Christian Baumgarten - Academia.edu (original) (raw)

Papers by Christian Baumgarten

It is demonstrated that energy conservation allows for a "heuristic" derivation of Newtonian mech... more It is demonstrated that energy conservation allows for a "heuristic" derivation of Newtonian mechanics, if the energy is presumed to be an additive function of position and velocity. It is shown that energy must be depicted as a function of position and momentum in order to allow for the correct relativistic equations. Accordingly it is argued that not only quantum theory but also special relativity is intrinsically Hamiltonian and requires a description by coordinates and momenta instead of coordinates and velocities. Furthermore it is argued that the usual historical order of the "formulations" of mechanics, from Newtonian via Lagrangian to Hamiltonian mechanics, is illogical and misleading. We suggest that it should be reversed.

arXiv (Cornell University), Jul 16, 2019

We give an exceptionally short derivation of Schrödinger's equation by replacing the idealization... more We give an exceptionally short derivation of Schrödinger's equation by replacing the idealization of a point particle by a density distribution.

arXiv (Cornell University), Oct 12, 2018

When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysi... more When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the Hamiltonian formulation of classical analytical mechanics is based on abstract generalized coordinates and momenta: It is a mathematical rather than a philosophical framework. If the metaphysical assumptions ascribed to classical mechanics are dropped, then there exists a presentation in which little of the purported difference between quantum and classical mechanics remains. This presentation allows to derive the mathematics of relativistic quantum mechanics on the basis of a purely classical Hamiltonian phase space picture. It is shown that a spatio-temporal description is not a condition for but a consequence of objectivity. It requires no postulates. This is achieved by evading spatial notions and assuming nothing but time translation invariance.

The usage of numerical models to study the evolution of particle beams is an essential step in th... more The usage of numerical models to study the evolution of particle beams is an essential step in the design process of particle accelerators. However, uncertainties of input quantities such as beam energy and magnetic field lead to simulation results that do not fully agree with measurements. Hence the machine will behave differently compared to the simulations. In case of cyclotrons such discrepancies affect the overall turn pattern or alter the number of turns. Inaccuracies at the PSI Ring cyclotron that may harm the isochronicity are compensated by 18 trim coils. Trim coils are often absent in simulations or their implementation is simplistic. A realistic trim coil model within the simulation framework OPAL is presented. It was used to match the turn pattern of the PSI Ring. Due to the high-dimensional search space consisting of 48 simulation input parameters and 182 objectives (i.e. turns) simulation and measurement cannot be matched in a straightforward manner. Instead, an evolut...

We describe a precise beam dynamics model of the production set up of the Injector 2 Cyclotron at... more We describe a precise beam dynamics model of the production set up of the Injector 2 Cyclotron at the Paul Scherrer Institut (PSI). Injector 2 is a 72 MeV separate-sector cyclotron producing a high intensity proton beam up to 2.7 mA CW, which is then injected into the 590 MeV Ring Cyclotron. The model includes space charge and is calculated for optimised matched initial conditions. It has been verified with measurements. Based on this model we estimate the limits to the intensity obtainable from Injector 2. The precise beam dynamics model is based on the OPAL (Object Oriented Parallel Accelerator Library) simulation code, a tool for charged-particle optics calculations in large accelerator structures and beam lines including 3D space charge.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2018

In a cyclotron-based proton therapy facility, the energy changes are performed by means of a degr... more In a cyclotron-based proton therapy facility, the energy changes are performed by means of a degrader of variable thickness. The interaction of the proton beam with the degrader creates energy tails and increases the beam emittance. A precise model of the degraded beam properties is important not only to better understand the performance of a facility already in operation, but also to support the development of new proton therapy concepts. The accuracy of the degraded beam properties, in terms of energy spectrum and transverse phase space, is influenced by the approximations in the model of the particle-matter interaction. In this work the model of a graphite degrader has been developed with four Monte Carlo codes: three conventional Monte Carlo codes (FLUKA, GEANT4 and MCNPX) and the multipurpose particle tracking code OPAL equipped with a simplified Monte Carlo routine. From the comparison between the different codes, we can deduce how the accuracy of the degrader model influences the precision of the beam dynamics model of a possible transport line downstream of the degrader.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2018

