spread MOSES decides which value should be taken through a rather complicated algorithm First it takes the initial value from the solution for the tune spread one step sinaller f NSTPS 1 from the solution for no tune spread at the same current We shall call it X0 If there is a solution within DXMAX around XO for the current one step smaller a the same tune spread the program replaces by this value In this process any two solutions whose distance is less than ESPC in complex tune space are supposed be the same solution and one of them is not therefore used as an initial estimate of the solution for the next current Hf the solution from the minimization program lies further away from the initial estimate than CXMAX it is rejected Sometimes the minimization program converges to the same local minimum or fails to find a local minimum at all If this happens the following recipe might be worth to try Set STPC negative and compute backwards from the largest current e Try a finer step size for changing the tune spread using NSTPS e Change the paramclers DXMAX CXMAX EX EY FEPS and ZEPS e If the m 0 m
35. nd 2k 000709 898478 000702 0 4 22 00079146 6EL te 00079 5 018 02 0007962 668761 0007942 2917981 0007912 LL 0007971 180791 00079514 SLE tre 000 96 96 ll 000796 0887 000791 68h 22 00072275 269712 0007266 ShL 02 000 262 151 61 000 252 Gn9 8l 0007212 066771 0007271 226744 0007261 9LL hL 000 26 219 11 000 2S 66174 000721 80h 000 896 694712 0007926 089 02 000 882 989761 000 8nc 126781 0007802 LET 000891 661761 0007821 606751 000788 496711 000 8 152 9 000 8 125722 000496 000 466702 0007482 086 61 000 hha 8087981 000 911741 0007191 6G GL 000 ticL 469761 000748 65071 00071 967 00078 u16ue1 Young vw u36u81 young yw wo young vu 1 young vu ya6ua7 young vu 1u3JJno 1 young vu 1ua4Jn2 young vu queuing young vu u35ue1 young u36ue1 young vu ualang H HE HF HE HH E HF HE HF HEHEHE HE HE HF gt gt SAO110 SV IN3WuS00 S IHVA HLONIT lt lt 16 0 0 684170 670070 6952791 00007081 HE C e6
36. ode is not found set NMODF to a larger value If solutions cannot be found even after all these tries and if the user is interested in finding all local minima if they exist he should use the parameter It gives a graphical picture of the function to be minimized as function of the real tune shift in the interval HMIN MMAX with distance 0 05 between neighboring points The user may then find what is going on by his inspection Next we consider the Besnicr s dispersion matrix method This method has the advan tage that all solutions are always obtained no matter whether solutions are stationary or unstable It has however the following two drawbacks 1 We need a large number of or thogonal polynomials to expand the transverse dipole distribution for accurate calculation A suitable NDISP is around SPRD x500 NUS 2 There is no stability threshold This might be explained physically as follows In this method a infinite set of amp functions or shell distributions each having a different tune determined by its phase space is approximated by a finite set of orthogonal coherent distributions In reality Landau damping is due to the fact that the energy of unstable coherent oscillations is absorbed by those shell distributions whose oscillation frequency resonates with the coherent one This situation is now described by only a few orthogonal distributions Therefore the share of cach orthogonal distribution becomes r
37. ou can get the same input data with the ICL job control card by typing in Wylbur mode EXEc FROm 1Z ZOT LIB MOSESTST and answering the questions We list all input variables with brief explanations their units or formats and default values in what follows TITLE VORMAT A712 The title of the program run which may be printed as header to the program If you do not want a title leave it blank but never eliminate the linc NAMELIST amp MPARM defines machine and beam parameters NUS Synchrotron tunc If NUS gt 0 the synchrotron tine is kept constant as input while the bunch current varies ENGY SGMZ BETAC REVFRQ ALFA CHROM SPRD NUSTOC i CTONUS i SGMTOC i GeV cnt meter defanlt 0 default 0 mA i lt 120 If NUS 0 the synchrotron tune varies with the bunch current according to the user specified arrays of the synchrotron tunes NUSTOC i and the bunch currents CTONUS i see also the explanation of NUSTOC and CTONUS for more details If NUS lt 0 the synchrotron tune varies with the bunch current according to a user defined function Phe user must supply synchrotron tune function into the source program Copy the source file into your file and edit the subroutine function FNUS X following the instruction written there Beain energy Bunch length If SGMZ gt 0 the bunch length kept constant as input while the bunch current varies If SGMZ 0
