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

hBN, eps = 4A. Grudiev14/09/2012

Geometry of TDI in HFSS. Horizontal plane of symmetry is used

Half gap = 8 mm

R/Q estimate from PEC impedance calculated in CST

00

)(4)0(;)cos()(2

)( dffZWdcsZsW RR

Reminder from classicalP. Wilson, SLAC-PUB-4547

For impedance of N modes with Q >> f/df, where df=c/s_max, for PEC Q~∞

N

nnR

N

n

dff

dff

R

N

nn

N

nn dffZdffZkWW

n

n1111

)(4)(42)0()0(

n

nRn

n

nRn

f

dffZk

Q

R

dffZk

)(44

)(2

R/Q estimated from longitudinal impedance calculated in CST,

hBN, b0, σz = 50 mm4(Zl-Zl0)*df/πf is plotted where Zl0 = 71 Ohm to make the real part positive

0 0.5 1 1.5 2 2.5 3 3.510

-4

10-2

100

102

104

f [GHz]

R/Q

[O

hm]

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

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110

-2

10-1

100

f [GHz]

R/Q

[O

hm]

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

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 210

0

101

102

103

f [GHz]

R/Q

[O

hm]

Table of longitudinal

mode parameters calculated in HFSS, hBN,

4S60@500MHzaccelerator

definition of R/Q: P=I2*R/Q*Q

f [GHz] Q R/Q [Ω], b0 R/Q [Ω], b1 R/Q [Ω], b21 0.031 164 0.513 0.539 0.3842 0.042 257 3.41E-05 0.005 0.09753 0.058 193 0.738 0.778 0.5774 0.066 221 0.0043 0.00247 0.1735 0.086 205 0.463 0.485 0.3596 0.097 256 0.00377 0.00597 0.2587 0.103 292 0.0486 0.0503 0.02898 0.118 240 0.199 0.217 0.1859 0.122 228 0.0121 0.00123 0.112

10 0.149 226 0.138 0.154 0.13211 0.153 262 0.0167 0.006 0.038712 0.181 278 0.0385 0.041 0.042113 0.183 271 0.00917 0.0054 0.01314 0.241 564 0.0637 0.065 0.042315 0.281 74 0.0734 0.067 0.022116 0.324 352 0.0521 0.057 0.036717 0.325 354 0.00608 0.004 0.012318 0.484 319 0.093 0.096 0.051719 0.515 460 0.135 0.137 0.07820 0.721 465 0.108 0.11 0.06621 0.819 547 2.362 2.359 0.74822 0.845 759 0.0436 0.0796 0.059623 0.852 590 0.853 0.846 0.3124 1.07 563 2.102 2.1 0.73325 1.096 700 0.379 0.375 0.11926 1.126 751 3.32 3.301 1.03927 1.2224 358 2.138 2.149 0.60828 1.2225 2025 2.304 2.315 0.66429 1.2247 873 17.193 17.4 4.9230 1.225 726 5.029 5.055 1.15231 1.227 862 3.763 3.794 1.10332 1.26 737 7.401 7.447 2.06233 1.277 869 0.958 0.975 0.26

Power loss on the different surfaces normalized to the total power loss:P_vt - power loss on the vacuum tank wallsP_bs – power loss on the beam screen surfaceP_fc1,2 – power loss on the surfaces of the flexible contacts 1 and 2, respectively

-?-?

Low frequency mode at 31 MHzElectric field distribution in horizontal and vertical planes (log scale)

f = 31 MHz; Q = 164; RT = 80 Ohm; Ploss for Ib=0.36A: ~10W

All volume filled with EM fieldsInside and outside of beam screen

Low frequency mode at 58.6 MHzElectric field distribution in horizontal plane

f = 58.6 MHz; Q = 195; RT = 150 Ohm; Ploss for Ib=0.36A: ~19Wpower loss distribution:50% -> Al keeper43% -> Cu beam screen2 x 2% -> Cu flexible contacts2% -> SS jaw support1% -> SS vacuum tank

All volume filled with EM fieldsInside and outside of beam screen

High frequency mode at 1224 MHz Electric field distribution in horizontal plane

Localized field distribution

f = 1224 MHz; Q = 755; RT = 14 kOhmpower loss distribution:49% -> Al keeper38% -> Cu beam screen1.5% -> Cu flexible contact4% -> SS jaw support7.5% -> SS vacuum tank

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

1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 210

0

101

102

103

f [GHz]

