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RF Heating in the SLAC Rotatable Collimator Design Liling Xiao Advanced Computations Department SLAC National Accelerato

RF Heating in the SLAC Rotatable Collimator Design Liling Xiao Advanced Computations Department SLAC National Accelerator Laboratory. Outline. Simulation Model Rectangular vacuum tank, Circular vacuum tank Longitudinal Trapped Modes (loss factor, Q 0 )

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RF Heating in the SLAC Rotatable Collimator Design Liling Xiao Advanced Computations Department SLAC National Accelerato

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  1. RF Heating in the SLAC Rotatable Collimator Design Liling Xiao Advanced Computations Department SLAC National Accelerator Laboratory L. Xiao, LARP-CM12, April 9, 2009

  2. Outline • Simulation Model Rectangular vacuum tank, Circular vacuum tank • Longitudinal Trapped Modes (loss factor, Q0) Beam energy loss, Power dissipation • Transverse Trapped Modes (kick factor, Q0) Beam instability, Power dissipation • Ferrite-Loaded Collimator Damped trapped modes in circular vacuum collimator • Summary L. Xiao, LARP-CM12, April 9, 2009

  3. Omega3P calculates the trapped modes below 2GHz andprovides HOM parameters for beam heating and coupled-bunch stability studies Beam Frequency Spectrum F(Hz) L. Xiao, LARP-CM12, April 9, 2009

  4. Rotatable Collimator Rectangular Vacuum Tank Design Circular Vacuum Tank Design Easier for fabrication Beampipe R = 42mm, Fc(TE11) = 2.1GHz, Fc(TM01) = 2.7GHz The collimator jaw will move in and out with a 2mm to 42mm gap. L. Xiao, LARP-CM12, April 9, 2009

  5. Simulation Model Circular Design Rectangular Design x z y ¼ Omega3P Model L. Xiao, LARP-CM12, April 9, 2009

  6. Finite Element Mesh • Tetrahedras with 2nd order curved surface • Denser mesh along beam path plus 3rd order basis functions for better accuracy L. Xiao, LARP-CM12, April 9, 2009

  7. Trapped Mode Excitation Longitudinal Modes With magnetic boundary conditions on x and y symmetric planes, modes with Ez component on z beam axis are excited resulting in energy loss and collimator power dissipation. Transverse Modes With magnetic/electric boundaries on y/x symmetry planes, modes with Ey component between the two jaws are excited when the beam crosses the collimator at an y-offset generating a transverse kick in the y-direction as well as beam energy loss. Due to the small gap of the jaws, this Ey is very strong over the full length of the collimator. L. Xiao, LARP-CM12, April 9, 2009

  8. Longitudinal Trapped Modes Loss Parameters vs. Jaw’s Opening Rectangular Tank Circular Tank When the two jaws move out, more and more EM fields will be generated along the beam path. The loss factors are getting the largest for fully retracted jaws with gap=42mm. L. Xiao, LARP-CM12, April 9, 2009

  9. Longitudinal Trapped Modes RF Parameters for fully retracted jaws, gap=42mm Q0 R Vacuum tank is made of stainless steel, σ=0.116e7s/m. Two jaws are made of copper, σ=5.8e7s/m L. Xiao, LARP-CM12, April 9, 2009

  10. E-field B-field Longitudinal Trapped Modes Lowest Trapped Mode Field Pattern E-field B-field Rec. Tank: f1=82MHz, Q=279 The trapped mode locates between the jaw and chamber wall. Q is lower. Cir. Tank: f1=93MHz, Q=1662 The trapped mode spreads around the jaws. Q is higher. L. Xiao, LARP-CM12, April 9, 2009

  11. Longitudinal Trapped Modes Transient Heating Effects Transient beam energy losses is total energy left by the passage of the bunch train through the collimator. The transient heating power normally causes no problem for structures with good thermal conduction. L. Xiao, LARP-CM12, April 9, 2009

  12. Longitudinal Trapped Modes Resonant Heating Effects Resonant power losses are due to the excitation of these trapped modes. Assuming all bunches are in phase with them and mode decay is lower from bunch to bunch (Td>>Tb): The trapped mode frequencies should be shifted away from 40MHz beam harmonic thus reducing the resonant heating power. L. Xiao, LARP-CM12, April 9, 2009

  13. Transverse Trapped Modes RF Parameters for fully inserted jaws, gap=2mm Kick Q0 When the two jaws are fully inserted with gap=2mm, the kick factors are highest due to the strongest Ey between the two jaws. L. Xiao, LARP-CM12, April 9, 2009

  14. Transverse Trapped Modes Lowest Trapped Mode Field Patterns E-field E-field B-field B-field Rec. Tank: f1=79MHz, Q=382 The trapped mode is between the two jaws and the jaw and chamber wall. Q is lower. Cir. Tank: f1=85MHz, Q=1344 The trapped mode is between the two jaws. Q is higher. L. Xiao, LARP-CM12, April 9, 2009

  15. Transverse Trapped Modes Loss Parameters CircularTank Rectangular Tank Loss factors of transverse modes depend on the beam offset. L. Xiao, LARP-CM12, April 9, 2009

  16. Trapped Mode Heating To be safe, beam heating due to the longitudinal trapped modes in the circular vacuum design needs to be reduced. L. Xiao, LARP-CM12, April 9, 2009

  17. Ferrite-Loaded Collimator Chosen Lossy Material At room temperature and 100K Re. ε Im.ε Re. μ Im. μ F=0~2GHz, ε~10-j0.2, μ~2-j10 at 297k “Measurements of ε and μ of Lossy Materials for the Low Temperature HOM LOAD”, V. Shemelin, et al. “First Studies for a Low Temperature Higher-Order-Mode Absorber For the Cornell ERL Prototype”, M. Liepe, et al. L. Xiao, LARP-CM12, April 9, 2009

  18. Ferrite-Loaded Collimator Damping Longitudinal Trapped Modes w/ Ferrites TT2-111R Ferrite Tile t=2mm t ε=10-j0.2, μ=2-j10 Jaw fully retracted gap=42mm Attaching ferrite tiles on vacuum wall above the top and bottom of the jaws can strongly damp the longitudinal trapped modes. L. Xiao, LARP-CM12, April 9, 2009

  19. E-field B-field Ferrite-Loaded Collimator Lowest Trapped Mode Field Patterns Without Ferrite Tiles With Ferrite Tiles E-field B-field Cir. Tank without ferrite tiles: f1=93MHz, Q=1662 Cir. Tank with ferrite tiles: f1=86MHz, Q=10 After adding ferrite tiles, the trapped mode is absorbed in the lossy material. L. Xiao, LARP-CM12, April 9, 2009

  20. Summary • All trapped modes below 2GHz in the SLAC design are calculated using Omega3P, and their RF heating effects are evaluated. • The longitudinal trapped modes in the circular vacuum chamber design have higher Q-value. In the worst case, the total power heating can reach 500W if they all interact with the beam in resonance. • The heating due to the transverse trapped modes are negligible but the transverse kick on the beam needs to be evaluated. • Adding ferrite tiles in the circular vacuum chamber collimator can strongly damp the trapped modes. Need effort on design and analysis of the tiles that include ferrite’s thermal/mechanical effects. • Using the amplitude ratio of longitudinal and transverse modes to determine the position of the beam is underway. Special thanks to Fritz Caspers for his helpful discussions and advice. L. Xiao, LARP-CM12, April 9, 2009

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