Off-momentum DA of RCS 3D_BM &amp; QFF &amp; CC

1 / 22

# Off-momentum DA of RCS 3D_BM & QFF & CC - PowerPoint PPT Presentation

AP meeting / December 8, 2004. Off-momentum DA of RCS 3D_BM &amp; QFF &amp; 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”.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Off-momentum DA of RCS 3D_BM & QFF & CC' - lluvia

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

AP meeting / December 8, 2004

### Off-momentum DA of RCS3D_BM & QFF & CC

Alexander Molodozhentsev

Etienne Forest

KEK

RCS_3DBM

Tune diagram

Structure resonances:

-QX+2Qy=6 “Sextupole”

Chromatic

tune_shift ~  0.08

(dp/p=  0.01)

-Qx+3Qy=12 “Octupole”

-Qx+4Qy=18 “Decapole”

-Qx+5Qy=24

“Bare” tunes:

Qx = 6.68

Qy = 6.27

--- scanning regions

Wkin = 181 MeV

…  = 0.54523

WHY?

as the independent parameter

MAX_Dx ~ 10 m !!!

RCS_3DBM

Off-momentum particle motion(lattice#1)

PTC tracking:

Observation point : SFX Dx ~ ???

p/p = 0.01

Dx (SFX) ~ 5.5 m

PTC:

Chromaticity (x/y) ~ -8

5.5 cm

-15cm

15 cm

Chromaticity definition

Sextupole field component

Path_length in ring

If the code uses the time instead of the path, the chromaticity

will be different in the case of the low kinetic energy: ds = (c) dt

Wkin = 181 MeV …  = 0.54523

… then PATH ~ 0.545 TIME !!!

Dispersion function definition

Periodic dispersion function can be written as

[Mario Conte, p.85]

… also depends on choice “path” or “time”

for Wkin=181 MeV …

Off-momentum particle motion(lattice#1)

PTC tracking:

Observation point : SFX Dx ~ 10 m

p/p = 0.01

TDR:

Bore radius of SFX is (330/2) mm=165 mm

SFX: x ~ 13m, y ~ 6m

xcenter->chamber ~ 16.5-10.0=6.5 cm

x,MAX ~ (x)2 / x ~ (6.5e-2)2/13 ~ 325 .mm.mrad

… Momentum Acceptance for p/p = 0.01

xp/p ~ 10 cm

-15cm

15 cm

RCS_3DBM

Effects of the quadrupole fringe field

ON-momentum particles…

(1) ‘Octupole-like’ effect …

… at the leading order – excitation of the normal octupole resonances

OFF-momentum particles…

(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

(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

Tune variation for off-momentum particles

Linear chromaticity ~ (-8)

Without sextupole magnets

for the chromaticity correction…

RCS_3DBM

Off-momentum DA (3D_BM)

3D_BM

Plus: QFFHE

NO Sextupole CC

Observation point:

BM1 entrance (#47)

dp/p=0

RCS_3DBM

Off-momentum DA (3D_BM)

3D_BM

Plus: QFFHE

Resonance [-1,2]

driving terms

NO Sextupole CC

Observation point:

BM1 entrance (#47)

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)

3D_BM

Plus: QFFHE

NO Sextupole CC

Observation point:

BM1 entrance (#47)

Increasing the resonance

4Qx=27 for the off-momentum

particles … by the feeding-down

the high-order field components

of the 3D_BM …

RCS_3DBM

3D_BM

Plus: QFFHE

NO Sextupole CC

• Contribution to the normal
• sextupole resonance by
• the sextupole ‘feeding-down’
• of the QFF “pseudo-octupole”…
• some compensation effect

(1)

(2)

(2) Increasing of the normal

octupole resonance…

RCS_3DBM

Off-momentum DA (3D_BM)

3D_BM

Plus: QFFHE

NO Sextupole CC

Observation point:

BM1 entrance (#47)

Main limitation of the off-momentum DA is

caused by the normal octupole resonance.

… synchrotron oscillation …

Some speculation … look at summary012-file …

RCS_3DBM

On-momentum particle motion

NO CC Sextupoles

Tune-scanning in the Qy direction

QX – fix

QY - vary

Main limitation of the

on-momentum DA is caused by the normal

sextupole resonance

RCS_3DBM

Off-momentum (3D_BM) plus chromatic sextupole magnets

Changing of the tune for

different (dp/p) before (1)

and after (2) the chromaticity

correction

RCS_3DBM

Off-momentum DA after chromatic correction

3D_BM

Plus: QFFHE

Sextupole CC

Observation point:

BM1 entrance (#47)

Twiss Parameters:

(βx)1/2 = 2.7848 m1/2, x = 0.2517

(βy)1/2 = 3.9030 m1/2, y = 0.1990

(X=Y)MIN = 2.75 cm

Ax = (Xmax)2x ~ 190  mm mrad

Ay = (Ymax)2y ~ 150  mm mrad

RCS_3DBM

On-momentum DA after chromatic correction

… result was presented October 27, 2004.

RCS_3DBM

To DO:
• … correction of the normal sextupole resonance …
• … off-momentum particle motion after the correction…

Presented for the AP-group

December 8, 2004