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Numerical Algorithms for Vlasov-Poisson Equation and Applications to Coherent Electron Cooling

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dc.contributor.advisor Samulyak, Roman V. en_US
dc.contributor.advisor Glimm, James en_US
dc.contributor.author Ma, Jun en_US
dc.contributor.other Department of Applied Mathematics and Statistics en_US
dc.date.accessioned 2017-09-20T16:52:16Z
dc.date.available 2017-09-20T16:52:16Z
dc.date.issued 2017-05-01 en_US
dc.identifier.uri http://hdl.handle.net/11401/77244 en_US
dc.description 219 pgs en_US
dc.description.abstract New algorithms for the particle-based numerical method, called AP-Cloud, for optimal solutions of Poisson-Vlasov equation have been developed and implemented in code SPACE, as well as a traditional particle-in-cell (PIC) electrostatic solver. While the traditional PIC method is based on a uniform Cartesian mesh, a linear charge deposition scheme, and Fast Fourier Transform solvers, the AP-Cloud method replaces the traditional PIC mesh with an adaptively chosen set of computational particles and is beneficial if the distribution of particles is non-uniform. The code SPACE is a parallel, relativistic, 3D electromagnetic PIC code developed for the simulations of relativistic particle beams, beam-plasma interactions, and plasma chemistry, and has been used in the simulation studies of coherent electron cooling experiments at the Brookhaven National Laboratory. Coherent electron cooling is a novel technique for rapidly cooling high-energy, high-intensity hadron beams, and consists of three major components: a modulator, where each ion imprints a modulation signal on the electron beam, an amplifier where the modulation signals are amplified by orders, and a kicker where the electrons carrying the amplified signals interact with ions resulting in cooling of ion beam. We have performed highly resolved numerical simulations to study the coherent electron cooling concept and support the relevant experiments. Modulator and kicker simulations are performed using code SPACE. Simulations of free electron laser, as the amplifier, are performed using the open source code GENESIS. Numerical convergence and verification test problems for modulator simulations have been studied using electron beam with uniform spatial distribution, where analytic solutions of density and velocity modulations exist. A good agreement of theory and simulations has been obtained for the case of stationary and moving ions in uniform electron clouds with realistic distributions of thermal velocities. Predictions of modulation process have been given for ions with reference and off-reference velocities and center and off-center locations in Gaussian electron beams with continuous focusing electric field and quadrupole magnetic field. Phase advance studies have been performed to explore the dynamics of electron beam in the transverse plane due to the quadrupole magnetic field, and to explain the behaviors of the transverse modulation signal in the modulator section. The dynamics of the electron beam and the evolutions of the modulation signal in the coherent electron cooling process have been simulated by the combination use of code SPACE and GENESIS, using electron beam with Gaussian distribution and realistic profiles relevant to the Relativistic Heavy Ion Collider at the Brookhaven National Laboratory. en_US
dc.description.sponsorship This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. en_US
dc.format Monograph en_US
dc.format.medium Electronic Resource en_US
dc.language.iso en_US en_US
dc.publisher The Graduate School, Stony Brook University: Stony Brook, NY. en_US
dc.subject.lcsh Applied mathematics en_US
dc.title Numerical Algorithms for Vlasov-Poisson Equation and Applications to Coherent Electron Cooling en_US
dc.type Dissertation en_US
dc.mimetype Application/PDF en_US
dc.contributor.committeemember Litvinenko, Vladimir N. en_US
dc.contributor.committeemember Reuter, Matthew G. en_US
dc.contributor.committeemember Wang, Gang en_US


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