Transverse resistive-wall impedance Elliptical pipe with semiaxes w , - - PowerPoint PPT Presentation

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Transverse resistive-wall impedance Elliptical pipe with semiaxes w , - - PowerPoint PPT Presentation

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Resistive-wall impedance of insertions 12 Bernard Riemann Zentrum fr Synchrotronstrahlung 2018-02-02 8th FCC-hh collective effects meeting 1 thanks to S. Arsenyev, A. Langner, R. Martin, D. Schulte and S. Khan 2 supported by German Federal

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SLIDE 1

Resistive-wall impedance of insertions12

Bernard Riemann

Zentrum für Synchrotronstrahlung

2018-02-02

8th FCC-hh collective effects meeting

1thanks to S. Arsenyev, A. Langner, R. Martin, D. Schulte and S. Khan 2supported by German Federal Ministry of Education and Research,

funding code 05P15PERB1

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SLIDE 2

Transverse resistive-wall impedance

Elliptical pipe with semiaxes w, b: ⇒ Use form factors G1⊥(w, b):34 ˜ Z⊥,n Ln = G1⊥(wn, bn)Z0δskin 1 + i 2πb3

n

Single-kick model5 for elements n of a latice ⇒ continuum: Z⊥ = 1 βsmooth

⊥

  • n

˜ Z⊥,n β⊥(sn) = 1 βsmooth

⊥

  • n

˜ Z⊥,n Ln

sn

∫

sn−1

β⊥(s) ds

Qadrature rule

Assume β is piece-wise cubic function of s. β, α = −β′/2 known at all element endpoints sn.

L

∫ β(s) ds ≈ L β(L) + β(0) 2 + L2 α(L) − α(0) 6 . Approximation is exact for drif spaces (quadratic dependence).

3R.L. Gluckstern, J. van Zeijts and B. Zoter, Phys. Rev. E 47 (1992)

  • 4K. Yokoya, Part. Acc. 41 (1993), p. 18 – 19
  • 5N. Mounet, PhD thesis, EPFL Lausanne (2012)

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SLIDE 3

Longitudinal case & Input data

Longitudinal resistive-wall impedance

Different dependence on b and f ,a no β Z⊥ = α(1 + i)

  • f, with

α = Z0 2πc

  • π

µ0µr

  • n

Ln √ρn G0(wn, bn) bn .

  • aA. Chao, Physics of Collective Instabilities… (Wiley, 2003)

Used updated optics data from repo6 Collision optics with β∗ = 0.3 m, injection optics with β∗ = 4.6 m. Used resistivities of copper7, individual assumptions for each insertion ρ(50 K) = 0.518 nΩ m, ρ(293 K) = 16.78 nΩ m. collimators etc. are ignored

  • 6A. Chance, R. Martin, A. Langner, M. Hofer et al.,

https://gitlab.cern.ch/fcc-optics/FCC-hh-lattice, commit 5443690ac... (2018).

7R.A. Matula, J. Phys. Chem. Ref. Data 8 (4) (1979)

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SLIDE 4

Total impedance, β∗ = 0.3 m

regions A, B, D, F, G, H, J, L

106 108 1010 x impedance / (Ω/m) Re,Im Zx (all insertions) Re Zx (cold beamscreen) Im Zx (cold beamscreen) 106 108 1010 y impedance / (Ω/m) Re,Im Zy (all insertions) Re Zy (cold beamscreen) Im Zy (cold beamscreen) 102 104 106 108 1010 f / Hz 10−1 101 103 long impedance / Ω Re,Im Zl (all insertions) Re Zl (cold beamscreen) Im Zl (cold beamscreen)

Transverse: strong contribution relative to cold beamscreen reference data.a Longitudinal contribution is significantly smaller than cold beamscreen → OK.

  • aS. Arsenyev, FCC impedance online database,

https://impedance.web.cern.ch/impedance/fcchh

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SLIDE 5

Major transverse contributions from main experiments

20 40 60 β / km

insertion A, β∗ = 0.3 m

x y 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 s / km 2 4 6 c.s. of ζ / (MΩ √ MHz/m) x y −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 b, w / cm

insertion A

50 K 293 K 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 s / km 0.0 0.2 0.4 0.6 0.8 1.0 c.s. of α / (Ω/ √ MHz) 5 / 20

