View
37
Download
0
Category
Preview:
DESCRIPTION
AP meeting / December 8, 2004. Off-momentum DA of RCS 3D_BM & QFF & CC. Alexander Molodozhentsev Etienne Forest KEK. RCS_3DBM. Tune diagram. Structure resonances:. -Q X +2Q y =6 “Sextupole”. Chromatic tune_shift ~ 0.08 (dp/p= 0.01). -Q x +3Q y =12 “Octupole”. - PowerPoint PPT Presentation
Citation preview
Off-momentum DA of RCS3D_BM & QFF & CC
AP meeting / December 8, 2004
Alexander Molodozhentsev
Etienne Forest
KEK
Tune diagram
-QX+2Qy=6 “Sextupole”
-Qx+3Qy=12 “Octupole”
-Qx+4Qy=18 “Decapole”
Structure resonances:
“Bare” tunes:Qx = 6.68Qy = 6.27
-Qx+5Qy=24
RCS_3DBM
--- scanning regions
Chromatic tune_shift ~ 0.08
(dp/p= 0.01)
MADX:RCS Twiss parameters (dp=0.0)
MADX_Chromaticity: ~ -15 !!!
MAX_Dx ~ 10 m !!! WHY?Because MADX uses ‘time”as the independent parameterinstead of ‘path-length’…
Wkin = 181 MeV … = 0.54523
Off-momentum particle motion(lattice#1)
Observation point : SFX Dx ~ ???
-15cm 15 cm
5.5 cm
p/p = 0.01
PTC tracking:Use “path” instead of “time”…SAD, MAD8
Dx (SFX) ~ 5.5 m
PTC: Chromaticity (x/y) ~ -8
RCS_3DBM
Chromaticity definition
dsssbsp
qppQ xxx )()()(
2
1)//( 2
0
Sextupole field component
Path_length in ring
If the code uses the time instead of the path, the chromaticitywill be different in the case of the low kinetic energy: ds = (c) dt
Wkin = 181 MeV … = 0.54523
TIMEPATH
… then PATH ~ 0.545 TIME !!!
Dispersion function definition
dQsQ
ss H
Ls
sH
])()(cos[)(
)(
)sin(2
)()(
Periodic dispersion function can be written as[Mario Conte, p.85]
… also depends on choice “path” or “time”
… MAD dispersion (“path”) is about two time bigger than SAD dispersion for Wkin=181 MeV …
Off-momentum particle motion(lattice#1)
p/p = 0.01
Observation point : SFX Dx ~ 10 m
xp/p ~ 10 cm
-15cm 15 cm
TDR: Bore radius of SFX is (330/2) mm=165 mm
SFX: x ~ 13m, y ~ 6mxcenter->chamber ~ 16.5-10.0=6.5 cmx,MAX ~ (x)2 / x ~ (6.5e-2)2/13 ~ 325 .mm.mrad… Momentum Acceptance for p/p = 0.01
PTC tracking:Use “time” instead of “path” …MADX
Effects of the quadrupole fringe field
(2) De-tuning effect for the off-momentum particles … … the end-field of the quadrupole magnet gives the beam two kicks in the opposite directions, which cancel for the paraxial trajectories, but which gives a net focusing to trajectories passing though at an angle. It means that the fringe field of the quadrupole magnets, which are located in the non- zero dispersion sections, will provide the de-tuning of the off-momentum particles. This effect depends on the particle momentum and the betatron amplitude, the dispersion and the slope of the dispersion at the location of the quadrupole magnet.
(1) ‘Octupole-like’ effect … … at the leading order – excitation of the normal octupole resonances
(3) Sextupole feeding-down component … … for the off-momentum particles the pseudo-octupole nonlinearity of the quadrupole magnet will be “feeding-down” due to the closed orbit displacement in the quadrupole magnets in the non-zero dispersion regions (in the ARCs). In this case the quadrupole fringe field can contribute additional excitation to the normal sextupole resonances.
