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Beam impedance of ATLAS unshielded Bellows

Beam impedance of ATLAS unshielded Bellows. Friday 8/7 2011 Thanks to B. Salvant and V. Vaccaro . Technical drawing of the current/old bellow. CST model of the current/old bellow. CST mesh with 4,424,509 cells. Assumptions: ultrarelativistic bunch

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Beam impedance of ATLAS unshielded Bellows

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  1. Beam impedance of ATLAS unshielded Bellows Friday 8/7 2011 Thanks to B. Salvant and V. Vaccaro

  2. Technical drawing of the current/old bellow

  3. CST model of the current/old bellow

  4. CST mesh with 4,424,509 cells • Assumptions: • ultrarelativistic bunch • background made of perfect conductor (instead of aluminum)

  5. Theoryhttp://cdsweb.cern.ch/record/118026/files/p1.pdf( page 87 ) This term vanishes at high energy (g large ) ZL = Longitudinal impedance. It is a function of frequency ZL(f) n = (f/frev) frev = Revolution frequency. For the LHC it is 11.2455 kHz = Relativistic beta ~ 1 = Relativistic gamma Z0 = Intrinsic impedance ( ) a = Radius of the beam b = Radius of the inner of the bellow (= radius of beam pipe) b’ = Radius of the outer fold of bellow L = Accumulated length of the bellow, with an outer radius. It is approximately half of the length of the bellow, since approximately half the length has an outer radius, and half of the length has an inner radius R = Radius of the accelerator. For LHC it is (26659 m / 2p)

  6. Theory This formula is only valid up to the first cut-off frequency ===== 0.086mΩ Where: p = 2.405 for the first zero of the TM mode [J0(p)=0 for cylindrical geometry c = speed of light b = radius of beam pipe

  7. The real part of the wake impedance is zero below cut-off frequency. The reason is that below cut-off the waves from the bellow cannot propagate out of the bellow, so there is no energy loss. Theory

  8. The effect of increasing #meshcells

  9. Effect of increasing length of pipe 150mm 100mm 90mm 80mm 70mm 60mm 50mm 45mm 40mm 35mm 30mm 25mm 20mm 15mm 10mm 5mm Open boundaries were used. A new series of simulations with ports are necessary!!

  10. Effect of increasing length of pipe 150mm 100mm 90mm 80mm

  11. Low frequency impedance INTERMEDIATE REVIEW OF SINGLE BUNCH COLLECTIVE EFFECTS IN THE LHC D Angal, D Brandt, L Vos. (2002) LHC Project Report 587 “In terms of impedance, ATLAS is rather optimal, with a very smooth vacuum chamber. Its contribution is therefore negligible.” “The unshielded bellows: such elements are extremely unfavourable from an impedance point of view, and a special effort was made to avoid such components whenever possible. As a result, their number could be restricted to a few elements in the surroundings of the LHC experiments. Their total length is expected to be around 3 m, with an impedance of 0.005 Ω.” Old bellow  0.086 mΩ*30=0.0026 Ω New bellow 0.15 mΩ*30=0.0048 Ω Theoretical value for the new bellow:

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