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SLIDE 6

Almost identical for IRA / IRG

IRA ζ / (MΩ √ MHz/m) elements x plane y plane α / (Ω/ √ MHz) drifs 6.43 6.31 0.88 quads 0.30 0.30 0.05 dipoles 0.14 0.14 0.02 kickers 0.02 0.02 0.00 total 6.89 6.76 0.97 IRG ζ / (MΩ √ MHz/m) elements x plane y plane α / (Ω/ √ MHz) drifs 6.43 6.31 0.88 quads 0.31 0.32 0.07 dipoles 0.14 0.14 0.02 kickers 0.01 0.01 0.00 total 6.89 6.79 0.98

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SLIDE 7

IRA/IRG with 40mm → 55mm default chamber radius

IRA ζ / (MΩ √ MHz/m) elements x plane y plane α / (Ω/ √ MHz) drifs 2.47 2.43 0.64 quads 0.28 0.28 0.05 dipoles 0.14 0.14 0.02 kickers 0.02 0.02 0.00 total 2.91 2.86 0.72 IRG ζ / (MΩ √ MHz/m) elements x plane y plane α / (Ω/ √ MHz) drifs 2.47 2.43 0.64 quads 0.30 0.32 0.07 dipoles 0.14 0.14 0.02 kickers 0.00 0.00 0.00 total 2.92 2.89 0.74

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SLIDE 8

IRA with 40mm → 55mm default chamber radius

20 40 60 β / km

insertion A, β∗ = 0.3 m

x y 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 s / km 0.0 0.5 1.0 1.5 2.0 2.5 3.0 c.s. of ζ / (MΩ √ MHz/m) x y −7.5 −5.0 −2.5 0.0 2.5 5.0 7.5 b, w / cm

insertion A

50 K 293 K 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 s / km 0.0 0.2 0.4 0.6 c.s. of α / (Ω/ √ MHz) 8 / 20

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SLIDE 9

Impedance coeffs vs β∗

summary ζ / (MΩ √ MHz/m) β∗ / m x plane y plane 0.15 31.58 33.05 0.20 25.02 25.25 0.30 18.47 18.42 1.10 8.03 8.18 4.60 4.66 4.80 6.00 4.56 4.65

Table: Overall transverse impedance coefficients for different optics setings.

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SLIDE 10

Total impedance, β∗ = 4.6 m

regions A, B, D, F, G, H, J, L

106 108 1010 x impedance / (Ω/m) Re,Im Zx (all insertions) Re Zx (cold beamscreen) Im Zx (cold beamscreen) 106 108 1010 y impedance / (Ω/m) Re,Im Zy (all insertions) Re Zy (cold beamscreen) Im Zy (cold beamscreen) 102 104 106 108 1010 f / Hz 10−1 101 103 long impedance / Ω Re,Im Zl (all insertions) Re Zl (cold beamscreen) Im Zl (cold beamscreen)

Overall contributions (40mm default radius) significantly smaller than cold beamscreen estimate for transverse and longitudinal case → OK. Reasonable, as there is an inverse relation between β∗ and max(β) which enters into transverse impedance…

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SLIDE 11

Transverse contribution from IRA, β∗ = 4.6 m

1 2 3 4 β / km

insertion A, β∗ = 4.6 m

x y 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 s / km 0.0 0.1 0.2 0.3 0.4 c.s. of ζ / (MΩ √ MHz/m) x y

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SLIDE 12

Betatron collimation (IRJ)

0.0 0.5 1.0 1.5 2.0 β / km

insertion J

x y 73.5 74.0 74.5 75.0 75.5 76.0 s / km 0.0 0.5 1.0 1.5 2.0 c.s. of ζ / (MΩ √ MHz/m) x y −4 −2 2 4 b, w / cm

insertion J

50 K 293 K 73.5 74.0 74.5 75.0 75.5 76.0 s / km 0.0 0.5 1.0 1.5 2.0 2.5 3.0 c.s. of α / (Ω/ √ MHz)

3rd-highest transverse contribution for collision optics (afer IRA and IRG, due to large β), no modification indicated IRJ is identical for both optics

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SLIDE 13

Extraction (IRD)

1 2 3 4 β / km

insertion D

x y 24.5 25.0 25.5 26.0 26.5 27.0 s / km 0.0 0.2 0.4 0.6 0.8 1.0 1.2 c.s. of ζ / (MΩ √ MHz/m) x y −4 −2 2 4 b, w / cm

insertion D

50 K 293 K 24.5 25.0 25.5 26.0 26.5 27.0 s / km 0.0 0.5 1.0 1.5 2.0 c.s. of α / (Ω/ √ MHz)

is a moderate increase of chamber radius possible? IRD is identical for both optics