38. representation on a line printer In the following sections we will explain the definitions of the input variables and how to interpret the output referring to an example for a test job The final section is devoted to some remarks on how to search coherent tune shifts in tlie presence of betatron tune spread and how to interpret the results 2 Input variables A sample input data for the clectron storage ring DCT of Orsay is given in Fig l consists of five NAMELIST formats and one headline If yon are a user of the CERN IBM VM CMS you must have access to the disk where you will find a of the files MOSES FORTRAN source code MOSES EXEC EXEC file for executing MOSES MOSES IIELPCMS file and a test data file TEST MOSDATA If you don t know about the LEPTH disk You need log in CERNVM and type GIME 195 o obtain access to the disk Then the command LEPTHDSK will allow you to take full advantage of the software on the disk including permanent access if you wish This command will also guide you to the on line HELP information which includes help for using MOSES In order to run the program you must have a data file on the A disk called MOSDATA If m is not specified it is assumed to be TEST For test purposes you could copy the TEST MOSDATA file from the LEPTIN disk Then type in MOSES fn The results will be on the file MOSES RESULTS on your A disk Hf you are a user of the MVS Wylbur y
39. rray to store the bunch lengths at the bunch currents CTOSGM i The bunch length between two points CTOSGM i and CTOSGM i 1 is calculated by linear interpolation defines parameters of the transverse impedance A resonator model is assumed for the impedance Resonant frequency of the impedance Impedance at the resonant frequency Quality factor parameters relevant to the computation of coherent tune shifts and control card for printout The first bunch current with which the computation starts The value must be larger than zero Step on increase in bunch current The bunch current varies as CRNT CRNT STPC STPC x NCR 1 Can be negative Number of steps on change in bunch current to he executed Must be less than 120 The lowest azimuthal mode number to be included in the calculation The highest azimuthal mode number to be included in the calculation Number of higher longitudinal radial modes to be used for expansion of the radial function for cach azimuthal mode Note that zero means that cach azimuthal mode has one radial mode When LPRINT TRUE numerical values of coherent ane shifts normalized by the synchrotron tune are printed with the bunch length aud the synchrotron tune for cach bunch current defines the window of graphical output of coherent tune shifts on a Tine printer A MMIN TAUMAX TAUMIN NSPL NAMELIST LMTRIX LINTGL LMAP NDISP defa
40. synchrotron tune fo r is the transverse unperturbed distribution and w r is the longitudinal weight function First we show how to solve Eq 1 according to the dispersion integral method If we divide both sides of Eq 1 by v v r multiply by r over we obtain 2 ES and integrate FA eX GT rar rign 4 where F v u 2 Jo Valte 5 We solve Eq 4 by expanding the unknown function g 7 into normalized orthogonal polynomials which satisfy the relation ow r SRE n r dr Sinn Opt 6 The kernel can also be expanded with the same orthogonal polynomials The results are g r wr Bins 7 k 0 GP 35 Ma AP 8 kl The explicit form of the matrix clement MX js given by Eq 2 44 in Ref 1 Multiplying Eq 4 by r and integrating over r we obtain d E 9 2 2 0 The of equations has a non trivial solution only if detA 0 10 where A is the matrix with elements AW bn F v Mj 11 The condition 10 may be called a generalized dispersion relation 10 W fo r is Gaussian distribution with a beam size 2 Te 2702 20 12 exp 2 and the tune spread 5 has a parabolic dependence on rz r SE 13 ox the integration of Fm is achieved readily with the result
