Betatron Phase Measurements using
Single-pass BPMs in KEKB
M. Tejima, K. Mori, M. Tobiyama, H. Ishii,
S. Hiramatsu, Y. Ohnishi*

KEKB Accelerator Review Committee
2007.Nov.29*Email: yukiyoshi.

IntroductionSingle-pass BPMs have been installed in LER and HER.


38 sets for each ring.

The system consists of log-amplifiers, peak-hold circuits,analog-digital converters(ADC), memory circuits, atiming control circuit.
Beam position

yBAx

beamC VV x = Cx  log A − log B VD  VC VV y = Cy  log A + log B VD  VCABCD€

DBlock diagram

Introduction (cont'd)Expected position resolution
100 µm resolution can be achieved for the bunch current of0.1~1 mA
 e+ injection beam(typically ~0.3 nC/pulse) can be measured
within 500 µm resolution.
0.3 nC
1 mA/bunchThe purpose of Single-pass BPMs is to measure injectedbeam positions and optics parameters(betatron phases,xy-couplings) using a oscillated beam.

Betatron Phase Measurement
Horizontal betatron phase measurements:
One of injection kickers can give a horizontal oscillation.
 Damped free oscillation is measured by single-pass BPMs.
 BxB feedback is OFF. Radiation damping is about 4000 turns.

Turn-by-turn beam positions are fitted by the following
formula:x n = Ae−Γn cos(2πν x ⋅ n + Ψx ) + xCOD€

M241QI8Px(mm)#turnsgreen: data
red: fitError of Measurement
xn = Ae−Γn cos(2πν ⋅n+ Ψx ) +Δxnsimulation
A = 1 mm
Γ = 4x10-4
N = 1000€σ Ψx =xσΨ (deg)ν=0.505, Γ=4x101 2⋅σxA Nxn = Acos(2πν ⋅n+ Ψx )€(Δxn )2 = A2 sin2 (2πν ⋅n+ Ψx )(ΔΨx )2€σx (mm)σx = 100 µm → ΔΨx ~ 0.4° @ A = 1 mm, N=1000

Betatron Phase Measurement
Horizontal betatron phase:

avda esahp a e r apmoc We

Ψx,i-1Ψx,iBetatron Phase Measurement (LER)Example 1

Betatron Phase Measurement (HER)Example 2

Tracking Simulation (LER)

x (m)M245QEAP#turnsΔX (mm) @ sextupoles

rfsw,rad,radcod,nofluc1 macro particle

Tracking Simulation (LER)
ΔX (mm) @ sextupoles

rfsw,rad,radcod,cod,nofluc1 macro particles
COD correction (steering+backleg)

K0

COD correction
with backleg

Tracking Simulation (LER)
ΔX (mm) @ sextupoles

K0

COD correction without backleg

2007.11.08 LER
green: design optics(model)
cyan/red: single-pass BPM(ONEPASS)
blue: global beta measurement(BETAPHASE)

meas-model (deg)No correlation between single-pass
and global beta measurement

2007.11.29 LER
green: design optics(model)
cyan/red: single-pass BPM(ONEPASS)
blue: global beta measurement(BETAPHASE)

Strength of QR4P is changed to makebig beta-beat. (as a known gradient error)

meas-model (deg)bad BPM

Strong correlation between
single-pass and global betameasurement

Orbit Measurement of Injected BeamHER

1

2

3

Beam was lost at
movable masks

Summary

Betatron phase measurements are performed using the singlepass BPMs.

Intrinsic resolution of the phase measurement is enough.

Scatters of deviation from the design phase looks like due to thehorizontal orbit displacement at sextupole magnets from thetracking simulation. The orbit displacement comes from radiationenergy-loss and RF acceleration. In the real machine, the orbit
correction has been done.

The discrepancy from the global beta measurement is found. But,
the result was consistent with each other for the large beta-beatwhich was made by the known gradient error.

Orbits of injected beam can be measured by the single-passBPMs.