Paper  Title  Other Keywords  Page 

SAPAF01  Genetic Algorithm Enhanced by Machine Learning in Dynamic Aperture Optimization  dynamicaperture, lattice, sextupole, resonance  8 


Funding: This work was supported by Department of Energy Contract No. DESC0012704 With the aid of machine learning techniques, the genetic algorithm has been enhanced and applied to the multiobjective optimization problem presented by the dynamic aperture of the NSLSII Ring. During the evolution employed by the genetic algorithm, the population is classified into different clusters. The clusters with top average fitness are given elite status. Intervention is implemented by repopulating some potentially competitive candidates based on the accumulated data. These candidates replace randomly selected candidates among the original data pool. The average fitness of the population is improved while diversity is not lost. The quality of the population increases and produces more competitive descendants accelerating the evolution process significantly. When identifying the distribution of optimal candidates, they appear to be located in isolated islands within the search space. Some of these optimal candidates have been experimentally confirmed at the NSLSII storage ring. The machine learning techniques that exploit the genetic algorithm can also be used in other populationbased optimization problems such as particle swarm algorithm. 

Slides SAPAF01 [6.696 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018SAPAF01  
About •  paper received ※ 15 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  polarization, electron, radiation, synchrotron  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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MOPAF02  Realistic Modeling of the Muon g2 Experiment Beamlines at Fermilab  simulation, target, experiment, proton  134 


Funding: This work is supported by the U.S. Department of Energy under Award No. DEFG0208ER41546, by the PhD Accelerator Program at Fermilab, and by a Strategic Partnership Grant from the MSU Foundation. The main goal of the Muon g2 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 g2 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 highorder 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. 

Slides MOPAF02 [14.110 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018MOPAF02  
About •  paper received ※ 22 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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MOPAF03  Polarization Lifetime in an Electron Storage Ring, an Ergodic Approach in eRHIC EIC  polarization, electron, simulation, resonance  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  polarization, electron, radiation, coupling  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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TUPAF12  Longitudinal Beam Dynamics With a HigherHarmonic Cavity for Bunch Lengthening  cavity, operation, simulation, synchrotron  202 


Funding: Work supported by Brookhaven Science Associates, LLC under Contract No. DEAC0298CH10886 with the U.S. Department of Energy We discuss the longitudinal beam dynamics in storage rings in the presence of a higherharmonic cavity (HHC) system for bunch lengthening. We first review the general conditions for HHC operations, either in active or passive mode, assuming the stability of the system. For uniform filling patterns, a distinction is made between operations with a normalconducting HHC, where optimal conditions for bunch lengthening can be satisfied, and operations with superconducting HHC, where optimal conditions can be met only approximately. The option to operate the NSLSII storage ring with a passive, superconducting third harmonic cavity (3HC) system is discussed next. The stability and performance of the system in the presence of a gap in the uniform filling, which corresponds to the present mode of operation of the NSLSII storage ring, is investigated with selfconsistent VlasovFokkerPlanck simulations performed with the code SPACE*. * G. Bassi, A. Blednykh and V. Smaluk, Phys Rev. Accel. Beams 19, 024401 (2016). 

Slides TUPAF12 [17.562 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAF12  
About •  paper received ※ 20 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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TUPAF16  Analysis of the Beam Loss Mechanism During the Energy RampUp at the SAGALS  powersupply, electron, acceleration, dataacquisition  227 


The accelerator of the SAGA Light Source consists of 255 MeV injector linac and 1.4 GeV storage ring. The accumulated electron beam current of the storage ring is about 300 mA. The energy of the electrons are raised up to 1.4 GeV in 4 minutes in the storage ring. At the moment of the beam acceleration (the beam energy is lower than 300 MeV), the electron beam is lost like the step function. The lost beam current is normally about 5 mA to 30 mA. The beam loss at the energy rampup is not observed, when the beam current is lower than 200 mA. To understand the beam loss mechanism, which depend on the beam current, we developed highspeed logging system of 100 kHz for monitoring the beam current and the magnets power supplies using National Instruments PXI. We investigated the relationship between the beam loss and the betatron tune shifts. The tune shifts during the beam acceleration were analyzed from the measured data of the output current of the magnets power supplies by using beam tracking code of TRACY2. By adopting the new highspeed logging system, the time structure of the beam loss process was clearly observed. We will present the highspeed logging system developed for monitoring the beam current and the power supplies at this meeting. The results of the investigation to find the relationship of the beam loss and the tune shifts will be also shown.  
Slides TUPAF16 [1.286 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAF16  
About •  paper received ※ 19 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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TUPAG22  Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g2 Experiment Storage Ring  quadrupole, multipole, experiment, FEL  313 


Funding: This work was supported by the U.S. Department of Energy under Contract DEFG0208ER41546 and by Fermi Research Alliance for U.S. Department of Energy under Contract DEAC0207CH11359. We consider semiinfinite electrostatic deflectors with plates of different thickness, including plates with rounded edges, and we calculate their electrostatic potential and field using conformal mappings. To validate the calculations, we compare the fringe fields of these electrostatic deflectors with fringe fields of finite electrostatic capacitors, and we extend the study to fringe fields of adjacent electrostatic deflectors with consideration of electrostatic induction, where field falloffs of semiinfinite electrostatic deflectors are slower than exponential and thus behave differently from most magnetic fringe fields. Building on the success with electrostatic deflectors, we develop a highly accurate and fully Maxwellian conformal mappings method for calculation of main fields of electrostatic particle optical elements. A remarkable advantage of this method is the possibility of rapid recalculations with geometric asymmetries and mispowered plates. We use this conformal mappings method to calculate the multipole terms of the high voltage quadrupole used in the storage ring of the Muon g2 Experiment (FNALE0989). Completing the methodological framework, we present a method for extracting multipole strength falloffs of a particle optical element from a set of Fourier mode falloffs. We calculate the quadrupole strength falloff and its effective field boundary (EFB) for the Muon g2 quadrupole, which has explained the experimentally measured tunes, while simple estimates based on a linear model exhibited discrepancies up to 2%. 

Slides TUPAG22 [3.780 MB]  
DOI •  reference for this paper ※ https://doi.org/10.18429/JACoWICAP2018TUPAG22  
About •  paper received ※ 15 October 2018 paper accepted ※ 28 January 2019 issue date ※ 26 January 2019  
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