Nondestructive beam energy-spread monitor
using multi-stripline electrodes

T. Suwada (e-mail:tsuyoshi.suwada@kek.jp)
Accelerator Laboratory,High Energy Accelerator Research Organization (KEK),
1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

1

Motivations

Beam feedback controls in daily operation of the linac•
Beam position feedback•Beam energy feedback•Beam energy-spread feedback (under construction)‡ A nondestructive energy-spread monitor contributes toward further stableoperation/injection of the linac.
‡ We developed the new beam energy-spread monitor with multi-striplineelectrodes.

sThis work was strongly motivated by a pioneering work by R. H.
Miller, et al.[HEAC’83, pp.602-605].
‡ They showed that a stripline-type BPM with four pickups could beutilized as a nonintercepting emittance monitor.

s

Also our previous work using similar stripline-type BPMs [Jpn.J.App.
Phys. 40 (2001), pp.890-897] demonstrated that the higher-order(second- and third-order) moments of an electron beam were directly
measured depending upon the transverse beam sizes.

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

2

Beam Energy-Spread Monitor with Eight
Stripline-Type Electrodes

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

3

Multi-Stripline Energy Spread Monitor:
Mechanical design parameters

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

4

Multipole Analysis of the Electromagnetic
Field Generated by a Charged Beam:
Beam-Induced Electric-Field Lines
Electric-Field Line ++++ Charged Particle+Image Charges++++ Pickup++++

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

5

Multipole Analysis of the Electromagnetic
Field Generated by a Charged Beam:
Wall current formula and its multipole expansions

For a conducting round duct, the image charge density by aline charge is formulated by,I(r,f )
R2 - r 2j(r,f,R,q ) =,2pR R 2 + r 2 - 2rRcos(q - f )sExpanding the image charge density in a power series ofr/R,n•˘I(r,f ) ÈÊr ˆj(r,f,R,q ) =1 + 2Â Ë ¯ cosn(q - f ) ˙.
Í2pR În =1 R
˚Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

6

Multipole Analysis of the Electromagnetic
Field Generated by a Charged Beam:
Wall current formula and its multipole expansion(cont’d)s Assuming the transverse r-distribution r(r) of a travelingcharged beam, the total image charge J is formulated by,
R 2p

J(R,q ) = Ú Ú j(r,f,R,q )r(r) rdrdf .
0 0sIt is easily expanded by the power series,
J(R,q ) ªIb Ï2[·xÒcosq + ·yÒsinq ]1+Ì2pR Ó R

222222 (·x Ò - ·y Ò + ·xÒ - ·yÒ ) cos2q + 2(·xy Ò + ·xÒ·yÒ) sin2q
R+higher orders}.
+Tsuyoshi Suwada/KEKB Injector Linac[8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003]
7

Multipole Analysis of the Electromagnetic
Field Generated by a Charged Beam:
Wall current formula and its multipole expansion(cont’d)sThe multipole moments are definedfor the 1st-order moment,·xÒ = Ú xj (x, y) r(x,y)dxdy, ·yÒ = Ú yj( x,y) r(x, y)dxdy,, for the 2nd-order moment,·x 2 Ò = Ú x 2 j(x,y) r(x, y)dxdy, ·y 2 Ò = Ú y 2 j(x, y)r(x,y)dxdy,
and for the xy coupling term,·xyÒ = Ú xyj(x,y) r(x, y)dxdy.

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

8

Multipole Analysis of the Electromagnetic
Field Generated by a Charged Beam:
Wall current formula and its multipole expansion(cont’d)sAssuming a gaussian function for the transverse charge distribution,
the total image charge density is formulated by,

Ib
J(R,q ) =2ps xs y
J(R,q ) ªÚÚ

È -( y - y 0 ) 2 ˘
È -( x - x 0 ) 2 ˘j(r,f ,R,q )exp Íexp Ídxdy,22˙˙I(r,f )
2s2sÎ
˚xyÎ
˚Ib ÏyÈx˘
Ì1 + 2 0 cosq + 0 sin q
2pR Ó
ÎRR˚
ÈÊ s x2 - s 2y x 02 - y 02 ˆ˘x0 y 0˜+ 2ÍÁ
+cos2q+2sin2q222˙RRRË¯Î˚È x 0 Ê 3(s 2x - s y2 ) x02 - 3y 02 ˆÊ 3(s 2x - s y2 ) 3x 20 - y 20 ˆ˘y0ÁÁ˜ cos3q +˜ sin 3q ˙+ 2Í
++2222RRRRRR¯Ë¯Î Ë˚+ higher orders},

