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High-Performance Electron Sources: Numerical Methods and Beam Dynamics at the Precision Frontier
Electron sources have a wide range of applications and there are many stakeholders that express continuing need for improvements and performance enhancements. Whether we consider ultra-cold, high-brightness, high-charge or high-average current source needs, there are some common themes from the point of view of the beam dynamics involved. These are the following ones: ability to model accurately the emission processes, including the presence of often complicated cathode and other boundary surfaces with a wide range of spatial scales; ability to deal accurately and efficiently with a large number of particles interacting pair-wise, including the stochastic part of these interactions with a wide range of spatial scales; and ability to propagate the particle distributions in time, including collisions with a wide range of temporal scales. These tasks require high precision and accuracy since the goal is usually generation, transport and preservation of very high-quality beams. This grant addressed one of the rem
Polarization transmission in the Hadron Storage Ring of the Electron-Ion Collider
The successful operation of the future Electron-Ion Collider is contingent on maintaining high hadron beam polarization up to 275 GeV. The Hadron Storage Ring lattice, however, features a symmetry-breaking interaction region that excites strong, nonsystematic spin resonances, posing a significant threat to polarization preservation. This paper systematically investigates two complementary strategies to ensure high polarization transmission. The first method involves optimizing the vertical betatron phase advance between Siberian snakes to orchestrate a cancellation of depolarizing kicks across the ring. We demonstrate through simulations that both dynamic and fixed-optics solutions based on this principle can successfully preserve polarization through the strongest resonances. The second, more powerful approach involves optimizing the snake rotation axes to suppress resonance driving terms at their source. We revisit established symmetric configurations, such as the Lee-Courant schemes, and introduce a novel, highly symmetric “Doubly Lee-Courant” (DLC) scheme, which enforces a local 𝜋 spin phase advance across every consecutive pair of snakes. Our analysis reveals a clear performance hierarchy, with the DLC configuration providing an exceptionally robust and energy-insensitive baseline for polarization preservation. We conclude that a hybrid strategy, using a DLC snake scheme as a symmetric foundation and betatron phase tuning for fine corrections, offers the most effective path forward for the EIC and future high-energy polarized-beam facilities.
Tomography of longitudinal phase space linearization for the generation of attosecond electron bunches
The generation of electron bunches on the attosecond timescale is important for a multitude of accelerator-based applications. Here, we report on a tomographic measurement of the (pre)linearized longitudinal phase space of a low charge 3 MeV electron bunch generated with the 1.6 cell Pegasus photoinjector for the generation of attosecond bunches. The nonlinear correlations in the longitudinal phase space induced by space charge at the photocathode, radiofrequency field curvature of the gun, and vacuum dispersion are compensated using a compact X-band linearizer. Then, the initial and compensated phase of the picosecond electron bunch is precisely reconstructed by neural network assisted tomographic reconstruction from momentum spectra at varying buncher linac phase. Finally, we combine the measured phase space shape with particle tracking simulations to show that electron bunches as short as 941 as develop downstream the beamline.
A Unified Beam-Dynamics and Hardware Design Framework for Hybrid Nonlinear-Kicker Injection in NSLS-II
Nonlinear kickers (NLKs) enable off-axis injection in ultralow-emittance storage rings by providing a strong kick to the injected beam while remaining nearly transparent to the stored beam. In hybrid schemes, a conventional four-kicker bump defines the injected trajectory, and the NLK reduces the first-turn action under constrained beam offset and optics conditions. Effective operation additionally requires stable and reproducible first-turn injection trajectories. We develop a compact action–angle framework that expresses NLK dynamics in terms of Courant–Snyder invariants and yields an analytical bound on achievable action reduction. This formulation provides direct design rules for NLK placement, phase advance, injected-beam offset, and kicker field profile. Within this framework, we identify the 8-wire NLK as a practical baseline and extend its design by relaxing the square-geometry constraint, enabling inward shifting of the off-axis field peak while preserving on-axis field and gradient cancellation. Application to the NSLS-II lattice shows how aperture, pulsed-power, and mechanical constraints combine to determine a coupled design solution. Multi-turn tracking confirms that candidate NLK locations maintain sufficient stay-clear (aperture-clearance) margin, while the optimized wire geometry reduces the required current and Lorentz force load. The results establish a unified approach for NLK-assisted injection design and provide a practical pathway for upgrades in diffraction-limited storage rings.
Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam
The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.
