SYNCHROTRON INJECTION
T. Mori
The 17th KEKB Accelerator Review Committee
Feb. 21, 2012

Why it necessary?
 Very low survival rate with betatron injection into HER is expected If offset ⊿𝑥 from IP for betatron oscillation,
 Kicked vertically by beam-beam force from the colliding beam
Tracking example with beam-beam interaction

𝑒+𝑒−IP

Offsetinteraction*
Injected oscillating beam

* Finite 𝑦-amplitude⟹ Large beam-beam kick∵ Hour-glass effect

Survive: 24%
Y. Ohnishi

 Synchrotron oscillation ⇒ no offset ⊿𝑥 (∵ 𝜂 ∗ = 0)

Synchrotron injection (as a backup option of betatron inj.)
T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 20122

Synchrotron Injection
Schematic view of injections
Betatron Injection

Synchrotron Injection

Injected beam

SeptumInjected beam

⊿𝐸

Parameter assumption

Injection bump

Injection bump𝑤𝑆 = 5[mm]𝛽𝑥𝑅 = 60[m]𝜀𝑥𝑅 = 4.6[nm]𝜎𝛿𝑅 = 0.059 %𝑛𝑅 = 3.0

 Generate dispersion (𝜂𝑥𝑅 )𝛽𝑥𝐼 = 20[m] Injection with energy difference (𝛿0 = ⊿𝑝/𝑝0 )𝜀𝑥𝐼 = 1.46[nm] ⊿𝑥 = 𝜂𝛿0 = 𝑛𝐼 𝜎𝑥𝐼 + 𝑤𝑆 + 𝑛𝑅 𝜎𝑥𝑅

𝜎𝛿I = 0.1[%]

𝑛𝐼 = 2.5

Q-magnet

Stored beam

Q-magnet

Stored beam

 Take advantage of synchrotron oscillation

𝜎𝑥 =𝛽𝑥 𝜀𝑥 + 𝜂𝑥 𝜎𝛿 2T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 20123

Synchrotron Injection
 What are requirements to realize?
 ⊿𝑥 = 𝜂𝑥𝑅 𝛿0 = 𝑛𝐼 𝛽𝑥𝐼 𝜀𝑥𝐼 + 𝜂𝑥𝐼 𝜎𝛿𝐼 2 + 𝑤𝑆 + 𝑛𝑅 𝛽𝑥𝑅 𝜀𝑥𝑅 + 𝜂𝑥𝑅 𝜎𝛿𝑅 2Orbit shift

Injected beam spread

Stored beam spread

Septum width𝑤𝑆 [m] Assumption from optics study: 𝛿0 + 2𝜎𝛿𝐼 = 0.65[%] 𝜎𝛿𝐼 = 0.1 % &𝜂𝑥𝑅 = 1.4[m]⟹ 𝑤𝑆 < 3[mm] required Important parameters
 𝑤𝑆 , 𝜂𝑥𝑅 , 𝜎𝛿𝐼 Have the 1st order effect𝜂𝑥𝑅 [m]T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 20124

Injection Septum（𝑤𝑆 ） Get thinner 𝑤𝑆𝑤𝑆

𝜂𝑥𝑅

𝜎𝛿𝐼

Magnification

 Suppress leak field Calculation (OPERA)
Transient analysis
 Sine wave(𝜏 = 0.3[ms])𝐵max = 1[T]𝐵max = 1[T]Schematic view of SuperKEKB HER septum
Main ring

Septum MagnetFe?
6mmB⨀

200μm Cu𝑤𝑆 = 2.5 + 1⊿𝑥Current：𝑤𝑆 = 3.5[mm]⨀CoreCu



Si-Steal

Non-uniform field region included
KEKB: 5mmIssues
Magnetic material for vacuum chamberShim shape To reduce non-uniform region

T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 20125Injection Septum Upgrade𝑤𝑆

𝜂𝑥𝑅𝜎𝛿𝐼 Alternation of septum conductor
 Thickness: 1.5mm ⟶ 1.0mm
 Skin depth: 1.2mm ⟹ Leakage field should be considered Perform field measurement
 3D transient field calculation is too heavy

