Reprint Server

Selected recent publications and some frequently cited older publications

Books

An Introduction to Beam Physics
M. Berz, K. Makino, W. Wan, Taylor & Francis, 2014, ISBN 978-0-7503-0263-0

Proceedings, Femtosecond Electron Imaging and Spectroscopy 2013, Key West, Florida
M. Berz, P. Duxbury, K. Makino, C.-Y. Ruan (Eds.), Advances in Imaging and Electron Physics 191, Elsevier, 2015

Special Issue on Taylor Model Methods
K. Jackson, M. Neher, M. Berz (Eds.), Communications of the Fields Institute

Proceedings, FFAG 2009 International Conference, Fermilab, Illinois
C. Johnstone, M. Berz, P. Snopok (Eds.), International Journal of Modern Physics A 26,10-11, World Scientific, 2011, DOI 10.1142/S0217751X11053079

Proceedings, p-Adic and Non-Archimedean Analysis 10, East Lansing, Michigan
M. Berz, K. Shamseddine (Eds.), Contemporary Mathematics 508, American Mathematical Society, 2009, ISBN 978-0-8218-4740-4

Proceedings, Fifteenth Int. Workshop on Beam Dynamics and Optimization, St. Petersburg, Florida
D. Ovsyannikov, M. Berz, P. Snopok (Eds.), International Journal of Modern Physics A 24,5, World Scientific, 2009, ISSN 0217-751X

Proceedings, Eighth Int. Conf. on Computational Accelerator Physics, Saint Petersburg, Russia
D. Ovsyannikov, M. Berz, K. Makino (Eds.), Nuclear Instruments and Methods A 558,xvii-xxi, Elsevier, 2006, ISBN 0-168-9002558

Proceedings, Seventh Int. Conf. on Computational Accelerator Physics, East Lansing, Michigan
M. Berz, K. Makino (Eds.), Institute of Physics CS 175, IOP Publishing, 2004, ISBN 0-75-030939-3

Modern Map Methods in Particle Beam Physics
M. Berz, Academic Press, 1999, ISBN 0-12-014750-5

Computational Differentiation: Techniques, Applications, and Tools, Proc. AD1996, Santa Fe, New Mexico
M. Berz, C. Bischof, A. Griewank, G. Corliss (Eds.), SIAM, 1996, ISBN 0-89871-385-4

Proceedings, Int. Workshop on Nonlinear Effects in Accelerators, Berlin, Germany
M. Berz, S. Martin, K. Ziegler (Eds.), Institute of Physics CS 131, IOP Publishing, 1993, ISBN 0-7503-0238-0

Papers

Storage Ring to Search for Electric Dipole Moments of Charged Particles -- Feasibility Study
CPEDM Collaboration, CERN Yellow Reports: Monographs, 3 (2021) CERN-2021-003. DOI: 10.23731/CYRM-2021-003

Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
Muon g-2 Collaboration, Physical Review Letters, 126 (2021) 141801. DOI: 10.1103/PhysRevLett.126.141801

Measurement of the Anomalous Precession Frequency of the Muon in the Fermilab Muon g-2 Experiment
Muon g-2 Collaboration, Physical Review D, 103 (2021) 072002. DOI: 10.1103/PhysRevD.103.072002

Magnetic-Field Measurement and Analysis for the Muon g-2 Experiment at Fermilab
Muon g-2 Collaboration, Physical Review A, 103 (2021) 042208. DOI: 10.1103/PhysRevA.103.042208

Beam Dynamics Corrections to the Run-1 Measurement of the Muon Anomalous Magnetic Moment at Fermilab
Muon g-2 Collaboration, Physical Review Accelerators and Beams, 24 (2021) 044002. DOI: 10.1103/PhysRevAccelBeams.24.044002

Measurement of Deuteron Carbon Vector Analyzing Powers in the Kinetic Energy Range 170–380 MeV
F. Müller et al. (JEDI Collaboration), The European Physical Journal A, 56 (2020) 211. DOI: 10.1140/epja/s10050-020-00215-8

Bounded Motion Design in the Earth Zonal Problem using Differential Algebra based Normal Form Methods
A. Weisskopf, R. Armellin, M. Berz, Celestial Mechanics and Dynamical Astronomy, 132 (2020) 14. DOI: 10.1007/s10569-020-9953-x

Muon Loss Rates from Betatron Resonances at the Muon g-2 Storage Ring at Fermilab
D. Tarazona, M. Berz, K. Makino, Int. Journal of Modern Physics A, 34, 36 (2019) 1942008. DOI: 10.1142/S0217751X19420089

Validation of Transfer Map Calculation for Electrostatic Deflectors in the Code COSY INFINITY
E. Valetov, M. Berz, K. Makino, Int. Journal of Modern Physics A, 34, 36 (2019) 1942010. DOI: 10.1142/S0217751X19420107

Derivation, Cross-Validation, and Comparison of Analytic Formulas for Electrostatic Deflector Aberrations
E. Valetov, M. Berz, Advances in Imaging and Electron Physics, 213 (2020) 145-203. DOI: 10.1016/bs.aiep.2019.11.007

Analysis and Fringe Field Scaling of a Legacy Set of Electrostatic Deflector Aberration Formulas
E. Valetov, Advances in Imaging and Electron Physics, 213 (2020) 205-224. DOI: 10.1016/bs.aiep.2019.11.008

Computation and Consequences of High Order Amplitude- and Parameter-Dependent Tune Shifts in Storage Rings for High Precision Measurements
A. Weisskopf, D. Tarazona, M. Berz, Int. Journal of Modern Physics A, 34, 36 (2019) 1942011. DOI: 10.1142/S0217751X19420119

Dynamical Simulations of the Muon Campus at Fermilab
D. Tarazona, M. Berz, K. Makino, D. Stratakis, M. J. Syphers, Int. Journal of Modern Physics A, 34, 36 (2019) 1942033. DOI: 10.1142/S0217751X19420338

