A1257787526bSBoI

1
BEAM-CAVITY INTERACTIONS IN HIGH CURRENT
CYCLOTRONS
L. Stingelin1, M. Bopp1, H. Fitze1, C. Ng2,
K. Ko2 1Paul Scherrer Institute, CH-5232
Villigen-PSI, Switzerland 2Stanford Linear
Accelerator Center, Stanford University,
Stanford, CA 94309, USA
Abstract Measurements on the main cavities of
the PSI 590MV ring cyclotron revealed a
higher-order mode excitation at 1.8mA operation
that coincides with the 10th beam harmonic. This
suggests that the beam-cavity interactions could
have an important effect in future high current
cyclotrons planned for use in Accelerator Driven
Systems so that more detailed studies are
warranted. This paper describes initial
calculations on the ring cyclotron using the E
(eigensolver), T3 (wakefield solver) and TS3
(particle-in-cell) modules in MAFIA. In order to
model the geometric deformations due to air
pressure and wall heating as calculated by ANSYS,
SLAC's Eigensolver Omega3P is used to take
advantage of its unstructured grid and parallel
computing features.
Introduction
Omega3P Simulations
Coupled Wakefield and PIC Simulations with MAFIA

• Motivation
• Measurements of a signal at 10th beam-harmonic
  with inductive pickup-probes at 30dB below signal
  of fundamental mode at 50.6MHz.
• Could this mode be excited by the beam and how
  does it affect the beam-quality?
• Analytical model
• Cavity as RCL-circuit with beam as
  current-source acting on it.

• Import of deformation data from ANSYS
• Linear interpolation of deformation data to
  CUBIT-mesh coordinates (330k Elements)
  
• Mean Shunt-Impedance Calculation at
  beam-positions and directions from Fixpo-file and
  B-field at pickup.
• Solver frequency shift is 10th beam harmonic
  frequency for the solution of f10

• Method
• Import of the Bunch positions and velocities
  from Fixpo-Calculations to MAFIA 1dcurrents
• Wake calculation with the T3 Module
• Import of the calculated fields as initial-data
  for PIC simulation in the TS3-module
• Comparison of phase space before and after
  cavity crossing

30x real Deformation
Top-view
beams
Bunchprofile
Fourier Transform of Wakeintegral
Fixpo Integrates elementary particles in
periodic structures. Fourier Transf. of magnetic
fields, integration with standard algorithms like
Runge-Kutta. Optimized for Cyclotron-fields with
acceleration structures.
Coupling loop
Electrodes
Layout
Original Deformed
f0 MHz 50.966 50.633
Q0 29421 28928
Zm0k? 830 796
Bpu0 0.34 0.34
f10 MHz 556.92 556.96
Zm10 k? 0.005 0.001
Q10 71439 67752
Bpu10 6.48 4.3

• Conclusions
• Mostly space-charge effects and
  field-deformation from cavity wall
• Low perturbation from neighbor bunches
• More bunch-crossings should be considered

Before cavity
After cavity

• 221 Bunches cross the cavity at the same time
  with Energies from 70MeV up to 590MeV and
  currents of 1.8 mA
• Particle Bunches spiral out counter clock wise
  and gain energy in the 4 main cavities. One
  cavity at the third harmonic serves as flat-top
  for better phase acceptance.

Coupled Eigenmode and PIC Simulation with MAFIA

Acknowledgements
Sector magnet
Help from M. Humbel for providing the fixpo data
and from J. Cherix for the measurement-assistance
is gratefully acknowledged
cavity
After cavity

• E3s select-solver finds a mode at 554MHz with
  magnetic boundary condition in beam plane (only
  one half of the cavity is modeled)
• Import as initial-field with amplitude of 10 of
  fundamental mode amplitude to TS3-module
• Visible deformation of phase space

References

• Stammbach T et al., Proc. Cyclotron 2001 Conf.
• East Lansing (2001)
• K. Ko, Proc. Snowmass 2001 conference T7
  Working Group (2001)
• G. Rudolf. Fixpo Bedienungsanleitung