Public Abstract

DE-SC0025476: Complementary Innovative Methods for Studying Electron Polarization in Storage Rings

Award Status: Active

Institution: University of New Mexico, Albuquerque, NM
UEI: F6XLTRUQJEN4
DUNS: 868853094

Most Recent Award Date: 09/17/2024
Number of Support Periods: 1
PM: Colby, Eric

Current Budget Period: 09/01/2024 - 08/31/2025
Current Project Period: 09/01/2024 - 08/31/2027
PI: Heinemann, Klaus

Supplement Budget Period: N/A

Public Abstract

Complementary Innovative Methods for Studying Electron Polarization in Storage Rings Klaus Heinemann, University of New Mexico (Principal Investigator) Georg Hoffstaetter, Cornell university (Co-Principal Investigator) Qi Tang, Los Alamos National Laboratory (Co-Principal Investigator) Our proposed work focuses on spin dynamics in electron or positron storage rings worldwide. It will be a study of the spin-polarization at high energy for those rings using the three main approaches to spin-polarization. Namely firstly, the Derbenev-Kondratenko formulas, using the invariant spin field (ISF) to evaluate the spin-flip polarization rates and depolarization rates as well as the equilibrium polarization of the beam, secondly, Monte-Carlo spin tracking or solving a stochastic ODE system (“SDE system”) and, thirdly, a Bloch equation for the polarization density. It is hoped that electron and positron beams will be polarized. On one hand, this will give an added knob in experimental studies and, on the other hand, can provide precise measurement of the beam energy by means resonant depolarization. The latter is important for precise mass measurements. With the aforementioned three main approaches to spin-polarization, independent methods of evaluating the polarization in storage rings will be available to address controversial questions that are hitherto not fully resolved, yet are critical for several large accelerator projects, e.g. the interaction of the beam-beam force with polarization and the poorly understood correction terms to the Derbenev-Kondratenko formula for the radiative depolarization time. The correction terms, which were introduced by Derbenev and Kondratenko shortly after they devised their formula, are of special interest for circular colliders with very high electron energies like FCC-ee. The aforementioned SDE system is believed to capture, unlike the Derbenev-Kondratenko formulas, all major effects (radiative depolarization, Sokolov-Ternov polarization buildup, Baier- Katkov correction, kinetic polarization). This SDE system was introduced by K. Heinemann et. al in 2019 and it is an extension of the reduced SDE system, which only captures the radiative depolarization effect. The aforementioned Bloch equation, together with an orbital Fokker-Planck equation, is equivalent to the SDE system. The so-called reduced Bloch equation is defined, by neglecting, in the Bloch equation, the Sokolov-Ternov terms and their Baier-Katkov correction as well as the kinetic polarization terms. Thus the reduced Bloch equation together with the orbital Fokker-Planck equation is equivalent to the reduced SDE system. Our main proposed work is thus focused on numerical and analytical studies of the aforementioned three main approaches with the emphasis on creating codes which, when feasible, will end up in the software library Bmad at Cornell University. For established notions like the ISF or the reduced SDE system we propose new computation methods, while for new notions, e.g., the SDE system we will just extend current software, e.g., codes of Monte-Carlo spin tracking. The solution of the reduced Bloch equation, which is an established equation, will be pursued by a new method, introduced by Beznosov in 2020, which is based on a Galerkin condition in a specially designed Hilbert space. For the ISF we propose three new methods. Two of these ISF methods will rely on a new variational approach to the ISF introduced by E. Hamwi and J. Devlin (both at Cornell University) and the third ISF method will rely on a new Machine Learning approach introduced by O. Beznosov of LANL. Note that for electron storage rings the ISF is needed since it is the key ingredient in the Derbenev-Kondratenko formulas. In fact several methods for com- puting the ISF are available since the 1990s, but more robust methods are needed in order to cope with delicate effects like the polarization under the influence of the beam-beam force.

Complementary Innovative Methods for Studying Electron Polarization in Storage Rings

Klaus Heinemann, University of New Mexico (Principal Investigator)

Georg Hoffstaetter, Cornell university (Co-Principal Investigator)

Qi Tang, Los Alamos National Laboratory (Co-Principal Investigator)

Our proposed work focuses on spin dynamics in electron or positron storage rings worldwide. It will be a study of the spin-polarization at high energy for those rings using the three main approaches to spin-polarization. Namely firstly, the Derbenev-Kondratenko formulas, using the invariant spin field (ISF) to evaluate the spin-flip polarization rates and depolarization rates as well as the equilibrium polarization of the beam, secondly, Monte-Carlo spin tracking or solving a stochastic ODE system (“SDE system”) and, thirdly, a Bloch equation for the polarization density. It is hoped that electron and positron beams will be polarized. On one hand, this will give an added knob in experimental studies and, on the other hand, can provide precise measurement of the beam energy by means resonant depolarization. The latter is important for precise mass measurements.

With the aforementioned three main approaches to spin-polarization, independent methods of evaluating the polarization in storage rings will be available to address controversial questions that are hitherto not fully resolved, yet are critical for several large accelerator projects, e.g. the interaction of the beam-beam force with polarization and the poorly understood correction terms to the Derbenev-Kondratenko formula for the radiative depolarization time. The correction terms, which were introduced by Derbenev and Kondratenko shortly after they devised their formula, are of special interest for circular colliders with very high electron energies like FCC-ee.

The aforementioned SDE system is believed to capture, unlike the Derbenev-Kondratenko formulas, all major effects (radiative depolarization, Sokolov-Ternov polarization buildup, Baier- Katkov correction, kinetic polarization). This SDE system was introduced by K. Heinemann et. al in 2019 and it is an extension of the reduced SDE system, which only captures the radiative depolarization effect. The aforementioned Bloch equation, together with an orbital Fokker-Planck equation, is equivalent to the SDE system. The so-called reduced Bloch equation is defined, by neglecting, in the Bloch equation, the Sokolov-Ternov terms and their Baier-Katkov correction as well as the kinetic polarization terms. Thus the reduced Bloch equation together with the orbital Fokker-Planck equation is equivalent to the reduced SDE system.

Our main proposed work is thus focused on numerical and analytical studies of the aforementioned three main approaches with the emphasis on creating codes which, when feasible, will end up in the software library Bmad at Cornell University. For established notions like the ISF or the reduced SDE system we propose new computation methods, while for new notions, e.g., the SDE system we will just extend current software, e.g., codes of Monte-Carlo spin tracking. The solution of the reduced Bloch equation, which is an established equation, will be pursued by a new method, introduced by Beznosov in 2020, which is based on a Galerkin condition in a specially designed Hilbert space. For the ISF we propose three new methods. Two of these ISF methods will rely on a new variational approach to the ISF introduced by E. Hamwi and J. Devlin (both at Cornell University) and the third ISF method will rely on a new Machine Learning approach introduced by O. Beznosov of LANL. Note that for electron storage rings the ISF is needed since it is the key ingredient in the Derbenev-Kondratenko formulas. In fact several methods for com- puting the ISF are available since the 1990s, but more robust methods are needed in order to cope with delicate effects like the polarization under the influence of the beam-beam force.