The First trial of XY-coupled Beam Phase Space
Matching for Three-dimensional Spiral Injection*
Muhammad Abdul Rehman#,1), H. Iinuma, S. Ohsawa1, H.
Nakayama1, K. Furukawa1, T. Mibe1, H. Hisamatsu1, H.
Hirayama2, K. Oda2, R. Matsushita3, N. Saito1, K. Sassaki1
1)KEK, 2)Ibaraki University, 3)The University of TokyoContent• Introduction• Spiral Injection Test Experiment (SITE) at KEK• Phase Space Matching• Conclusion

MOPAB162#rehman@post.kek.jp*Work supported by “Grant in Aid” for Scientific Research, JSPS
(KAKENHI#26287055, KAKENHI#19H00673).

9 September 2021

M. A. Rehman, KEK1

Muon g-2/EDM Experiment at J-PARC

Muon’s EDM
Muon’s g-2• Upper Limit; 0.9 × 10-19 e.cm
• 3.8σ discrepancy exist between• No finite EDM found YetExperiment and Standard Model• Excellent Probe for New Physics(NP) • Any Finite value of EDM  NP
𝝁=𝒈𝒒
𝒈−𝟐𝒔 𝒂𝝁 =𝟐𝒎𝟐𝒒
𝒅=𝜼
𝒔𝟐𝒎𝒄

J-PARC E34

Final Goal(g – 2)µ : 0.1 ppm
EDM: 1.5 × 10-21 e.cm
https://doi.org/10.1093/ptep/ptz030

9 September 2021

M. A. Rehman, KEK

2Why inject beam spirally?

Conventional 2D injection (BNL)

Inflector

E34 3T MRI type storage magnet

1.45 Tesla.

BKick

BNL E821
14 m orbit, To avoid beam hit
at inflector (77 mm), kickangle become 10.8 mrad
within 149 ns.
9 September 2021

E340.66 m orbit kick angle is 233 mrad
within 7.4 ns.
Impossible by any existent technology.
3 T is too high to be canceled byinflector.
M. A. Rehman, KEK

3

How to inject beam spirally?

To resolve technical challenges a new 3D Spiral Injection scheme has been invented

Yg

Yg (mm)

Yg=0

Yg=0𝑩𝒌𝒊𝒄𝒌Yg
BY (Gauss)

XY-Coupled

Xg

Zg

e𝑭𝒌𝒊𝒄𝒌Injection

Yg (mm)However,
The Elegance and Advantages
Unprecedented
 Smooth connection between injection
and storage sections: No need of Inflector Therefore, it is indispensable All in one storage magnet, reduceto prove the feasibility of thissource of error fields: No Electric Quad
 No need to kick within a single turn: Simple
newscheme.
kicker
9 September 2021

M. A. Rehman, KEK4

Spiral Injection Test Experiment (SITE)
Spiral Injection Test Experiment Setup at KEK Tsukuba Campus
Storage Magnet
82.5 Gauss

Electron Gun
80 keVe-e-e9 September 2021

M. A. Rehman, KEK5

Phase Space Matching for SITE
Due to the axial
symmetric field of thesolenoid magnet anappropriate XY coupled
beam is requiredMoreover, particles atdifferent vertical
positions face different
radial field andeventually verticalblow-upPhase space matchingis essential to avoid
vertical blow-up
9 September 2021

(Xg, Yg, Zg) aresolenoidal or global
coordinates

YZX(X, Y, Z) are beam coordinates

M. A. Rehman, KEK

6

Phase Space Matching for SITE
Apply transfer matrix consists of coupling parameters (R1,R2,R3,R4)
and Twiss parameters to input phase space

𝑿 = 𝑴. 𝑿𝟎
Twiss Parameters

𝑫𝒙
𝟎−𝟏−𝟏
𝑴 = 𝑼𝒐𝒖𝒕. 𝑫. 𝑼𝒊𝒏
Coupling Parameters

𝟎
𝑫𝒚−𝟏
𝑼𝒊𝒏
= 𝑰𝒅𝒆𝒏𝒕𝒊𝒕𝒚 in our case,
From Coupling Measurement.

𝑴 = 𝑼−𝟏𝒐𝒖𝒕 𝑫

Non-zero values of (R1, R2, R3, R4) shows coupling
9 September 2021

M. A. Rehman, KEK

7

The matching beamline

Iterate 𝜽 and k to match slope
𝑴𝒕𝒐𝒕𝒂𝒍 = 𝑳𝟓. 𝑩𝟏. 𝑳𝟒. 𝑸𝟑𝑹 . 𝑳𝟑. 𝑸𝟐𝑹 . 𝑳𝟐. 𝑸𝟏𝑹 . 𝑳𝟏

9 September 2021

M. A. Rehman, KEK8

Results
Without XY-couplingWith XY-coupling

Gas Monitor

9 September 2021

M. A. Rehman, KEK

9Conclusion

To overcome the vertical beam blow-up in the solenoid-type
storage magnet, a beam transport line consisting of threerotatable quadrupole magnets has been designed and built
The dramatic reduction in the vertical beam size was observedwith the appropriate setting of three rotatable quadrupolemagnets
Without any beam phase–space matching, the beam size grows
to 8.18±0.03 mm (1σ) at the kick point (Y ~100 mm). The verticalbeam blow–up was reduced to 2.56 ± 0.005 mm (1σ) at the kickpoint with the appropriate combination of the three rotation
quadrupole magnets.

9 September 2021

M. A. Rehman, KEK10