Simulation of the particle beam dynamics

Beam dynamics may be defined as the study of charged particle motion in static or time varying electromagnetic fields. These fields may be external or induced by the particle distribution. In the case of electrons, the effect of synchrotron radiation must also be taken into consideration. Obtaining an accurate model of beam dynamics raises many problems. Examples at the fundamental level include interactions with the residual gas, interactions with solid interfaces, the dynamics of ion source plasmas, beam optics in the presence of high-order electromagnetic components such as hexapoles and octupoles, and the control of halo formation and beam losses for the maintenance of future high-power accelerators. Overcoming these problems involves the development of analytical models and numerical methods that exploit available computer resources to the full. The validity of proposed models must then be tested by comparison with experimental results.

Simulation of the particle beam dynamics

Transverse distribution at the final detection plane of the S3 spectrometer used in the SPIRAL2 project. The separation of three isotopes of a super heavy element (Z = 116 and A = 291, 292 and 293) can be seen in five charge states. Each group of marks represents the three isotopes for a given charge state. The calculation is based on the S3 geometry with field maps for all components, including the MOSAR magnet.

Beam simulation in electron cyclotron resonance sources


The emergence of several projects over the last ten years has prompted the CEA and the CNRS to form a partnership in the field of high-current accelerators, focused specifically on developing a low-energy demonstrator in the form of the IPHI high-intensity proton injector. The projects that led to this collaboration include SPIRAL2 at GANIL, IFMIF which requires deuteron beams, the FAIR project at GSI in Germany, the ESS project at Lund in Sweden, and hybrid reactors requiring a source of protons. Other projects, including SPL at CERN, the Fermilab Proton Driver, and spallation sources, require a source of negative hydrogen ions for injection into the compression rings. All these machines require a powerful and reliable source of ions, which SACM is capable of designing and building.


Particle extraction from the source is modeled by calculating the plasma expansion meniscus and beam generation through a multi-electrode extraction system.

Simulation of the particle beam dynamics

Map of the space charge potential in the low energy line of the FAIR proton linac. The abscissa z = 0 represents the extraction from the ECR source. The region with no space charge compensation (potential ~ 500V) on the abscissas above 2.2 meters corresponds to the injection of the beam into the radio frequency quadrupole.

Particle transport in a low energy line


The low energy line of an accelerator is used to transport the beam from the point of extraction from the ion source, and to optimize its injection into the accelerating sections. In the case of high intensity accelerators such as IFMIF or IPHI, the main problem to overcome is the limitation of losses and increases in emittance during beam transport. The dynamics of these intense beams is dominated by the nonlinear effects of the space charge field. In a low energy line, the beam ionizes the residual gas in the vacuum vessel, leading to a partial compensation of the space charge. The SolMaxP computer code, developed at SACM, is designed to simulate beam transport under space charge compensation conditions.

The SolMaxP and TraceWin codes were used together to design and optimize the low energy line of the IFMIF deuteron accelerator, and in the preliminary studies for the low energy line of the FAIR proton linac. In both cases, the beam is focused by two solenoids, and the beamline dimensions have been optimized to around two meters in order to limit any increase in the emittance. The characteristics of the beams generated by the IFMIF and SILHI low energy lines have been measured with the aim of providing experimental data to validate the SolMaxP code.


Particle transport in the medium and high energy sections


Beyond the radio frequency quadrupole, the problems caused by the space charge are less significant, but the level of beam losses must still be controlled in order to minimize the power dissipated in the cryostatic components and the activation of the structure. Beam power in high power machines can reach several megawatts, and the main challenge is to develop extremely accurate calculation methods to estimate the probabilities of very low losses, which can often be well below one watt. SACM has focused its efforts on the development of simulation codes that are capable of defining the highest performance accelerators, and on carrying out large scale simulations based on the most realistic description of the accelerator, including tuning and construction errors. The reliability studies must also include an estimation of the impact of the failure of one or more accelerator components, and of any measures taken to reduce the consequences of such failure.


SACM is involved in a large number of projects that demand every aspect of its expertise. These include IFMIF, Betabeam, MYRRHA, EURISOL, LINAC4, SPL, ESS, SPIRAL2, ILC and S3.

Simulation of the particle beam dynamics

Density of electrons of more than 1.5 MeV at t = 107 fs. The target is initially at x = 0. The laser pulse impacts a thin target consisting of 30 nm of hydrogen at an angle of incidence of 30°. The oscillation of the target plasma can clearly be seen. The arrangement of the wave front of the electrons ejected from the target corresponds to the laser wave.

Laser plasma acceleration


SACM is involved in projects in which particles are accelerated by a plasma wave resulting from the wake of a laser beam, such as the Interdisciplinary Center for Extreme Light (CILEX) where the laser is expected to be fired for the first time in 2016. SACM is contributing in two areas: the specification of the transfer lines between the various accelerator stages, together with their associated diagnostics, and simulations of the interactions between the laser and the plasma. The second of these will make use of experience already gained in the development of the Particles in Cell (PIC) codes. Initial simulations have been carried out using the SolMaxP code in order to predict the acceleration of ions when a layer of just a few nanometers is impacted by an intense laser.


Improvements to the LHC


SACM is contributing to beam dynamics studies aimed at increasing the luminosity of the LHC by a factor of five by 2020. Using the Achromatic Telescopic Squeezing (ATS) approach developed by S. Fartoukh at CERN, this improvement will only require modifications to two interaction regions. One of these modifications requires the replacement of the NbTi quadrupoles in the final focusing triplets with quadrupoles manufactured from Nb3Sn. The second requires the use of crab cavities in order to compensate the beam crossing angle. SACM is participating in the development of the mesh and has proposed a structure that would reduce the voltage requirement of the cavities by 25 %. SACM is also involved in studies to specify the tolerances of the new components, which will affect the long term stability of the beam.


Applications for beam transport software


The development of these codes began in 1995 and since 2000, they have been used by many laboratories in the majority of high intensity accelerator studies throughout the world. The predictability of these codes has been verified by experimental comparisons carried out at SNS in the USA, J-PARC in Japan, and GSI in Germany. This suite of professional software is now distributed under license from the CEA via a download website that promotes the software to internet search engines:




Last update : 06/22 2018 (3372)


Retour en haut