Beam Dynamics Problems Research Articles

Symplectic neural surrogate models for beam dynamics

Development of robust machine-learning (ML) based surrogates for particle accelerators can significantly benefit the modeling, design, optimization, monitoring and control of such accelerators. It is desirable that the surrogate models embed fundamental physical constraints to the interaction and dynamics of the beams, for which an accelerator must be designed to operate upon. We implement and train a class of phase space structure-preserving neural networks — Henon Neural Networks (HenonNets) [1], for nonlinear beam dynamics problems. It is demonstrated that the trained HenonNet model predicts the beam transfer matrix to a reasonably good accuracy while strongly maintaining the symplecticity. To explore such model’s applicability and flexibility for high brightness or intensity beams, we further test it with beam dynamics in the presence of electrostatic and radiative collective effects. Our results indicate that HenonNet may be used as a base ML model for the surrogate of complex beam dynamics, thus opening up a wide range of applications.

Evolutionary Integro-Differential Equation Solution of Self-Consistent Beam Dynamics in Dielectric-Filled Wakefield Accelerating Structure

Self-coordinated transverse dynamics of the high current relativistic electronic bunches used for generation of wake fields in accelerating structures with dielectric filling is investigated. The Laplace transform method is used to find the analytical solution of the problem of self-consistent beam dynamics.

Numerical simulations of colliding beams dynamics with nonzero crossing angle

The work is devoted to the problem of charged particle beam dynamics in self‐consistent electromagnetic fields in the modern colliders. The colliding beams move in vacuum with highly relativistic speeds (γ∼103 − 105). The achievement of the high luminosities for the high energy beams finds difficulties due to the beam disruption under the strong electromagnetic fields. We present our first results on the numerical simulations for the beams with the nonzero crossing angle with our parallel fully three‐dimensional algorithm. The results of the numerical modelling demonstrate qualitative and quantitative coincidence with theory for noncritical beam parameters.

On Nonlocal Computation of Eigenfrequencies of Beams Using Finite Difference and Finite Element Methods

In this paper, we show that two numerical methods, specifically the finite difference method and the finite element method applied to continuous beam dynamics problems, can be asymptotically investigated by some kind of enriched continuum approach (gradient elasticity or nonlocal elasticity). The analysis is restricted to the vibrations of elastic beams, and more specifically the computation of the natural frequencies for each numerical method. The analogy between the finite numerical approaches and the equivalent enriched continuum is demonstrated, using a continualization procedure, which converts the discrete numerical problem into a continuous one. It is shown that the finite element problem can be transformed into a system of finite difference equations. The convergence rate of the finite numerical approaches is quantified by an equivalent Rayleigh's quotient. We also present some exact analytical solutions for a first-order finite difference method, a higher-order finite difference method or a cubic Hermitian finite element, valid for arbitrary number of nodes or segments. The comparison between the exact numerical solution and the approximated nonlocal approaches shows the efficiency of the continualization methodology. These analogies between enriched continuum and finite numerical schemes provide a new attractive framework for potential applications of enriched continua in computational mechanics.

High performance computation on beam dynamics problems in high intensity compact cyclotrons

This paper presents the research progress in the beam dynamics problems for future high intensity compact cyclotrons by utilizing the state-of-the-art high performance computation technology. A “Start-to-Stop” model, which includes both the interaction of the internal particles of a single bunch and the mutual interaction of neighboring multiple bunches in the radial direction, is established for compact cyclotrons with multi-turn extraction. This model is then implemented in OPAL-CYCL, which is a 3D object-oriented parallel code for large scale particle simulations in cyclotrons. In addition, to meet the running requirement of parallel computation, we have constructed a small scale HPC cluster system and tested its performance. Finally, the high intensity beam dynamics problems in the 100 MeV compact cyclotron, which is being constructed at CIAE, are studied using this code and some conclusions are drawn.

Analytical treatment of the nonlinear electron cloud effect and the combined effects with beam-beam and space charge nonlinear forces in storage rings

In this paper we treat first some nonlinear beam dynamics problems in storage rings, such as beam dynamic apertures due to magnetic multipoles, wiggles, beam-beam effects, nonlinear space charge effect, and then nonlinear electron cloud effect combined with beam-beam and space charge effects, analytically. This analytical treatment is applied to BEPC II. The corresponding analytical expressions developed in this paper are useful both in understanding the physics behind these problems and also in making practical quick hand estimations.

Discrete spectral analysis of beam oscillation

For a range of beam dynamics problems, high-precision measurement of frequency, amplitude and phase of a beam oscillation mode is required. The problem of extraction of oscillation modes from a series of equally time-spaced data samples is studied. Discrete Fourier Transform and methods of its refinement are analyzed in the view of accuracy limitations and applicability.

Applications of parallel computational methods to charged-particle beam dynamics

The availability of parallel computation hardware and the advent of standardized programming interfaces has made a new class of beam dynamics problems accessible to numerical simulations. We describe recent progress in code development for simulations of coherent synchrotron radiation and the weak–strong and strong–strong beam–beam interaction. Parallelization schemes will be discussed, and typical results will be presented.

