1. H. Yamamoto IRENG07 1 Heating of IR region Image current HOM heating ‘GLD’ IR

2. H. Yamamoto IRENG07 2 Fields of relativistic charge Electric field  Nearly perpendicular to velocity  Spread at r~10cm: 0.2  m (  z =300  m) assume spread=0 Magnetic field   Energy of E ~ Energy of B β θ 1/η θ r

3. H. Yamamoto IRENG07 3 Image current I Skin depth  Effective wavelength:  Cu pipe, 2X10 10 /bunch, σ z =300μm. E ++++++

4. H. Yamamoto IRENG07 4 Image current II Assume the bunch current flows uniformly in depth δ, radius r, and length 4σ z. Current density j: Heat by one bunch passing L(m) of beampipe Heat per second over L(m) of beampipe (radius r) (q: bunch charge) (t sp : bunch spacing)

5. H. Yamamoto IRENG07 5 Image current III With the duty factor of 1/200, t sp =308ns,  Image heating = 0.075 W (per m of beampipe) Formula by Saito-san → 0.056 W (per m of beampipe)

6. H. Yamamoto IRENG07 6 HOM loss I Iris step r = a to b a b a b EM energy bounced back = HOM loss

7. H. Yamamoto IRENG07 7 HOM loss II Assume gaussian line charge Energy in B = Energy in E. u: energy density Energy from r = a to b(per bunch): lost by hitting iris

8. H. Yamamoto IRENG07 8 HOM loss III Loss factor k : HOM loss by an iris of a=1cm to b=10cm This is to turn to heat somewhere

9. H. Yamamoto IRENG07 9 HOM loss IV Two beams & FCAL/BCAL 5.6 x 2 x 2 ~ 22.4 W SiD

10. H. Yamamoto IRENG07 10 Things to do Numerical calculation Estimation of distribution of energy deposit  HOM absorbers Include all items  BPM  Flanges  etc. Effects on final quads