RCS QM shuffling

平成１８年６月９日發知　英明

GL data of QMA (QFN,QDN,QDX)QFN

QDN

QDX

GLac

GLmax

GLdc

0.181 to 3 GeV

GLmin

GL/

<G

L>

MAG#

GL data of QMB (QFM)

GL data of QMC (QFX)

GLac

GLmax

GLdc

0.181 to 3 GeV

GLmin

GL/

<G

L>

MAG#

GL/

<G

L>

MAG#

GL data of QMD (QFL,QDL)

GLac

GLmax

GLdc

0.181 to 3 GeV

GLmin

QFL

QDL

GL/

<G

L>

MAG#

Which data should we use for the QM shuffling?

GLmin, GLmax, GLdc & GLac ?We will perform the shufflingso as to minimize the beta modulation at “injection”.

Grouping of QMA(33) into QFN(12), QDN(12), QDX(9)

QFN

QDN

QDX

QD

N

GLm

in/<

GLm

in>

QFNGLmin/<GLmin> QFNGLmin/<GLmin>

QD

X

GLm

in/<

GLm

in>

QDXQFN

QDN

Grouping of QMD(12) into QFL(6), QDL(6)

QD

LG

Lmin

/<G

Lmin

>

QFLGLmin/<GLmin>

QFL

QDL

GL of QMA (QFN,QDN,QDX)QFN

QDN

QDX

GL/

<G

L>

MAG#

GLac

GLmax

GLdc

0.181 to 3 GeV

GLmin

～ 1E-3

～ 1E-3

～ 1E-3

GL of QMB (QFM)

GL of QMC (QFX)

GL/

<G

L>

MAG#

GL/

<G

L>

MAG#

GLac

GLmax

GLdc

0.181 to 3 GeV

GLmin

～ 5E-4

～ 1E-3

GL of QMD (QFL, QDL)QFL

QDL

GL/

<G

L>

MAG#

GLac

GLmax

GLdc

0.181 to 3 GeV

GLmin

～ 1E-3

～ 1E-3

|GLmin/<GL>| < 1.0E-3

x,y

(m)

s (m)

s (m)

x,y/

x,y |/|< 0.8%

HorizontalVertical

Beta modulation at (6.68,6.27) assuming the allocation in the order of Pro.#

Beta modulation caused by GLmin

BEFORE shuffling

x /x ～ -2.0E-5y /y ～ 4.3E-7

1 QFL 32.92 51.1282 QFL 230.155 241.3183 QFL 834.52 803.5284 QFL 1031.755 993.7185 QFL 1636.12 1555.9286 QFL 1833.355 1746.118

1 QDL 82.334 104.6332 QDL 180.741 187.8143 QDL 883.934 857.0334 QDL 982.341 940.2145 QDL 1685.534 1609.4336 QDL 1783.941 1692.614

1 QFM 131.538 146.2232 QFM 933.137 898.6233 QFM 1734.737 1651.023

1 QFN 291.543 336.6352 QFN 471.704 477.9413 QFN 592.971 566.9054 QFN 773.132 708.2115 QFN 1093.143 1089.0356 QFN 1273.304 1230.3417 QFN 1394.571 1319.3058 QFN 1574.732 1460.6119 QFN 1894.743 1841.435

10 QFN 2074.904 1982.74111 QFN 2196.171 2071.70512 QFN 2376.332 2213.011

1 QDN 361.64 376.5752 QDN 441.499 431.5023 QDN 623.176 613.3454 QDN 703.035 668.2725 QDN 1163.24 1128.9756 QDN 1243.099 1183.9027 QDN 1424.776 1365.7458 QDN 1504.635 1420.6729 QDN 1964.84 1881.375

10 QDN 2044.699 1936.30211 QDN 2226.376 2118.14512 QDN 2306.235 2173.072

1 QFX 412.337 395.3252 QFX 419.064 411.1913 QFX 645.611 633.6554 QFX 652.338 649.5225 QFX 1213.937 1147.7256 QFX 1220.664 1163.5917 QFX 1447.211 1386.0558 QFX 1453.938 1401.9229 QFX 2015.537 1900.125

