Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Space-Charge Effects During Half-Integer Resonance Crossing in the CERN PSB

Tirsi Prebibaj, Fanouria Antoniou, Foteini Asvesta, Hannes Bartosik, Giuliano Franchetti

TL;DR

This study addresses how space-charge effects interact with half-integer resonances during crossing in a high-brightness synchrotron. Using a coasting beam in the CERN PSB and 6D tracking with PIC space-charge, the authors dissected the dynamics when crossing the non-structural resonance $2Q_y=9$, comparing compensated and excited cases from above and from below. Key findings show that trapping in resonance islands dominates when crossing from above, while centroid oscillations and inward island motion drive growth and losses when crossing from below; an empirical scaling law links losses to stopband width, crossing rate, and space-charge tune shift. The results quantify coherent versus incoherent space-charge effects, offering mitigation strategies (e.g., fast crossing) for high-intensity PSB operations and informing similar accelerators operating near half-integer tunes.

Abstract

The survival of charged particles in synchrotrons requires avoiding setting the beam on machine resonances, the most dangerous of which are the integer and half-integer. Nevertheless, operationally, the transverse tunes may change dynamically, crossing these resonances, and resulting in unwanted beam quality degradation and beam loss. For high intensity beams the process of resonance crossing is even more critical as space charge, in addition to the incoherent effects, may generate also coherent effects on the beam envelope dynamics. The interplay of the speed of resonance crossing, the space charge incoherent tune spread, and half-integer resonance width are fundamental for the beam behavior. In this paper we study the crossing of the half-integer resonance $2Q_y=9$ in the CERN Proton Synchrotron Booster~(PSB) for a range of parameters using a coasting beam. We take advantage of the newly commissioned PSB to investigate the beam response experimentally. The experimental findings are also discussed with the support of simulations.

Space-Charge Effects During Half-Integer Resonance Crossing in the CERN PSB

TL;DR

This study addresses how space-charge effects interact with half-integer resonances during crossing in a high-brightness synchrotron. Using a coasting beam in the CERN PSB and 6D tracking with PIC space-charge, the authors dissected the dynamics when crossing the non-structural resonance , comparing compensated and excited cases from above and from below. Key findings show that trapping in resonance islands dominates when crossing from above, while centroid oscillations and inward island motion drive growth and losses when crossing from below; an empirical scaling law links losses to stopband width, crossing rate, and space-charge tune shift. The results quantify coherent versus incoherent space-charge effects, offering mitigation strategies (e.g., fast crossing) for high-intensity PSB operations and informing similar accelerators operating near half-integer tunes.

Abstract

The survival of charged particles in synchrotrons requires avoiding setting the beam on machine resonances, the most dangerous of which are the integer and half-integer. Nevertheless, operationally, the transverse tunes may change dynamically, crossing these resonances, and resulting in unwanted beam quality degradation and beam loss. For high intensity beams the process of resonance crossing is even more critical as space charge, in addition to the incoherent effects, may generate also coherent effects on the beam envelope dynamics. The interplay of the speed of resonance crossing, the space charge incoherent tune spread, and half-integer resonance width are fundamental for the beam behavior. In this paper we study the crossing of the half-integer resonance in the CERN Proton Synchrotron Booster~(PSB) for a range of parameters using a coasting beam. We take advantage of the newly commissioned PSB to investigate the beam response experimentally. The experimental findings are also discussed with the support of simulations.

Paper Structure

This paper contains 13 sections, 3 equations, 16 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Half-Integer Resonance Control
  3. Half-Integer Crossing from Above the Resonance
  4. Crossing without external resonance excitation
  5. Particle trapping in resonance islands
  6. Centroid oscillations during resonance crossing
  7. Scaling of beam losses
  8. Half-Integer Crossing from Below the Resonance
  9. Conclusions
  10. Details of the experimental and simulation setup
  11. Controlling the orientation of the beamlets
  12. Remerging of trapped beamlets
  13. Limitations of the wire scanner measurements

Figures (16)

  • Figure 1: Experimentally determined half-integer stopband upper and lower boundaries (purple), and comparison with analytical estimations (green), for different resonance excitation levels. The excitation corresponds to the absolute current shift of the QNO816 quadrupole family with respect to its compensating value. A shift of $| \delta I_\textrm{816}| = 2$ A corresponds to $|\delta (k_\textrm{1} l)| = 0.62\times 10^{-3}$$\textrm{m}^{-1}$.
  • Figure 2: Left: working point evolution (blue arrow) and analytically estimated space charge tune spread (orange polygons) PySCRDT. Right: measured vertical tune as a function of time during the crossing of the half-integer resonance $2Q_y=9$. 1 ms at PSB flat-bottom energy corresponds to approximately 1000 beam revolutions.
  • Figure 3: Top: evolution of the measured vertical beam profile as a function of the vertical tune during the crossing of the compensated$2Q_y=9$ resonance (white arrow points the direction of crossing). The vertical axis corresponds to the measured tune, the horizontal axis to the $y$-position along the beam profile, and the color to the density of the profile in arbitrary units. Bottom: simulation of the same process using a 6D tracking simulation.
  • Figure 4: Top: evolution of the measured vertical beam profile as a function of the vertical tune during the crossing of the excited$2Q_y=9$ resonance (white arrow points the direction of crossing). Bottom: simulation of the same process using a 6D tracking simulation.
  • Figure 5: Top: Measured (blue) and simulated (orange) vertical beam profile during the crossing of the half-integer resonance at $Q_y=4.51$. Bottom: simulated vertical phase space at the same tune.
  • ...and 11 more figures