November 14, 2004 First ILC Workshop 1

CESR-c Wiggler DynamicsD.Rubin

-Objectives-Specifications-Modeling and simulation-Machine measurements/ analysis

November 14, 2004 First ILC Workshop 2

CESR-c Superconducting Wigglers

- Damping and emittance wigglers for 1.8GeV operation Reduce radiation damping time by X 10 (500ms->50ms)

•Injection repitition transfer rate from synchrotron is limited by damping time in storage ring

•Single and multi-bunch instability thresholds scale inversely with damping rate

•Beam beam tune shift limit ~ (damping rate)1/3

•Tolerance to parasitic beambeam effects ~ (damping rate)1/3

Increase horizontal emittance Beam beam current limit ~ emittance

November 14, 2004 First ILC Workshop 3

CESR-c

Electrostatically separated electron-positron orbits accomodate counterrotating trains

Electrons and positrons collide with ±~3 mrad horizontal crossing angle

9 5-bunch trains in each beam

(768m circumference)

November 14, 2004 First ILC Workshop 4

Wiggler specifications:

- 2.1T peak field (vs 0.2T max bending field) -Uniform over 9cm horizontal aperture, -Long period (40cm) to minimize vertical cubic nonlinearity -Complete installation is 12, 1.6m superconducting wigglers

- CESR-c is a wiggler dominated storage ring (>90% of synchrotron radiation in 768m ring in 19m of superconducting wigglers)

- 3kW/wiggler synchrotron radiation with IB = 200 mA

November 14, 2004 First ILC Workshop 5

Ideal Wiggler

πλϑ20

0 w

E

ceB=

Vertical kick ~ Bs

€

Δ ′ y = −B0

2L

2(E0 /ce)2y +

2

3

2π

λ

⎛

⎝ ⎜

⎞

⎠ ⎟2

y 3 + ... ⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

€

Bs = −B0 sinh(ky y)sin(kss)

November 14, 2004 First ILC Workshop 6

7-pole, 1.3m 40cm period, 161A, B=2.1T

Superconducting wiggler prototype

November 14, 2004 First ILC Workshop 7

Wiggler model:

- Phase space mapping through wigglers required for simulation of dynamical effects - Create field vs position table for wiggler geometry with OPERA-3D finite element code - Measured field in good agreement with computed field table

November 14, 2004 First ILC Workshop 8

7 and 8 pole wiggler transfer functions

November 14, 2004 First ILC Workshop 9

€

Bx = Ckx

ky

sinh(kx x)sinh(ky y)cos(kss + φs)

By = C cosh(kx x)cosh(ky y)cos(kss + φs)

Bs = −Cks

ky

cosh(kx x)sinh(ky y)sin(kss + φs)

€

Bx = Ckx

ky

sinh(kx x)sin(ky y)cos(kss + φs)

By = C cosh(kx x)cos(ky y)cos(kss + φs)

Bs = −Cks

ky

cosh(kx x)sin(ky y)sin(kss + φs)

Wiggler Field Model

€

B fit = Bn

n=1

N

∑ (x,y,s;Cn ,kxn ,ksn ,φsn, fn )

-Finite element code -> 3-d field table-Fit analytic form to table

€

( fn = 3)

€

ky2 = ks

2 − kx2

€

ky2 = kx

2 − ks2

€

( fn = 2)

€

( fn =1)

€

Bx = −Ckx

ky

sin(kx x)sinh(ky y)cos(kss + φs)

By = C cos(kx x)cosh(ky y)cos(kss + φs)

Bs = −Cks

ky

cos(kx x)sinh(ky y)sin(kss + φs)

€

ky2 = kx

2 + ks2

November 14, 2004 First ILC Workshop 10

Wiggler modeling

-Phase space mapping

Fit parameters of series to field table

Analytic form ofHamiltonian -> symplectic integration -> taylor map

November 14, 2004 First ILC Workshop 11

7-pole wiggler

November 14, 2004 First ILC Workshop 12

Measurement and correction of linear lattice

Measured - modeled

Betatron phase

and transverse coupling

November 14, 2004 First ILC Workshop 13

Measurement of wiggler nonlinearity

-Measurement of betatron tune vs displacement consistent with modeled field profile and transfer functon

November 14, 2004 First ILC Workshop 14

Wiggler Beam Measurements

-Injection

1 sc wiggler (and 2 pm CHESS wigglers) -> 8mA/min

6 sc wiggler -> 50mA/min

1/ = 4.5 s-1

1/ = 10.9s-1

November 14, 2004 First ILC Workshop 15

Wiggler Beam Measurements 6 wiggler lattice

-Injection

30 Hz 68mA/80sec 60 Hz 67ma/50sec

November 14, 2004 First ILC Workshop 16

Wiggler Beam Measurements

-Single beam stability

1/ = 4.5 s-1 1/ = 10.9s-1

2pm + 1 sc wigglers 6 sc wigglers

November 14, 2004 First ILC Workshop 17

Sextupole optics

Modeled pretzel dependence of betatron phase due to sextupole feeddown

Difference between measured and modelled phase with pretzel after correction of sextupoles

November 14, 2004 First ILC Workshop 18

Optimization of sextupole distributioneliminates synchro-betatron resonance

November 14, 2004 First ILC Workshop 19

Summary

CESR-c is a wiggler dominated storage ring

• Wigglers reduce damping time by a factor of 10• Injection rate and multibunch instability thresholds are increased as anticipated• Analytic form for magnetic field (including ends) yields accurate phase space mapping• Measured and modeled

•Linear and nonlinear focusing effects•Emittance•Damping rate•Dynamic aperture

in good agreement

Conclusion: Good understanding of dynamics of wiggler dominated damping ring

November 14, 2004 First ILC Workshop 20

Acknowledgement

A. Mikhailichenko, S.Temnykh, D. Rice, J. Crittenden, D.Sagan, E. Forest and the CESR operations group

November 14, 2004 First ILC Workshop 21

ILC Damping Ring R&D

• Evaluate dynamic aperture of various alternatives

• Determine dependence of acceptance on - linear lattice parameters - sextupole distribution to minimize energy dependence and optimize aperture

• Consider dependence on wiggler period/peak field/unit length

• Continue study of transverse RF for separation of closely space bunches

November 14, 2004 First ILC Workshop 22

Transverse RF introduces bunch dependent offsets

Transverse RF compensates offsets

Circumference = 4km

Linear collider damping ring

Rich Helms