 Producing
 1mm septum conductor
 Mockup of beam chamber
50𝜇m20turns

𝐵 = 10−4 [T]𝜙1.2mm

Pickup coil𝑉0 = 30[mV]

Septum conductor（before alternation）
T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 2012

6

Dispersion (𝜂𝑥𝑅 )

𝑤𝑆

𝜂𝑥𝑅

𝜎𝛿𝐼

 Optics calculationMatching 𝜂 = −1.6[m] 𝜀𝑥 = 4.6[nm] Kicker bump:
25mm

Injection point

T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 20127

Energy Spread（𝜎𝛿𝐼 ）𝑤𝑆𝜂𝑥𝑅𝜎𝛿𝐼

 Simple calculation with Linac parameters Acceleration field：2856MHz Bunch length：FWHM = 3[mm] On crest acceleration
 Space charge & wake field are not considered
Gaussian beam

Rectangular beam𝜎𝛿𝐼 [%]

0.410.12

Injection efficiency

0.70.9• Assuming only 𝛿𝐼 ≤ 0.1[%] part of beam is successfully injected Study is on going in Linac groupto reduce energy spread
T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 20128

Result & Summary Due to hour-glass effect, very low survival rate with betatron

injection into HER is expected⟹ synchrotron injection
 Considered requirements for synchrotron injection scheme𝑤𝑆 [m]

 Effective septum width: 3.5mm
 Dispersion: −1.6m
 Energy spread:𝜎𝛿𝐼 = 0.1%

 In progress Septum Shim of pole
 Storage beam chamber
 1mm septum conductor
 Injection tracking
 Check survival rate
T. Mori, The 17th KEKB Accelerator Review Committee

𝜂𝑥𝑅 [m]21 Feb., 20129

Thank you!
T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 201210

BackupT. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 201211

Motivation
 Betatron injection is impossible Because of low emittance More phase space expected in synchrotron oscillation ⊿𝑥 ∼ 7[mm]

Dynamic Aperture for HER

 𝜀𝑥 = 4.6[nm] 𝛽𝑥 ∼ 100[m] 𝜎𝑥 ∼ 700[μm]Y. Ohnishi

T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 201212

Synchrotron Injection
 Take advantage of synchrotron oscillation
 Generate dispersion (𝜂) at injection point Injection with energy difference (𝛿0 ) ⊿𝑥 = 𝜂𝛿0 = 𝑛𝐼 𝜎𝑥𝐼 + 𝑤𝑆 + 𝑛𝑅 𝜎𝑥𝑅 𝛿0 + 2𝜎𝛿𝐼 = 0.65[%]

𝜎𝑥 =Schematic view of KEKB HER septum

𝑤𝑆 = 5[mm]𝛽𝑥𝑅 = 60[m]𝜀𝑥𝑅 = 4.6[nm]𝜎𝛿𝑅 = 0.059 %𝑛𝑅 = 3.0𝛽𝑥𝐼 = 20[m]𝜀𝑥𝐼 = 1.46[nm]𝜎𝛿I = 0.1[%]

𝑛𝐼 = 2.5

T. Mori, The 17th KEKB Accelerator Review Committee

21 Feb., 2012

11mmCu⨀⨀CoreCu

KEKB parameters

Main ring

Septum Magnet

B

𝛽𝑥 𝜀𝑥 + 𝜂𝑥 𝜎𝛿 2Si-steel
sheet × 2𝑤𝑆⊿𝑋

13

Gaussian BeamE-field (𝐸 𝐸max ) 𝜎𝛿 = 0.4[%]
 Obtain 𝜎𝛿 = 0.1[%]Bunch 𝛿cut = 0.4[%]

 Efficiency : 0.7

𝛿

𝜎 - efficiency𝜎 - 𝛿cut

RectangularBeam

E-field (𝐸 𝐸max ) 𝜎𝛿 = 0.12[%]Bunch

 Obtain 𝜎𝛿 = 0.1[%]
 𝛿cut = 0.4[%]
 Efficiency: 0.9
𝛿

𝜎 - 𝛿cut𝜎 - efficiency

セプタム磁場の温度依存性