Computation of the Main and Fringe Fields for the Electrostatic Quadrupoles of the Muon g-2 Storage Ring
E. Valetov, M. Berz, K. Makino, Int. Journal of Modern Physics A, 34, 36 (2019) 1942041. DOI: 10.1142/S0217751X19420417

Accurate Taylor Transfer Maps for Large Aperture Iron Dominated Magnets Used in Charged Particle Separators and Spectrometers
E. Kazantseva, H. Weick, M. Berz, K. Makino, O. Boine-Frankenheim, Nuclear Instruments and Methods A 935 (2019) 56-64. DOI: 10.1016/j.nima.2019.04.086

Phase Measurement for Driven Spin Oscillations in a Storage Ring
N. Hempelmann et al. (JEDI Collaboration), Physical Review Accelerators and Beams 21 (2018) 042002. DOI: 10.1103/PhysRevAccelBeams.21.042002

Hybrid Methods for Muon Accelerator Simulations with Ionization Cooling
J. Kunz, P. Snopok, M. Berz, K. Makino, Journal of Instrumentation (JINST), 13 (2018) P07026. DOI: 10.1088/1748-0221/13/07/P07026

Spin Tune Mapping as a Novel Tool to Probe the Spin Dynamics in Storage Rings
A. Saleev et al. (JEDI Collaboration), Physical Review Accelerators and Beams 20 (2017) 072801. DOI: 10.1103/PhysRevAccelBeams.20.072801

Phase Locking the Spin Precession in a Storage Ring
N. Hempelmann et al. (JEDI Collaboration), Physical Review Letters 119 (2017) 014801. DOI: 10.1103/PhysRevLett.119.014801

Verified Computations Using Taylor Models and Their Applications
K. Makino, M. Berz, Lecture Notes in Computer Science 10381 (2017) 3-13

Rigorous Reachability Analysis and Domain Decomposition of Taylor Models
M. Berz, K. Makino, Lecture Notes in Computer Science 10381 (2017) 90-97

Active Control of Bright Electron Beams with RF Optics for Femtosecond Microscopy
J. Williams, F. Zhou, T. Sun, Z. Tao, K. Chang, K. Makino, M. Berz, P. M. Duxbury, C.-Y. Ruan, Structural Dynamics 4 (2017) 044035

BRho-Dependent Taylor Transfer Maps for the Super-FRS Dipole Magnets
E. Kazantseva, O. Boine-Frankenheim, H. Weick, J. S. Winfield, M. Berz, R. Jagasia, K. Makino, in: 8th International Particle Accelerator Conference, (2017) 2631

Quasi-Frozen Spin Concept of Deuteron Storage Ring as an Instrument to Search for Electric Dipole Moment
Y. Senichev, A. Aksentyev, S. Chekmenev, J. Pretz, S. Andrianov, A. Ivanov, M. Berz, E. Valetov, on behalf of the JEDI Collaboration, in: 8th International Particle Accelerator Conference, (2017) 2275

Spin Dynamics Investigation of Quasi-Frozen Spin Lattice for EDM Searches
E. Valetov, Y. Senichev, M. Berz, on behalf of the JEDI Collaboration, in: Proceedings of Spin'16, University of Illinois at Urbana-Champaign, in print

A Storage Ring Experiment to Detect a Proton Electric Dipole Moment
V. Anastassopoulos et al., Review of Scientific Instruments 87 (2016) 115116

How to Reach a Thousand-Second In-Plane Polarization Lifetime with 0.97-GeV/c Deuterons in a Storage Ring
G. Guidoboni et al. (JEDI Collaboration), Physical Review Letters 117 (2016) 054801

Hybrid Methods for Simulation of Muon Ionization Cooling Channels
J. Kunz, P. Snopok, M. Berz, in: 2016 North American Particle Accelerator Conference (NAPAC16), (2016) 775

Comparison of Tracking Codes for the Determination of Dynamic Aperture in Storage Rings
R. Hipple, M. Berz, in: 7th International Particle Accelerator Conference, (2016) 3114

Muon Beam Tracking and Spin-Orbit Correlations for Precision g-2 Measurements
D. Tarazona, M. Berz, R. Hipple, K. Makino, M.J. Syphers, in: 7th International Particle Accelerator Conference, (2016) 3397

Hybrid Methods for Simulation of Muon Ionization Cooling Channels
J. Kunz, P. Snopok, M. Berz, K. Makino, in: 7th International Particle Accelerator Conference, (2016) 1568

Systematic Errors Investigation in Frozen and Quasi-Frozen Spin Lattices of Deuteron EDM Ring
Y. Senichev, B. Lorentz, S. Andrianov, A. Ivanov, S. Chekmenev, J. Pretz, M. Berz, E. Valetov, on behalf of the JEDI Collaboration, in: 7th International Particle Accelerator Conference, (2016) 3394

Computation of Nonlinear Fields and Orbit and Spin Transfer Maps of Electrostatic Elements using Differential Algebras
K. Makino, E. Valetov, M. Berz, in: 12th International Computational Accelerator Physics Conference 2015, (2016) 168

Implementation of Benchmarks for Precision Tracking in Storage Rings
R. Hipple, M. Berz, in: 12th International Computational Accelerator Physics Conference 2015, (2016) 13

Search for the Optimal Spin Decoherence Effect in a QFS Lattice
E. Valetov, M. Berz, Yu. Senichev, on behalf of the JEDI Collaboration, in: 12th International Computational Accelerator Physics Conference 2015, (2016) 172

Hybrid Methods for Muon Accelerator Simulations with Ionization Cooling
J. Kunz, P. Snopok, M. Berz, in: 12th International Computational Accelerator Physics Conference 2015, (2016) 66

