arXiv subjects

Sergei Nagaitsev

Publications and source records attributed to Sergei Nagaitsev.

At least 19 recordsLinked to original sources

arXiv2026

Construction of Approximate Invariants Across Nonlinear Resonances

Our previous work [Y.~Li, D.~Xu, and Y.~Hao, Phys. Rev. Accel. Beams \textbf{28}, 074001 (2025)] introduced a square-matrix method for constructing approximate invariants recursively, order by order, from the one-turn map of non-integrable Hamiltonian systems. At fourth and higher even orders, the recursive construction is intrinsically non-unique because rotationally invariant polynomials generate a null space in the corresponding homological equations. In the resonant regime, this ambiguity can lead to an incorrect description of the resonance-island topology and is therefore particularly relevant to accelerator applications that rely on stable resonance islands. In this work, we select the null-space contributions by explicitly incorporating the null-space basis vectors and determining their coefficients through an averaging procedure over a prescribed region of interest. The method is demonstrated using the Kobayashi map near a third-order resonance, extending the square-matrix construction to resonant Hamiltonian dynamics.

physics.acc-ph↗

arXiv2026

Experimental Demonstration of a Two-Dimensional Nonlinear Integrable System in a Particle Accelerator

A two-dimensional nonlinear integrable system was experimentally demonstrated at the Fermilab Integrable Optics Test Accelerator. The system was implemented by inserting a special nonlinear magnet in a conventional accelerator lattice. We characterized the system by measuring lifetimes, transverse profiles and transverse oscillation frequencies of the 150-MeV electron beam as a function of the strength of the nonlinear insert. The measured shift of the working point and the amplitude-dependent detuning were consistent with theoretical predictions. We also observed the predicted bifurcation of the stable closed orbit. A striking consequence of the system's implementation was the possibility to operate the storage ring with integer tunes without lifetime degradation. This research opens up novel ways to design particle accelerators and to stabilize particle beams.

physics.acc-ph↗

arXiv2026

Intrabeam scattering studies with large-emittance-ratio ion beams in the Relativistic Heavy Ion Collider, and implications for the Electron-Ion Collider

The Electron-Ion Collider (EIC), to be constructed at Brookhaven National Laboratory, will collide polarized, high-energy electron beams with hadron beams, achieving peak luminosities of up to $1.0 \times 10^{34}$ cm$^{-2}$ s$^{-1}$. To reach such luminosity, the EIC will employ flat-beam collisions at the interaction point. The design transverse emittance ratio will be about 10:1 in the Hadron Storage Ring (HSR). Thanks to stochastic cooling and precise decoupling, we successfully generated and accelerated gold ion beams with a large emittance ratio of 11:1 in the Relativistic Heavy Ion Collider (RHIC). In this article, we present results of intrabeam scattering (IBS) measurements and modeling for large-emittance-ratio gold ion beam, both with and without controlled betatron coupling. To model the IBS growth, we use the formulas developed by Lebedev and Nagaitsev.

physics.acc-ph↗

arXiv2026

Approximate Invariant Analysis: An Efficient Framework for Nonlinear Beam Dynamics, Part I: Geometric Approaches of the Poincaré Rotation Number

We present the first part of an efficient framework for nonlinear beam dynamics, termed Approximate Invariant Analysis (AIA). The framework is based on the construction of approximate invariants~[Y.~Li, D.~Xu, and Y.~Hao, Phys.\ Rev.\ Accel.\ Beams \textbf{28}, 074001 (2025)] and on the extraction of the betatron frequency with the geometric foundations of Poincaré rotation number~[S.~Nagaitsev and T.~Zolkin, Phys.\ Rev.\ Accel.\ Beams \textbf{23}, 054001 (2020)]. The method is demonstrated using the National Synchrotron Light Source~II (NSLS-II) storage ring as an illustrative example.

physics.acc-ph↗

arXiv2026

Geometry of Almost-Conserved Quantities in Symplectic Maps. Part III: Approximate Invariants in Nonlinear Accelerator Systems

We present a perturbative method for constructing approximate invariants of motion directly from the equations of discrete-time symplectic systems. This framework offers a natural nonlinear extension of the classic Courant-Snyder (CS) theory for systems with one degree of freedom -- a foundational cornerstone in accelerator physics now spanning seven decades and historically focused on linear phenomena. The original CS formalism emerged under conditions where nonlinearities were weak, design goals favored linear motion, and analytical tools -- such as the Kolmogorov-Arnold-Moser (KAM) theory -- had not yet been fully developed. While various normal form methods have been proposed to treat near-integrable dynamics, the approach introduced here stands out for its conceptual transparency, minimal computational overhead, and direct applicability to realistic systems. We demonstrate its power and versatility by applying it to several operational accelerator configurations at the Fermi National Accelerator Laboratory (FermiLab), illustrating how the method enables fast, interpretable diagnostics of nonlinear behavior across a broad range of machine conditions.