10 QFX 2022.264 1915.99111 QFX 2248.811 2138.45512 QFX 2255.538 2154.322

1 QDX 4.637 1.5862 QDX 258.438 290.863 QDX 532.338 522.4234 QDX 806.237 753.9865 QDX 1060.038 1043.266 QDX 1333.937 1274.8237 QDX 1607.837 1506.3868 QDX 1861.638 1795.669 QDX 2135.537 2027.223

Shuffling for QM11

Cs

s11 ds)](2cos[)s(k)s(

)2sin(21

)s()s(

197°()

83°()

180°()

7°(0)

182°()

292°(3)

463°(5)

[ k(s)= k(s’) ] if n[ k(s)=k(s’) ] ifn

x y

Phase advance at (6.68,6.27)

s (m)

s (m)

y/

y

|/| 1%→ 0.8%→ 0.4%

BEFORE shufflingAFTER shuffling

Beta modulation at (6.68,6.27)

x/

xBeta modulation caused by

GLminAFTER shuffling

AFTER “BAD” shuffling

BEFORE shufflingAFTER shufflingAFTER “BAD” shuffling

Max[

x,y/

x,y]

Max[

x,y/

x,y] Horizontal (BEFORE shuffling)

Horizontal (AFTER shuffling)

Vertical (BEFORE shuffling)

Vertical (AFTER shuffling)

x (y=6.27 fixed)

y (x=6.68 fixed)x

y

2x=13

2y=13

11

Cs

s11 ds)](2cos[)s(k)s(

)2sin(21

)s()s(

Possible operating points

Possible operating points

Tune dependence of /at INJ (GLmin)

Comparison of / at INJ(GLmin) & EXT(GLmax)

Horizontal, INJ

Horizontal, EXT

Vertical, INJ

Vertical, EXT

x (y=6.27 fixed)

y (x=6.68 fixed)

Possible operating points

Possible operating points

2x=13

2y=13

|/| ～ 0.5% at INJ ～ 1% at EXTfor the possible operating area.

“AFTER shuffling (using GLmin)”

Max[

x,y/

x,y]

Max[

x,y/

x,y]

x

y

Single-particle trackingwith GLmin & GLmax (SAD)

x

y

We looked for the maximum x=y

for which the beam survives withinthe physical apertures up to 5000 turns.

x= y

- Multipole field in the BM and QM : OFF- Chromatic correction : OFF- Quadrupole field error : GLmin

AFTER shuffling (using GLmin)

x

y

Surveyed lines

Max.

x=

y

Max.

x=

y

With GLmaxWith no error

＊

x (y=6.27 fixed)

y (x=6.68 fixed)

With GLminWith no error

＊

Single-particle trackingwith GLmin & GLmax

AFTER shuffling (using GLmin)2

X-2

Y=

0

2X

-=1

3 X-2

Y-=

-6

4X

-=2

7

X-2

Y-=

-6

2Y-=

13

Max.

x=

y

Max.

x=

y x (y=6.27 fixed)

y (x=6.68 fixed)

Horizontalunstable

Horizontalunstable

Verticalunstable

Verticalunstable

|ds)jpexp()s(k)s(21

||J|Cs

sp

~ 0.0007 for 2X=13~ 0.0004 for 2Y=13

~ 0.0020 for 2X=13~ 0.0013 for 2Y=13

STOPBAND:

Multi-particle tracking simulation

(SIMPSONS) - Errors included in the simulations -

(1) Multipole field components of BM & QM

BM : MEASURED data & TOSCAQM : TOSCA

(2) Field errors of BM & QM

BM : MEASURED data, ShufflingQM : No data → Random error [ Gauss(2) with =5E-4 ]

(3) Alignment errors of BM & QM

Random error [ Gauss(2) with =0.1 mm for dx & dy, =0.2 mrad for d

GL/GL| <1.0E-3

Field & Alignment errors of QM

G

L)/(

GL)

x (

m)

y (

m)

(r

ad)

QM No.

GL/GL| <1.0E-3

Result from multi-particle tracking(6.72, 6.35)

0.6 MW @ Extr.Chromatic cor. : ACC

Beam

surv

ival

turns

(0) W/O Mult

(1) W/ Mult (COD=0)(3) W/ Mult, ERRORS, COD cor. (COD<0.8mm )

(2) W/ Mult, ERRORS(COD~5mm)

The QM field error of |GL/GL|<1.0E-3 may not lead to large beam loss.

