MOPAF01
Northern Illinois University, DeKalb, Illinois, USA
MSU, East Lansing, Michigan, USA
Fermilab, Batavia, Illinois, USA
Northern Illinois University, DeKalb, Illinois, USA
The main goal of the Muon g-2 Experiment at Fermilab (E989) is to measure the muon anomalous magnetic moment (a, also dubbed as the "anomaly’’) to unprecedented precision. This new measurement will allow to test the completeness of the Standard Model (SM) and to validate other theoretical models beyond the SM. Simulations of the beamlines from the pion production target to the entrance of the g-2 Storage Ring using COSY INFINITY contribute to the understanding and characterization of the muon beam production in relation to the statistical and systematics uncertainties of the E989 measurement. The effect of nonlinearites from fringe fields and high-order contributions on the beam delivery system performance are considered, as well as interactions with the beamline elements apertures, particle decay channels, spin dynamics, and beamline misalignments.
BNL, Upton, Long Island, New York, USA
Electron polarization in a storage ring is subject to two very long term effects: Sokolov-Ternov polarization and depolarization by diffusion. This leads to an equilibrium state over a very long time scale, and, simulation-wise, is highly CPU-time and -memory consuming. Simulations aimed at determining optimal ring storage energy in an electron-ion collider in this context, are always based on tracking bunches with thousands of particles, and in addition for short time scales in comparison, due to HPC limitations. Based on considerations of ergodicity of electron bunch dynamics in the presence of synchrotron radiation, and on the very slow depolarization aimed at in a collider, tracking a single particle instead is investigated, here. This saves a factor of more than 2 orders of magnitudes in the parameter CPU-time*Memory-allocation, it allows much longer tracking and thus improved accuracy on the evaluation of polarization and time constants. The concept is illustrated with polarization lifetime and equilibrium polarization simulations at the eRHIC electron-ion collider.
UNM, Albuquerque, New Mexico, USA
University of Colorado at Boulder, Boulder, USA
DESY, Hamburg, Germany
In this talk we present some numerical results from our work on the spin polarization in high energy electron storage rings. The motivation of our work is to understand spin polarization in very high energy rings like the proposed Future Circular Collider* (FCC-ee) and Circular Electron Positron Collider** (CEPC). This talk is a supplement to K. Heinemann’s talk and gives further numerical details and results. As discussed in Heinemann’s talk our work is based on the initial value problem of the full Bloch equations*** (FBEs) which in turn determines the polarization vector of the bunch. The FBEs take into account spin diffusion effects and spin-flip effects due to synchrotron radiation. The FBEs are a system of three uncoupled Fokker-Planck equations plus coupling terms. Neglecting the spin flip terms in the FBEs one gets the reduced Bloch equations (RBEs) which poses the main computational challenge. Our numerical approach has three parts. Firstly we approximate the FBEs analytically using the method of averaging, resulting in FBEs which allow us to use large time steps (without the averaging the time dependent coefficients of the FBEs would necessitate small time steps). The minimum length of the time interval of interest is of the order of the orbital damping time. Secondly we discretize the averaged FBEs in the phase space variables by applying the pseudospectral method, resulting in a system of linear first-order ODEs in time. The phase space variables come in d pairs of polar coordinates where d = 1, 2, 3 is the number of degrees of freedom allowing for a d-dimensional Fourier expansion. The pseudospectral method is applied by using a Chebychev grid for each radial variable and a uniform Fourier grid for each angle variable. Thirdly we discretize the ODE system by a time stepping scheme. The presence of parabolic terms in the FBEs necessitates implicit time stepping and thus solutions of linear systems of equations. Dealing with 2d + 1 independent variables p
* See http://tlep.web.cern.ch
** See http://cepc.ihep.ac.cn
*** See http://ipac2018.vrws.de/papers/thpak144.pdf
BNL, Upton, Long Island, New York, USA
We present our experiences in optimizing the proposed Rapid Cycling Synchrotron (RCS) injector for the eRHIC Storage ring and the RHIC 2017 lattice. We have develop python code to drive lattice calculations in MADX which are then used to calculate spin resonances using the DEPOL algorithm. This approach has been used to minimize intrinsic spin resonances during the RCS acceleration cycle while controlling lattice parameters such as dispersion and beta functions. This approach has also been used to construct localized imperfection bumps using a spin response matrix and SVD. This approach has also been used to reduce interfering intrinsic spin resonances during the RHIC acceleration ramp.