Gyrodampers for large space structures
The problem of controlling the vibrations of a large space structures by the use of actively augmented damping devices distributed throughout the structure is addressed. The gyrodamper which consists of a set of single gimbal control moment gyros which are actively controlled to extract the structural vibratory energy through the local rotational deformations of the structure, is described and analyzed. Various linear and nonlinear dynamic simulations of gyrodamped beams are shown, including results on self-induced vibrations due to sensor noise and rotor imbalance. The complete nonlinear dynamic equations are included. The problem of designing and sizing a system of gyrodampers for a given structure, or extrapolating results for one gyrodamped structure to another is solved in terms of scaling laws. Novel scaling laws for gyro systems are derived, based upon fundamental physical principles, and various examples are given.
Aeroelastic Analysis Using Deforming Cartesian Grids
Ongoing work in air-vehicle design illustrates the potential of advanced concepts to provide significant improvements in efficiency; but with their incorporation of lightweight flexible structures, such configurations may require active control systems to ensure reliability and safety. However, many contemporary analysis methods are inefficient for aeroelastic analysis and design of such configurations. This paper describes the development of a new approach that automates the geometry setup, mesh generation, and assembly of fluid–structural coupling interfaces to enable efficient aeroelastic and aeroservoelastic analysis of advanced concepts. The core elements for this approach are a cut-cell Cartesian grid-based computational fluid dynamics solver, a nonlinear beam element structural model, a conservative fluid–structural interface treatment, and the formulation and implementation of a new deforming grid capability within the cut-cell Cartesian grid solver. In this paper, emphasis is on this latter component with detailed description given of the mesh motion strategy, evaluation of fluxes and structural loads at the surface, and computation of geometrical properties such as cell volume, directed face areas, centroids, and motion-induced fluxes for deforming Cartesian grids required to advance the flow states. Aeroelastic simulations exercising the capability show favorable agreement with data and predictions in the literature for subsonic and supersonic applications.
Final Physics Design of Proton Improvement Plan-II at Fermilab
This paper presents the final physics design of the Proton Improvement Plan-II (PIP-II) at Fermilab, focusing on the linear accelerator (Linac) and its beam transfer line. We address the challenges in longitudinal and transverse lattice design, specifically targeting collective effects, parametric resonances, and space charge nonlinearities that impact beam stability and emittance control. The strategies implemented effectively mitigate space charge complexities, resulting in significant improvements in beam quality—evidenced by reduced emittance growth, lower beam halo, decreased loss, and better energy spread management. This comprehensive study is pivotal for the PIP-II project's success, providing valuable insights and approaches for future accelerator designs, especially in managing nonlinearities and enhancing beam dynamics.
Final Physics Design of Proton Improvement Plan-II At Fermilab
This paper presents the final physics design of the Proton Improvement Plan-II (PIP-II) at Fermilab, focusing on the linear accelerator (Linac) and its beam transfer line. We address the challenges in longitudinal and transverse lattice design, specifically targeting collective effects, parametric resonances, and space charge nonlinearities that impact beam stability and emittance control. The strategies implemented effectively mitigate space charge complexities, resulting in significant improvements in beam quality -- evidenced by reduced emittance growth, lower beam halo, decreased loss, and better energy spread management. This comprehensive study is pivotal for the PIP-II project's success, providing valuable insights and approaches for future accelerator designs, especially in managing nonlinearities and enhancing beam dynamics.
Advanced storage ring lattice options based on hybrid six-bend achromat for Stanford Synchrotron Radiation Lightsource upgrade
Three storage ring lattices have been designed as options for a future upgrade of the Stanford synchrotron radiation lightsource (SSRL). The three options differ in circumference and targeted future site, with one to be built in the tunnel of the present SPEAR3 ring, one as a green field ring on the SLAC campus, and the third in the tunnel of the decommissioned PEP-II ring. The lattices are based on the newly proposed hybrid 6-bend achromat (H6BA) lattice cells, which is ideal for pushing the photon beam brightness while achieving excellent nonlinear dynamics performance. The transparent matching conditions are enforced to minimize the negative impact of the loss of periodicity due to insertion of various long straight sections. Numerical optimization is performed to further improve the nonlinear dynamics. Finally, in addition to reaching very low emittances, the lattices can accommodate traditional off-axis injection and achieve beam lifetimes similar to or exceeding that of typical third generation rings.