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

9

Multipole Analysis of 8-Electrode BESM
sThe multipole moments are defined• for the 1st-order (dipole) moments,
8Vi cosq
2p2pÂ·xÒi =1J dx ≡= Ú J(R,q )cosqdq Ú J(R,q )dq @,8R00
Â Vii =18Vi sinq2pÂ·yÒ 2p
J dy ≡= Ú J(R,q )sinqdq Ú J(R,q )dq @ i =1 8,R00
ÂVii=1• and for the 2nd-order (quadrupole and skew) moments,82p2p
Â Vi cos2q
1 2222J q ≡ (·x Ò - ·y Ò + ·xÒ - ·yÒ ) = Ú J(R,q )cos2qdq Ú J(R,q )dq @ i =1 8,R00
Â Vii =182p2p
Â Vi sin2q1J s ≡ 2 (·xyÒ + ·xÒ·yÒ) = Ú J(R,q)sin2qdq Ú J(R,q )dq @ i =1 8,R00
Â ViTsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

i =110Multipole Analysis of 8-Electrode
BESM (cont’d)• Using the 2nd-order (quadrupole and skew) moments, theskew angle (x-y coupling) of the beam is formulated by

qskew = J s / 2J q ,• and the beam energy spread is also formulated using theoptics parameters and transverse emittances by2

Ê DE ˆ·x Ò - ·y Ò @ b xe x + Ë hx
- b ye y + g.
¯E22

where g is the offset due to the gain imbalance and thegeometrical errors of the pickups.
Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

11

Multi-Stripline Energy Spread Monitor:
Charge Simulation Method

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

12

Multi-Stripline Energy Spread Monitor:
Jquad-Sensitivity Calculation
0.3

4Pickups(SmallR)
0.2

8Pickups(SmallR)

Jquad

0.1

8Pickups(LargeR)
08pu/Jq@Sigma_Y=0.1
8pu/Jq@Sigma_Y=2.1
4pu/Jq@Sigma_Y=0.1
4pu/Jq@Sigma_Y=2.1
Jq@Sigma_Y=0.1/8pu(smallR)
Jq@Sigma_Y=2.1/8pu(smallR)

-0.1

-0.2
00.5

11.5

Energy Spread (sE /E) [%]Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

13

Beam Test at the 180-degree J-arc
section of the injector linac

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

14

Beam Test:Experiment and beam condition
1. Beam Conditions:•single bunch (KEKB) electron and high-current e-/e+ production
beam (bunch width=12ps, bunch charge=0.9 and 8nC, repetition
rate=25Hz)•beam energies (Eb=1.7GeV) at the linac J-arc.
2. Second-order moments (quadrupole and skew moments) were measured
by the BESM depending upon the rf phase of the booster klystronand the transverse beam positions.
3. Beam-size calibration was performed by a fluorescent screen monitor
with a high-resolution image processing system.
4. Data-acquisition system of the BESM comprises a signal-digitizing
system of a fast oscilloscope(LeCroy WavePro 950) with a sampling
rate of 8-GS/s (BW=1GHz) and a PC/Linux-based computer with aPentium IV microprocessor at 2.2GHz.

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

15

Experimental Results:
phase=0deg (0.9-nC e- beam)Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

16

Experimental Results:
phase=+3deg (0.9-nC e- beam)Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

17Experimental Results:
Beam-size measurement by the screen monitor
system depending on the rf phase (0.9-nC e- beam)Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

18

Experimental Results:
Variations of the horizontal and verticalbeam-position dependence of Jquad

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

19

Experimental Results:
Variations of Jquad and the rf phase resolution
depending on the rf phase(0.9 and 8-nC e- beams)

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

20

Experimental Results:
Variations of the skew angles depending upon the rfphase(0.9 and 8-nC e- beams)s

Tsuyoshi Suwada/KEKB Injector Linac

The obtained skew angles inaverage are• 21 and 20 mrad for the
0.9- and 8-nC e- beamover the measured
region of the rf phase.

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

21

Experimental Results:
Variations of the beam energy spread depending
upon the rf phasesThe obtained beam energyspreads were• 0.150±0.007% for the0.9-nC e-,• and 0.264±0.004% for
the 8-nC e-/e+ production
at the rf phase of theenergy-spread minimum
The resolution of themeasurement is on the order of10-3 depending upon the beam
charge and the rf phase.

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

22

Experimental Results:
Time trend of the beam energy spread and the rf
phase of the booster klystron

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

23

Conclusionsss•Result of the beam-size measurement by the BESM is consistent well withthat obtained by the fluorescent screen monitor system, where the 2ndorder moments need to be corrected with the transverse beam positions.
•RF phase resolutions were• less than 1 deg. for the high-current primarly electron(8-nC) beam,and less than 1 deg. over the region of ±1 deg. apart from the rf phase at theenergy-spread minimum.

s•Beam energy spreads were
• 0.150±0.007% for the 0.9-nC electron beam,• and 0.264±0.004% for the 8-nC e- beam, and the resolution is on the order of10-3 depending upon the beam charge and the rf phase.

s•Skew angles of the electron beam were• 21 and 20 mrad in average over the measured region of the rf phase for the 0.9and 8-nC electron beam, respectively.

Tsuyoshi Suwada/KEKB Injector Linac

8th KEKB Acc. Rev. Committe, Feb.
10-11, 2003

24