Investigation of Lattice for Deuteron EDM Ring
Y. Senichev, S. Andrianov, A. Ivanov, S. Chekmenev, M. Berz, E. Valetov, on behalf of the JEDI Collaboration, in: 12th International Computational Accelerator Physics Conference 2015, (2016) 17

Ionization Cooling Channels in COSY INFINITY
B. Loseth, M. Berz, P. Snopok, in: 6th International Particle Accelerator Conference, (2015) 2652

The Advancement of Cooling Absorbers in COSY INFINITY
J. Kunz, P. Snopok, M. Berz, K. Makino, in: 6th International Particle Accelerator Conference, (2015) 2655

Quasi-Frozen Spin Method for EDM Deuteron Search
Y. Senichev, A. Lehrach, B. Lorentz, R. Maier, S. Andrianov, A. Ivanov, S. Chekmenev, M. Berz, E. Valetov, on behalf of the JEDI Collaboration and JARA-FAME, in: 6th International Particle Accelerator Conference, (2015) 213

Dynamics in Electrostatic Rings via High-Order Transfer Maps
K. Makino, M. Berz, Microscopy and Microanalysis 21 Suppl. 4 (2015) 36

A Comparison of Storage Ring Modeling with COSY INFINITY, ZGOUBI, and MAD8
R. Hipple, M. Berz, Microscopy and Microanalysis 21 Suppl. 4 (2015) 2

The Poincaré Section Method for Accelerator Element Maps
R. Jagasia, M. Berz, B. Loseth, Microscopy and Microanalysis 21 Suppl. 4 (2015) 14

Optics of Ionization Cooling Channels Under the Influence of Space Charge
B. Loseth, M. Berz, H. Zhang, P. Snopok, J. Kunz, Microscopy and Microanalysis 21 Suppl. 4 (2015) 20

Matter-Dominated Muon Accelerator Lattice Simulation Tools for COSY INFINITY
J. Kunz, P. Snopok, M. Berz, K. Makino, Microscopy and Microanalysis 21 Suppl. 4 (2015) 8

The Differential Algebra Based Multiple Level Fast Multipole Algorithm for 3D Space Charge Field Calculation and Photoemission Simulation
H. Zhang, J. Portman, Z. Tao, P. Duxbury, C.-Y. Ruan, K. Makino, M. Berz, Microscopy and Microanalysis 21 Suppl. 4 (2015) 224

New Method for a Continuous Determination of the Spin Tune in Storage Rings and Implications for Precision Experiments
D. Eversmann et al. (JEDI Collaboration), Physical Review Letters 115 (2015) 094801

Space Charge Simulations of Photoemission Using the Differential Algebra-based Multiple-Level Fast Multipole Algorithm
H. Zhang, Z. Tao, C.-Y. Ruan, M. Berz, Advances in Imaging and Electron Physics 191 (2015) 56-66

Multiscale Modeling of the Ultrafast Electron Microscope: From the Photocathode to the Sample
J. Portman, H. Zhang, K. Makino, C.-Y. Ruan, M. Berz, P. Duxbury, Advances in Imaging and Electron Physics 191 (2015) 117-130

Propagation of Large Uncertainty Sets in Orbital Dynamics by Automatic Domain Splitting
A. Wittig, P. Di Lizia, R. Armellin, K. Makino, F. Bernelli-Zazzera, M. Berz, Celestial Mechanics and Dynamical Astronomy 122 (2015) 239-261

Untangling the Contributions of Image Charge and Laser Profile for Optimal Photoemission of High-Brightness Electron Beams
J. Portman, H. Zhang, K. Makino, C.-Y. Ruan, M. Berz, P. M. Duxbury, Journal of Applied Physics 116 (2014) 174302

The Perspectives of Femtosecond Imaging and Spectroscopy of Complex Materials using Electrons
C.-Y. Ruan, P. M. Duxbury, M. Berz, Proc. SPIE Ultrafast Nonlinear Imaging and Spectroscopy II 9198 (2014) 91980Q

High Order Optimal Control of Space Trajectories with Uncertain Boundary Conditions
P. Di Liziaa, R. Armellina, F. Bernelli-Zazzeraa, M. Berz, Acta Astronautica 93 (2014) 217-229

Space Charge Simulation in COSY using The Fast Multipole Method
B. Loseth, M. Berz, K. Makino, H. Zhang, P. Snopok, in: 5th International Particle Accelerator Conference, (2014) 460

The Development of Stochastic Processes in COSY INFINITY
J. Kunz, P. Snopok, M. Berz, K. Makino, in: 5th International Particle Accelerator Conference, (2014) 457

Differential Algebraic Techniques
M. Berz, Chapter in: "Handbook of Accelerator Physics and Engineering", A. Chao, K. H. Mess, M. Tigner, F. Zimmermann (Eds.), 2013

Differential Algebra based Magnetic Field Computations and Accurate Fringe Field Maps
B. Erdelyi, M. Berz, M. Lindemann, Vestnik Mathematica 10,4 (2015) 36-55

Computational and Experimental Characterization of High-Brightness Beams for Femtosecond Electron Imaging and Spectroscopy
J. Portman, H. Zhang, Z. Tao, K. Makino, M. Berz, P.M. Duxbury, C.-Y. Ruan, Applied Physics Letters 103 (2013) 253115

Efficient Treatment of Space Charge Effects Using DA-based FMM Methods
H. Zhang, M. Berz, Vestnik Mathematica 10,4 (2014) 97-107

Rigorous Global Optimization of System Parameters
K. Makino, M. Berz, Vestnik Mathematica 10,2 (2014) 61-71

Affine Invariant Measures in Levi-Civita Vector Spaces and the Erdös Obtuse Angle Theorem
M. Berz, S. Troncoso, AMS Contemporary Mathematics 596 (2013) 1-21

