Modification of the vacuum chamber in ATLAS Effect on impedance and related quantities E. Métral, N. Mounet and B. Salvant with the help of R. Veness and M. A. Gallilee E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Context and motivation There is a proposition to reduce the diameter of the Beryllium vacuum chamber inside the ATLAS pixel detector: Radius should change from 29 mm to 22.5 mm, Need also to insert two new conical transitions (=tapering) from the existing 29 mm to the 22.5 mm radius, using the available 100 mm length. Transition angle = arctan(6.5/100) ≈ 3.7 deg << 15 deg (value set by L. Vos in the past). Issues to assess: Longitudinal and transverse impedance for beam stability, Longitudinal impedance for power loss. E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Current situation 7.1 m, inner diameter 58 mm NEG coating (1 μm) Beryllium (0.8 mm at -15°C) Isolating aerogel (4 mm) E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Current situation E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Future situation inner diameter 58 mm 7.1 m, inner diameter 45 mm 100 mm transition with the same layers of materials inside (NEG 1 μm – Be 0.8 mm – aerogel 4 mm) E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Impedance contributions Two different contributions are to be distinguished: Resistive wall impedance, due to the resistivity of the beam pipe. Models assume a perfectly smooth cylindrical geometry. Geometrical impedance, due to the conical transitions (tapering) in the modified situation. Models assume a perfectly conductive chamber. E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Material parameters used for the resistive wall impedance Beryllium: Resistivity: 4.24 10-8 Ω.m (from specifications) Permittivity: 1 Aerogel: Resistivity: Infinity (approximation) Permittivity: 1.1 (from specifications) NEG: Resistivity: 2.5 10-5 Ω.m (David Seebacher, F. Caspers, NEG properties in the microwave range, SPSU Meeting, 17th February, CERN) Permittivity: 10 E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Resistive wall models Two models used here: Exact multilayer analytical formula for an axisymmetric geometry (assumptions: linear materials, infinite length i.e. no side effects). Implemented in a Mathematica code (ReWall – http://impedance.web.cern.ch/impedance/Codes/ReWall/ReWall_to_date.zip) Classic thick wall formula (Chao’s book) giving a simple impedance formula for a resistive beam pipe, valid at “intermediate” frequencies: Longitudinal impedance: Transverse impedance: with L the length of the element, b its radius, s the wall conductivity, m0 the vacuum permeability, Z0= m0 c the vacuum impedance (c=speed of light), and w the angular frequency. E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Power loss due to the impedance General expression for any impedance: loss is a function of the real part of the longitudinal impedance and of the bunch spectrum l(w) (=line density in frequency domain, here for a parabolic bunch): with f0=w0 /2p the revolution frequency, M the number of bunches and e the electron charge. For a classic resistive wall impedance and a parabolic line density, we can get an analytic formula: for a bunch of total length 4sz=4stc (in meters), L=26658.883 being the circumference of the LHC and Lelem the length of the element considered for the impedance (here 7.1 m). G. Rumolo, USPAS 2009 Power loss per unit length : E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Beam parameters (for power loss computation) Energy Bunch length (4 σt) Number of bunches Intensity per bunch 450 GeV 1.4 ns (during MD) 2808 *2 beams 1.15 1011 p/b 3.5 TeV 0.8 ns (during MD) 2808*2 beams 7 TeV 1 ns (nominal) E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Contribution of the aerogel to the power loss? The skin depth of Beryllium at 20 kHz is 0.8 mm  above 20 kHz, what is behind the 0.8 mm thick beam pipe contributes much less Curve to integrate to get power loss  below 20 kHz, the contribution to power loss is negligible As a consequence, the material behind 0.8 mm beam pipe does not contribute (also checked by multilayer calculations) E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Resistive wall contribution: power loss Energy Inner radius Number of layers taken into account Bunch length (4st) Power loss (W/m) – exact Power loss (W/m) – classic approx. 450 GeV 29 mm 1 (Be) 1.4 ns (MD) 0.62 22.5 mm 0.80 (+29%) 0.80 3.5 TeV 0.8 ns (MD) 1.44 1.86 (+29%) 1.86 7 TeV 1 ns (nominal) 1.03 1.33 (+29%) 1.33 2 (Be 0.8mm +air) N/A 2 (NEG 1 μm + Be) → about 30% increase in the power loss, confirmed by classic approximation. Maximum at 3.5 TeV (~1.9 W/m). E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Geometric impedance: ABCI electromagnetic simulations Geometry simulated (perfect conductor): 1 m, inner diameter 58 mm 7.1 m, inner diameter 45 mm 100 mm transition Other parameters for the simulation: 1 mm mesh size, 5 cm rms bunch length, Napoly integration with moving mesh and 4 m wake length. E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

ABCI cavity shape E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Power loss ~ 10-7 W/m (analytic formula: exactly zero) E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011

Effect on beam stability: Longitudinal effective impedance Sacherer longitudinal effective impedance (first headtail mode) for parabolic bunches: Energy Inner radius Nb. of layers taken into account Bunch length (4st) (Z||/n)eff [W] resistive part (exact) (Z||/n)eff [W] total (LHC ring) 450 GeV 29 mm 1 (Be) 1.4 ns (MD) j 1.1 10-5 j 0.09 22.5 mm j 1.3 10-5 7 TeV 1 ns (nominal) j 0.65 10-5 j 0.085 j 0.8 10-5 → Longitudinal effective impedances for both current and future situations are estimated to be negligible with respect to the rest of the ring.

Effect on beam stability: Transverse effective impedance Sacherer transverse effective impedance for water-bag bunches: Energy Inner radius Nb. of layers taken into account Bunch length (4st) Im(Zteff ) [W/m] resistive part (exact) Im(Zteff ) [W/m] geom. part (ABCI) Im(Zteff ) [MW/m] total (LHC ring) 450 GeV 29 mm 1 (Be) 1.4 ns (MD) 169 ~2.4 22.5 mm 361 282 7 TeV 1 ns (nominal) 141 ~25 302 284 → Transverse effective impedances for both current and future situations are estimated to be negligible with respect to the rest of the ring.

Conclusion Power loss (from resistive-wall): at most 1.9 W/m (with bunches of 0.8 ns at 3.5 TeV), increased by 30% with respect to the previous configuration. With our current understanding, there is a very little effect of the vacuum pipe modification on the beam stability (longitudinal and transverse). E. Métral, N. Mounet & B. Salvant - BE/ABP/ICE - Effect on impedance of ATLAS pipe modifications - 21/01/2011