nlin.CD↗

arXiv2026

Multiple intrabeam scattering in X-Y coupled focusing systems

This paper describes an analytical method to calculate the emittance growth rates due to intra-beam scattering in a circular accelerator with arbitrary x-y coupling. The underlying theory is based on the Landau collision integral and the extended Mais-Ripken parametrization of a coupled betatron motion. The presented results are based on calculations of average emittance growth rates for an initially Gaussian distribution. They are applicable to both bunched and continuous beams.

physics.acc-ph↗

arXiv2026

Dynamics of McMillan mappings III. Symmetric map with mixed nonlinearity

This article extends the study of the dynamical properties of the symmetric McMillan map, emphasizing its utility in understanding and modeling complex nonlinear systems. Although the map features six parameters, we demonstrate that only two are irreducible: the linearized rotation number at the fixed point and a nonlinear parameter representing the ratio of terms in the biquadratic invariant. Through a detailed analysis, we classify regimes of stable motion, provide exact solutions to the mapping equations, and derive a canonical set of action-angle variables, offering analytical expressions for the rotation number and nonlinear tune shift. We further establish connections between general standard-form mappings and the symmetric McMillan map, using the area-preserving Hénon map and accelerator lattices with thin sextupole magnet as representative case studies. Our results show that, despite being a second-order approximation, the symmetric McMillan map provides a highly accurate depiction of dynamics across a wide range of system parameters, demonstrating its practical relevance in both theoretical and applied contexts.

nlin.SI↗

arXiv2025

Frequency Extraction from Invariant Flows

In non-degenerate integrable Hamiltonian systems, invariant tori can be parameterized equivalently by action variables or by their fundamental frequencies. We introduce an invariant-flow formulation for extracting fundamental frequencies of integrable Hamiltonian systems. By treating invariants as generators of commuting Hamiltonian flows, the frequencies are obtained from time-of-flight parameters along these flows, providing a direct alternative to action-angle constructions and spectral methods based on long time series. The approach yields an explicit numerical procedure that extends naturally to systems with multiple degrees of freedom. Its effectiveness is demonstrated using the McMillan map, where machine-precision accuracy is achieved.

nlin.SI↗

arXiv2025

Realizing the Scientific Program with Polarized Ion Beams at EIC

Polarized ion beams at the Electron Ion Collider are essential to address some of the most important open questions at the twenty-first century frontiers of understanding of the fundamental structure of matter. Here, we summarize the science case and identify polarized $^2$H, $^3$He, $^6$Li and $^7$Li ion beams as critical technology that will enable experiments which address the most important science. Further, we discuss the required ion polarimetry and spin manipulation in EIC. The current EIC accelerator design is presented. We identify a significant R\&D effort involving both national laboratories and universities that is required over about a decade to realize the polarized ion beams and estimate (based on previous experience) that it will require about 20 FTE over 10 years (or a total of about 200 FTE-years) of personnel, including graduate students, postdoctoral researchers, technicians and engineers. Attracting, educating and training a new generation of physicists in experimental spin techniques will be essential for successful realization. AI/ML is seen as having significant potential for both acceleration of R\&D and amplification of discovery in optimal realization of this unique quantum technology on a cutting-edge collider. The R\&D effort is synergistic with research in atomic physics and fusion energy science.

nucl-ex↗

arXiv2025

Dynamic Focusing to Suppress Emittance Transfer in Crab-Crossing Flat Beam Collisions

Flat hadron beam collisions, though expected to enhance peak luminosity by about an order of magnitude, have not yet been demonstrated. Our study reveals a critical limitation: realistic fluctuations, when amplified by synchro-betatron resonance, lead to transverse emittance transfer in flat-beam collisions. Using beam-beam simulations based on Electron-Ion Collider design parameters, we show that this effect leads to vertical emittance growth, which can distort the flat-beam profile and degrade luminosity. We propose a dynamic focusing scheme that combines sextupoles with crab cavities to suppress the hourglass-induced resonance. This approach increases tolerance to fluctuations and improves the robustness of flat-beam collisions. This practical mitigation facilitates the adoption of flat-beam collisions in next-generation lepton-hadron colliders.

physics.acc-ph↗

arXiv2025

Geometry of Almost-Conserved Quantities in Symplectic Maps. Part I: Perturbation Theory