Rigorous High Precision Interval Arithmetic in COSY INFINITY
A. Wittig, M. Berz, Proceedings of the Fields Institute, in print

Computer Assisted Proofs of the Existence of High-Period Fixed Points
A. Wittig, M. Berz, S. Newhouse, Proceedings of the Fields Institute, in print

Space Charge Simulation in COSY Using Fast Multipole Method
B. Loseth, M. Berz, K. Makino, H. Zhang, P. Snopok, in: Particle Accelerator Conference 2013, (2013) 195

Global Optimization of Interplanetary Transfers with Deep Space Maneuvers Using Differential Algebra
P. Di Lizia, R. Armellin, F. Topputo, F. Bernelli-Zazzera, M. Berz, Springer Optimization and Its Applications, 73 (2013) 187-213

Space Charge Effects in Ultrafast Electron Diffraction and Imaging
Z. Tao, H. Zhang, P. M. Duxbury, M. Berz, C.-Y. Ruan, Journal of Applied Physics 111 (2012) 044316

Rigorous Global Optimization of Impulsive Planet-to-Planet Transfers in the Patched-Conics Approximation
R. Armellin, P. Di Lizia, K. Makino, M. Berz, Engineering Optimization 44,2 (2012) 133-155

Advanced Computational Methods for Nonlinear Spin Dynamics
M. Berz, K. Makino, IOP Journal of Physics 295 (2011) 012143

High-Order Out-of-Plane Expansion for 3D Fields
K. Makino, M. Berz, C. Johnstone, Int. Journal of Modern Physics A 26 (2011) 1807-1821

Isochronous (CW) Non-Scaling FFAGs: Design and Simulation
C. Johnstone, M. Berz, K. Makino, P. Snopok, American Institute of Physics CP 1299 (2011) 682-687

Advances in Nonlinear Non-Scaling FFAGs
C. Johnstone, M. Berz, K. Makino, S. Koscielniak, P. Snopok, Int. Journal of Modern Physics A 26 (2011) 1690-1712

High Order Optimal Feedback Control of Lunar Landing and Rendezvous Trajectories
P. Di Lizia, R. Armellin, F. Bernelli-Zazzera, M. Berz, in: CEAS 2011 The International Conference of the European Aerospace Societies, (2011)

Optics and Nonlinear Effects in Repetitive Systems
M. Berz, K. Makino, Nuclear Instruments and Methods A645 (2011) 175-181

Optimal Correction and Design Parameter Search by Modern Methods of Rigorous Global Optimization
K. Makino, M. Berz, Nuclear Instruments and Methods A645 (2011) 332-337

The Fast Multipole Method in the Differential Algebra Framework
H. Zhang, M. Berz, Nuclear Instruments and Methods A645 (2011) 338-344

Rigorous and Accurate Enclosure of Invariant Manifolds on Surfaces
A. Wittig, M. Berz, J. Grote, K. Makino, S. Newhouse, Regular and Chaotic Dynamics 15,2-3 (2010) 107-126

Analysis on the Levi-Civita Field, a Brief Overview
K. Shamseddine, M. Berz, Contemporary Mathematics 508 (2010) 215-237

Progress of Dynamical Nanomaterial Imaging Using Ultrashort Electron Pulses
Z. Tao, H. Zhang, R.K. Raman, T.-T. Han, K. Chang, M. Berz, C.-Y. Ruan, Microscopy and Microanalysis, 16,S2 (2010) 498-499

Asteroid Close Encounters Characterization using Diffferential Algebra: the Case of Apophis
R. Armellin, P. Di Lizia, F. Bernelli-Zazzera, M. Berz, Celestial Mechanics and Dynamical Astronomy, 107,4 (2010) 451-470

Computing the Critical Points of the Distance Function Between Two Keplerian Orbits via Rigorous Global Optimization
R. Armellin, P. Di Lizia, M. Berz, K. Makino, Celestial Mechanics and Dynamical Astronomy, 107,3 (2010) 377-395

Nonlinear Mapping of Uncertainties: A Differential Algebra Approach
R. Armellin, P. Di Lizia, F. Bernelli-Zazzera, M. Berz, 4th International Conference on Astrodynamics Tools and Techniques (2010)

Gravity Assist Space Pruning Based on Differential Algebra
R. Armellin, P. Di Lizia, F. Topputo, M. Lavagna, F. Bernelli-Zazzera, M. Berz, Celestial Mechanics and Dynamical Astronomy, 106,1 (2010) 1-24

Rigorous Global Search using Taylor Models
M. Berz, K. Makino, Symbolic Numeric Computation 2009, (2009) 11-19

Rigorous Integration of Flows and ODEs using Taylor Models
K. Makino, M. Berz, Symbolic Numeric Computation 2009, (2009) 79-84

High-Order Description of the Dynamics in FFAGs and Related Accelerators
K. Makino, M. Berz, P. Snopok, C. Johnstone, Int. Journal of Modern Physics A 24,5 (2009) 908-922

Calculation of Nonlinear Tune Shift Using Beam Position Measurement Results
P. Snopok, M. Berz, C. Johnstone, Int. Journal of Modern Physics A 24,5 (2009) 974-986

Taylor Models and Computaions in the Complex Plane
A. Ovsyannikov, M. Berz, Bulletin of St. Petersburg University, 10,4 (2009) 172-185

Field Reconstruction in Large Aperture Quadrupole Magnets
A. Lazzaro, F. Cappuzzello, A. Cunsolo, M. Cavallaro, A. Foti, S. Orrigo, M. Rodrigues, J. Winfield, M. Berz, Nuclear Instruments and Methods A 602 (2009) 494-500

