Multiparticle Tracking Simulations Research Articles

Differentiable self-consistent space-charge simulation for accelerator design

The nonlinear space-charge effects in a high intensity or high brightness accelerator can have a significant impact on the beam properties through the accelerator. These effects are included in the accelerator design via self-consistent multi-particle tracking simulations. In order to study the sensitivity of the final beam's properties with respect to the accelerator design parameters, one has to carry out the time-consuming space-charge simulation multiple times. In this paper, we propose a differentiable self-consistent space-charge simulation model that enables the study of the beam sensitivity through only one simulation. Such a model can also be used with gradient-based numerical optimizers for accelerator design optimizations including the self-consistent space-charge effects.

Equilibrium electron beam parameters of the High Energy Photon Source

PurposeThe physics design of the High Energy Photon Source (HEPS) was finished after many times of iteration. Hereby, the typical equilibrium electron beam parameters corresponding to the proposed two baseline operation modes in the baseline design of HEPS are presented.MethodsTo compute the equilibrium parameters of the electron beam, the lattice parameters, RF parameters, and the parameters of the insertion devices (IDs) were determined first. Furthermore, it is more precise to use the full-current electron beam parameters in the estimations of the performance of the synchrotron light. Therefore, not only the single-particle dynamics but also the current-dependent collective effects need to be considered in the computations of the full-current, equilibrium parameters of the electron beam. Both analytic computations and multi-particle tracking simulations were carried out.ResultsThe full-current, equilibrium parameters of the electron beams in the HEPS storage ring are presented in this paper. Moreover, the main beam parameters in the injector (the booster and the LINAC), corresponding to the two baseline operation modes of the storage ring, are also presented.ConclusionThe typical electron beam parameters corresponding to the two baseline operation modes are given in detail in this paper.

Vlasov description of the beam response to noise in the presence of wakefields in high-energy synchrotrons: beam transfer function, diffusion, and loss of Landau damping

Noise can have severe impacts on particle beams in high-energy synchrotrons. In particular, it has recently been discovered that noise combined with wakefields can cause a diffusion that leads to a loss of Landau damping after a latency. Such instabilities have been observed in the Large Hadron Collider. This paper, therefore, studies the beam response to noise in the presence of wakefields, within the framework of the Vlasov equation. First, a wakefield beam eigenmode transfer function (MTF) is derived, quantifying the amplitude of a wakefield eigenmode when excited by noise. Then, the MTFs of all the wakefield eigenmodes are combined to derive the beam transfer function (BTF) including the impact of wakefields. It is found to agree excellently with multi-particle tracking simulations. Finally, the MTFs are also used to derive the single-particle diffusion driven by the wakefield eigenmodes. This new Vlasov-based theory for the diffusion driven by noise-excited wakefields is found to be superior to an existing theory by comparing to multi-particle tracking simulations. Through sophisticated simulations that self-consistently model the evolution of the distribution and the stability diagram, the diffusion is found to lead to a loss of Landau damping after a latency. The most important technique to extend the latency and thereby mitigate these instabilities is to operate the synchrotron with a stability margin in detuning strength relative to the amount of detuning required to barely stabilize the beam with its initial distribution.

Enforced stripping of negative muons from $\mu$He+ ions to stimulate muon-catalyzed fusion by cyclotron resonance acceleration

Abstract The addition (sticking) of a negative muon to an $\alpha$ particle to form a $\mu$He$^+$ ion limits the number of chain reactions in muon-catalyzed fusion (MuCF), making scientific break-even in MuCF difficult. The reduction in the sticking probability by boosting the negative muon stripping using resonance radio-frequency (RF) acceleration of $\mu$He$^+$ ions has been examined with multi-particle tracking simulations. It was found that the stripping efficiency was largely depressed by ion–electron capture processes that have not been considered so far. Improvement of the fusion chain cycles is rather difficult with an RF electric field strength of 50 MV m$^{-1}$ even at a small deuterium/tritium (D/T) gas pressure of approximately 5 atm. However, in the scheme of using spatially localized D/T mixture gas streams, the sticking probability could be reduced almost tenfold even at a large gas density of 100 atm with a modest RF field strength of less than 50 MV m$^{-1}$.

