Undulator Tolerance Budget Introduction Heinz-Dieter Nuhn, SLAC / SSRL January 27, 2005

1. Undulator Tolerance BudgetIntroduction Heinz-Dieter Nuhn, SLAC / SSRLJanuary 27, 2005 • Present Undulator Tolerances • Tolerance Budget Issues 1

2. Undulator Tolerances Based on Linear Simulations • RON Simulation • Tolerance Criterion: • Saturation length increase stays below one gain length • Tolerance Requirement: • Limit phase error to 10 degrees per segment,i.e., the actual phase slippage per segment should notdeviate from ideal phase slippage by more than 10 degrees 2

3. Electron Beam Phase Slippage Budget Contributions • Undulator Magnet Tuning Tolerance • Temperature Stability Tolerance • Horizontal and Vertical Segment Alignment Tolerance • Residual BBA Trajectory Straightness Tolerance • Beam Trajectory Control Tolerance • BPM Position Tracking Tolerance • Ground Motion Amplitude • Launch Condition Stability Tolerance 3

4. Phase Error Estimates from Undulator Tolerances Resulting Phase Error Vertical Segment Position ± 70 mm + 9 deg / seg Horizontal Segment Position ± 180 mm ± 6 deg / seg Segment Yaw Tolerance (rms) 50 mrad Segment Pitch Tolerance (rms) 14 mrad Segment Roll Tolerance (rms) 1000 mrad Horz. RMS Beam Based Alignment Trajectory 8.2 rad + 5.1 deg / seg Vert. RMS Beam Based Alignment Trajectory 4.9 rad + 4.8 deg / seg Undulator Environment Temperature Tolerance ± 0.2 oC ± 8 deg / seg Effective Undulator Parameter K Tolerance ± 0.015% ± 10 deg / seg BPM Tracking Error ± 1 mm Launch Position Tolerance (rms) ± 7.3 mm Launch Angle Tolerance (rms) ± 0.24 mrad Horz. / Vert. b-Function Matching Tolerance 2 % 4

5. Undulator Tolerances Based on SASE Simulations • Saturation length increase difficult to extract from SASE simulation data • New Performance Measure: • Evaluate total fundamental FEL power at two fixed points along undulator • 90 m (Before target saturation point, end of linear regime) • 132 m (End of Undulator) • Tolerance Requirement: • See: GENESIS 1.3 Simulation presentation by Sven Reiche • Beta-Function Mismatch • Beam Offset • Module Detuning • Horizontal Module Offset • Vertical Module Offset • Quadrupole Gradient Error • Transverse Quadrupole Position Misalignment 5

6. Conclusions • A number of individual tolerances are being used, each set to keep saturation length increase to one gain length. • Effect of different tolerances add up in different ways. • Budget considerations are required. 6

7. End of Presentation 7