Apophis Encounter 2029: Differential Algebra and Taylor Model Approaches
R. Armellin, P. Di Lizia, F. Bernelli-Zazzera, K. Makino, M. Berz, 1st IAA Planetary Defense Conference: Protecting Earth from Asteroids (2009)

Validated Integration in Solar System Dynamics
P. Di Lizia, R. Armellin, F. Bernelli-Zazzera, R. Jagasia, K. Makino, M. Berz, 1st IAA Planetary Defense Conference: Protecting Earth from Asteroids (2009)

Computation of High-Order Maps to Multiple Machine Precision
A. Wittig, M. Berz, Int. Journal of Modern Physics A 24,5 (2009) 1019-1039

Evolutionary Algorithm for the Neutrino Factory Front End Design
A. Poklonskiy, D. Neuffer, Int. Journal of Modern Physics A 24,5 (2009) 959-973

Conceptual Design of a Superconducting Quadrupole with Elliptical Acceptance and Tunable Higher Order Multipoles
S. Manikonda, J. Nolen, M. Berz, K. Makino, Int. Journal of Modern Physics A 24,5 (2009) 923-940

Effects of the Wiggler on the Hefei Light Source Storage Ring
H. Zhang, M. Berz, Int. Journal of Modern Physics A 24,5 (2009) 1057-1067

On the Estimation of Topological Entropy on Surfaces
S. Newhouse, M. Berz, J. Grote, K. Makino, Contemporary Mathematics 469 (2008) 243-270

Taylor Model-based Enclosure of Invariant Manifolds for Planar Diffeomorphisms and Applications
J. Grote, M. Berz, K. Makino, S. Newhouse, Proc. Applied Mathematics and Mechanics 7 (2008) 1022907

Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field
K. Shamseddine, M. Berz, Bulletin of the Belgian Mathematical Society 14 (2007) 1001-1015

Long-Term Stability of Large Particle Accelerators
M. Berz, K. Makino, Y.-K. Kim, P. Snopok, in: ECMI Newsletter 39 (2007) (A. Frommer, B.Lang, Guest Editors)

Long-Term Stability of the Tevatron by Verified Global Optimization
M. Berz, K. Makino, Y.-K. Kim, Nuclear Instruments and Methods A558 (2006) 1-10

Generalized Power Series on a Non-Archimedean Field
K. Shamseddine, M. Berz, Indagationes Mathematicae 17,3 (2006) 457-477

High-Order DA Methods for the Determination of Poincaré Sections
J. Grote, M. Berz, K. Makino, Nuclear Instruments and Methods A558,1 (2006) 106-111

Staging Acceleration and Cooling in a Neutrino Factory
C. Johnstone, M. Berz, K. Makino, M. Berz, Nuclear Instruments and Methods A558,1 (2006) 282-291

Multipole Expansion Solution of the Laplace Equation using Surface Data
S. Manikonda, M. Berz, Nuclear Instruments and Methods A558,1 (2006) 175-183

Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: The Single Step
K. Makino, M. Berz, International Journal of Pure and Applied Mathematics 36(2) (2006) 175-197

Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: Long-term Stabilization by Preconditioning
K. Makino, M. Berz, International Journal of Differential Equations and Applications 10(4) (2005) 353-384. This paper won the 3rd Moore Prize for Applications of Interval Analysis in 2008.

Suppression of the Wrapping Effect by Taylor Model-based Verified Integrators: Long-term Stabilization by Shrink Wrapping
M. Berz, K. Makino, International Journal of Differential Equations and Applications 10(4) (2005) 385-403

Simulation and Optimization of the Tevatron Accelerator
P. Snopok, C. Johnstone, M. Berz, in: Lecture Notes on Computational Science and Engineering 50 (2005) 199-209, Springer

Study and Optimal Correction of a Systematic Skew Quadrupole Field in the Tevatron
P. Snopok, C. Johnstone, M. Berz, D. Ovsyannikov, A. Ovsyannikov, Nuclear Instruments and Methods A558 (2005) 142-146

Exploring the bunching section of the Neutrino Factory
A.A. Poklonskiy, D.A. Ovsyannikov, A.D. Ovsyannikov, D. Neuffer, M. Berz, in: Proceedings, Physics and Control (2005) 272-277

Optimization of the Buncher and Phase Rotator for a Neutrino Factory
A. A. Poklonskiy, D. Neuffer, M. Berz, D. A. Ovsyannikov, A. D. Ovsyannikov in: Proceedings, Stability and Control Processes (2005) 282-291 (D. A. Ovsyannikov, L. A. Petrosyan, Editors)

Performance of Taylor Model Methods for Validated Integration of ODEs
M. Berz, K. Makino, Lecture Notes in Computer Science 3732 (2005) 65-74

Verified Global Optimization with Taylor Model-based Range Bounders
K. Makino, M. Berz, Transactions on Computers 11,4 (2005) 1611-1618

Taylor Models and Floating-Point Arithmetic: Proof that Arithmetic Operations are Validated in COSY
N. Revol, K. Makino, M. Berz, Journal of Logic and Algebraic Programming 64 (2005) 135-154 University of Lyon LIP Report RR 2003-11, MSU HEP report 30212

COSY INFINITY Version 9
K. Makino, M. Berz, Nuclear Instruments and Methods A558 (2005) 346-350

Optimizing the Adiabatic Buncher and Phase Rotator
A. Poklonskiy, D. Neuffer, C. Johnstone, M. Berz, K. Makino, D. Ovsyannikov, A. Ovsyannikov, Nuclear Instruments and Methods A558 (2005) 135-141

High-Order Verified Solutions of the 3D Laplace Equation
S. Manikonda, M. Berz, K. Makino, Transactions on Computers 11,4 (2005) 1604-1610

An Accurate High-Order Method to Solve the Helmholtz Boundary Value Problem for the 3D Laplace Equation
S. Manikonda, M. Berz, International Journal of Pure and Applied Mathematics 23,3 (2005) 365-378

