arXiv subjects

Desmond P. Barber

Publications and source records attributed to Desmond P. Barber.

11 recordsLinked to original sources

arXiv2026

A generalization of the Froissart-Stora formula to piecewise-linear spin-orbit resonance crossings

Spin-polarized beams are important for some nuclear and high-energy physics experiments, such as those planned for the future Electron-Ion Collider (EIC). However, maintaining polarization during the acceleration of a charged-particle beam is difficult because the periodic nature of circular accelerators leads to spin-orbit resonances where the spin-precession frequency is a sum of integer multiples of the orbital frequencies. Usually, the dominant depolarization mechanisms are first-order spin-orbit resonances and the depolarization associated with crossing such a resonance can be computed using the Froissart-Stora formula. However, accelerating polarized hadron beams to high energy requires special magnet structures called Siberian snakes. When these are implemented to maintain a spin-precession frequency of one-half the revolution frequency, there will be no first-order spin-orbit resonance crossings. The dominant depolarization mechanisms are then higher-order spin-orbit resonances. The Froissart-Stora formula can be applied to higher-order resonances when the slope of the amplitude-dependent spin tune is constant. However, the slope of the amplitude-dependent spin tune often changes at the moment of resonance crossing. This work introduces a generalization of the Froissart-Stora formula which is applicable when the slope changes in this manner. The applicability of this formula is demonstrated through tracking simulations of a higher-order resonance crossing in both a toy model and the Relativistic Heavy Ion Collider (RHIC). It is additionally shown that the Froissart-Stora formula is mathematically equivalent to the Landau-Zener formula for the diabatic transition probability in two-level systems with a linearly increasing energy gap and constant coupling. This work therefore also extends the Landau-Zener formula to the case of changing slope.

physics.acc-ph↗

arXiv2026

Elaboration on the kinetic approach of Derbenev and Kondratenko to spin-polarized beams in electron storage rings

We present a detailed account of the kinetic approach for describing the effect of synchrotron radiation on electron and positron spin polarization in storage rings. This approach was introduced in 1974 by Derbenev and Kondratenko and was extended by us since 2001. The kinetic approach is much less frequently utilized but it is more general than the original non-kinetic approach of Derbenev and Kondratenko from 1972 since the kinetic approach is not centered on the invariant spin field. As with the non-kinetic approach the kinetic approach covers the radiative depolarization effect, the Sokolov-Ternov effect and its Baier-Katkov correction as well as the kinetic polarization effect but it enables the calculation of corrections to the original Derbenev-Kondratenko formulas and thereby provides estimates of the reliability of the latter. The kinetic approach is applicable to storage rings with energies from a few GeV up to the energies of the FCC-ee and CEPC and beyond. The kinetic approach is based on the spin-orbit Wigner functions which lead to the so-called Bloch equation for the polarization density which is a generalization of Fokker-Planck equations to spin motion. In turn, as discovered in 2019, the Bloch equation is based on stochastic ordinary differential equations which can be used to develop Monte-Carlo spin tracking codes covering the key effects beyond the radiative depolarization effect. These stochastic ordinary differential equations lead to a new viewpoint of the physical effects, in particular the kinetic polarization effect.

physics.acc-ph↗

arXiv2026

A detailed and unified treatment of spin-orbit systems using tools distilled from the theory of bundles

We return to our study \cite{BEH} of invariant spin fields and spin tunes for polarized beams in storage rings but in contrast to the continuous-time treatment in \cite{BEH}, we now employ a discrete-time formalism, beginning with the $\rm{Poincar\acute{e}}$ maps of the continuous time formalism. We then substantially extend our toolset and generalize the notions of invariant spin field and invariant frame field. We revisit some old theorems and prove several theorems believed to be new. In particular we study two transformation rules, one of them known and the other new, where the former turns out to be an $SO(3)$-gauge transformation rule. We then apply the theory to the dynamics of spin-$1/2$ and spin-$1$ particle bunches and their density matrix functions, describing semiclassically the particle-spin content of bunches. Our approach thus unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics. This unifying aspect of our approach relates the examples elegantly and uncovers relations between the various underlying dynamical systems in a transparent way. As in \cite{BEH}, the particle motion is integrable but we now allow for nonlinear particle motion on each torus. Since this work is inspired by notions from the theory of bundles, we also provide insight into the underlying bundle-theoretic aspects of the well-established concepts of invariant spin field, spin tune and invariant frame field. Since we neglect, as is usual, the Stern-Gerlach force, the underlying principal bundle is of product formso that we can present the theory in a fashion which does not use bundle theory. Nevertheless we occasionally mention the bundle-theoretic meaningof our concepts and we also mention the similarities with the geometrical approach to Yang-Mills Theory.