Experimental Studies of Nonlinear Integrable Optics with Elliptic Potentials
The stable transport of charged particle beams is the core challenge in designing and operating accelerators. The current paradigm for transverse focusing is based on quadrupole and dipole elements, described as a linear integrable Hamiltonian by Courant and Snyder. The operational limits of high intensity accelerators are often determined by collective instabilities within the beam. Nonlinear elements may be added to suppress certain forms of these collective effects, but restrict the range of stable trajectories. These shortcomings motivate extending to a nonlinear integrable system which can offer the benefits of suppressing collective instabilities without limiting the stable trajectories. Danilov and Nagaitsev proposed a novel nonlinear integrable system with elliptical potentials, which could be implemented as magnetic elements in an accelerator. Such a system has been implemented for practical verification in the integrable optics test accelerator (IOTA), a small storage ring constructed for beam dynamics studies. Electron beam studies in IOTA treat the low-emittance beam as a macroparticle for detailed probing of the expected single particle dynamics. This dissertation details new measurements of the nonlinear integrable system relevant for practical implementation. Turn-by-turn measurements of the kicked beam responses are used for phase space reconstruction and analysis of the predicted nonlinear dynamics. The stability and aperture for various nonlinear configurations are measured with beam losses. Amplitude dependent detuning, a core figure of merit for suppressing instabilities, is measured and compared with high fidelity particle tracking simulations. The synchrotron radiation images of circulating beam allow direct measurements of the topology and lifetime in configurations where nonlinear focusing terms dominate.
Investigations of nonlinear polarization transfer between obliquely intersecting beams
Electromagnetic waves propagating through plasma can interact nonlinearly through a variety of different mechanisms. The excitation of a plasma beat wave (ions or electrons) can create a refractive index modulation that changes the dispersion of the interacting beams. Alternatively, high-intensity beams can enter the regime where relativistic nonlinearities influence the propagation dynamics. In recent studies [ Opt. Express 29 , 1162 ( 2021 ) OPEXFF 1094-4087 10.1364/OE.413064 ], it was proposed that two beams propagating along the same axis can exchange their polarization state due to nonlinear interaction. Here we present a numerical analysis of two laser beams intersecting in a nonlinear medium at varying angles. Polarization transfer is observed as predicted by analytical theory for a range of angles. For small angles, it is found that filamentation of the interacting beams becomes important. Analytical estimates of the filamentation threshold are presented, and good agreement is found with the simulation data.
Nonlinear flap-lag-axial equations of a rotating beam with arbitrary precone angle
In an attempt both to unify and extend the analytical basis of several aspects of the dynamic behavior of flexible rotating beams, the second-degree nonlinear equations of motion for the coupled flapwise bending, lagwise bending, and axial extension of an untwisted, torsionally rigid, nonuniform, rotating beam having an arbitrary angle of precone with the plane perpendicular to the axis of rotation are derived using Hamilton's principle. The derivation of the equations is based on the geometric nonlinear theory of elasticity and the resulting equations are consistent with the assumption that the strains are negligible compared to unity. No restrictions are imposed on the relative displacements or angular rotations of the cross sections of the beam other than those implied by the assumption of small strains. Illustrative numerical results, obtained by using an integrating matrix as the basis for the method of solution, are presented both for the purpose of validating the present method of solution and indicating the range of applicability of the equations of motion and the method of solution.
Vibration response of geometrically nonlinear elastic beams to pulse and impact loading
The governing equations for the geometrically nonlinear deformation of elastic beams subjected to dynamic bending loads are developed and solved for various initial conditions. Of primary interest is the response to pulse loading and simulated impact. Both transient and several cycle solutions are generated for the free vibration response to pulse loading. The results obtained are compared to a first mode analysis approximation. A model is developed to simulate impact loading by the distribution of additional mass to the elastic system and subjecting it to a velocity pulse. The governing equations are solved using second order finite differences in space and time. The solutions obtained are in reasonable agreement with experimental results.
Application of GRASP (General Rotorcraft Aeromechanical Stability Program) to nonlinear analysis of a cantilever beam
The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyse the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformations. The correlation is excellent in all cases.
Application of GRASP to nonlinear analysis of a cantilever beam
The General Rotorcraft Aeromechanical Stability Program (GRASP) was developed to analyze the steady-state and linearized dynamic behavior of rotorcraft in hovering and axial flight conditions. Because of the nature of problems GRASP was created to solve, the geometrically nonlinear behavior of beams is one area in which the program must perform well in order to be of any value. Numerical results obtained from GRASP are compared to both static and dynamic experimental data obtained for a cantilever beam undergoing large displacements and rotations caused by deformation. The correlation is excellent in all cases.
A computational procedure for multibody systems including flexible beam dynamics
A computational procedure suitable for the solution of equations of motions for flexible multibody systems has been developed. A fully nonlinear continuum approach capable of accounting for both finite rotations and large deformations has been used to model a flexible beam component. The beam kinematics are referred directly to an inertial reference frame such that the degrees of freedom embody both the rigid and flexible deformation motions. As such, the beam inertia expression is identical to that of rigid body dynamics. The nonlinear coupling between gross body motion and elastic deformation is contained in the internal force expression. Numerical solution procedures for the integration of spatial kinematic systems can be directily applied to the generalized coordinates of both the rigid and flexible components. An accurate computation of the internal force term which is invariant to rigid motions is incorporated into the general solution procedure.