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Beam Dynamics in Cyclotrons


Numerical Simulation and Optimization of Beam Dynamics in Cyclotrons

Tech Area / Field

  • PHY-PFA/Particles, Fields and Accelerator Physics/Physics
  • INF-SOF/Software/Information and Communications

3 Approved without Funding

Registration date

Leading Institute
Joint Institute of Nuclear Research, Russia, Moscow reg., Dubna

Supporting institutes

  • VNIIEF, Russia, N. Novgorod reg., Sarov


  • Institute of Physical and Chemical Research (RIKEN), Japan, Saitama, Wako\nUniversity of British Columbia / TRIUMF, Canada, BC, Vancouver

Project summary

The goal of the Project, proposed to the ISTC, is the development of the theoretical and numerical methods of three dimension (3D) simulation of the high-intensity beam dynamics in isochronous cyclotrons and synchrocyclotrons with space charge effects.

An isochronous cyclotron is the widely used type of cyclical accelerator. During last years a role of these accelerators sufficiently increase due to a wide scope of investigations with ion beams in nuclear physics and in apply and medical researchers. A series of new generation cyclotrons is under construction now in Japan, France, Italy and some other countries. The progress in the cyclotron development increases the beam intensity and the beam space charge has a strong influence on the beam dynamics now in the modern accelerators. These effects have especially strong influence on the beam injection and extraction and on the emittance of the beam in the cyclotron. X-ray radiation and radiation pollution of the elements of accelerator construction due to the beam losses from cyclotrons as the result of space charge effects have an addition serious sense of the considerate problem. All of this makes the problem of numerical simulation of beam dynamics with all space charge effects in cyclotrons very important and actual for design and constructions of next generation cyclotrons.

At present the art of theoretical and experimental investigation of the high-intensity beam in isochronous cyclotrons is developed in several accelerating laboratories of the world. As a rule the problem is subpided into two parts: transverse and longitudinal space charge effects. The basic efforts of researchers are concentrated on the solution of the second part of the problem, since in the cyclotron there is no longitudinal beam focusing. In this case the task becomes two-dimensional (2D) and the problem is solved by the particle-in-cell (PIC) method. For the transverse space charge effects are mainly used analytical estimations.

The goal of proposed Project is the creation of the new codes for the numerical simulation of the beam dynamics in cyclotrons and synchrocyclotrons with space charge effects in three dimensions. In order to get large confidence in the correctness of the obtained results, two methods will be applied for the solution of the problem namely: particle-to-particle and particle-in-cell ones. These new numerical codes will be used to study both the transverse and longitudinal beam characteristics in injection, main acceleration and extraction areas of the cyclotrons.

It is well known that the main drawback of such codes is that they are time-consuming especially in the case when an optimisation of accelerator and beam parameters is required. For overcoming this difficulty it is assumed the solution of the problem using the parallel computers.

At calculation of the beam dynamics one of the major directions is the numerical modelling of the beam behaviour at presence of perturbations in the cyclotron magnetic field. The reasons of these magnetic field perturbations are the various sorts of manufacturing and installation errors for ferromagnetic and current elements of the cyclotrons magnetic system. In view of these reasons the beam dynamics codes have to be supplied with the structure that processes the some kinds of errors in the geometry of cyclotron magnetic structure. The most important zones of a cyclotron are ones of the first revolutions of the beam, zone of the beam extraction and areas of passage through the various kinds of resonances. The most essential effect on the dynamics of beam in such zones have the lowest harmonics of the vertical and radial components of the magnetic field of cyclotron as well as the average value of radial one. Calculation of the beam dynamics taking into account the space charge effects and the field perturbations in such zones is pretty unexplored area of the theory of cyclotrons.

The new codes will be equipped by the databases with main magnetic fields, trim coils and injection/extraction element fields of cyclotrons. By the help of these databases the working magnetic fields will be shaped and tested without space charge effects making use the special subroutines. For simulation of the injection/extraction to/from cyclotron procedures the associated databases will be used. Special procedures will be used for calculation of the effects of beam interaction with the elements of cyclotrons and synchrocyclotrons design (the vacuum chamber, magnet poles, RF system).

Capabilities of the Project participants are confirmed by the following high qualification and experience of the JINR, VNIIEF and RIKEN scientific experts in numerical simulations, cyclotrons and particle beam physics as well as by the experience in the ISTC project elaboration. The really working code on the base of particle-to-particle method of the beam dynamics with space charge effects has been developed in JINR. The method of particle-in-cell was sufficiently developed in RIKEN for the simulation of charge particle beam transportation. The VNIIEF has a great experience in numerical simulation with parallel codes at multiprocessor computers.

The presented Project could be carried out in particular in the frame of RIKEN Project of Radioactive Ion Beam Factory (RIBF). The RI Beam Factory Project was approved by the Japanese Government and has been started at RIKEN, Saitama since 1997. In the first phase, a new multistage acceleration system consisting of three ring cyclotrons (FRC, IRC and SRC) with K=510 MeV, 980 MeV and 2500 MeV in each will build up in 2005. The RIBF as a next generation facility will be capable of providing the world’s most intense radioisotope beams over the whole range of atomic masses. The beam intensity is expected to be about 1 pA for a wide range of the ions.

During the Project realization a new level code library for the cyclotrons beam dynamics will be developed and applied for the scientific research program at RIKEN in the frame of RIKEN Project of Radioactive Ion Beam Factory. The outcome of the collaboration will have the following benefits:

· the creation a new level code library for the cyclotrons and synchrocyclotrons beam dynamic with space charge effects based on the particle-to-particle and particle-in-cell methods;

· the providing of the beam dynamics calculations for three stages RIKEN RIBF complex for intense beams of heavy ions and preparing the recommendations to optimize the beam characteristics of every cyclotron.


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ISTC facilitates international science projects and assists the global scientific and business community to source and engage with CIS and Georgian institutes that develop or possess an excellence of scientific know-how.

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