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K. Heinemann

Publications and source records attributed to K. Heinemann.

9 recordsLinked to original sources
arXiv2015

Spin decoherence in electron storage rings --- more from a simple model

This is an addendum to the paper "Some models of spin coherence and decoherence in storage rings" by one of the authors [1] in which spin diffusion in simple electron storage rings is studied. In particular, we illustrate in a compact way, a key implication in the Epilogue of [1], namely that the exact formalism of [1] delivers a rate of depolarisation which can differ from that obtained by the conventional treatments of spin diffusion which rely on the use of the derivative $\partial \hat n/\partialη$ [2,3,4]. As a vehicle we consider a ring with a Siberian Snake and electron polarisation in the plane of the ring (Machine II in [1]). For this simple setup with its one-dimensional spin motion, we avoid having to deal directly with the Bloch equation [5,6] for the polarisation density. Our treatment, which is deliberately pedagogical, shows that the use of $\partial \hat n/\partialη$ provides a very good approximation to the rate of spin depolarisation in the model considered. But it then shows that the exact rate of depolarisation can be obtained by replacing $\partial \hat n/\partialη$ by another derivative as suggested in the Epilogue of [1], while giving a heuristic justification for the new derivative.

physics.acc-ph↗
arXiv2004

Quasiperiodic spin-orbit motion and spin tunes in storage rings

We present an in-depth analysis of the concept of spin precession frequency for integrable orbital motion in storage rings. Spin motion on the periodic closed orbit of a storage ring can be analyzed in terms of the Floquet theorem for equations of motion with periodic parameters and a spin precession frequency emerges in a Floquet exponent as an additional frequency of the system. To define a spin precession frequency on nonperiodic synchro-betatron orbits we exploit the important concept of quasiperiodicity. This allows a generalization of the Floquet theorem so that a spin precession frequency can be defined in this case too. This frequency appears in a Floquet-like exponent as an additional frequency in the system in analogy with the case of motion on the closed orbit. These circumstances lead naturally to the definition of the uniform precession rate and a definition of spin tune. A spin tune is a uniform precession rate obtained when certain conditions are fulfilled. Having defined spin tune we define spin-orbit resonance on synchro--betatron orbits and examine its consequences. We give conditions for the existence of uniform precession rates and spin tunes (e.g. where small divisors are controlled by applying a Diophantine condition) and illustrate the various aspects of our description with several examples. The formalism also suggests the use of spectral analysis to ``measure'' spin tune during computer simulations of spin motion on synchro-betatron orbits.

physics.acc-ph↗
arXiv1997

Some models of spin coherence and decoherence in storage rings

I present some simple exactly solvable models of spin diffusion caused by synchrotron radiation noise in storage rings. I am able to use standard stochastic differential equation and Fokker-Planck methods and I thereby introduce, and exploit, the polarization density. This quantity obeys a linear evolution equation of the Bloch type, which is, like the Fokker-Planck equation, universal in the sense that it is independent of the state of the system. I also briefly consider Bloch equations for other local polarization quantities derived from the polarization density. One of the models chosen is of relevance for some existing and proposed low energy electron (positron) storage rings which need polarization. I present numerical results for a ring with parameters typical of HERA and show that, where applicable, the results of my approach are in satisfactory agreement with calculations using SLIM. These calculations provide a numerical check of a basic tenet of the conventional method of calculating depolarization using the n-axis. I also investigate the equilibrium behaviour of the spin ensemble when there is no synchrotron radiation. Finally, I summarize other results which I have obtained using the polarization density and which will be published separately.

physics.acc-ph↗
arXiv1996

On Stern-Gerlach forces allowed by special relativity and the special case of the classical spinning particle of Derbenev-Kondratenko

This work is devoted to an examination of Stern-Gerlach forces consistent with special relativity and is motivated by recent interest in the relativistic Stern-Gerlach force acting on polarized protons in high-energy particle accelerators. The equations for the orbital and spin motion of a classical charged particle with arbitrary intrinsic magnetic dipole moment in an external electromagnetic field are considered and by imposing the constraints of special relativity and restricting to first order in spin (= first order $\hbar$) a well-defined class of spin-orbit systems is obtained. All these systems can be treated on an equal footing including such prominent cases as those considered by Frenkel and by Good. The Frenkel case is considered in great detail because I show that this system is identical with the one introduced by Derbenev and Kondratenko for studying spin motion in accelerators. In particular I prove that the spin-orbit system of Derbenev and Kondratenko is (nonmanifestly) Poincaré covariant and identify the transformation properties of this system under the Poincaré group. The Derbenev-Kondratenko Hamiltonian was originally proposed as a way to combine relativistic spin precession and the Lorentz force. The aforementioned findings now demonstrate that the Derbenev-Kondratenko Hamiltonian also provides a legitimate framework for handling the relativistic Stern-Gerlach force. Numerical examples based on the Frenkel and Good cases for the HERA proton ring and electromagnetic traps are provided.

physics.acc-ph↗
arXiv1996

A tracking algorithm for the stable spin polarization field in storage rings using stroboscopic averaging

Polarized protons have never been accelerated to more than about $25$GeV. To achieve polarized proton beams in RHIC (250GeV), HERA (820GeV), and the TEVATRON (900GeV), ideas and techniques new to accelerator physics are needed. In this publication we will stress an important aspect of very high energy polarized proton beams, namely the fact that the equilibrium polarization direction can vary substantially across the beam in the interaction region of a high energy experiment when no countermeasure is taken. Such a divergence of the polarization direction would not only diminish the average polarization available to the particle physics experiment, but it would also make the polarization involved in each collision analyzed in a detector strongly dependent on the phase space position of the interacting particle. In order to analyze and compensate this effect, methods for computing the equilibrium polarization direction are needed. In this paper we introduce the method of stroboscopic averaging, which computes this direction in a very efficient way. Since only tracking data is needed, our method can be implemented easily in existing spin tracking programs. Several examples demonstrate the importance of the spin divergence and the applicability of stroboscopic averaging.

acc-phys↗
arXiv1995

Construction of Nonlinear Symplectic Six-Dimensional Thin-Lens Maps by Exponentiation

The aim of this paper is to construct six-dimensional symplectic thin-lens transport maps for the tracking program SIXTRACK, continuing an earlier report by using another method which consistes in applying Lie series and exponentiation as described by W. Groebner and for canonical systems by A.J. Dragt. We firstly use an approximate Hamiltonian obtained by a series expansion of the square root. Furthermore, nonlinear crossing terms due to the curvature in bending magnets are neglected. An improved Hamiltonian, excluding solenoids, is introduced in Appendix A by using the unexpanded square root mentioned above, but neglecting again nonlinear crossing terms...

acc-phys↗