Noether's theorem, which connects continuous symmetries to exact conservation laws, remains one of the most fundamental principles in physics and dynamical systems. In this work, we draw a conceptual parallel between two paradigms: the emergence of exact invariants from continuous symmetries, and the appearance of approximate invariants from discrete symmetries associated with reversibility in symplectic maps. We demonstrate that by constructing approximating functions that preserve these discrete symmetries order by order, one can systematically uncover hidden structures, closely echoing Noether's framework. The resulting functions serve not only as diagnostic tools but also as compact representations of near-integrable behavior. The first article establishes the formal foundations of the method. Using the symmetric form of the map as a flexible test case, we benchmark the perturbative construction against established techniques, including the Lie algebra method for twist coefficients. To resolve the inherent ambiguity in the perturbation series, we introduce an averaging procedure that naturally leads to a resonant theory -- capable of treating rational rotation numbers and small-denominator divergences. This enables an accurate and structured description of low-order resonances, including singular and non-singular features in the quadratic and cubic Hénon maps. The approach is systematic, requiring only linear algebra and integrals of elementary functions, yet it yields results in striking agreement with both theory and numerical experiment. We conclude by outlining extensions to more general maps and discussing implications for stability estimates in practical systems such as particle accelerators.

nlin.CD↗

arXiv2025

Dynamics of McMillan mappings II. Axially symmetric map

In this article, we investigate the transverse dynamics of a single particle in a model integrable accelerator lattice, based on a McMillan axially-symmetric electron lens. Although the McMillan e-lens has been considered as a device potentially capable of mitigating collective space charge forces, some of its fundamental properties have not been described yet. The main goal of our work is to close this gap and understand the limitations and potentials of this device. It is worth mentioning that the McMillan axially symmetric map provides the first-order approximations of dynamics for a general linear lattice plus an arbitrary thin lens with motion separable in polar coordinates. Therefore, advancements in its understanding should give us a better picture of more generic and not necessarily integrable round beams. In the first part of the article, we classify all possible regimes with stable trajectories and find the canonical action-angle variables. This provides an evaluation of the dynamical aperture, Poincaré rotation numbers as functions of amplitudes, and thus determines the spread in nonlinear tunes. Also, we provide a parameterization of invariant curves, allowing for the immediate determination of the map image forward and backward in time. The second part investigates the particle dynamics as a function of system parameters. We show that there are three fundamentally different configurations of the accelerator optics causing different regimes of nonlinear oscillations. Each regime is considered in great detail, including the limiting cases of large and small amplitudes. In addition, we analyze the dynamics in Cartesian coordinates and provide a description of observable variables and corresponding spectra.

nlin.SI↗

arXiv2025

Dynamics of McMillan mappings I. McMillan multipoles

In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symmetric McMillan maps, characterized by a single intrinsic parameter. While these systems find numerous applications across various domains of mathematics and physics, some of their dynamical properties remain unexplored. We aim to bridge this gap by providing a comprehensive description of all stable trajectories, including the parametrization of invariant curves, Poincaré rotation numbers, and canonical action-angle variables. In the second part, we establish connections between these maps and general chaotic maps in standard form. Our investigation reveals that the McMillan sextupole and octupole serve as first-order approximations of the dynamics around the fixed point, akin to the linear map and quadratic invariant (known as the Courant-Snyder invariant in accelerator physics), which represents zeroth-order approximations (referred to as linearization). Furthermore, we propose a novel formalism for nonlinear Twiss parameters, which accounts for the dependence of rotation number on amplitude. This stands in contrast to conventional betatron phase advance used in accelerator physics, which remains independent of amplitude. Notably, in the context of accelerator physics, this new formalism demonstrates its capability in predicting dynamical aperture around low-order resonances for flat beams, a critical aspect in beam injection/extraction scenarios.

nlin.SI↗

arXiv2025

Near-Infrared noise in intense electron bunches

This article investigates electron bunch density fluctuations in the 1 - 10 $μm$ wavelength range, focusing on their impact on coherent electron cooling (CEC) in hadron storage rings. In this study, we thoroughly compare the shot-noise model with experimental observations of optical transition radiation (OTR) generated by a relativistic electron bunch ($γ\approx$ 50), transiting an Aluminium metal surface. The bunch parameters are close to those proposed for a stage in an Electron-Ion Collider (EIC), where the bunch size is much larger than the OTR wavelength being measured. Here we present measurements and particle tracking results of both the low-level noise for the EIC bunch parameters and longitudinal space-charge-induced microbunching for the chicane-compressed bunch with coherent OTR enhancements up to 100 times in the various bandwidth-filtered near-infrared (NIR) OTR photodiode signals. We also discuss the corresponding limitations of the OTR method.

