Damping ring

K. Ohmi

LC説明会@KEKB

Layout

• Single tunnel

• Circumference 6.7 km

• Energy 5 GeV

2 km

35 km

Parameters

• 5 GeV, 400 mA storage ring

Role of the damping ring

• : 0.045 m 8x10-6 , 2x10-8 m at E=5 GeV• x=0.5 nm, y=2 pm, z =9 mm, dp/p=1.28x10-3.• Storage bunches every 3~6 ns spacing, where H

=14,516 ( frf=650MHz, 1.5 ns).• x=25 ms.• Fast injection and extraction kicker, ~3 ns.• LINAC Repetition: 5 Hz, storage time<200 ms.• Main Linac pulse : 2625-5534 every 370 ns.• Linac pulse length=1 ms, Rev. freq. frev=22 s.

Injection beam

( )x yJ Jψ +

0 0( ) 1

yJ

x y x yJ J dJ dJ

ψ + ≈∫∫

• Ne=2x1010 -1x1010.

• Initial distribution of the beam

• Initial emittance

• Energy deviation <0.5%0.045 4.5 m = =

Damping ring shape• L=6695 m. 6 角形• Radiation damping time, x=25 ms. 　 Stra

ge time <200 ms. Storage 8 damping time in maximum.

Ring lattice• Arc: TME cell• Straight, wiggler, RF, injection and extraction:

FODO cell.

Arc cell

Whole ring lattice

wig wig inj wig wig

Dynamic aperture• Injection beam,

2(Jx+Jy)=0.09, energy deviation 0.05%

赤： error有青： error無

OCS

TESLA org.

PPA

MCH

Injection and extraction• Bunch spacings are 6 ns and 370 ns in the ring and the main linac, re

spectively.• Each bunch has to be injected and extracted individually.• Measurement with 33 cm stripline and 5 kV 3MHz pulser.

Kicker and septum

• 30 cm stripline operating at 22 kV.

• 20 modules are required.

• The kickers pulse every 300 (150) ns during 1ms.

• Kicker amplitude jitter tolerance 10-3.

• Septum should have 1ms plateau flat to 10-4 with a half-sin pulse of 10ms.

Magnets

• Super conducting damping wiggler with B=1.6T. Common cryogenic infra. with RF-cavity.

Magnet field error

Vertical emittance and misalignment

• Design y=20 nm

RF system (superconducting)

VRF=24 MV

s=0.067

=4.2x10-4

Cryogenic Plant

Fast feedback system

• The pickups are 4-button monitor

• 16 bit signal processor

• Bunches in all bucket can be controlled, H=14,516 input channel. >50 taps

• Damping time <30 turn (resistive wall inst.).

Vacuum system

• Ante-chamber in arc

• Wiggler chamber

• NEG coated grooved aluminum chamber. Clearing electrodes are equipped.

• 0.5 nTorr CO

Intrabeam scattering

Bunch filling• Ne=0.97x1010-2.02x1010

• Several bunch filling patterns are prepared.

• The filling pattern

Ion instability• Instability growth for P=0.3 nTorr (CO).• Number of bunches in a train<40• Train gap>28x1.5ns• Feedback noise was not essential.

Ne=2.02x1010, Lsp=6 ns

No noise

1% feedback noise

Ion instability for various filling patterns

• Ne=0.99x1010 Lsp=3 ns Nb=49, Lgap=25x1.5 ns

• Ne=1.29x1010 Lsp=3 ns Nb=53, Lgap=71x1.5 ns

• Ne=1.54x1010 Lsp=4.5 ns Nb

=25, Lgap=25x1.5 ns

Table 1. Electron cloud density near beam (m-3) before bunch passage, compared with threshold density for secondary electron yield 2,max=1.2.

SEY=1.2 TESLA MCH DAS 2 x OCS OCS BRU OTW PPA PEP-II LER KEKB LERLb,tot 695.2 1445.4 653.6 434.0 433.6 1445.4 460.0 767.2 86 102

BEND ρe 2.8E+10 2.8E+10 2.8E+10 3.9E+10 4.0E+11 4.0E+11 1.0E+11 8.0E+11ρe Lb/L 1.15E+09 2.54E+09 1.08E+09 2.77E+09 2.84E+10 9.13E+10 0.00E+00 0.00E+00 3.93E+09 2.70E+10Lquad,tot 200.0 310.8 323.2 177.5 177.5 254.4 148.1 153.6 174.4