R/Q

[O

hm]

hBN modesTable of

longitudinal mode

parameters calculated in HFSS, hBN,

4S60@500MHzaccelerator

definition of R/Q: P=I2*R/Q*Q

f [GHz] Q R/Q [Ω], b0 R/Q [Ω], b1 R/Q [Ω], b234 1.622 3253 9.311 6.840 0.25635 1.661 6103 13.166 10.115 0.08736 1.662 4597 7.086 5.476 0.08937 1.670 4740 43.689 32.888 0.24938 1.677 5415 51.575 38.545 0.84939 1.679 5047 47.415 37.023 1.07040 1.688 1987 16.703 13.460 0.42041 1.688 1879 12.721 10.454 0.31142 1.753 10625 16.671 13.055 0.00043 1.759 9755 20.653 16.216 0.00244 1.803 10871 107.638 82.588 0.00245 1.808 10697 83.385 65.536 0.00146 1.816 11285 15.719 12.747 0.00347 1.876 9054 13.629 11.121 0.00048 1.884 8635 11.129 8.504 0.09749 1.886 7297 13.315 10.550 0.05550 1.893 5281 30.365 24.038 0.01851 1.896 7181 23.283 18.478 0.09252 1.902 8565 102.385 82.797 0.00553 1.903 9017 30.960 24.344 0.03154 1.904 9759 83.113 65.495 0.07455 1.906 6995 31.454 26.369 0.10056 1.906 10485 90.156 71.705 0.04657 1.908 4766 24.324 19.623 0.06758 1.908 9855 376.136 301.014 0.21059 1.910 12041 112.859 89.382 0.05760 1.910 3097 43.045 34.022 0.10361 1.912 6054 35.682 27.617 0.14462 1.949 5062 12.672 10.352 0.09263 1.958 6306 11.813 8.951 0.06364 1.961 4167 19.523 14.613 0.44065 1.962 1961 13.477 10.656 0.00166 1.965 4746 17.500 13.711 0.22367 1.968 10299 519.195 417.127 0.11968 1.969 4863 122.052 95.551 0.02869 1.970 3324 30.248 23.151 0.11070 1.970 8094 338.797 270.687 0.30071 1.974 6416 13.013 10.728 0.190

Coupling to beam 2 is zero since the field is between the hBN blocks

hBN mode, f=1.9675 GHz, Q=10299Most of the field is in the hBN blocksR/Q [0,b1,b2] = [645, 518, 0] OhmR [0,b1,b2] = [6.64, 5.33, 0] MOhm

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

RF losses distribution for hBN mode, 1st order tetr.: f=1.9675 GHz, Q=10299

/2nd order tetr.: f =1.9664 GHz, Q= 9275

Objects Stored energy [fJ] Volume loss [nW] Surface loss [nW]

Ferrites (4s60@0.5GHz) 1st/2nd ~0 0.29 / 0.12 ~0

Beam screen (Cu) 0 0 0.093 / 0.037

Flex contacts (Cu) 0 0 0.004 / 0.0004

Keeper (Al) 0 0 2.225 / 0.67

Support (SS) 0 0 0.026 / 0.013

Blocks hBN (eps = 4) 16.63 / 4.55 ~0 1.77 / 0.53 (not real, must be 0)

Block Al 0 0 0.012 / 0.005

Block Cu 0 0 0.0005 / 0.0002

Vacuum Tank (SS) 4.75 / 1.37 (vac) ~0 1.00 / 0.31 (double counting)

Total (all objects HFSS) 5.10 / 1.56 (double counting)

Total real 21.38/ 5.92 0.29 / 0.12 1.00 + 1.77 = 2.77 / 0.31 + 0.53 = 0.84

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

RF losses distribution for hBN mode, Keeper in Al: f=1.9675 GHz, Q=10299

/Keeper in Cu: f =1.9675 GHz, Q=11309

R/Q [Ω]: b0 = 518, b1 = 414, b2 = 0Objects Stored energy [fJ] Volume loss [nW] Surface loss [nW] Surface loss [%]

Ferrites (4s60@0.5GHz) ~0 0.29 / 0.19 ~0

Beam screen (Cu) 0 0 0.093 / 0.049 3.4 / 3.7

Flex contacts (Cu) 0 0 0.004 / 0.003 0.1 / 0.2

Keeper (Al / Cu) 0 0 2.225 / 1.00 80.3 / 75.2Support (SS) 0 0 0.026 / 0.022 0.9 / 1.7

