Studies on orbit corrections error analysis Cai Meng Institute of High Energy Physics Joint IHEP-IMP group on C-ADS accelerator physics

Main topics Alignment errors and rf errors The correction scheme of Injector-I The correction scheme of middle β spoke cavity section Summary

Alignment errors and RF dynamics errors The maximum cold misalignment of elements is 1 mm, which is larger than warm misalignment 0.4 mm. The maximum rotation angle is 2 mrad. For the dynamic errors, the field amplitude error is 0.5% and the field phase error is 0.5 degree (reference to SNS). Simulation code is TraceWin. In the correction scheme, the BPMs uncertainty are 100 micron (um). These errors are reasonable ? Error Tolerance Distribution cold element displacement ±1 mm Uniform warm element displacement ±0.4 mm element rotation ±2 mrad BPM uncertainty 0.1 mm RF amplitude fluctuation ±0.5% Gaussian RF phase fluctuation ±0.5º

Preliminary correction scheme of Injector-I The phase advance per period of Injector-I is about 40~90 degree, so there are a pair of correctors and BPMs in one period. Considering the structure of Injector-I, the correctors are attached to solenoid and BPMs are installed in the drift between Spoke cavity and solenoid.

Spoke012 section with anti-symmetric lattice Spoke012 section with anti-symmetric lattice in two cryomodule. Different percent error means that percent of the maximum error. For example, 60% error is 0.6 mm element displacement and 1.2 mrad rotation angle, the rf dynamic error is unchanged. Centroid orbit distribution of 100 linacs with different percent error.

Spoke012 section with the anti-symmetric lattice Control the centroid orbit well Under 0.35 mm(RMS), that means the maximum centroid displacement is about 0.7mm.

Spoke012 section with the anti-symmetric lattice before correction after correction Average emittance (normalized rms emittance ) growth percent with different percent statistics errors (100 linacs) at the lattice end After correction scheme, the transverse emittance growth is under 14 % and longitudinal emittance is under 10% After correction scheme, there is no beam loss.

Spoke012 section with the anti-symmetric lattice  

Spoke012 section with one cryomodule scheme Correction scheme RMS centroid orbit 0.4 mm, the maximum centroid orbit is about 0.8 mm

Spoke012 section with one cryomodule scheme before correction after correction Average emittance (normalized rms emittance ) growth percent with different percent statistics errors (100 linacs) at the lattice end After correction scheme, the transverse emittance growth is under 3 % and longitudinal emittance is under 8%

Spoke012 section with one cryomodule scheme  

Spoke011T section with one cryomodule scheme Maximum centroid orbit is about 0.8 mm

Spoke011T section with one cryomodule scheme After correction scheme, the transverse emittance growth is under 5.7 % and longitudinal emittance is under 8.7%

Spoke011T section with one cryomodule scheme  

Comparative correction results of Injectors Maximum rms centroid orbit after correction is controlled under 0.4 mm The maximum centroid displacement is smaller than 0.8 mm with the maximum errors. Maximum rms centroid orbit(horizontal/vertical) (mm) correction Spoke012 two CM one CM Spoke011T 20% error without 1/0.98 0.76/0.7 0.65/0.62 with 0.14/0.14 0.12/0.11 0.11/0.11 40% error 1.78/1.92 1.34/1.45 1.37/1.27 0.2/0.21 0.18/0.17 0.17/0.18 60% error 2.52/3.15 2.12/2.3 1.7/2.26 0.24/0.22 0.24/0.25 0.23/0.24 80% error 4.34/3.94 2.81/2.92 2.72/2.41 0.33/0.31 0.32/0.33 100% error 5.1/4.3 3.34/3.5 3.64/3.22 0.35/0.38 0.42/0.42 0.42/0.38

Comparative correction results of Injectors Average emittance growth percent Two CM scheme has larger emittance growth, especially transverse. Average emittance growth percent (x / y / z) (%) correction Spoke012 two CM one CM Spoke011T 20% error without 11.9/11.8/5.95 1.78/1.84/5.47 4.1/4/ 4.92 with 11.3/11.1/5.04 1.38/1.72/ /4.3 4.03/3.84/4.83 40% error 14.1/ 13.8/ 9.6 2.9/3.03/9.11 4.3/4.6/6.2 11.6/11.5/5.65 1.74/1.76/4.69 4.14/4.1/5.2 60% error 16.8/16.9/15.7 4.19/4.57/13.7 4.8/4.7/8.2 12/12/6.46 1.86/2.13/5.56 4.6/4.4/6.1 80% error 24.3/24.2/29.5 5.92/6.89/19.3 5.8/ 5.7/11.3 12.7/12.7/8.1 2.24/ 2.5/6.25 5/4.8/7.1 100% error 31.4/32.2/41.4 8.08/10.2/27.5 6.8/ 6.9/15.8 13.8/13.8/9.8 2.78/3.08/7.83 5.6/5.4/8.7

Preliminary correction scheme of middle β spoke section Spoke021 section with two cavities and one solenoid one period Spoke040 section with four cavities and one solenoid one period A pair of correctors and a BPM in one period Spoke040 section: BPM maybe put in the drift between CMs

Preliminary correction scheme of middle β spoke section Maximum centroid orbit is about 0.5mm

Preliminary correction scheme of middle β spoke section After correction scheme, the transverse emittance growth is under 2 % and longitudinal emittance is under 11% After correction, there is no beam loss.

Preliminary correction scheme of middle β spoke section  

Summary According to the phase advance of lattice, a pair of correctors and a BPM are put in one period for solenoid section. The correctors are attached to solenoid. According to the results of centroid obit and emittance growth, the performance of one cryomodule scheme is better than two cryomodule scheme. The correction scheme can control the centroid obit in 0.8 mm even with 1 mm misalignment of elements, meanwhile it can depress the emittance growth greatly.

Further work Repeat the simulation with Track code to compare the results with TraceWin Reduce the number of BPMs to study the correction scheme Simulate detailed and overall error analysis and so on…

Thanks for your attention !