RCS_3DBM
ON-momentum particles…
OFF-momentum particles…
Tune variation for off-momentum particles
-0.010 -0.005 0.000 0.005 0.0106.15
6.20
6.25
6.30
6.35
6.40
6.45
6.50
6.55
6.60
pp
Qx /
Qy
#3D_BM Q
x
Qy
# IDEAL Q
x
Qy
Without sextupole magnets for the chromaticity correction…
Linear chromaticity ~ (-8)
RCS_3DBM
Off-momentum DA (3D_BM)
6.3 6.4 6.5 6.6 6.7 6.83.0
3.5
4.0
4.5
5.0
5.5
6.0-Q
x+2Q
y=6
* Tunes include the chromatic tune shift
4Qx=
27
-Qx+
3Q
y=1
2
QV * ~ 6.222... 6.224
dp/p=0.005
Max
imum
X=
Y [c
m]
"Chromatic" horizontal tune *
3D_BMPlus: QFFHE
NO Sextupole CC
Observation point:BM1 entrance (#47)
RCS_3DBM
6.3 6.4 6.5 6.6 6.7 6.82.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
-Qx+
3Q
y=1
2
4Q
X=
27
-QX+
2Q
y=6
QV ~ 6.2620 ... 6.2630
BM_3D & QFF (1000 turns / entrance BM1)
Ma
xim
um
X=
Y [cm
]
Horizontal Tune
dp/p=0
6.3 6.4 6.5 6.6 6.7 6.83.0
3.5
4.0
4.5
5.0
5.5
6.0
Lattice tune
-Qx+
2Q
y=6
-Qx+
3Q
y=1
2
4Q
x=2
7
QV ~ 6.26
dp/p= 0.005
Ma
xim
um
X=
Y [cm
]
Horizontal tune
Off-momentum DA (3D_BM)
3D_BMPlus: QFFHE
NO Sextupole CC
Observation point:BM1 entrance (#47)
Resonance [-1,2]driving terms
Resonance [-1,2]driving terms for this case is 3 times smaller than for the corresponding tunes of the on-momentum particles
RCS_3DBM
Off-momentum DA (3D_BM)
6.3 6.4 6.5 6.6 6.7 6.83.0
3.5
4.0
4.5
5.0
5.5
6.0
* Tunes include the chromatic tune shift
QV
* ~ 6.183 ...6.188
-Qx+
2Q
y=6
-Qx+
3Q
y=1
2
4Q
x=2
7
dp/p=0.010
Ma
xim
um
X=
Y [
cm
]
'Chromatic' horizontal tune*
3D_BMPlus: QFFHE
NO Sextupole CC
Observation point:BM1 entrance (#47)
RCS_3DBM
Increasing the resonance4Qx=27 for the off-momentumparticles … by the feeding-downthe high-order field componentsof the 3D_BM …
Effect of the quadrupole fringe field for the off-momentum particles
6.3 6.4 6.5 6.6 6.7 6.83.0
3.5
4.0
4.5
5.0
5.5
6.0
4Q
x=2
7
-Qx+
2Q
y=6Ma
xim
um
X=
Y [
cm
]
'Chromatic' horizontal tune*
3DBM & QFF 3DBM
dp/p=0.01 3D_BMPlus: QFFHE
NO Sextupole CC
RCS_3DBM
(1)
(1) Contribution to the normal sextupole resonance by the sextupole ‘feeding-down’ of the QFF “pseudo-octupole”… some compensation effect (2)
(2) Increasing of the normal octupole resonance…
Off-momentum DA (3D_BM)
6.2 6.3 6.4 6.5 6.6 6.7 6.83.0
3.5
4.0
4.5
5.0
5.5
6.0
Lattice tune
-Qx+
3Q y=
12
-Qx+
2Q y=
6
4Q
x=2
7Ma
xim
um
X=
Y [cm
]
QV ~ 6.263 ... 6.265
dp/p=0.01
Horizontal tune
3D_BMPlus: QFFHE
NO Sextupole CC
Observation point:BM1 entrance (#47)
RCS_3DBM
Main limitation of the off-momentum DA iscaused by the normal octupole resonance.