Blocks hBN (eps = 4) 16.63 / 9.31 ~0 1.77 / 0.8 (not real) 61.4 / 60.1

Block Al 0 0 0.012 / 0.008 0.4 / 0.6

Block Cu 0 0 0.0005 / 0.00015 0.0 / 0.0

Vacuum Tank (SS) 4.75 / 2.65 (vac) ~0 1.00 / 0.53 (not only SS) 36 / 39.9

Total (all objects HFSS) 5.10 / 2.4 (double count) 184 / 180

Total real 21.38 / 11.96 0.29 / 0.19 1.00 + 1.77 = 2.77 / 0.53 + 0.8 = 1.33

100 / 100

Power loss for HL-LHC beams

0 0.5 1 1.5 2 2.5 310

-2

100

102

104

106

f [GHz]

R [

Ohm

]

b0

b1b2

Gauss

cos2

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

t [ns]

I/I pe

ak

Gauss

cos2

Gaussian bunch (GB): RMS sigma_z = 85mmRMS sigma_t = 0.284 nsCos^2 bunch (CB): the same width at half hight as GB: HWHH_t = sqrt(2*ln(2))*sigma_t = 0.334 nsTotal bunch length 4*HWHH_t = 1.336 ns

Measurements on B1 by ThemisM and PhilippeB on fill # 2261

?

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

22 )2(22/)/( )}({)(;)( tt ftpeak etIFfSeItI

2

2

2

2

])(1[

)sin()}({)(

2ln24;)/cos()(

tt

t

tttpeak

fLfL

fLtIFfS

LLtItI

Power loss for 50 and 25 ns

HL-LHC beamsGaussian bunches: sigma_z = 85 mm

power loss gausin bunch sz = 85 mm or 0.284 ns3.5e+11 p/b, 1404 bunches 2.2e+11 p/b, 2808 bunchesP [W], b1 P [W], b2 P [W], b1+b2 P [W], b1 P [W], b2 P [W], b1+b2

1 69.06 49.30 235.06 109.15 77.91 371.502 1.00 19.55 29.37 1.57 30.90 46.423 116.43 86.36 403.34 184.01 136.48 637.454 0.42 29.68 37.18 0.67 46.90 58.765 76.22 56.44 263.82 120.45 89.19 416.946 1.16 50.30 66.76 1.84 79.49 105.517 11.14 6.40 34.41 17.60 10.11 54.388 39.19 33.36 144.87 61.94 52.72 228.959 0.21 19.14 23.35 0.33 30.25 36.91

10 25.51 21.80 94.48 40.32 34.46 149.3211 1.15 7.39 14.38 1.82 11.68 22.7312 8.06 8.27 32.66 12.74 13.07 51.6113 1.03 2.48 6.71 1.63 3.92 10.6114 23.90 15.58 78.07 37.77 24.62 123.3815 3.03 1.00 7.50 4.78 1.58 11.8516 11.33 7.27 36.75 17.90 11.49 58.0717 0.80 2.44 6.02 1.26 3.85 9.5118 11.43 6.14 34.31 18.06 9.70 54.2319 21.34 12.26 65.94 33.72 19.37 104.2120 7.67 4.62 24.20 12.13 7.30 38.2521 120.26 38.14 293.83 190.05 60.27 464.3822 4.90 3.67 17.05 7.75 5.80 26.9523 39.08 14.31 100.70 61.77 22.62 159.1524 24.50 8.55 61.99 38.72 13.51 97.9625 4.55 1.44 11.11 7.19 2.28 17.5626 34.70 10.93 84.57 54.85 17.27 133.6627 5.26 1.49 12.34 8.31 2.35 19.5028 32.02 9.19 75.50 50.60 14.52 119.3229 102.01 28.84 239.33 161.21 45.58 378.2430 24.58 5.60 53.65 38.85 8.85 84.7931 21.63 6.29 51.24 34.18 9.94 80.9732 27.88 7.72 64.95 44.06 12.20 102.6433 3.74 1.00 8.62 5.92 1.58 13.62

P [W], b1 P [W], b2 P [W], b1+b2 P [W], b1 P [W], b2 P [W], b1+b2

Power loss for 50 and 25 ns

HL-LHC beamscos^2 bunch:

total bunch 1.336 ns

power loss cos^2 bunch total bunch length : 1.336 ns3.5e+11 p/b, 1404 bunches 2.2e+11 p/b, 2808 bunchesP [W], b1 P [W], b2 P [W], b1+b2 P [W], b1 P [W], b2 P [W], b1+b2

