Paper  Title  Page 

SUPAF04  Symplectic and SelfConsistent Algorithms for Particle Accelerator Simulation  42 


This paper is a review of algorithms, applicable to particle accelerator simulation, which share the following two characteristics: (1) they preserve to machine precision the symplectic geometry of the particle dynamics, and (2) they track the evolution of the selffield consistently with the evolution of the charge distribution. This review includes, but is not limited to, algorithms using a ParticleinCell discretization scheme. At the end of this review we discuss to possibility to derived algorithms from an electrostatic Hamiltonian.  
Slides SUPAF04 [0.424 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018SUPAF04  
About •  paper received ※ 19 October 2018 paper accepted ※ 24 October 2018 issue date ※ 26 January 2019  
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MOPLG03  Spin Dynamics in Modern Electron Storage Rings: Computational and Theoretical Aspects  127 


Funding: U.S. Department of Energy, Office of Science, Office of High Energy Physics, Award Number DESC0018008 In this talk we present some numerical and analytical results from our work on the spin polarization in high energy electron storage rings. Our work is based on the initial value problem of what we call the full Bloch equations (FBEs). The solution of the FBEs is the polarization density which is proportional to the spin angular momentum density per particle in phase space and which determines the polarization vector of the bunch. The FBEs take into account spin diffusion effects and spinflip effects due to synchrotron radiation including the SokolovTernov effect and its BaierKatkov generalization. The FBEs were introduced by Derbenev and Kondratenko in 1975 as a generalization of the BaierKatkovStrakhovenko equations from a single orbit to the whole phase space. The FBEs are a system of three uncoupled FokkerPlanck equations plus two coupling terms, i.e., the TBMT term and the BaierKatkov term. Neglecting the spin flip terms in the FBEs one gets what we call the reduced Bloch equations (RBEs). The RBEs are sufficient for computing the depolarization time. The conventional approach of estimating and optimizing the polarization is not based on the FBEs but on the socalled DerbenevKondratenko formulas. However, we believe that the FBEs offer a more complete starting point for very high energy rings like the FCCee and CEPC. The issues for very high energy are: (i) Can one get polarization, (ii) are the DerbenevKondratenko formulas satisfactory at very high energy? If not, what are the theoretical limits of the polarization? Item (ii) will be addressed both numerically and analytically. 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. Seco 

Slides MOPLG03 [0.465 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018MOPLG03  
About •  paper received ※ 20 October 2018 paper accepted ※ 24 October 2018 issue date ※ 26 January 2019  
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MOPAF03  Polarization Lifetime in an Electron Storage Ring, an Ergodic Approach in eRHIC EIC  140 


Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DEAC0298CH10886 with the U.S. Department of Energy Electron polarization in a storage ring is subject to two very long term effects: SokolovTernov polarization and depolarization by diffusion. This leads to an equilibrium state over a very long time scale, and, simulationwise, is highly CPUtime and memory consuming. Simulations aimed at determining optimal ring storage energy in an electronion 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 CPUtime*Memoryallocation, 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 electronion collider. 

Slides MOPAF03 [1.758 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018MOPAF03  
About •  paper received ※ 23 October 2018 paper accepted ※ 27 January 2019 issue date ※ 26 January 2019  
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MOPAF04  Spin Dynamics in Modern Electron Storage Rings: Computational Aspects  146 


Funding: This material is based on work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DESC0018008. 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* (FCCee) 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 spinflip effects due to synchrotron radiation. The FBEs are a system of three uncoupled FokkerPlanck 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 firstorder 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 ddimensional 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 

Slides MOPAF04 [0.993 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018MOPAF04  
About •  paper received ※ 20 October 2018 paper accepted ※ 24 October 2018 issue date ※ 26 January 2019  
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MOPAF05  Approaches to Optimizing Spin Transmission in Lattice Design  151 


Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DEAC0298CH10886 with the U.S. Department of Energy. 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. 

Slides MOPAF05 [1.333 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018MOPAF05  
About •  paper received ※ 17 October 2018 paper accepted ※ 24 October 2018 issue date ※ 26 January 2019  
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TUPAG09 
Electron Beam Longitudinal Phase Space Restoration From the Image After Beam Pass Deflector Cavity and Spectrometer Arm  


Recently commissioned Xband deflector cavity at Brookhaven National Laboratory Accelerator Test Facility (BNL ATF) is used for electron bunch longitudinal profile measurements in both  at zerodegree beamline and at spectrometer arm directions to measure the ebeam longitudinal phase space profile. The deflector cavity induces energy distortions on the offaxis particles and corrupt real picture of the beam energy profile at spectrometer screen. A special computational phase space restoration technique which is under development at BNL ATF to reveal undistorted ebeam parameters will be discussed.  
Slides TUPAG09 [1.766 MB]  
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