physics.acc-ph↗

arXiv2024

Isochronous and period-doubling diagrams for symplectic maps of the plane

Symplectic mappings of the plane serve as key models for exploring the fundamental nature of complex behavior in nonlinear systems. Central to this exploration is the effective visualization of stability regimes, which enables the interpretation of how systems evolve under varying conditions. While the area-preserving quadratic Hénon map has received significant theoretical attention, a comprehensive description of its mixed parameter-space dynamics remain lacking. This limitation arises from early attempts to reduce the full two-dimensional phase space to a one-dimensional projection, a simplification that resulted in the loss of important dynamical features. Consequently, there is a clear need for a more thorough understanding of the underlying qualitative aspects. This paper aims to address this gap by revisiting the foundational concepts of reversibility and associated symmetries, first explored in the early works of G.D. Birkhoff. We extend the original framework proposed by Hénon by adding a period-doubling diagram to his isochronous diagram, which allows to represents the system's bifurcations and the groups of symmetric periodic orbits that emerge in typical bifurcations of the fixed point. A qualitative and quantitative explanation of the main features of the region of parameters with bounded motion is provided, along with the application of this technique to other symplectic mappings, including cases of multiple reversibility. Modern chaos indicators, such as the Reversibility Error Method and the Generalized Alignment Index, are employed to distinguish between various dynamical regimes in the mixed space of variables and parameters. These tools prove effective in differentiating regular and chaotic dynamics, as well as in identifying twistless orbits and their associated bifurcations.

nlin.CD↗

arXiv2023

Integrable symplectic maps with a polygon tessellation

The identification of integrable dynamics remains a formidable challenge, and despite centuries of research, only a handful of examples are known to date. In this article, we explore a special form of area-preserving (symplectic) mappings derived from the stroboscopic Poincare cross-section of a kicked rotator. Notably, Suris' theorem constrains the integrability within this category of mappings, outlining potential scenarios with analytic invariants of motion. In this paper, we challenge the assumption of the analyticity of the invariant, by exploring piecewise linear transformations on a torus and associated systems on the plane, incorporating arithmetic quasiperiodicity and discontinuities. By introducing a new automated technique, we discovered previously unknown scenarios featuring polygonal invariants that form perfect tessellations and, moreover, fibrations of the plane/torus. In this way, this work reveals a novel category of planar tilings characterized by discrete symmetries that emerge from the invertibility of transformations and are intrinsically linked to the presence of integrability. Our algorithm relies on the analysis of the Poincare rotation number and its piecewise monotonic nature for integrable cases, contrasting with the noisy behavior in the case of chaos, thereby allowing for clear separation. Some of the newly discovered systems exhibit the peculiar behavior of integrable diffusion, marked by infinite and quasi-random hopping between tiles while being confined to a set of invariant segments. Finally, through the implementation of a smoothening procedure, all mappings can be generalized to quasi-integrable scenarios with smooth invariant motion, thereby opening doors to potential practical applications.

nlin.SI↗

arXiv2023

Report of the 2021 U.S. Community Study on the Future of Particle Physics (Snowmass 2021) Summary Chapter

The 2021-22 High-Energy Physics Community Planning Exercise (a.k.a. ``Snowmass 2021'') was organized by the Division of Particles and Fields of the American Physical Society. Snowmass 2021 was a scientific study that provided an opportunity for the entire U.S. particle physics community, along with its international partners, to identify the most important scientific questions in High Energy Physics for the following decade, with an eye to the decade after that, and the experiments, facilities, infrastructure, and R&D needed to pursue them. This Snowmass summary report synthesizes the lessons learned and the main conclusions of the Community Planning Exercise as a whole and presents a community-informed synopsis of U.S. particle physics at the beginning of 2023. This document, along with the Snowmass reports from the various subfields, will provide input to the 2023 Particle Physics Project Prioritization Panel (P5) subpanel of the U.S. High-Energy Physics Advisory Panel (HEPAP), and will help to guide and inform the activity of the U.S. particle physics community during the next decade and beyond.

hep-ex↗

arXiv2023

Machine-assisted discovery of integrable symplectic mappings

We present a new automated method for finding integrable symplectic maps of the plane. These dynamical systems possess a hidden symmetry associated with an existence of conserved quantities, i.e. integrals of motion. The core idea of the algorithm is based on the knowledge that the evolution of an integrable system in the phase space is restricted to a lower-dimensional submanifold. Limiting ourselves to polygon invariants of motion, we analyze the shape of individual trajectories thus successfully distinguishing integrable motion from chaotic cases. For example, our method rediscovers some of the famous McMillan-Suris integrable mappings and discrete Painlevé equations. In total, over 100 new integrable families are presented and analyzed; some of them are isolated in the space of parameters, and some of them are families with one parameter (or the ratio of parameters) being continuous or discrete. At the end of the paper, we suggest how newly discovered maps are related to a general 2D symplectic map via an introduction of discrete perturbation theory and propose a method on how to construct smooth near-integrable dynamical systems based on mappings with polygon invariants.

nlin.SI↗