physics.acc-ph↗

arXiv2023

Evaluation of radiative depolarization in the future Circular Electron-Positron Collider

Polarized lepton beams are an important aspect in the design of the future 100 km-scale Circular Electron-Positron Collider (CEPC). Precision beam energy calibration using resonant depolarization, as well as longitudinally polarized colliding beams are being actively investigated. The achievable beam polarization level for various beam energies and application scenarios depends on the radiative depolarization in the collider rings. In this paper the radiative depolarization effects are evaluated for a CEPC collider ring lattice with detailed machine imperfections and corrections. Simulations with the SLIM and Monte-Carlo approaches using the Bmad/PTC codes are compared with the theory of the effects of spin diffusion for ultra-high beam energies and the validity of the theories is thereby addressed. The paper concludes with a summary and suggestions for further investigations.

physics.acc-ph↗

arXiv2021

Re-evaluation of Spin-Orbit Dynamics of Polarized e+ e- Beams in High Energy Circular Accelerators and Storage Rings: an approach based on a Bloch equation

We give an overview of our current/future analytical and numerical work on the spin polarization in high-energy electron storage rings. Our goal is to study the possibility of polarization for the CEPC and FCC-ee. Our work is based on the so-called Bloch equation for the polarization density introduced by Derbenev and Kondratenko in 1975. We also give an outline of the standard approach, the latter being based on the Derbenev-Kondratenko formulas.

physics.acc-ph↗

arXiv2020

The Bloch equation for spin dynamics in electron storage rings: computational and theoretical aspects

In this paper we describe our work on spin polarization in high-energy electron storage rings which we base on the Bloch equation for the polarization density and which aims towards the e-/e+ option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The Bloch equation takes into account non spin-flip and spin-flip effects due to synchrotron radiation including the spin-diffusion effects and the Sokolov-Ternov effect with its Baier-Katkov generalization as well as the kinetic-polarization effect. This mathematical model is an alternative to the standard mathematical model based on the Derbenev-Kondratenko formulas. For our numerical and analytical studies of the Bloch equation we develop an approximation to the latter to obtain an effective Bloch equation. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations underlying the Bloch equation and by approximating that system via the method of averaging from perturbative ODE theory. We also give an overview of our algorithm for numerically integrating the effective Bloch equation. This discretizes the phase space using spectral methods and discretizes time via the additive Runge-Kutta method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

physics.acc-ph↗

arXiv2019

Polarization and Centre-of-mass Energy Calibration at FCC-ee

The first stage of the FCC (Future Circular Collider) is a high-luminosity electron-positron collider (FCC-ee) with centre-of-mass energy ranging from 88 to 365 GeV, to study with high precision the Z, W, Higgs and top particles, with samples of $5 \times 10^{12}$ Z bosons, $10^8$ W pairs, $10^6$ Higgs bosons and $10^6$ top quark pairs. A cornerstone of the physics program lays in the precise (ppm) measurements of the W and Z masses and widths, as well as forward-backward asymmetries. To this effect the centre-of-mass energy distribution should be determined with the high precision. This document describes the capacity offered by FCC-ee, starting with transverse polarization of the beams around the Z pole and the W pair threshold. A running scheme based on regular measurements of the beam energy by resonant depolarization of pilot bunches, during physics data taking, is proposed. The design for polarization wigglers, polarimeter and depolarizer is outlined. The $e^\pm$ beam energies will be monitored with a relative precision of $10^{-6}$. The centre-of-mass energy is derived subject to further corrections, related to the beam acceleration, synchrotron radiation and beamstrahlung; these effects are identified and evaluated. Dimuon events $e^+e^- \to μ^+ μ^-$, recorded in the detectors, provide with great precision the beam crossing angle, the centre-of-mass energy spread, and the $e^+$ and $e^-$ energy difference. Monitoring methods to minimize absolute error and relative uncertainties are discussed. The impact on the physics measurements is given. A programme of further simulations, design, monitoring and R&D is outlined.