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SLIDE 14

Tabular summary (β∗ = 0.3 m)

summary ζ / (MΩ √ MHz/m) insertion x plane y plane α / (Ω/ √ MHz) A 6.89 6.76 0.97 B 0.71 0.62 1.17 D 1.27 1.25 1.93 F 0.17 0.22 1.22 G 6.89 6.79 0.98 H 0.13 0.14 1.28 J 1.81 1.97 3.29 L 0.61 0.68 1.20 all 18.47 18.42 12.03 cold bs. (50 TeV, S. Arsenyev) 23.41 43.25 72.81

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SLIDE 15

Tabular summary (β∗ = 4.6 m)

summary ζ / (MΩ √ MHz/m) insertion x plane y plane α / (Ω/ √ MHz) A 0.42 0.40 0.97 B 0.23 0.22 1.17 D 1.27 1.25 1.93 F 0.17 0.22 1.22 G 0.44 0.41 0.98 H 0.13 0.13 1.28 J 1.81 1.97 3.29 L 0.20 0.20 1.20 all 4.66 4.80 12.03 cold bs. (3 TeV, S. Arsenyev) 17.48 32.15 54.20

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SLIDE 16

Summary

Transverse and longitudinal resistive-wall impedance contributions of major warm parts have been computed for present state of collision

  • ptics and injection optics.

Overall impedance of warm parts for collision optics is non-negligible. Major contributions in collision optics stem from

1 drif spaces in main experiments (IRA & IRG) 2 betatron collimation system (IRJ, possible “implicit” overlap with

collimator computations, no change indicated)

3 extraction (IRD)

Contributions can be reduced by aperture increase (see computation with modified default apertures and inverse cubic scaling law). Results will be published in IPAC18 proceedings and in the FCC-hh CDR.

Tank you for your atention!

Next page and following: missing insertions (backup slides)

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SLIDE 17

Injection & additional experiments (IRB, IRL)

0.0 0.5 1.0 1.5 2.0 2.5 3.0 β / km

insertion B, β∗ = 0.3 m

x y 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 s / km 0.0 0.2 0.4 0.6 c.s. of ζ / (MΩ √ MHz/m) x y −4 −2 2 4 b, w / cm

insertion B

50 K 293 K 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 s / km 0.0 0.2 0.4 0.6 0.8 1.0 1.2 c.s. of α / (Ω/ √ MHz)

β∗ = 0.3 m IRL is symmetric to IRB

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SLIDE 18

Injection & additional experiments (IRB, IRL)

0.0 0.2 0.4 0.6 0.8 β / km

insertion B, β∗ = 4.6 m

x y 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 s / km 0.00 0.05 0.10 0.15 0.20 c.s. of ζ / (MΩ √ MHz/m) x y −4 −2 2 4 b, w / cm

insertion B

50 K 293 K 6.2 6.4 6.6 6.8 7.0 7.2 7.4 7.6 s / km 0.0 0.2 0.4 0.6 0.8 1.0 1.2 c.s. of α / (Ω/ √ MHz)

β∗ = 4.6 m IRL is symmetric to IRB

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SLIDE 19

Momentum collimation (IRF)

0.0 0.2 0.4 0.6 0.8 β / km

insertion F

x y 43.8 44.0 44.2 44.4 44.6 44.8 45.0 s / km 0.00 0.05 0.10 0.15 0.20 c.s. of ζ / (MΩ √ MHz/m) x y −4 −2 2 4 b, w / cm

insertion F

50 K 293 K 43.8 44.0 44.2 44.4 44.6 44.8 45.0 s / km 0.0 0.2 0.4 0.6 0.8 1.0 1.2 c.s. of α / (Ω/ √ MHz)

IRF is identical for both optics

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SLIDE 20

RF acceleration (IRH)

0.0 0.1 0.2 0.3 0.4 β / km

insertion H

x y 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 s / km 0.000 0.025 0.050 0.075 0.100 0.125 c.s. of ζ / (MΩ √ MHz/m) x y −4 −2 2 4 b, w / cm

insertion H

50 K 293 K 55.2 55.4 55.6 55.8 56.0 56.2 56.4 56.6 s / km 0.0 0.2 0.4 0.6 0.8 1.0 1.2 c.s. of α / (Ω/ √ MHz)

IRH is identical for both optics

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