Self-polarization in Storage Rings

Gianfelice-Wendt, E.

doi:10.22323/1.346.0013

Cited by 1 publication

(10 citation statements)

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“…It is straightforward to show via the Fokker-Planck equation for P that f and η evolve according to (2) and (8). Thus indeed (14) and (16) lead to (2) and (8). Note that | S(t)| in (16) is not conserved in time.…”

Section: Be Rbe and Associated Sdes In The Laboratory Framementioning

confidence: 99%

“…The terms M (t, Z), B kin (t, z) and D spin (t, z) in (16) are chosen so that they deliver the required BE (8) by the end of the path for obtaining the FPE described below. As can be expected from the discussion after (9) above, the term Ω(t, Z) S will account for the Thomas-BMT spin-precession effect, the terms −λ(t, Z) 5 √ 3…”

Section: Be Rbe and Associated Sdes In The Laboratory Framementioning

confidence: 99%

“…To show that (14) and (16) lead to (2) and 8one proceeds as follows. The SDEs for the joint process (Z, S) can be written as…”

Section: Be Rbe and Associated Sdes In The Laboratory Framementioning

confidence: 99%

“…Since (2) and (8) follow from (14) and (16) one can use (14) and (16) as the basis for a Monte-Carlo spin tracking algorithm for P (t). Thus this would extend the standard Monte-Carlo spin tracking algorithms by taking into account all physical effects described by (8), like the Sokolov-Ternov effect, the Baier-Katkov correction, the kinetic-polarization effect and, of course, spin diffusion.…”

Section: Be Rbe and Associated Sdes In The Laboratory Framementioning

confidence: 99%

“…Thus, we study the initial-value problem of the system of coupled orbital Fokker-Planck equation and the BE. The third model is based on the system of coupled spin-orbit SDEs (14) and (16) and its associated Fokker-Planck equation which governs the evolution of the (joint) spin-orbit probability density. The third model is equivalent to the second model, i.e., the one based on Ref.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

Heinemann

Appelö

Barber

et al. 2019

Int. J. Mod. Phys. A

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In this paper, we describe our work on spin polarization in high-energy electron storage rings which we base on the Full Bloch equation (FBE) for the polarization density and which aims towards the [Formula: see text] option of the proposed Future Circular Collider (FCC-ee) and the proposed Circular Electron Positron Collider (CEPC). The FBE 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 FBE, we develop an approximation to the latter to obtain an effective FBE. This is accomplished by finding a third mathematical model based on a system of stochastic differential equations (SDEs) underlying the FBE 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 FBE. This discretizes the phase space using spectral methods and discretizes time via the additive Runge–Kutta (ARK) method which is a high-order semi-implicit method. We also discuss the relevance of the third mathematical model for spin tracking.

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