Beta modulation for the case (3)

s (m)

s (m)

y/

y

x/

x

|/|< 1.5%

HorizontalVertical

Shuffling for RCS QM （配置案）

QDX.1 (START)

INJ EXT RF

QFN.12 (END)

QFL.1 5 5.5266E-04 -7.0815E-04QFL.2 3 -3.0916E-04 -4.1831E-04QFL.3 1 1.7112E-04 1.7504E-04QFL.4 4 -3.0144E-04 -3.4764E-04QFL.5 11 5.4409E-05 1.2491E-03QFL.6 2 -1.6759E-04 4.9989E-05

QDL.1 10 2.2648E-04 1.2574E-03QDL.2 9 1.7828E-04 -5.5927E-04QDL.3 12 2.0154E-05 9.0040E-04QDL.4 6 -8.6928E-05 -6.6625E-04QDL.5 8 -1.0578E-04 -7.0846E-04QDL.6 7 -2.3221E-04 -2.2384E-04

QFM.1 2 -1.8764E-04 -1.1459E-04QFM.2 3 3.3658E-04 2.8479E-04QFM.3 1 -1.4894E-04 -1.7020E-04

QFN.1 21 6.8416E-04 2.5681E-04QFN.2 33 -5.6110E-04 2.8760E-04QFN.3 25 3.6266E-04 -1.1600E-04QFN.4 16 -4.9984E-04 6.7884E-05QFN.5 32 2.9784E-04 -4.3077E-04QFN.6 17 -3.9251E-04 -7.2008E-04QFN.7 26 2.3367E-04 2.1653E-04QFN.8 12 -2.3459E-04 2.2009E-04QFN.9 20 1.1034E-04 1.5672E-04QFN.10 1 -9.0733E-05 -8.2401E-04QFN.11 23 9.8060E-05 1.1141E-04QFN.12 28 -7.9741E-06 7.7382E-04

QDN.1 29 2.4049E-04 1.9960E-04QDN.2 8 -3.6880E-04 -4.9946E-04QDN.3 22 2.6735E-04 -1.7662E-04QDN.4 30 1.9254E-04 -1.1933E-03QDN.5 9 1.1788E-04 -4.7090E-04QDN.6 7 -4.8937E-04 -2.6461E-04QDN.7 3 3.9168E-04 8.0692E-04QDN.8 4 5.7125E-05 5.6111E-04QDN.9 5 -1.2421E-04 9.5204E-04QDN.10 10 -6.2276E-04 4.1786E-05QDN.11 18 5.2912E-04 1.9383E-04QDN.12 6 -1.9106E-04 -1.5036E-04

QFX.1 5 9.1200E-04 1.6012E-04QFX.2 3 -7.6459E-04 8.3371E-04QFX.3 4 8.3024E-04 -1.2219E-04QFX.4 11 -5.9420E-04 -6.1390E-04QFX.5 10 4.7182E-04 -7.2714E-04QFX.6 12 -5.0363E-04 -8.3727E-04QFX.7 8 1.2200E-04 -1.0202E-04QFX.8 1 -3.9519E-04 3.0826E-04QFX.9 2 1.0264E-04 1.1932E-03QFX.10 6 -1.5811E-04 -4.3630E-04QFX.11 7 3.4655E-05 3.8310E-04QFX.12 9 -5.7640E-05 -3.9587E-05

QDX.1 31 -9.1535E-04 -5.8434E-04QDX.2 13 -4.5136E-05 4.3229E-04QDX.3 14 3.8744E-04 6.8645E-04QDX.4 11 -5.6827E-05 -8.2704E-06QDX.5 19 -1.2889E-04 -5.3440E-04QDX.6 15 4.5602E-04 5.3885E-04QDX.7 2 -3.0060E-04 -7.8283E-04QDX.8 24 -3.2695E-04 -2.0867E-04QDX.9 27 9.3029E-04 4.6092E-04

QMA 1-33 QMB 1-3

QMC 1-12

QMD 1-12

Location Prod. # GLmin GLmax Location Prod. # GLmin GLmax