physics.acc-ph↗

arXiv2015

A Monte-Carlo simulation of the equilibrium beam polarization in ultra-high energy electron (positron) storage rings

With the recently emerging global interest in building a next generation of circular electron-positron colliders to study the properties of the Higgs boson, and other important topics in particle physics at ultra-high beam energies, it is also important to pursue the possibility of implementing polarized beams at this energy scale. It is therefore necessary to set up simulation tools to evaluate the beam polarization at these ultra-high beam energies. In this paper, a Monte-Carlo simulation of the equilibrium beam polarization based on the Polymorphic Tracking Code(PTC) (Schmidt et al., 2002 [1]) is described. The simulations are for a model storage ring with parameters similar to those of proposed circular colliders in this energy range, and they are compared with the suggestion (Derbenev et al., 1978 [2]) that there are different regimes for the spin dynamics underlying the polarization of a beam in the presence of synchrotron radiation at ultra-high beam energies. In particular, it has been suggested that the so-called "correlated" crossing of spin resonances during synchrotron oscillations at current energies, evolves into "uncorrelated" crossing of spin resonances at ultra-high energies.

physics.acc-ph↗

arXiv2015

An Informal Summary of a New Formalism for Classifying Spin-Orbit Systems Using Tools Distilled from the Theory of Bundles

We give an informal summary of ongoing work which uses tools distilled from the theory of fibre bundles to classify and connect invariant fields associated with spin motion in storage rings. We mention four major theorems. One ties invariant fields with the notion of normal form, the second allows comparison of different invariant fields and the two others tie the existence of invariant fields to the existence of certain invariant sets. We explain how the theorems apply to the spin dynamics of spin-$1/2$ and spin-$1$ particles. Our approach elegantly unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics and suggests an avenue for addressing the question of the existence of the invariant spin field.

physics.acc-ph↗

arXiv2015

Accurate and efficient spin integration for particle accelerators

Accurate spin tracking is a valuable tool for understanding spin dynamics in particle accelerators and can help improve the performance of an accelerator. In this paper, we present a detailed discussion of the integrators in the spin tracking code gpuSpinTrack. We have implemented orbital integrators based on drift-kick, bend-kick, and matrix-kick splits. On top of the orbital integrators, we have implemented various integrators for the spin motion. These integrators use quaternions and Romberg quadratures to accelerate both the computation and the convergence of spin rotations. We evaluate their performance and accuracy in quantitative detail for individual elements as well as for the entire RHIC lattice. We exploit the inherently data-parallel nature of spin tracking to accelerate our algorithms on graphics processing units.

physics.acc-ph↗

arXiv2014

A New and Unifying Approach to Spin Dynamics and Beam Polarization in Storage Rings

With this paper we extend our studies [1] on polarized beams by distilling tools from the theory of principal bundles. Four major theorems are presented, one which ties invariant fields with the notion of normal form, one which allows one to compare different invariant fields, and two that relate the existence of invariant fields to the existence of certain invariant sets and relations between them. We then apply the theory to the dynamics of spin-1/2 and spin-1 particles and their density matrices describing statistically the particle-spin content of bunches. Our approach thus unifies the spin-vector dynamics from the T-BMT equation with the spin-tensor dynamics and other dynamics. This unifying aspect of our approach relates the examples elegantly and uncovers relations between the various underlying dynamical systems in a transparent way.

physics.acc-ph↗