IPAC2014 - List of Authors (Berz, M.)

Paper	Title	Page
MOPME037	The Development of Stochastic Processes in COSY Infinity	457
	J.D. Kunz IIT, Chicago, Illinois, USA M. Berz, K. Makino MSU, East Lansing, Michigan, USA P. Snopok Illinois Institute of Technology, Chicago, Illlinois, USA
	Funding: Work supported by U.S. Department of Energy. COSY Infinity is an arbitrary-order beam dynamics simulation code. It can determine high-order transfer maps of combinations of particle optical elements. New features are being developed for inclusion in COSY to follow the distribution of particles through matter. To study in detail the properties of muons passing through material, the transfer map approach alone is not sufficient. The interplay of beam optics and atomic processes must be studied by a hybrid transfer map–Monte-Carlo approach in which transfer map methods describe the average behavior of the particles including energy loss, and Monte-Carlo methods are used to provide small corrections to the predictions of the transfer map accounting for the stochastic nature of scattering and straggling of particles. The advantage of the new approach is that the vast majority of the dynamics is represented by fast application of the high-order transfer map of an entire element and accumulated stochastic effects. The gains in speed will aid the optimization of muon cooling channels. Progress on the development of the required algorithms is reported.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2014-MOPME037
Export •	reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

MOPME038	Space Charge Simulation in COSY using The Fast Multipole Method	460
	B.T. Loseth, M. Berz, K. Makino MSU, East Lansing, Michigan, USA P. Snopok Fermilab, Batavia, Illinois, USA H. Zhang JLab, Newport News, Virginia, USA
	A method is implemented in COSY Infinity that allows the computation of space charge effects of arbitrary and large distributions of particles in an efficient and accurate way based on a variant of the Fast Multipole Method (FMM). It relies on an automatic multigrid-based decomposition of charges in near and far regions and the use of high-order differential algebra methods to obtain decompositions of far fields that lead to an error that scales with a high power of the order. Given an ensemble of N particles, the method allows the computation of the self-fields of all particles on each other with a computational expense that scales as O(N). Furthermore, the method allows the computation of all high-order multipoles of the space charge fields that are necessary for the computation of high-order transfer maps and all resulting aberrations. Space charge effects are crucial in modeling the latter stages of the six-dimensional (6D) cooling channel for the Muon Collider. Results of simulating the 6D cooling channel for the Muon Collider using the FMM method and other tools and improvements implemented for ionization cooling lattices are presented.
DOI •	reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2014-MOPME038
Export •	reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

Paper

Title

Page

The Development of Stochastic Processes in COSY Infinity

457

J.D. Kunz
IIT, Chicago, Illinois, USA
M. Berz, K. Makino
MSU, East Lansing, Michigan, USA
P. Snopok
Illinois Institute of Technology, Chicago, Illlinois, USA

Funding: Work supported by U.S. Department of Energy.
COSY Infinity is an arbitrary-order beam dynamics simulation code. It can determine high-order transfer maps of combinations of particle optical elements. New features are being developed for inclusion in COSY to follow the distribution of particles through matter. To study in detail the properties of muons passing through material, the transfer map approach alone is not sufficient. The interplay of beam optics and atomic processes must be studied by a hybrid transfer map–Monte-Carlo approach in which transfer map methods describe the average behavior of the particles including energy loss, and Monte-Carlo methods are used to provide small corrections to the predictions of the transfer map accounting for the stochastic nature of scattering and straggling of particles. The advantage of the new approach is that the vast majority of the dynamics is represented by fast application of the high-order transfer map of an entire element and accumulated stochastic effects. The gains in speed will aid the optimization of muon cooling channels. Progress on the development of the required algorithms is reported.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2014-MOPME037

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)

MOPME038

Space Charge Simulation in COSY using The Fast Multipole Method

460

B.T. Loseth, M. Berz, K. Makino
MSU, East Lansing, Michigan, USA
P. Snopok
Fermilab, Batavia, Illinois, USA
H. Zhang
JLab, Newport News, Virginia, USA

A method is implemented in COSY Infinity that allows the computation of space charge effects of arbitrary and large distributions of particles in an efficient and accurate way based on a variant of the Fast Multipole Method (FMM). It relies on an automatic multigrid-based decomposition of charges in near and far regions and the use of high-order differential algebra methods to obtain decompositions of far fields that lead to an error that scales with a high power of the order. Given an ensemble of N particles, the method allows the computation of the self-fields of all particles on each other with a computational expense that scales as O(N). Furthermore, the method allows the computation of all high-order multipoles of the space charge fields that are necessary for the computation of high-order transfer maps and all resulting aberrations. Space charge effects are crucial in modeling the latter stages of the six-dimensional (6D) cooling channel for the Muon Collider. Results of simulating the 6D cooling channel for the Muon Collider using the FMM method and other tools and improvements implemented for ionization cooling lattices are presented.

DOI •

reference for this paper ※ https://doi.org/10.18429/JACoW-IPAC2014-MOPME038

Export •

reference for this paper using ※ BibTeX, ※ LaTeX, ※ Text/Word, ※ RIS, ※ EndNote (xml)