41. ted in the header line If SPRD 0 the method used for finding solutions is also typed 4 Some remarks In this final chapter we add some remarks on the computation algorithm and on the interpretation of results for the case of nonzero betatron tune spread First we consider the case where the dispersion integral method is used There is no uniquely defined way to to calculate coherent tune shifts for stationary modes only when the imaginary part of tune shifts becomes nonzero solutions can be rigorously obtained This corresponds to the fact that there is no method of the mapping from the complex tune shift plane to the stable region in the stability diagram In MOSES it is assumed that such a stationary solution may be approximated by a purely real tune which corresponds a local mininium of the absolute value of the determinant of the matrix A see Appendix for its definition This assumption is reasonable since zeros of this determinant are true eigensolutions when the tune spread is zero Therefore one may expect that this function will still have well defined local minima around solutions as long as the tune spread is small However it is not clear how good or bad this approximation is for large tune spreads There is even no physical foundation for the existence of local minima The user has to keep in mind that tunes of stationary solutions provided by MOSES have meaning only as guide for the user s convenience When MOSES fa
42. ult NMODF defanlt NMODE default 0 1 default 0 1 default 1 amp SPARM Logical 1 default F Logical 1 default T Logical default T default 9 The maximum coordinate of the figure of the real part of coherent tune shifts The minimum coordinate of the figure of the real part of coherent tune shifts The maximum coordinate of the figure of the imaginary part of coherent tune shifts The minimum coordinate of the figure of the imaginary part of coherent tune shifts Number of split pictures of the real part of coherent tunc shifts defines parameters necessary for scarching coherent une shifts in the presence of betatron tune spread If SPRD 0 this NAMELIST is nof read Scc also remarks in Scc 4 When LMTRIX TRUE Besuier s dispersion matrix method is used The user has to specify NDISP number of higher transverse radial modes for expansion of the transverse dipole distribution When LINTGL TRUE lie dispersion integral method is used The user has to specify all variables from NSTPS down CXMAX described in this NAMELIST Solutions are identified as points which give zeros or local minima of the absolute value of the determinant of the matrix A defined in the Appendix The simplex method and the Miller method are used for minimum search For a large tune spread it is recommended to increase the dane spread gradually from a small value to the desired one using N
43. v3s A 3Nnl OVWI NI 4315 HOHV3S X 3Nnl 1V3M NI 4315 Qv3uds 3 1 SNIINUVIS qv3uds NI 54315 40 4 dMN 53004 IVIGVY SNVNL 30 YIBWNN 1NvNIWH3130 SO9V JO 1014 VJ931NI NOISYIdSIG GOHL3W XINIVM NOISM3JdSIQ MdVdSS 51014 03111145 30 H38W N 1014 Nvi 3i1VNIOHOOD WAWINIW 1014 AVL NI 31VNIQMOOD 1014 NI 300W 2 WAWINIW 1014 NI 300W TWHINWIZY MnN1XVM MHVdHS S3 Y1VAN3913 40 1NIHd 5300 lViQVH SNOT 30 Ju3gSWnN 300 IWHINWIZV 1S HO1H 300W VHInMIZV 153 07 AN3YUND NI 54315 30 YISWAN 1N3HHf D 4315 1NHHnO ONIJIUVIS 405 INYA b AON3n03U4 LNVNOS3Y Wuvd 15 VNOIS 0 3845 3 NOWIVI3U 11911VNOHHO 019V NOIIOVdWOO MLN MOM AON 0D 3 NOIIQ10A3U iV NOI1ONn3 V13H NVISSNVS V 40 VWOIS NONIOUHONAS NddVMS HEHE HE HE HE A HE HE HEHEHE HE HE HE AEH HE HE HE E HE HE HEHE HF HF HEHE HE HE EAE HE HE HE HE HE S SOM 11 072 NOISYJA OZ Lh G1 3Wl1 88 0 6L 31VO M3SOMHOA MVN 0F SISON Indu 5uiJ uoJ4329 3 ue U 3 11522501 young 9I5uIS Hu dnoo spow A VY 5830 JO 130 E HEHE HE HE HE E HE E HE HE E HE HEHEHE HE E EH HE HE HEE E HE HE HE E HEHE SE E HE HE HF HF AE HE HF HE HE HE HEH HE HE HF HE E HE
Download Pdf Manuals
Related Search