Analytical Properties of Power Series on Levi-Civita Fields
K. Shamseddine, M. Berz, Annales Mathematiques Blaise Pascal 12 (2005) 309-329

Verified Computation of High-Order Poincaré Maps
J. Grote, K. Makino, M. Berz, Transactions on Systems 11,4 (2005) 1986-1992

High-Order Representation of Poincaré Maps
J. Grote, M. Berz, K. Makino, in: Lecture Notes on Computational Science and Engineering 50 (2005) 59-66, Springer

Solenoid Elements in COSY Infinity
K. Makino, M. Berz, Institute of Physics CS 175 (2004) 219-228

High Order Map Treatment of Superimposed Cavities, Absorbers, and Magnetic Multipole and Solenoid Fields
K. Makino, M. Berz, C. J. Johnstone, D. Errede, Nuclear Instruments and Methods A519 (2004) 162-174

The COSY Language Independent Architecture: Porting COSY Source Files
L. M. Chapin, J. Hoefkens, M. Berz, Institute of Physics CS 175 (2004) 37-45

Muon Beam Ionization Cooling in a Linear Quadrupole Channel
C. Johnstone, M. Berz, D. Errede, K. Makino, Nuclear Instruments and Methods A519 (2004) 472-482

Muon Beam Ring Cooler Simulations Using COSY Infinity
C. Maidana, M. Berz, K. Makino, Institute of Physics CS 175 (2004) 211-218

Stochastic Processes in Muon Ionization Cooling
D. Errede, K. Makino, M. Berz, C. Johnstone, A. van Ginneken, Nuclear Instruments and Methods A519 (2004) 466-471

Higher Order Multivariate Automatic Differentiation and Validated Computation of Remainder Bounds
M. Berz, K. Makino, Transactions on Mathematics 3(1) (2004) 37-44

COSY Infinity's EXPO Symplectic Tracking for LHC
M. L. Shashikant, M. Berz, B. Erdelyi, Institute of Physics CS 175 (2004) 299-306

Local Theory and Applications of Extended Generating Functions
B. Erdelyi, M. Berz, International Journal of Pure and Applied Mathematics 11(3) (2004) 241-282

New Approaches for the Validation of Transfer Maps using Remainder-Enhanced Differential Algebra
M. Berz, K. Makino, Nuclear Instruments and Methods A519 (2004) 53-62

Computing Validated Solutions of Implicit Differential Equations
J. Hoefkens, M. Berz, K. Makino, Advances in Computational Mathematics 19 (2003) 231-253

Taylor Models and Other Validated Functional Inclusion Methods
K. Makino, M. Berz, International Journal of Pure and Applied Mathematics 4(4) (2003) 379-456

Constructive Generation and Verification of Lyapunov Functions around Fixed Points of Nonlinear Dynamical Systems
M. Berz, K. Makino, International Journal of Computer Research 12,2 (2003) 235-244

Recent Progress in Neutrino Factory and Muon Collider Research within the Muon Collaboration
M. Alsharoa et al., Physical Review STAB 6(081001) (2003) 1-52

High-Order Maps with Acceleration for Optimization of Electrostatic and Radio-Frequency Ion-Optical Elements
A. Geraci, T. Barlow, M. Portillo, J. Nolen, K. Shepard, K. Makino, M. Berz, Review of Scientific Instruments 73(9) (2002) 3174-3180

Measure Theory and Integration on the Levi-Civita Field
K. Shamseddine, M. Berz, Contemporary Mathematics 319 (2002) 369-387

Cauchy Theory on Levi-Civita Fields
M. Berz, Contemporary Mathematics 319 (2002) 39-52

Intermediate Values and Inverse Functions on Non-Archimedean Fields
K. Shamseddine, M. Berz, International Journal of Mathematics and Mathematical Sciences 30(3) (2002) 165-176

Verification of Invertibility of Complicated Functions over Large Domains
J. Hoefkens, M. Berz, Reliable Computing 8(1) (2002) 1-16

Verified High-Order Inversion of Functional Dependencies and Interval Newton Methods
M. Berz, J. Hoefkens, Reliable Computing 7(5) (2001) 379-398

Verified Integration of Dynamics in the Solar System
M. Berz, K. Makino, J. Hoefkens, Nonlinear Analysis 47 (2001) 179-190

Verified High-Order Integration of DAEs and Higher-order ODEs
J. Hoefkens, M. Berz, K. Makino, in "Scientific Computing, Validated Numerics and Interval Methods", W. Kraemer, J. W. v. Gudenberg (Eds.) (2001) Kluwer

New Applications of Taylor Model Methods
K. Makino, M. Berz, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, U. Naumann (Eds.) (2001) Springer

Higher Order Verified Inclusions of Multidimensional Systems by Taylor Models
K. Makino, M. Berz, Nonlinear Analysis 47 (2001) 3503-3514

Towards a Universal Data Type for Scientific Computing
M. Berz, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, U. Naumann (Eds.) (2001) Springer

Efficient High-Order Methods for ODEs and DAEs
J. Hoefkens, M. Berz, K. Makino, in: "Automatic Differentiation: From Simulation to Optimization", G. Corliss, C. Faure, A. Griewank, L. Hascoet, U. Naumann (Eds.) (2001) Springer

Optimal Symplectic Approximation of Hamiltonian Flows
B. Erdelyi, M. Berz, Physical Review Letters 87(11) (2001) 114302

Towards Accurate Simulation of Fringe Field Effects
M. Berz, B. Erdelyi, K. Makino, Nuclear Instruments and Methods A472(3) (2001) 533-540

The WebCOSY System for Course Management in Distance Education
J. Hoefkens, L. Diening, M. Berz, B. Erdelyi, Journal of Computers in Mathematics and Science Teaching 20(3) (2001) 307-321

