Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2605.12267

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

Yongjun Li·Sergei Nagaitsev·Derong Xu·Yue Hao·Chad Mitchell
View original source ↗Read source document ↗Export metadata ↓

Abstract

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 Poincar\'e 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.

Explore related subjects

physics.acc-phnlin.CD

Keep this discovery

BibTeXRIS

Yongjun Li, Sergei Nagaitsev, Derong Xu, Yue Hao, Chad Mitchell. 2026-05-12. Approximate Invariant Analysis: An Efficient Framework for Nonlinear Beam Dynamics, Part I: Geometric Approaches of the Poincar\'e Rotation Number. https://arxiv.org/abs/2605.12267

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Coupling periodic-cell and finite-bunch dynamics for structured photocathodes

Patterning a photocathode with submicrometre features can enhance nonlinear photoemission by concentrating the optical field, but the surface geometry can also increase the transverse momentum spread of the emitted electrons. Resolving nanoscale surface fields across an injector-scale illuminated area within a full rf gun simulation is computationally demanding. To couple these scales, we developed an approach which combines a self-consistent finite flat-cathode calculation with the particle-resolved difference between matched structured and flat periodic calculations. The finite calculation determines the macroscopic bunch evolution and space-charge field. The periodic difference determines the local change caused by the surface. For a finite but relatively small test problem, comparison with a fully resolved finite-array WarpX calculation gives differences of 1.3% in rms energy spread and less than 0.1% in projected normalized emittance. We then apply the method to representative FEL photoinjector parameters with a 100 pC emitted source distributed over more than half a million periods, and track the composed bunch through an L-band rf gun and solenoid. The initial difference between the projected horizontal and vertical emittances becomes much smaller after rf acceleration and solenoid focusing. At 1.52 m downstream of the cathode, the projected emittances are nearly equal and exceed those of the matched flat-cathode reference by less than 2% in both planes. The central-slice emittances exceed the reference values by approximately 3% horizontally and 5% vertically.

physics.acc-ph↗
arXiv2026

Physics-Informed Drift Diagnosis for Laser-Plasma Accelerator Operations

Laser-plasma accelerators (LPAs) sustain accelerating gradients of order $100\,\mathrm{GV/m}$, but routine operation remains difficult: electron beam metrics drift over an operating shift, and the root physical cause is often invisible to the available diagnostics. We formulate LPA operation as a latent state-space model in which three effective interaction-point variables, the normalized laser amplitude $a_0$, the normalized plasma electron density $\tilde n_e$ and the residual pulse chirp $\mathcal{C}$, are inferred from routine electron beam observations by an extended Kalman filter. The emission model, which maps the latent state to the diagnostics, is kept structurally separate from the {transition} model, which describes how the latent state evolves between shots. The separation supports diagnosis in two stages, one asking which latent variable moved and one asking what moved it. The implemented emission model is a toy model, yielding an expected performance in line with current facilities and using 3D blow-out regime dependencies where relevant. We conduct synthetic sessions to test the effectiveness of the detection and attribution protocols, finding that attribution is limited by excitation rather than by shot count or diagnostic resolution. Because the construction needs only a set of physical latent variables, an emission model and a family of hardware-derived transition models, it transfers to other drift-prone subsystems. We argue that the accuracy of the whole procedure is limited by the emission model rather than by the inference method.

physics.acc-ph↗
arXiv2026

Turn-by-turn Tune Analysis Using Adaptive BPM Ensembles in the Fermilab Mu2e Delivery Ring*

The Mu2e experiment at Fermilab requires stable resonant slow extraction from the Delivery Ring, making reliable tune monitoring an important operational diagnostic. This work investigates BPM-based tune-candidate extraction using synchronized turn-by-turn position data distributed across multiple digitizers. Each spill contains approximately 50,000 turns from many BPMs in both transverse planes, enabling spectral analysis of tune-like structure. The analysis captures coherent spill snapshots, verifies synchronization using stream timestamps, and computes tune candidates in configurable horizontal and vertical tune bands. Rather than relying on a single BPM or fixed BPM list, it evaluates BPM quality on a spill-by-spill basis and selects small adaptive BPM ensembles. A multi- spill study shows that tune observability is distributed and dynamic rather than concentrated in one globally optimal BPM. Adaptive ensembles improve tune-candidate quality compared with single-BPM selections, with the clearest results in the vertical plane. The horizontal plane shows useful ranking structure but weaker visibility under present thresholds. Direct evaluation of fixed global BPM sets shows that static selections do not reproduce dynamic per-spill performance. These results motivate an adaptive BPM-ensemble approach for Delivery Ring tune analysis using selected BPM subsets, confidence metrics, and quality flags rather than a single preferred BPM or fixed BPM list.

physics.acc-ph↗