1 69.12 49.34 235.26 109.24 77.98 371.812 1.00 19.58 29.42 1.58 30.95 46.493 116.78 86.62 404.54 184.56 136.89 639.344 0.42 29.79 37.32 0.67 47.08 58.985 76.71 56.80 265.52 121.23 89.77 419.636 1.17 50.71 67.31 1.85 80.14 106.377 11.24 6.45 34.73 17.76 10.20 54.898 39.66 33.76 146.62 62.68 53.36 231.729 0.21 19.39 23.66 0.34 30.64 37.39

10 26.01 22.23 96.33 41.10 35.13 152.2411 1.18 7.54 14.67 1.86 11.91 23.1912 8.29 8.51 33.60 13.11 13.44 53.0913 1.06 2.55 6.91 1.68 4.04 10.9214 25.12 16.38 82.06 39.70 25.88 129.6915 3.24 1.07 8.02 5.12 1.69 12.6716 12.38 7.94 40.15 19.56 12.55 63.4517 0.87 2.66 6.58 1.38 4.21 10.4018 13.81 7.42 41.47 21.83 11.73 65.5519 26.37 15.15 81.50 41.68 23.95 128.8120 11.14 6.70 35.12 17.60 10.60 55.5021 187.31 59.40 457.67 296.02 93.88 723.3022 7.76 5.81 27.00 12.27 9.18 42.6723 62.13 22.76 160.09 98.19 35.96 253.0024 40.34 14.07 102.06 63.75 22.24 161.3025 7.37 2.34 18.01 11.64 3.70 28.4626 54.70 17.22 133.29 86.44 27.21 210.6627 6.93 1.96 16.26 10.95 3.10 25.7028 42.18 12.10 99.47 66.66 19.13 157.2029 133.54 37.76 313.32 211.05 59.67 495.1730 32.15 7.33 70.17 50.81 11.58 110.9031 28.14 8.18 66.68 44.48 12.93 105.3832 32.40 8.97 75.47 51.20 14.18 119.2733 4.04 1.08 9.30 6.39 1.71 14.70

Power loss for 50 and 25 ns HL-

LHC beamsguassian bunch:sigam_z = 85mm

andcos^2 bunch: total

bunch 1.336 ns(b1 only, since b2 ~ 0)

GB 50 ns, GB 25 ns CB 50 ns CB 25 ns34 4.11 6.50 6.88 10.8735 7.65 12.10 25.90 40.9336 3.08 4.87 10.64 16.8237 17.60 27.81 68.80 108.7338 21.67 34.24 95.88 151.5339 19.12 30.22 86.38 136.5240 2.49 3.94 12.85 20.3141 1.81 2.87 9.47 14.9742 6.31 9.97 77.18 121.9743 6.71 10.61 88.29 139.5444 23.25 36.75 490.89 775.8045 17.25 27.27 380.97 602.0846 3.20 5.06 77.10 121.8447 1.11 1.76 45.76 72.3148 0.74 1.17 32.37 51.1549 0.76 1.20 33.69 53.2450 1.14 1.80 53.81 85.0451 1.16 1.83 55.64 87.9452 5.75 9.08 289.48 457.5053 1.77 2.79 89.35 141.2154 5.05 7.98 258.39 408.3755 1.43 2.25 73.95 116.8856 5.79 9.15 300.92 475.5857 0.71 1.11 37.13 58.6758 22.26 35.18 1175.29 1857.4459 7.94 12.54 423.49 669.2960 0.78 1.23 41.42 65.4761 1.20 1.90 65.11 102.9062 0.24 0.38 16.62 26.2763 0.23 0.36 16.87 26.6764 0.24 0.38 17.90 28.2865 0.08 0.13 6.08 9.6166 0.24 0.38 18.50 29.2367 15.55 24.57 1203.71 1902.3568 1.65 2.61 128.99 203.8669 0.27 0.43 21.27 33.6170 7.72 12.21 604.93 956.0471 0.23 0.36 18.45 29.16

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

0 0.5 1 1.5 2 2.5 3 3.510

-4

10-2

100

102

104

f [GHz]

Q,

R/Q

[O

hm]

CST estimate

HFSS R/QHFSS Q

HFSS Q estimate

0 0.5 1 1.5 2 2.5 3 3.510

-2

100

102

104

106

f [GHz]

R [

Ohm

]

CST estimate

HFSS

Comparison of the power estimate from CST and HFSS calculations

0 0.5 1 1.5 2 2.5 3 3.510

-1

100

101

102

103

104

f [GHz]

P [

W]

Beam: Mb = 2808, Nb = 2.2e+011

CST estimate

HFSS

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