1. Update on the TDI impedance simulations and RF heating for HL- LHC beams Alexej Grudiev on behalf of the impedance team TDI re-design meeting 30/10/2012

2. outline Geometry of TDI and the source of impedances Simulation of the trapped modes Calculation of the impedance of the absorber blocks Summary

3. Geometry of TDI in HFSS. Horizontal plane of symmetry is used Half gap = 8 mm Big size and complex shape results in a huge number of the trapped modes with sharp narrow band impedance Proximity of the absorber blocks to the beam results in the broad band impedance, i.e. resistive wall impedance

4. R/Q estimated from longitudinal impedance calculated in CST, hBN, b0, σ z = 50 mm 4(Zl-Zl0)*df/πf is plotted where Zl0 = 71 Ohm to make the real part positive BUT the Q-factor cannot be found in time-domain CST simulations

5. R/Q estimated from longitudinal impedance, hBN, b0, σ z = 100 mm, and HFSS eigenmode results 4(Zl-Zl0)*df/πf is plotted where Zl0 = 71 Ohm to make the real part positive

6. Table of longitudinal mode parameters calculated in HFSS, hBN, 4S60@500MHz accelerator definition of R/Q: P=I 2 *R/Q*Q -?

7. Low frequency mode at 31 MHz Electric field distribution in horizontal and vertical planes (log scale) f = 31 MHz; Q = 164; RT = 80 Ohm; P loss for I b =0.36A: ~10W All volume filled with EM fields Inside and outside of beam screen

8. Low frequency mode at 58.6 MHz Electric field distribution in horizontal plane f = 58.6 MHz; Q = 195; RT = 150 Ohm; P loss for I b =0.36A: ~19W power loss distribution: 50% -> Al keeper 43% -> Cu beam screen 2 x 2% -> Cu flexible contacts 2% -> SS jaw support 1% -> SS vacuum tank All volume filled with EM fields Inside and outside of beam screen

9. High frequency mode at 1224 MHz Electric field distribution in horizontal plane Localized field distribution f = 1224 MHz; Q = 755; RT = 14 kOhm power loss distribution: 49% -> Al keeper 38% -> Cu beam screen 1.5% -> Cu flexible contact 4% -> SS jaw support 7.5% -> SS vacuum tank

10. Power loss for 50 and 25 ns HL-LHC beams Gaussian bunches: sigma_z = 85 mm

11. Power loss for 50 and 25 ns HL-LHC beams cos^2 bunch: total bunch 1.336 ns

12. A way to estimate shunt impedance for other gaps and boundary conditions w/o lengthy HFSS simulations

13. Comparison of the power estimate from CST and HFSS calculations Shunt impedance for other gaps and boundary conditions (BC) can be estimated using CST R/Q estimate calculated for specific gap and BC and assuming HFSS Q estimate calculated for gap=16mm is valid for other gaps and BC, then the power loss estimate can be done without long HFSS simulations

14. Power estimated from ReZl, hBN, hgap=8mm, σ z = 85 mm, same HWHH: b0,b1,b2

15. Power estimated from ReZl, hBN, hgap=8->20->55mm, cos^2 bunch, HL-LHC 25 ns beam : b0,b1,b2 hgap=8mm hgap=20mm hgap=55mm The impedance of the low frequency modes (<200MHz) weakly (far from linear) depends on the gap! At fully open jaws position a few 100s of Watts can be dissipated mainly on the block keepers and beam screen. The impedance of the higher frequency modes (> 1 GHz) depends on the gap, roughly linear with the gap. Power dissipation is reduced from a few kilowatts down to the level of 100 Watts.

16. Coating simulations Reasonable agreement in Real part, less good in imaginary. Convergence ??? This is preliminary results of the on-going work. At this moment we can not simulate the coating s directly in 3D simulation codes. Some model have to be used. OR analytical formalism for parallel plate geometry.

17. Re. Wall Power loss for HL-LHC beam 50 ns 1404, 3.5e11 N. Mounet

18. Re. Wall Power loss for HL-LHC beam 25 ns 2808, 2.2e11 N. Mounet

19. RF heating of the hBN blocks coated with 5 um of Ti flash coating ~1 kW power is dissipated in 5 um coating over a surface of ~Lx4b = 2.8m x 20mm The surface power deposition density: 18 kW/m 2 The volume power deposition density: 3.6 GW/m 3 Is it an issue??? 2b

20. Summary Trapped modes can results in few 100s of Watt RF heating even for fully open TDI position. Deposited ~ 50/50 on the jaws and beam screen. The power loss could be much (x10) higher for closed position. Broad band resistive impedance results in higher RF heating for small gap ~1kW and much smaller (x10) for fully open. Power deposition in very thin coating could be an issue especially if the beam passes close to one jaw.