Distance Education in Beam Physics
B. Erdelyi, J. Hoefkens, K. Makino, M. Berz, in: "Towards the Virtual University - International On-Line Learning Perspectives", Mihai Jalobeanu, Nicolae Nistor, Susan English, Steve Wheeler (Eds.) (2001) Information Age Publishing

The Michigan State University M.Sc. and Ph.D. Online Degree Programs in Beam Physics
B. Erdelyi, J. Hoefkens, L. Diening, K. Makino, M. Berz, Quarterly Review of Distance Education 1(4) (2000) 345-350

Perturbative Equations of Motion and Differential Operators in Nonplanar Curvilinear Coordinates
K. Makino, M. Berz, International Journal of Applied Mathematics 3(4) (2000) 421-440

Preservation of Canonical Structure in Nonplanar Curvilinear Coordinates
M. Berz, K. Makino, International Journal of Applied Mathematics 3(4) (2000) 401-419

Analytical and Computational Methods for the Levi-Civita Field
M. Berz, Lecture Notes in Pure and Applied Mathematics 222 (2000) 21-34

Convergence on the Levi-Civita Field and Study of Power Series
K. Shamseddine, M. Berz, Lecture Notes in Pure and Applied Mathematics 222 (2000) 283-299

The Differential Algebraic Structure of the Levi-Civita Field and Applications
K. Shamseddine, M. Berz, International Journal of Applied Mathematics 3(4) (2000) 449-464

Non-Archimedean Analysis and Rigorous Computation
M. Berz, International Journal of Applied Mathematics 2(5) (2000) 889-930

Fringe Field Effects in Small Rings of Large Acceptance
M. Berz, B. Erdelyi, K. Makino, Physical Review STAB 3, 124001 (2000)

Effects of Kinematic Correction on the Dynamics in Muon Rings
K. Makino, M. Berz, American Institute of Physics CP 530 (2000) 217-227

Fringe Field Effects in Muon Rings
M. Berz, K. Makino, B. Erdelyi, American Institute of Physics CP 530 (2000) 38-47

The Influence of Fringe Fields on Particle Dynamics in the Large Hadron Collider
W. Wan, C. Johnstone, J. Holt, M. Berz, K. Makino, M. Lindemann, B. Erdelyi, Nuclear Instruments and Methods A427, 74-78 (1999)

High-Accuracy Field Description of Particle Spectrographs,
R. Degenhardt, M. Berz, Nuclear Instruments and Methods A427, 151-156 (1999)

Differential Algebraic Techniques
M. Berz, Chapter in: "Handbook of Accelerator Physics and Engineering", M. Tigner, A.Chao (Eds.) (1999) World Scientific

Differential Algebraic Determination of High-Order Off-Energy Closed Orbits, Chromaticities, and Momentum Compactions
M. Berz, B. Erdelyi, W. Wan, K.-Y. Ng, Nuclear Instruments and Methods A427 (1999) 310-314

COSY Infinity Version 8
K. Makino, M. Berz, Nuclear Instruments and Methods A427 (1999) 338-343

Design of a Fifth-Order Achromat
W. Wan, M. Berz, Nuclear Instruments and Methods A423, 1 (1999) 1-6

Experiences with Interactive Remote Graduate Instruction in Beam Physics
M. Berz, B. Erdelyi, J. Hoefkens, Journal of Interactive Learning Research 10,1 (1999) 49-58

New Methods for High-Dimensional Verified Quadrature
M. Berz, K. Makino, Reliable Computing 5 (1999) 13-22

Efficient Control of the Dependency Problem Based on Taylor Model Methods
K. Makino, M. Berz, Reliable Computing 5 (1999) 3-12

Computation and Application of Taylor Polynomials with Interval Remainder Bounds
M. Berz, G. Hoffstätter, Reliable Computing 4 (1998) 83-97

From Taylor Series to Taylor Models
M. Berz, Chapter in: "Nonlinear Problems in Accelerator Physics" (1997) 1-27, American Institute of Physics CP405

Arbitrary Order Maps, Remainder Terms, and Long Term Stability in Particle Accelerators
M. Berz, K. Makino, Proc. SPIE Charged Particle Optics III 3155 (1997) 186-192

Arbitrary Order Aberrations for Elements Characterized by Measured Fields
K. Makino, M. Berz, Proc. SPIE Charged Particle Optics III 3155 (1997) 221-227

Remainder Differential Algebras and their Applications
K. Makino, M. Berz, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 63-75, SIAM

Calculus and Numerics on Levi-Civita Fields
M. Berz, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 19-37, SIAM

Exception Handling in Derivative Computation with Nonarchimedean Calculus
K. Shamseddine, M. Berz, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 37-52, SIAM

Rigorous Lower Bounds on the Survival Time in Particle Accelerators
G. Hoffstätter, M. Berz, Particle Accelerators 54 (1996) 193-202

COSY Infinity Version 7
K. Makino, M. Berz, American Institute of Physics CP 391 (1996) 253-258

Symplectic Scaling of Transfer Maps including Fringe Fields
G. Hoffstätter, M. Berz, Physical Review E 54,5 (1996) 5664-5672

Analytical Theory of Arbitrary-Order Achromats
W. Wan, M. Berz, Physical Review E 54,3 (1996) 2870-2883

COSY Infinity and its Applications to Nonlinear Dynamics
M. Berz, K. Makino, K. Shamseddine, G. Hoffstätter, W. Wan, in: "Computational Differentiation: Techniques, Applications, and Tools", M. Berz, C. Bischof, G. Corliss, A. Griewank (Eds.) (1996) 363-367, SIAM

Modern Map Methods for Charged Particle Optics
M. Berz, Nuclear Instruments and Methods A363 (1995) 100-104