Bending Dominated Beam Dynamics: Continuous Shape Functions, Boundary Conditions and Internal Loads

Predicted solutions to flexible beam dynamics problems involving large overall prescribed motion are investigated using two existing continuous shape function approaches. The beam is cantilevered to a rigid rotating table at one end and attached to the table by way of a tether spring at the other end. It is demonstrated that the free-interface component mode approach provides a significantly more accurate solution than the traditional cantilever beam eigenfunction approach. The chief difference between the two approaches is the continuous shape functions used and the handling of the boundary conditions. The beam in this study, in contrast to a previous study, is oriented such that the steady-state response of the beam is dominated by its bending behavior. It is shown that the internal loads acting on the beam must be considered in order to demonstrate the distinctive differences between the two approaches. Finally, it is demonstrated that adding a new static shape function to the existing free-interface component mode synthesis approach yields a significantly more accurate solution to the problem.

Mathematical Modeling and Optimization of Beam Dynamics

Nowadays mathematical methods of modeling and optimization are extensively used in many fields of science and technology. Development of specialized software for various applications is of more and more importance. A special class of the problems attracting attention of numerous researches is represented by the problems associated with the beam dynamics formation in accelerators. The paper deals with optimization problems of charged particle beam dynamics in accelerators. The optimization methods are developed for the presented functionals. They are used for solution of various beam dynamics problems in different accelerating and focusing structures. The realization of these methods shows their effectiveness. In this paper we demonstrate the power of new BDO-RFQ code. The comparative analysis of various structures: LEDA-RFQ (USA), IPHI-RFQ (France) and RFQ structure found with BDO-RFQ code (Russia) is given.

Stochastic dynamics and Fokker-Planck equation in accelerator physics

The aim of this contribution is to study the particle dynamics in a storage ring under the influence of noise. Some simplified stochastic beam dynamics problems are treated by solving the corresponding Fokker-Planck equations numerically.

Dynamics of beams in a periodically corrugated plasma-filled waveguide with a polynomial corrugation profile

The problem of beam dynamics in a periodically corrugated plane waveguide filled partially with nonmagnetized plasma is considered. Short-period beam trajectories of purely waveguide type and plasma-waveguide types are found. The distribution function of beam reflection points from the waveguide surface in the case of chaotic trajectories is calculated.

The problem of an elastic-plastic beam dynamics and an incomplete co-dimension two bifurcation

In this paper, a continuous fourth-order ordinary differential equation Shanley-type model is suggested for analytical analysis of the problem of elastic-plastic beam dynamics. A codimension three bifurcation problem and its simplified case, an incomplete co-dimension two bifurcation of a pair of pure imaginary eigenvalues and a simple zero eigenvalue are presented and analyzed, and the normal form analysis and the unfoldings of 2-jet and 4-jet cases of the incomplete normal forms are provided. Since elastic-plastic beam dynamics are of great non-linear complexity and the vector fields are multiple degeneracies, small differences of physical parameters cause dramatic essential changes of behavior of the motion. Through these results the rich dynamical behaviors of the elastic-plastic beam dynamics, including the counterintuitive behavior and its sensitivity to small parameters of this problem, can be illustrated.

Outline of a 15–20 GeV CEBAF like machine

Transverse beam dynamics problems in a recirculating linac and synchrotron radiation effects in beam transport lines are briefly summarized. A broad outline of a CEBAF like accelerator capable of producing electron beams with energies of up to 15–20 GeV is given.

Counterintuitive Behavior in a Problem of Elastic-Plastic Beam Dynamics

In a particular example of short pulse loading on a pin-ended beam, the permanent deflection is predicted by a numerical solution to be in the direction opposite that of the load. Analysis of a Shanley-type model shows that this surprising behavior may occur as a consequence of plastic irreversibility combined with geometric nonlinearity, when the peak deflection produced by the pulse lies in a certain range of small magnitudes. Results from a number of well-known structural dynamics codes are shown. These exhibit a wide spread in the predicted final deflections, indicating strong sensitivities of both physical and computational nature.

Some Interaction Effects in a Problem of Plastic Beam Dynamics—Part 3: Experimental Study

An experimental study is made of the permanent deformation of clamped beams with and without constraints against axial displacements at the ends. The beams carry a concentrated mass at the center and are subjected to blast loading at the central mass. Experimental results are compared with the theoretical predictions developed in earlier papers, Parts 1 and 2, and show general agreement.

Some Interaction Effects in a Problem of Plastic Beam Dynamics—Part 2: Analysis of a Structure as a System of One Degree of Freedom

A theoretical study is made of the permanent deformation of a clamped beam with constraints against axial displacements at the ends. The beam carries a concentrated mass at its center and is subjected to large transverse impact loading at the mass. The analysis is based on the assumption of one degree of freedom and takes account of the interaction between bending and extension, of strain-rate sensitivity, of elastic vibration, and of load duration, in an approximate manner.

Some Interaction Effects in a Problem of Plastic Beam Dynamics—Part 1: Interaction Analysis of a Rigid, Perfectly Plastic Beam

An analysis is presented to determine the permanent deformation of a rigid-plastic clamped beam with constraints against axial displacements at the ends. The beam carries a concentrated mass at its center and is subjected to large transverse impulsive loading at the mass. Plastic interaction is considered for the combined action of bending moments, axial forces, and shearing forces, based on a fixed yield surface.

Beam Dynamics Problems in a High-Energy Electron Linac

Beam Dynamics Problems in a High-Energy Electron Linac