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TDI impedance and power loss

TDI impedance and power loss. O. Aberle, F. Caspers, A. Grudiev, E. Metral, N. Mounet, B. Salvant. Context. TDI power loss Follow up of E. Metral’s talk at LCE meeting 11/06/2004 for Flat chamber with large aspect ratio  Form factor for longitudinal = 1

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TDI impedance and power loss

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  1. TDI impedance and power loss O. Aberle, F. Caspers, A. Grudiev, E. Metral, N. Mounet, B. Salvant

  2. Context • TDI power loss • Follow up of E. Metral’s talk at LCE meeting 11/06/2004 for • Flat chamber with large aspect ratio  Form factor for longitudinal = 1 • Formula for multilayer round pipe without approximation • inner radius=4.6 mm for y=43 m • Inner radius=7.7 mm for y=118 m 2nd Block (0.6 m) 3rd Block (0.7 m) 1st Block (2.8 m) Vacuum Vacuum Vacuum hBN (54 mm) Al (54 mm) Cu (54 mm) Ti 3 m Cu 10 m hBN (54 mm) Al (54 mm) Cu(54 mm) Vacuum Vacuum Vacuum

  3. Material properties • Copper DC= 17 10^-9 Ω.m rel= 1 rel= 1 H1 = 0 relaxationTime= 27 10^-15 s • Titanium DC= 58 10^-8 Ω.m rel= 1 rel= 1 H1 = 0 relaxationTime= 0 • Hexagonal Boron Nitride (hBN) DC= 4 10^12 Ω.m rel= 5 rel= 1 H1 = 0 relaxationTime= 0 • Aluminum DC= 28 10^-9 Ω.m rel= 1 rel= 1 H1 = 0 relaxationTime= 0

  4. Total longitudinal impedance (y=43 m) Linear scale Log scale Ztotal~Z(1st block) Z(2nd block)~Z(3rd block) Ztotal 1st block (Ti+hBN+vacuum) 2nd block (Cu+Al+vacuum) 3rd block (Cu+vacuum) Ploss (1st block) ~ 162 W Ploss (2nd block) ~ 0.6 W Ploss (3rd block) ~ 0.7 W Ploss (total) ~ 163 W Losses occur mainly in the first block

  5. Total longitudinal impedance (y=118 m) Linear scale Log scale Ztotal~Z(1st block) Z(2nd block)~Z(3rd block) Ztotal 1st block (Ti+hBN+vacuum) 2nd block (Cu+Al+vacuum) 3rd block (Cu+vacuum) Ploss (1st block) ~97 W Ploss (2nd block) <1 W Ploss (2nd block) <1 W Ploss (total) ~ 98 W Losses occur mainly in the first layer

  6. 1st block (Ti-hBN-Vacuum)  Z 1 layer (Ti) 2 layers (Ti+hBN) 3 layers (Ti+hBN+vacuum) Infinite thick wall (Ti)

  7. Power loss in the first block From F. Ruggiero, Single-beam collective effects in the LHCCERN-SL-95-09-AP (1995) Formula assumes a gaussian bunch 1 layer (Ti) 2 layers (Ti+hBN) 3 layers (Ti+hBN+vacuum) Infinite thick wall (Ti) for Ploss = 163 W Ploss ~ 98 W for Significant losses in the hBN?

  8. Losses in the hBN 1 layer (Ti) 2 layers (Ti+hBN) 3 layers (Ti+hBN+vacuum) Infinite thick wall (Ti) 2 layers (Ti+vacuum) At f=1010 Hz, the skin depth in titanium is ~ 3 m… A single layer of titanium surrounded with vacuum leads to Ploss ~0.04 W This 3 m layer surrounded with 54 mm of hBN leads to Ploss~ 162 W This means that all the power (162 W) is lost in the hBN.

  9. Effect of hBN conductivity on impedance of the 1st block (hBN)=8 1012 Ω.m (hBN)=4 1012Ω.m (hBN)=2 1012Ω.m  No effect of hBN conductivity on the power loss (in this 1012 Ω.mrange…)

  10. Effect of hBN permittivity on impedance of the 1st block r(hBN)=1 r(hBN)=1.1 r(hBN)=2 r(hBN)=5  strong effect of hBN permittivity on the power loss, but only if r ~ 1. If r >2, the effect is small, as Alexej already observed

  11. Conclusion • Significant power loss dissipated in the hBN (162 W) • r = 1 leads to suppressing almost all the losses in the hBN (and therefore everywhere). • However r >2 for instance f leads to very small changes (P=160W instead of 163W) for Ploss ~ 163 W In surprising agreement with previous estimates (Ploss ~ 165 W and Ploss ~ 100 W ) Ploss ~ 98 W for

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