Reconstructive Correction of Aberrations in Nuclear Particle Spectrographs
M. Berz, K. Joh, J. A. Nolen, B. M. Sherrill, A. F. Zeller, Physical Review C 47,2 (1993) 537-544

Differential Algebraic Formulation of Normal Form Theory
M. Berz, in "Proc. Nonlinear Effects in Accelerators", M. Berz, S. Martin, K. Ziegler (Eds.) (1992) 77-86, IOP Publishing

High-Order Computation and Normal Form Analysis of Repetitive Systems
M. Berz, Chapter in: "Physics of Particle Accelerators", Melvin Month (Ed.) (1992) 456-489, AIP Publishing

Automatic Differentiation as Nonarchimedean Analysis
M. Berz, in: "Computer Arithmetic and Enclosure Methods" (1992) 439-450, Elsevier

Design Overview of a Highly Stable Infrared Free Electron Laser at LBL
K.J. Kim, M. Berz, S. Chattopadhyay, C. Kim, J. Edighofer, R. Gough, C. Kim, A.H. Kung, W. Stein, M. Xie, Nuclear Instruments and Methods A304 (1991) 233-237

Algorithms for Higher Order Automatic Differentiation in Many Variables with Applications to Beam Physics
M. Berz, in: "Automatic Differentiation of Algorithms: Theory, Implementation and Application" (1991) SIAM

Symplectic Tracking in Circular Accelerators with High Order Maps
M. Berz, in: "Nonlinear Problems in Future Particle Accelerators" (1991) 288-296, World Scientific

Isochronous Beamlines for Free Electron Lasers
M. Berz, Nuclear Instruments and Methods A298 (1990) 106-112

Arbitrary Order Description of Arbitrary Particle Optical Systems
M. Berz, Nuclear Instruments and Methods A298 (1990) 426-440

Computational Aspects of Optics Design and Simulation: COSY INFINITY
M. Berz, Nuclear Instruments and Methods A298 (1990) 473-479

The Computation of the Aberrations of Fringing Fields of Magnetic Multipoles and Sector Magnets Using Differential Algebra
B. Hartmann, M. Berz, H. Wollnik, Nuclear Instruments and Methods A297 (1990) 343-353

Differential Algebraic Description of Beam Dynamics to Very High Orders
M. Berz, Particle Accelerators 24 (1989) 109-124

Simulation of Intense Particle Beams with Regularly Distributed Gaussian Subbeams
M. Berz, H. Wollnik, Nuclear Instruments and Methods A267 (1988) 25-34

The Method of Power Series Tracking for the Mathematical Description of Beam Dynamics
M. Berz, Nuclear Instruments and Methods A258 (1987) 431-436

COSY 5.0 - The Fifth Order Code for Corpuscular Optical Systems
M. Berz, H. C. Hoffmann, H. Wollnik, Nuclear Instruments and Methods A258 (1987) 402-406

Relations between Elements of Transfer Matrices due to the Condition of Symplecticity
H. Wollnik, M. Berz, Nuclear Instruments and Methods A238 (1985) 127-140

Theses

A Timeline of Major Particle Accelerators
A. R. Steere (2005) (Master's Thesis)

Other

Realistic Modeling of the Muon g-2 Experiment Beamlines at Fermilab
D. Tarazona, M. Berz, K. Makino, D. Stratakis, M. J. Syphers, in: Proceedings of 13th International Computational Accelerator Physics Conference 2018, (2019) 141-146.
See here for enhanced version.

Main and Fringe Field Computations for the Electrostatic Quadrupoles of the Muon g-2 Experiment Storage Ring
E. Valetov, M. Berz, in: Proceedings of 13th International Computational Accelerator Physics Conference 2018, (2019) 307-313.
See here for enhanced version.

Direct Calculation of the Transfer Map of Electrostatic Deflectors, and Comparison with the Codes COSY INFINITY and GIOS
E. Valetov, M. Berz, K. Makino, MSUHEP-171023, Michigan State University (2017)

The COSY INFINITY Graphical User Interface Subsystem
A. Wittig, M. Berz, K. Makino, MSUHEP-111101, Michigan State University (2011)

Survey of FORTRAN Compiler Options and Their Impact on COSY INFINITY
R. Jagasia, A. Wittig, MSUHEP-090422, Michigan State University (2009)

Design and Implementation of a High Precision Arithmetic with Rigorous Error Bounds
A. Wittig, M. Berz, MSUHEP-081126, Michigan State University (2008)

Taylor Model Methods and Computer Assisted Proofs
M. Berz, K. Makino, Lecture Notes, Course Presented at Department of Mathematics, University of Barcelona, June 2008, MSUHEP-080609, Michigan State University (2008)

Studies on Performance of the COSY Infinity Optimizers on Constraint Satisfaction
A. Poklonskiy, MSUHEP-083117, Michigan State University (2008)

The COSY 8th Order Runge Kutta Integrator
K. Makino, MUC-NOTE-COOL_THEORY-238 (2002)

Detailed Analysis of Fringe Field Effects in the Large Hadron Collider
B. Erdelyi, M. Berz, K. Makino, MSUCL-1129, Michigan State University (1999).

Analysis on a Nonarchimedean Extension of the Real Numbers
M. Berz, Lecture Notes, 1992 and 1995 Mathematics Summer Graduate Schools of the German National Merit Foundation, MSUCL-933, Department of Physics and Astronomy, Michigan State University (1994)

Analysis auf einer Nichtarchimedischen Erweiterung der Reellen Zahlen
M. Berz, Monograph, in German MSUCL-753, Department of Physics and Astronomy, Michigan State University (1990)

Introduction to Beam Physics
M. Berz, Lecture Notes, MSUPA PHY861

COSY Infinity

In addition to these publications you can access the COSY Infinity Reference Manual online.

This page is maintained by Kyoko Makino. Please contact her if there are any problems with it.