An Effective Space Charge Solver. for DYNAMION Code

Transcription

1 A. Orzhehovsaya W. Barth S. Yaramyshev GSI Hemhotzzentrum für Schweronenforschung (Darmstadt) An Effectve Space Charge Sover for DYNAMION Code

2 Introducton Genera space charge agorthms based on the effectve method of the ntegra cacuaton Impementaton of the space charge agorthms nto DYNAMION code Concusons

3 Standard Space Charge Approaches Posson Sovers anaytca soutons for smpe modes partce partce ( + speca routne to avod artfca partce coson grd methods FFT PIC-sovers

4 Standard Space Charge Approaches Posson Sovers anaytca soutons for smpe modes partce partce ( + speca routne to avod artfca partce coson grd methods FFT PIC-sovers Advanced methods study of the partcuar cases for fast and precse ntegra cacuatons

5 Studed Modes study of the study partcuar of the partcuar cases for cases faster and more precse for the faster ntegra and cacuatons precser ntegra cacuatons Epsoda bunch a-symmetrca bunch anaytca method The bunch of the arbtrary eptca cross secton sem-anaytca method arbtrary as numerca method

6 Space Charge of the Epsoda Bunch z Keogg s formuae abc bunch as t= /a +y /b +z /c ( y z) n( t) 4 abc n ( r ) r dr 1 y E E y E z n( T ) ds 1/ ( a 3/ ( b 1/ ( c y ( a ( b n( T ) ds 1/ 1/ 3 / z ( a ( b n( T ) ds ( c ( c 3 / 1/ 1/ a s y b s z c T s

7 Space Charge of the Epsoda Bunch z Keogg s formuae y E n( T ) ds 1/ ( a 3/ ( b 1/ ( c E y y ( a ( b n( T ) ds 1/ 1/ 3 / ( c Many partces Many steps: E z z ( a ( b n( T ) ds 3 / 1/ 1/ ( c NOT EFFECTIVE!!! a s y b s z c T s

8 Space Charge of the Epsoda Bunch Poynoma representaton n( t) n N c n t n E E y Keogg s formuae n( T ) ds 1/ ( a 3/ ( b 1/ ( c y ( a ( b n( T ) ds 1/ 1/ 3 / ( c t= /a +y /b +z /c E z z ( a ( b n( T ) ds 3 / 1/ 1/ ( c a s y b s z c T s

9 Sem-Anaytca space charge Sover (SAS) NOW EASY TO CALCULATE! E N! c!!! y z I 1

10 N I z y c E 1!!!! Sem-Anaytca space charge Sover (SAS) N n n c n t t n ) (

11 N I z y c E 1!!!! Sem-Anaytca space charge Sover (SAS) N n n c n t t n ) ( 1/ 1/ 1/ ) ( ) ( ) ( 1 d c b a I Gaussan uadrature (or Anaytca Souton)

12 N I z y c E 1!!!! Sem-Anaytca space charge Sover (SAS) N n n c n t t n ) ( 1/ 1/ 1/ ) ( ) ( ) ( 1 d c b a I Error <.1%

13 Sem-Anaytca space charge Sover (SAS) 1/ 1/ 1/ ) ( ) ( ) ( 1 d c b a I Integra does not depend on (yz) Can be cacuated ONCE for a partces MUCH FASTER fed cacuatons N I z y c E 1!!!!

14 Anaytca method Appcatons of the Agorthms HIPPI Proect Hgh Intensty Pused Proton Inector Perfect concdence! benchmarng of the nac codes DYNAMION (ITEP GSI) HALODYN (Unversty of Boogna) IMPACT (LANL LBNL) LORASR (IAP) PARMILA (LANL) PARTRAN (CEA) PATH (CERN) TOUTATIS (CEA) CPU - TIME (n unt A-symmetrc Epsoda Bunch Statc Case 1 5 partces

15 Appcatons of the Agorthms MICROMAP Guano Franchett GSI (Darmstadt) Lbrary of codes for beam dynamcs smuaton n crcuar acceerators anaytca method for the D eptca cross secton or for the a-symmetrca epsoda bunch sem-anaytca methods for the bunches of an arbtrary eptca cross secton grd method for the D cross secton hgh speed and hgh accuracy of cacuaton beam dynamcs smuatons and beam osses nvestgatons for SIS18 and FAIR

16 The mutpartce DYNAMION code DYNAMION ITEP (Moscow) GSI (Darmstadt) created n ITEP (1985) deveoped n coaboraton ITEP and GSI snce 1991 end-to-end beam dynamcs smuatons for nacs Advanced code for beam dynamcs smuaton n near acceerators was used for smuatons n dfferent aboratores partce partce method for space charge cacuatons wth speca routne to avod artfca partce cosons PIC sover (ITEP) s under tests

17 Interpoaton of the charge densty Chebyshev nodes n(t) N n c n t t 1 1 cos ( N 1) n t= /a +y /b +z /c = 1.. N Mnmzaton of the mamum nterpoaton error for poynoms of order N N ~! EPAC 4 Orzhehovsaya Franchett

18 Impementaton nto DYNAMION code reconstructon of the charge densty from the dscrete partce coordnates (yz) 3 d t= /a +y /b +z /c t 1

19 Impementaton nto DYNAMION code reconstructon of the charge densty from the dscrete partce coordnates (yz) 3 d t= /a +y /b +z /c t 1 t Chebyshev node n ( t ) -?

20 Impementaton nto DYNAMION code reconstructon of the charge densty from the dscrete partce coordnates (yz) 3 d t= /a +y /b +z /c t 1 t TOO Large n(t) a partces nsde t How Large?

21 Impementaton nto DYNAMION code reconstructon of the charge densty from the dscrete partce coordnates (yz) 3 d t= /a +y /b +z /c t 1 t TOO Large n(t) a partces nsde t How Large? TOO Sma n(t) ust 1 partce nsde t

22 Impementaton nto DYNAMION code reconstructon of the charge densty from the dscrete partce coordnates (yz) 3 d t= /a +y /b +z /c t 1 t - D t t + D N p partce -? D = 1. / N p

23 Impementaton nto DYNAMION code M E ( y z) E E 1 ( y z) ( y z) = 5!

24 Comparson wth p-p method (statc case) Dfference n the eectrc fed vaues s ess than 1%!!!

25 Beam dynamcs smuatons wth DYNAMION code GSI Hemhotzzentrum für Schweronenforschung UNInversa Lnear ACceerator (UNILAC) 1-st Avarez Tan

26 Beam dynamcs smuatons wth DYNAMION code CPU tme for beam dynamcs smuatons (1-st Avarez tan) 1 3 partces 1 4 partces 1 5 partces P-P 1 mn 48 hours - SAS 1 hour hours 1 hours

27 Beam dynamcs smuatons wth DYNAMION code RMS emttance behnd 1-st Avarez Tan of UNILAC

28 Concuson Fast and precse Sem-Anaytca Space Charge Sover (SAS) s mpemented nto DYNAMION code Good concdence wth other codes for statc and dynamcs Up to 1 6 partces can be smuated -step scheme: 1) fast nvestgaton wth SAS ) fna proof wth hgh precson by more tme consumng space charge sovers

29 Outoo The frst resuts are promsng! Optmzaton of the parameters n SAS Impementaton for bunches of dfferent shape Benchmarng of DYNAMION (new space charge sover) wth other beam dynamcs codes