Off-momentum DA (3D_BM):dp/p= 0.005
6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.03.0
3.5
4.0
4.5
5.0
5.5
6.0
-QX
* +3Q
Y
* =12
HV-coupling
-QX
* +2Q
Y
* =6 H-unstable
4QX
* =27
HV-coupling
Qy
*=6.301...6.303
dp/p=-0.005
Ma
xim
um X
=Y
[cm
]
"Chromatic" horizontal tune *
6.3 6.4 6.5 6.6 6.7 6.83.0
3.5
4.0
4.5
5.0
5.5
6.0
-Qx* +
2Qy* =
6
* Tunes include the chromatic tune shift
4Qx* =
27
-Qx* +
3Qy* =
12
QV * ~ 6.222... 6.224
dp/p=0.005
Max
imum
X=
Y [c
m]
"Chromatic" horizontal tune *
Off-momentum DA (3D_BM):dp/p= 0.01
6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.03.0
3.5
4.0
4.5
5.0
5.5
6.0
4Q
X
* =2
7
-QX
* +2
QY
* =6
Overlapping ofresonances
HV-unstable
H-unstable
QV
* ~ 6.344 ...6.346
dp/p=-0.01
Max
imu
m X
=Y
[cm
]
'Chromatic' horizontal tune*
6.3 6.4 6.5 6.6 6.7 6.83.0
3.5
4.0
4.5
5.0
5.5
6.0
* Tunes include the chromatic tune shift
QV
* ~ 6.183 ...6.188
-Qx* +
2Qy* =
6
-Qx* +
3Qy* =
12
4Qx* =
27
dp/p=0.010
Max
imum
X=
Y [c
m]
'Chromatic' horizontal tune*
… synchrotron oscillation …
Some speculation … look at summary012-file …
On-momentum particle motion
6.0 6.1 6.2 6.3 6.4 6.53.0
3.5
4.0
4.5
5.0
5.5
6.0-Q
x+5
Qy=
24
-Qx+
2Q
y=6
-Qx+
3Q
y=1
2
-Qx+
4Q
y=1
8
3DBM & QFF / dp=0Q
X ~ 6.69
Ma
xim
um
X=
Y [cm
]
Vertical tune
QX – fixQY - vary
RCS_3DBM
Tune-scanning in the Qy direction
Main limitation of theon-momentum DA is caused by the normalsextupole resonance
NO CC Sextupoles
Off-momentum (3D_BM) plus chromatic sextupole magnets
-0.010 -0.005 0.000 0.005 0.0106.10
6.15
6.20
6.25
6.30
6.35
6.40
6.45
6.50
6.55
6.60
Qx /
Qy
pp
3D_BM:(1) NO_CC
B C
(2) YES_CC D E
Changing of the tune fordifferent (dp/p) before (1)and after (2) the chromaticitycorrection
RCS_3DBM
Off-momentum DA after chromatic correction
6.3 6.4 6.5 6.6 6.7 6.82.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
4Q
x=2
7
-Qx+
2Q
y=6
3D_BM & QFF & CCQ
V ~ 6.25...6.26
#47
dp/p=0.01
Ma
xim
um
X=
Y [
cm]
Horizontal tune
3D_BMPlus: QFFHE
Sextupole CC
Observation point:BM1 entrance (#47)
(X=Y)MIN = 2.75 cm
Twiss Parameters:(βx)1/2 = 2.7848 m1/2, x = 0.2517(βy)1/2 = 3.9030 m1/2, y = 0.1990
Ax = (Xmax)2x ~ 190 mm mrad
Ay = (Ymax)2y ~ 150 mm mrad
RCS_3DBM
On-momentum DA after chromatic correction
6.3 6.4 6.5 6.6 6.7 6.82.0
2.5
3.0
3.5
4.0
4.5
5.0
5.5
6.0
4Q
H=
27
-QH+
2Q V
=6
QV=6.2620...6.2630
Ma
xim
um
X=
Y [cm
]
Horizontal Tune
BM_3D&QFF BM_3D&QFF&CC
… result was presented October 27, 2004.
RCS_3DBM
To DO:
• … correction of the normal sextupole resonance …
• … off-momentum particle motion after the correction…
RCS_3DBM
Presented for the AP-groupDecember 8, 2004
Recommended