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 • 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

1st Block (2.8 m)

Vacuum

Vacuum

hBN (54 mm)

hBN (54 mm)

Ti3 m

2nd Block (0.6 m)

Vacuum

Vacuum

Al (54 mm)

Al (54 mm)

Cu10 m

3rd Block (0.7 m)

Vacuum

Vacuum

Cu (54 mm)

Cu(54 mm)

Material properties• Copper

DC= 17 10^-9 Ω.mrel= 1rel= 1H1 = 0relaxationTime= 27 10^-15 s

• TitaniumDC= 58 10^-8 Ω.mrel= 1rel= 1H1 = 0relaxationTime= 0

• Hexagonal Boron Nitride (hBN)DC= 4 10^12 Ω.mrel= 5rel= 1H1 = 0relaxationTime= 0

• AluminumDC= 28 10^-9 Ω.mrel= 1rel= 1H1 = 0relaxationTime= 0

Total longitudinal impedance (y=43 m)

Linear scale Log scale

Losses occur mainly in the first block

Ztotal1st block (Ti+hBN+vacuum)2nd block (Cu+Al+vacuum)3rd block (Cu+vacuum)

Z(2nd block)~Z(3rd block)

Ztotal~Z(1st block)

Ploss (1st block) ~ 162 W

Ploss (2nd block) ~ 0.6 W

Ploss (3rd block) ~ 0.7 W

Ploss (total) ~ 163 W

Total longitudinal impedance (y=118 m)

Linear scale Log scale

Losses occur mainly in the first layer

Ztotal1st block (Ti+hBN+vacuum)2nd block (Cu+Al+vacuum)3rd block (Cu+vacuum)

Z(2nd block)~Z(3rd block)

Ztotal~Z(1st block)

Ploss (1st block) ~97 W

Ploss (2nd block) <1 W

Ploss (2nd block) <1 W

Ploss (total) ~ 98 W

1st block (Ti-hBN-Vacuum) Z

1 layer (Ti)2 layers (Ti+hBN)3 layers (Ti+hBN+vacuum)Infinite thick wall (Ti)

1 1 0 0 0 1 0 6 1 0 9 1 0 1 21 0 6

1 0 4

0 .0 1

1

1 0 0

F re q ue nc y H z

ReZ long

1 1 0 0 0 1 0 6 1 0 9 1 0 1 21 0 6

1 0 4

0 .0 1

1

1 0 0

F re q ue nc y H zIm

Z long

Power loss in the first block

1

200//

2 2expRe2p

bloss pfpfZMIP

From F. Ruggiero, Single-beam collective effects in the LHCCERN-SL-95-09-AP (1995)

Formula assumes a gaussian bunch

for m118y

m43y

Ploss = 163 W

Ploss ~ 98 W for

0 2 . 1 0 8 4 . 1 0 8 6 . 1 0 8 8 . 1 0 80 .0 0

0 .0 5

0 .1 0

0 .1 5

F re q ue nc y H z

Power

Spec

trum

0 2 . 1 0 8 4 . 1 0 8 6 . 1 0 8 8 . 1 0 80

5

1 0

1 5

2 0

F re q ue nc y H z

ReZ long

1 layer (Ti)2 layers (Ti+hBN)3 layers (Ti+hBN+vacuum)Infinite thick wall (Ti)

Significant losses in the hBN?

Losses in the hBN

1 1 0 0 1 0 4 1 0 6 1 0 8 1 0 1 0 1 0 1 21 0 1 0

1 0 8

1 0 6

1 0 4

0 .0 1

1

1 0 0

F re q ue nc y H z

ReZ long

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.

Effect of hBN conductivity on impedance of the 1st block

1 1 0 0 1 0 4 1 0 6 1 0 81 0 1 0

1 0 8

1 0 6

1 0 4

0 .0 1

1

1 0 0

F re q ue nc y H z

ReZ long

(hBN)=8 1012 Ω.m(hBN)=4 1012 Ω.m(hBN)=2 1012 Ω.m

No effect of hBN conductivity on the power loss (in this 1012 Ω.m range…)

Effect of hBN permittivity on impedance of the 1st block

r(hBN)=1r(hBN)=1.1r(hBN)=2r(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

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 m118y

m43y

Ploss ~ 163 W

Ploss ~ 98 W for

In surprising agreement with previous estimates(Ploss ~ 165 W and Ploss ~ 100 W )