11 citations · 64 across the 19 of their papers we have counts for
19 papers
Geometry of Almost-Conserved Quantities in Symplectic Maps. Part II: Recovery of approximate invariant
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
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, w…
Geometry of Almost-Conserved Quantities in Symplectic Maps. Part I: Perturbation Theory
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
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, w…
Geometry of Almost-Conserved Quantities in Symplectic Maps. Part III: Approximate Invariants in Nonlinear Accelerator Systems
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
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…
Isochronous and period-doubling diagrams for symplectic maps of the plane
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +2
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 vis…
Dynamics of McMillan mappings III. Symmetric map with mixed nonlinearity
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov +1
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…
Dynamics of McMillan mappings II. Axially symmetric map
Tim Zolkin, Brandon Cathey, Sergei Nagaitsev
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. Althoug…
Dynamics of McMillan mappings I. McMillan multipoles
Tim Zolkin, Sergei Nagaitsev, Ivan Morozov
In this article, we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings, originally proposed by Edwin McMillan. Both represent the simplest symm…
Integrable symplectic maps with a polygon tessellation
Timofey Zolkin, Yaroslav Kharkov, Sergei Nagaitsev
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 explo…
Symplectic Particle Tracking in a Thick Nonlinear McMillan Lens for the Fermilab Integrable Optics Test Accelerator (IOTA)
B. Cathey, G. Stancari, T. Zolkin
The McMillan system is a novel method to increase the tune spread of a beam without decreasing its dynamic aperture due to the systems integrability. While the ideal system is base…
McMillan map and nonlinear Twiss parameters
Timofey Zolkin, Sergei Nagaitsev, Ivan Morozov
In this article we consider two dynamical systems: the McMillan sextupole and octupole integrable mappings originally introduced by Edwin McMillan; the second one is also known as…
Accelerator and Beam Physics: Grand Challenges and Research Opportunities
S. Nagaitsev, V. Shiltsev, A. Valishev +18
Accelerator and beam physics (ABP) is the science of the motion, generation, acceleration, manipulation, prediction, observation and use of charged particle beams. It focuses on fu…
Machine-assisted discovery of integrable symplectic mappings
Timofey Zolkin, Yaroslav Kharkov, Sergei Nagaitsev
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 q…
Extracting Dynamical Frequencies from Invariants of Motion in Finite-Dimensional Nonlinear Integrable Systems
Chad E. Mitchell, Robert D. Ryne, Kilean Hwang +2
Integrable dynamical systems play an important role in many areas of science, including accelerator and plasma physics. An integrable dynamical system with degrees of freedom (…
Accelerator and Beam Physics Research Goals and Opportunities
S. Nagaitsev, Z. Huang, J. Power +20
This report is a summary of two preparatory workshops, documenting the community vision for the national accelerator and beam physics research program. It identifies the Grand Chal…
Betatron frequency and the Poincare rotation number
Sergei Nagaitsev, Timofey Zolkin
Symplectic maps are routinely used to describe single-particle dynamics in circular accelerators. In the case of a linear accelerator map, the rotation number (the betatron frequen…
TMCI with Resonator Wakes
Alexey Burov, Timofey Zolkin
Transverse mode-coupling instability (TMCI) with a high-frequency resonator wake is examined by the Nested Head-Tail Vlasov solver (NHT), where a Gaussian bunch in a parabolic pote…
TMCI and Space Charge
T. Zolkin, A. Burov
Transverse mode-coupling instability (TMCI) is known to limit bunch intensity. Since space charge (SC) changes the spectra of the collective modes, it affects the TMCI threshold as…
Rotation number of integrable symplectic mappings of the plane
Timofey Zolkin, Sergei Nagaitsev, Viatcheslav Danilov
Symplectic mappings are discrete-time analogs of Hamiltonian systems. They appear in many areas of physics, including, for example, accelerators, plasma, and fluids. Integrable map…
On sector magnets or transverse electromagnetic fields in cylindrical coordinates
Timofey Zolkin
The Laplace's equations for the scalar and vector potentials describing electric or magnetic fields in cylindrical coordinates with translational invariance along azimuthal coordin…