Longitudinal equilibrium density distribution of arbitrary filled bunches in presence of a passive harmonic cavity and the short range wakefield

We propose a novel scheme for the calculation of bunch profiles and synchronous phase shifts for arbitrary fill patterns in electron storage rings considering both the effects of the passive harmonic cavity and the short range wakefield. This scheme treats the bunch as a charge distribution rather than a point charge with a bunch form factor, and divides the voltage induced in the cavity into two groups: that induced by the previous passages and that by the present passage, where the latter is integrated with the short range wakefield from all the other vacuum components. An iteration loop for computing the bunch profiles, including a subloop using Newton iteration for calculating the synchronous phase deviations, is built and implemented into a matlab-based code. Using this code, we study the bunch lengthening and centroid transient effects for several possible fill patterns in the Hefei Advanced Light Facility storage ring under design. We find the method is very efficient, and the CPU time for the whole calculation on a regular personal computer is less than 30 seconds for each case even with more than 700 bunches. Using the case of a long gap fill as a benchmark example, both the results given by our code and the multiparticle tracking simulation with elegant are in very good agreement.

Change of beam distribution due to decoherence in the presence of transverse feedback

The effect of Landau damping is often calculated based on a Gaussian beam distribution in all degrees of freedom. The stability of the beam is however strongly dependent on the details of the distribution. The present study focuses on the change of bunch distributions caused by the decoherence of the excitation driven by an external source of noise, in the presence of both amplitude detuning and a transverse feedback. Both multiparticle tracking simulations and theoretical models show a similar change of the distribution. The possible loss of Landau damping driven by this change is discussed.

Collimation and decoupling of ECR source beams for brilliance optimization

The four-dimensional transport of the transverse phase space of the extracted beam was calculated for the CAPRICE electron cyclotron resonance (ECR) ion source at GSI. It is especially of interest for an ECR ion source, where asymmetric beams of the transverse phase spaces are extracted in the presence of a strong solenoidal field, and this axial magnetic field adds an angular momentum to extracted beam, resulting in a strong horizontal and vertical (x–y) coupled beam. The paper presents multi-particle tracking simulations using the well-established particle-in-cell code BEAMPATH. The results illustrate that the beam brilliance can be improved by combination of multi-stage collimation with skew quadrupole decoupling.

Compact Storage Ring for Far-Infrared Coherent Synchrotron Radiation Source

We present the results of design studies for a compact storage ring that may produce coherent synchrotron radiation in the far-infrared frequency range. The momentum compaction factor in the ring is easily varied by controlling dispersion function and thus a short bunch length of a few picoseconds can be achieved. We have performed a detailed analysis of beam dynamics for a short bunch length in the ring. Within the controllable range of the second-order momentum compaction factor in the ring, it was shown that the alpha bucket and the rf bucket were created. It is shown that the compact ring with conservative machine errors has a sufficient dynamic aperture after the correction of closed orbit distortion. Multi-particle tracking simulations are performed to investigate longitudinal beam instability due to the broadband impedance in the ring. We investigated the effects of coherent synchrotron radiation wake in the ring on longitudinal beam distribution. From these studies, it is shown that the designed compact ring may provide stable electron beams of approximately around 2 ps rms.

Quasi-Isochronous Optics for Sub-Picosecond Bunch Length at Pohang Light Source

A lattice design was developed for a quasi-isochronous storage ring, which may produce a sub-picosecond bunch length at the 2.5 GeV Pohang Light Source (PLS) and the analysis of transverse and longitudinal particle dynamics in the designed ring was performed. Small momentum compaction factors in the PLS storage ring were obtained by varying the dispersion function to be negative in bending magnets. The shortest bunch length in the designed ring was estimated to be less than 1 ps, which is three-tenths that of a normal operation. The effects of the second-order momentum compaction factor on the transverse and longitudinal particle dynamics in the quasi-isochronous ring were investigated. The relationship between the momentum compaction factor and the bunch length, which can be obtained in the quasi-isochronous PLS storage ring was also investigated. Multiparticle tracking simulations were performed to investigate the longitudinal beam instability in the quasi-isochronous ring using a broadband impedance model.