Collective effects for FCC-ee high energy booster

Adnan Ghribi, Mauro Migliorati, Ali Rajabi, Antoine Chance, Barbara Dalena, Quentin Bruant

CNRS/GANIL, Univ. La Sapienza/INFN, DESY, CEA/IRFU

February 2, 2024

Outline

  1. Context
    Purpose of the study ; Baseline for machine and beam parameters ; Assumptions of the study.
  2. Single bunch Instabilities
    TMCI ; MI ; Mitigation ; dependencies.
  3. What comes next
    Todos, questions, news.

Context

Purpose

Context

  • Investigate collective effects instabilities in the booster ;
    • See previous booster collective effects studies here.
  • Perform parametric analysis ;
  • Investigate mitigation strategies if needed ;
  • Give feedback to appropriate working groups.

Parameters table

Context

Booster Baseline - Table 1.

Modes \(z\) \(w\) \(h\) \(t\bar{t}\)
\(\psi\) deg
60
90
Phase advance
\(I5\) \(10^{-11}\)
5.21
1.79
5th synchrotron integral
\(\alpha_c\) \(10^{-6}\)
14.9
7.34
Momentum compaction
\(\delta_{p}\) %
1.63
3.63 		Momentum acceptance
\(Q_{x/y}\) .225/.29
278/277
415/416
Horizontal tune
C km
91.174
Circumference
\(\nu\) MHz
800
RF Frequency
\(R_p\) mm
25
Pipe radius

​

Parameters table

Context

Beam baseline at injection - Table 2.

LINAC SPS
\(E\) GeV 20 16 Injection energy
\(\varepsilon_{nx}\) \(\mu\)m 10 190 \(\rightarrow\) 1000 Normalised horizontal emittance
\(\varepsilon_{ny}\) \(\mu m\) 2 \(\rightarrow\) 15 4 \(\rightarrow\) 20 Normalised vertical emittance
\(\sigma_{z}\) mm 1 \(\rightarrow\) 10 4 bunch length
\(\sigma_{e}\) % 0.1 \(\rightarrow\) 0.5 0.4 energy spread
\(V_{rf}\) MV 104.9/52.85 82.97/41.36 RF voltage 60º/90º
\(N_{max/b}\) \(10^{10}\)
2.45
Maximum particles per bunch

Assumptions

Context

  • Single bunch instabilities ;
  • Only resistive wall effects ;
  • Longitudinal impedance and wake potential of a 0.4 mm Gaussian bunch used as Green function in beam dynamics simulations ;
  • Only wake fields and synchrotron radiation ;
  • PA31 baseline lattice ;

Single bunch instabilities

TMCI & MI

Results : at nominal parameters for the 90 deg phase advance lattice

Instabilities

Transverse exponential growth

Tranverse Mode Coupling Instabilities.

Longitudinal instabilities

Microwave Instabilities.

TMCI & MI

Curation strategies1

Instabilities

Tranverse Mode Coupling Instabilities

\[ N_{b,th}^{TMCI} = \frac{Q_{x,y}Q_{s}E\sigma_{z}}{\Im{Z_{\perp}}} \]

\(E \nearrow\) \(\Rightarrow\) LINAC vs SPS
\(Z \searrow\) \(\Rightarrow\) Geometry, material

Microwave Instabilities

\[ N_{b,th}^{MI} \propto \frac{n\alpha_cE\sigma_{E}\sigma_z}{\lvert{Z_{\parallel}\rvert}} \]

\(\sigma_z, \sigma_E \nearrow\) \(\Rightarrow\) Wigglers ?
\(\alpha_c \nearrow\) \(\Rightarrow\) Lattice

TMCI

\(N_b\) scans - SPS Copper, d=50mm, \(\alpha_c=7.34~10^{-6}\) | \(E=16GeV\) | \(\sigma_e=0.4\%\) | \(\sigma_z=4mm\) | \(\varepsilon_x=190\mu m\) | \(\varepsilon_y=4\mu m\)

Instabilities

\(\Rightarrow\) Threshold is below the nominal current.

TMCI

\(N_b\) scans - LINAC Copper, d=50mm, \(\alpha_c=7.34~10^{-6}\) | \(E=20GeV\) | \(\sigma_e=0.1\%\) | \(\sigma_z=4mm\) | \(\varepsilon_{n,xy}=10\mu m\)

Instabilities

\(\Rightarrow\) Threshold is higher than the SPS but still below the nominal 2.4e10 particles.

TMCI

\(\alpha_c\) scans Copper, d=50mm, \(N_b=2.43~10^{10}\) | \(E=20GeV\) | \(\sigma_e=0.1\%\) | \(\sigma_z=4mm\) | \(\varepsilon_{n,xy}=10\mu m\)

Instabilities

\(\Rightarrow\) Increasing the momentum compaction does help but we don’t need to double it.

TMCI

\(R_p\) scans Stainless steel, \(N_b=2.43~10^{10}\) | \(\alpha_c=7.34~10^{-6}\) | \(E=20GeV\) | \(\sigma_e=0.1\%\) | \(\sigma_z=4mm\) | \(\varepsilon_{n,xy}=10\mu m\)

Instabilities

\(\Rightarrow\) We would need to increase the pipe diameter from 50 mm to 100 mm.
What would be the real cost/performance compromise ?

TMCI

Instabilities

To summarize

  • With \(N_b=2.5e10\), at \(h/t\bar{t}\) and a copper beam pipe of \(R_p=25mm\), we reach the TMCI threshold, We need to :
    • reduce the maximum bunch population
    • or increase the momentum compaction factor
    • or increase the beam pipe diameter
    • or add a feedback system - would avoid the 0 / -1 mode coupling but needs a detailed study
  • If we decide to use stainless steel instead of copper
    • We need to increase the beam pipe diameter to up to 100 mm but we need to check other impedance contributors
  • But the results still need consolidation and options need to be frozen in order to have a complete study for the deliverable.

What comes next

Todos

Next

Remaining questions we need to answer

  • What is our real margin with a complete impedance budget ?
    • How does the thickness of a copper coating affect TMCI ?
    • How do the different parameters scale the cost ?
    • We need to have more realistic impedance budget ?
    • Do we need to investigate eddy current ? See notes from 2022 here
    • We need to freeze the beam pipe diameter and material.
  • TCBI studies to start soon
    • How increasing the number of bunches affects TCBI ?
    • How a feedback system affects TMCI ?
  • Collective effects interplay
    • We need to study the interplay between IBS, wakefield and synchrotron radiation ;
    • We begin at injection energy (march 2024) and extend to the energy ramp-up and extraction strategy (june 2024) ;
    • We need an up-to date lattice !

Other news, updates, questions

Next

  • Dora Gibellieri beginning her PhD on collective effects in ~ April 2024 ;
  • Ali Rajabi finishing his position at DESY August 2024 ;
  • MOU signed between CERN and GANIL for FCC-ee ;
  • Where should we centralize impedance studies ? DESY or CERN ? Should we mutualise it with main ring studies ?
    • Gitlab repo at CERN to freeze the actual status of impedance studies then take it from there

FCC-ee booster meeting
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