QUAD ρe 8.0E+09 8.0E+09 8.0E+09 2.1E+10 3.0E+11 3.0E+11 8.0E+10ρe Lq/L 9.41E+07 1.56E+08 1.52E+08 6.10E+08 8.71E+09 1.21E+10 0.00E+00 0.00E+00 0.00E+00 4.63E+09Lsext, tot 100.0 100.8 22.4 96.0 96.0 100.8 60.0 22.4 41.6

SEXT ρe 8.0E+09 8.0E+09 8.0E+09 2.1E+10 3.0E+11 3.0E+11 8.0E+10(~Quad) ρe Ls/L 4.71E+07 5.06E+07 1.05E+07 3.30E+08 4.71E+09 4.77E+09 0.00E+00 0.00E+00 0.00E+00 1.10E+09

Lwig 417.4 441.0 432.9 196.0 196.0 441.0 144.0 92.8 96WIGG ρe 6.5E+11 6.5E+11 6.5E+11 1.2E+12 9.2E+12 9.2E+12

ρe Lw/L 1.60E+10 1.80E+10 1.65E+10 3.85E+10 2.95E+11 6.41E+11 0.00E+00 0.00E+00 0.00E+00 0.00E+00Ldrift,arc 499.2 499.2 499.2 5210.5 5210.9 4091.9 2410.9 1788.0 1372.8 2602.2

DRIFT ρe 4.0E+10 4.0E+10 4.0E+10 7.9E+10 3.0E+11 3.0E+11 8.7E+11 8.7E+11 1.5E+12(ARC) ρe Ld/L 1.17E+09 1.25E+09 1.17E+09 6.73E+10 2.56E+11 1.94E+11 6.51E+11 5.51E+11 0.00E+00 1.29E+12

Ldrift 15088.2 13137.8 15082.7 0.0 0.0 0.0 0.0 0.0 739.8DRIFT ρe 2.0E+09 2.0E+09 2.0E+09(LONG*) ρe Ld/L 1.78E+09 1.65E+09 1.77E+09 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00

L 17000.0 15935.0 17014.0 6114.0 6114.0 6333.5 3223.0 2824.0 2199 3016AVERAGE ρe,ave 2.02E+10 2.36E+10 2.07E+10 1.10E+11 5.92E+11 9.43E+11 0.00E+00 0.00E+00 3.93E+09 1.33E+12SOLEN ON ρe,ave 1.72E+10 2.07E+10 1.78E+10 4.22E+10 3.37E+11 7.49E+11 0.00E+00 0.00E+00 3.93E+09 3.40E+10

ρe,th (sim) 1.10E+11 3.00E+11 1.20E+11 1.40E+11 1.40E+11 3.00E+11 3.50E+11 3.26E+11 4.66E+11 3.64E+11

Electron cloud build-up

Electron cloud instabilityThreshold of the strong head-tail instability

• Stability condition for ez/c>1

• Since ρe=e/2xy,

• Q=min(Qnl, ez/c) Qnl=5-10? Depending on the nonlinear interaction• K~3 Cloud size effect.• ez/c~12-15 for damping rings.• KQ=60-70 for analytical estimation. KEKB KQ~15

0 0

0

3 3( )1

4 ( )p pe e

s e z s e z p y x y

r rZ KQ LU

c Z c

,

0

2

3s e z

e th

c

KQr L

ρ

Above or below the threshold? ρth=1.2x1011 m-3

The density is above the threshold due to the multipactoring in bending magnets.

OCSx2 was proposed at the first stage (BCD).

Electron cloud instabilityClearing electrode

• Electrode with 100V suppress the electron cloud build up

Electron cloud instabilityGrowth rate of the coupled bunch instability

• Slow growth rate (~1000 turn), if the conditions (average density =10m down stream) are kept.

• At injection, growth rate increases 10-20 times, (~50-100 turn)

OTW OCS

Resistive wall impedance• Resistive wall wake integrated along the ring with

considering chamber radius and beta function. • The resistive wall instability is serous for large

circumference rings, because low frequency component of the resistive wake is the source, impedance of the slowest fractional tune, Z(1-).

Broad band impedance• Longitudinal

• Transverse

Single bunch instability

• Longitudinal unstable, bu

nch lengthing

• Transverse

stable

Coupled bunch instability• There is no reason that OCS is

so bad. Tune should be chosen better. Growth time >30 turn. Transverse feedback system to suppress is required.

• Longitudinal, no problem (KEKB type SC cav.).