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TDI trapped modes for hgap =8mm, HFSS eigenmode simulation results hBN , eps = 4

TDI trapped modes for hgap =8mm, HFSS eigenmode simulation results hBN , eps = 4. Grudiev 14/09/2012. Geometry of TDI in HFSS. Horizontal plane of symmetry is used. Half gap = 8 mm. R/Q estimate from PEC impedance calculated in CST. Reminder from classical P. Wilson, SLAC-PUB-4547.

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TDI trapped modes for hgap =8mm, HFSS eigenmode simulation results hBN , eps = 4

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  1. TDI trapped modes for hgap=8mm, HFSS eigenmode simulation resultshBN, eps = 4 Grudiev 14/09/2012

  2. Geometry of TDI in HFSS. Horizontal plane of symmetry is used Half gap = 8 mm

  3. R/Q estimate from PEC impedance calculated in CST Reminder from classical P. Wilson, SLAC-PUB-4547 For impedance of N modes with Q >> f/df, where df=c/s_max, for PEC Q~∞

  4. R/Q estimated from longitudinal impedance calculated in CST, hBN, b0, σz = 50 mm 4(Zl-Zl0)*df/πf is plotted where Zl0 = 71 Ohm to make the real part positive

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

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

  7. Table of longitudinal mode parameters calculated in HFSS, hBN, 4S60@500MHzaccelerator definition of R/Q: P=I2*R/Q*Q -? -? Power loss on the different surfaces normalized to the total power loss: P_vt - power loss on the vacuum tank walls P_bs – power loss on the beam screen surface P_fc1,2 – power loss on the surfaces of the flexible contacts 1 and 2, respectively

  8. Low frequency mode at 31 MHzElectric field distribution in horizontal and vertical planes (log scale) All volume filled with EM fields Inside and outside of beam screen f = 31 MHz; Q = 164; RT = 80 Ohm; Plossfor Ib=0.36A: ~10W

  9. Low frequency mode at 58.6MHzElectric field distribution in horizontal plane All volume filled with EM fields Inside and outside of beam screen f = 58.6 MHz; Q = 195; RT = 150 Ohm; Ploss for Ib=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

  10. 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

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

  12. hBN modesTable of longitudinal mode parameters calculated in HFSS, hBN, 4S60@500MHzaccelerator definition of R/Q: P=I2*R/Q*Q Coupling to beam 2 is zero since the field is between the hBN blocks

  13. hBN mode, f=1.9675 GHz, Q=10299 Most of the field is in the hBN blocks R/Q [0,b1,b2] = [645, 518, 0] Ohm R [0,b1,b2] = [6.64, 5.33, 0] MOhm

  14. Electric field distribution forhBN mode, f=1.9675 GHz, Q=10299

  15. RF losses distribution for hBNmode, 1st order tetr.: f=1.9675 GHz, Q=10299/2nd order tetr.: f =1.9664 GHz, Q=9275 1st : Q=Wω/(Pv+Ps) =21.4e-16*2*3.14*1.97e9/(0.29e-9+2.77e-9) = 8652 2nd: Q=Wω/(Pv+Ps) = 5.9e-16*2*3.14*1.97e9/(0.12e-9+0.84e-9) = 7600

  16. RF losses distribution for hBNmode, Keeper in Al: f=1.9675 GHz, Q=10299/Keeper in Cu: f =1.9675 GHz, Q=11309R/Q [Ω]: b0 = 518, b1 = 414, b2 = 0

  17. Power loss for HL-LHC beams Gaussian bunch (GB): RMS sigma_z = 85mm RMS sigma_t = 0.284 ns Cos^2 bunch (CB): the same width at half hight as GB: HWHH_t = sqrt(2*ln(2))*sigma_t= 0.334 ns Total bunch length 4*HWHH_t = 1.336 ns ? Measurements on B1 by ThemisM and PhilippeB on fill # 2261

  18. Power loss for HL-LHC beams50 ns / 25 ns • Power loss assuming that the mode frequency is a harmonic of the beam spectrum: P=(Mb*Nb*q*frev)2*R/Q*Q*S(f0) • Power Spectrum functions: • Gaussian bunch: • Cos^2 bunch: • Parameters used: • Mb - number of bunches: 1404 / 2808 • Nb - bunch population: 3.5e11 / 2.2e11 • Frev - revolution frequency: 11.246 kHz

  19. Power loss for 50 and 25 ns HL-LHC beamsGaussian bunches: sigma_z = 85 mm

  20. Power loss for 50 and 25 ns HL-LHC beamscos^2 bunch: total bunch 1.336 ns

  21. Power loss for 50 and 25 ns HL-LHC beamsguassian bunch:sigam_z = 85mmandcos^2 bunch: total bunch 1.336 ns(b1 only, since b2 ~ 0)

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

  23. 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

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