We investigate limits on the current of the PSI Injector II high intensity separate-sector isochr... more We investigate limits on the current of the PSI Injector II high intensity separate-sector isochronous cyclotron, in its present configuration and after a proposed upgrade. Accelerator Driven Subcritical Reactors, neutron and neutrino experiments, and medical isotope production all benefit from increases in current, even at the ∼ 10% level: the PSI cyclotrons provide relevant experience. As space charge dominates at low beam energy, the injector is critical. Understanding space charge effects and halo formation through detailed numerical modelling gives clues on how to maximise the extracted current. Simulation of a space-charge dominated low energy high intensity (9.5 mA DC) machine, with a complex collimator set up in the central region shaping the bunch, is not trivial. We use the OPAL code, a tool for charged-particle optics calculations in large accelerator structures and beam lines, including 3D space charge. We have a precise model of the present (production) Injector II, operating at 2.2 mA current. A simple model of the proposed future (upgraded) configuration of the cyclotron is also investigated. We estimate intensity limits based on the developed models, supported by fitted scaling laws and measurements. We have been able to perform more detailed analysis of the bunch parameters and halo development than any previous study. Optimisation techniques enable better matching of the simulation setup with Injector II parameters and measurements. We show that in the production configuration the beam current scales to the power of three with the beam size. However, at higher intensities, 4th power scaling is a better fit, setting the limit of approximately 3 mA. Currents of over 5 mA, higher than have been achieved to date, can be produced if the collimation scheme is adjusted.

arXiv (Cornell University), Aug 31, 2020

Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by ... more Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report here about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobi's method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary "decoupling" transformations.

Proceedings of the 3rd J-PARC Symposium (J-PARC2019), 2021

The high intensity proton accelerator (HIPA) at the Paul Scherrer Institut (PSI) delivers a 590 M... more The high intensity proton accelerator (HIPA) at the Paul Scherrer Institut (PSI) delivers a 590 MeV c.w. proton beam with currents of up to 2.4 mA, i.e. 1.4 MW beam power, which is at the forefront of current particle accelerators. The challenge of this high power is to reduce unwanted beam losses and subsequent activation and damage as well as to dissipate the beam power at certain loss points like targets, collimators and beam dumps. Diagnostics and the interlock system have to provide the necessary tools to switch off the beam in case of unwanted beam loss or dangerous tunes. In the cyclotrons, beam losses can efficiently be reduced by increasing the accelerating voltage per turn. This concept was realized by replacing four aluminum cavities by copper cavities in the Ring cyclotron 2008 (s. Fig. 1). Following the same idea, the exchange of two cavities in the Injector II cyclotron (72 MeV) is underway with the aim to reduce beam losses and to increase the reliability. Beam dynamics studies, providing a better understanding of the mechanisms causing beam loss, may result in a further decrease of losses. After the damage of the SINQ Target no. 11 the diagnostics in front of the spallation neutron source SINQ was improved to detect unusual beam conditions in a faster and more reliable way. The talk will focus on the present status of HIPA, its challenges and further projects.

We discuss factors that have potential influence on the space charge induced vortex motion of par... more We discuss factors that have potential influence on the space charge induced vortex motion of particles within high intensity bunches (curling of bunches, Gordon 1969) in isochronous cyclotrons. The influence of the phase slip due to deviations from strict isochronism determines if the bunches of a specific turn are above, below or at "transition", and hence whether stable vortex motion of the bunches is possible at all. Secondly there are possible longitudinal and transverse effects of rf acceleration, the former depending on the bunch phase ("bunching" or "debunching"), the latter depending on the gradient of the accelerating voltage. High accelerating voltages in the first turns call the applicability of adiabatic approximations and analytic methods into question. The influence of the rf acceleration is expected to be significant only at low beam energy, i.e. should have small or even negligible effect beyond the central region of compact machines.

arXiv (Cornell University), Jan 10, 2020

We discuss the key role that Hamiltonian notions play in physics. Five examples are given that il... more We discuss the key role that Hamiltonian notions play in physics. Five examples are given that illustrate the versatility and generality of Hamiltonian notions. The given examples concern the interconnection between quantum mechanics, special relativity and electromagnetism. It will be demonstrated that a derivation of these core concepts of modern physics requires little more than a an abstract classical analysis of linear Hamiltonian theory.

JINST, 2023

One of the decisive issues in the design and operation of cyclotrons is the choice of the beam ex... more One of the decisive issues in the design and operation of cyclotrons is the choice of the
beam extraction method. Typical methods are extraction by electrostatic extractors and by stripping.
The former method requires DC high voltage electrodes which are notorious for high-voltage breakdowns. The latter method requires beams of atomic or molecular ions which are notorious for rest gas and Lorentz stripping. Here we discuss the conditions to be met such that a beam will leave the magnetic field of an isochronous cyclotron purely by fast acceleration.

Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei d... more Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei der Erstellung dieser Arbeit, ebenso bei Dr. G. Court, Dr. U. Stoesslein und M. Henoch für die vielen Anregungen und Diskussionen. Bei den Mitarbeitern und dem Direktorium des DESY bedanke ich mich für die Möglichkeit, diese Arbeit durchführen zu können. Allen Mitgliedern des HERMES Experiments danke ich für die freundliche Aufnahme in der HERMES Kollaboration und die herzliche und produktive Zusammenarbeit. Allen am Targetaufbau und Betrieb beteiligten Personen, insbesondere auch in den am Target beteiligten Instituten und ihren Werkstätten, die ich hier weder vollständig aufzählen noch angemessen würdigen kann, spreche ich meinen herzlichen Dank für ihre Beiträge aus. Besonders genannt seien Dr. J. Stenger und Dr. C. Grosshauser für ihren Beitrag am Aufbau des Target Gas Analysators, B.

Paul Scherrer Institute extends its proton therapy facility PROSCAN by a third gantry. It is deli... more Paul Scherrer Institute extends its proton therapy facility PROSCAN by a third gantry. It is delivered by Varian Medical Systems (VMS) as part of a joint research project. Gantry 3 is equipped with a cone beam CT and allows 360 degrees of rotation while occupying a 10.5 m diameter. The integration of a gantry into the existing PSI system typically being designed for a complete Varian system is a challenging project, since also the certification is to be maintained. Especially the interfaces between the PROSCAN control system and the one of Gantry 3 have been a major development. Gantry 3 is designed to deliver proton beam of up to 8 nA with an accuracy better than a mm, while having a high level of over-current protection. This comprises a new current monitoring unit, several levels of interlock controllers and a beam energy dependent intensity compensation concept. One challenge concerns the specified layer switching time of 200 ms, required to reduce the treatment time to enable f...

The High Intensity Proton Accelerator Facility at PSI routinely produces a proton beam with up to... more The High Intensity Proton Accelerator Facility at PSI routinely produces a proton beam with up to 1.4 MW power at a kinetic energy of 590 MeV. The beam is used to generate neutrons in spallation targets, and pions in meson production targets. The pions decay into muons and neutrinos. Pions and muons are used for condensed matter and particle physics research at the intensity frontier. This section presents the main physics and technology concepts utilized in the facility. It includes beam dynamics and the control of beam losses and activation, power conversion, efficiency aspects, and performance figures, including the availability of the facility.

Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices... more Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report here about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobi's method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary ``decoupling'' transformations.

Physical Review Accelerators and Beams

The usage of numerical models to study the evolution of particle beams is an essential step in th... more The usage of numerical models to study the evolution of particle beams is an essential step in the design process of particle accelerators. However, uncertainties of input quantities such as beam energy and magnetic field lead to simulation results that do not fully agree with measurements, hence the final machine will behave slightly differently than the simulations. In case of cyclotrons such discrepancies affect the overall turn pattern or may even alter the number of turns in the machine. Inaccuracies at the PSI Ring cyclotron facility that may harm the isochronism are compensated by additional magnetic fields provided by 18 trim coils. These are often absent from simulations or their implementation is very simplistic. In this paper a newly developed realistic trim coil model within the particle accelerator framework OPAL is presented that was used to match the turn pattern of the PSI Ring cyclotron. Due to the high-dimensional search space consisting of 48 design variables (simulation input parameters) and 182 objectives (i.e. turns) simulation and measurement cannot be matched in a straightforward manner. Instead, an evolutionary multi-objective optimization with a population size of more than 8000 individuals per generation together with a local search approach were applied that reduced the maximum absolute error to 4.5 mm over all 182 turns.

Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei d... more Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei der Erstellung dieser Arbeit, ebenso bei Dr. G. Court, Dr. U. Stoesslein und M. Henoch für die vielen Anregungen und Diskussionen. Bei den Mitarbeitern und dem Direktorium des DESY bedanke ich mich für die Möglichkeit, diese Arbeit durchführen zu können. Allen Mitgliedern des HERMES Experiments danke ich für die freundliche Aufnahme in der HERMES Kollaboration und die herzliche und produktive Zusammenarbeit. Allen am Targetaufbau und Betrieb beteiligten Personen, insbesondere auch in den am Target beteiligten Instituten und ihren Werkstätten, die ich hier weder vollständig aufzählen noch angemessen würdigen kann, spreche ich meinen herzlichen Dank für ihre Beiträge aus. Besonders genannt seien Dr. J. Stenger und Dr. C. Grosshauser für ihren Beitrag am Aufbau des Target Gas Analysators, B.

Double-spin asymmetries in the cross section of ρ 0 and φ production at intermediate energies.

It is demonstrated that energy conservation allows for a "heuristic" derivation of Newtonian mech... more It is demonstrated that energy conservation allows for a "heuristic" derivation of Newtonian mechanics, if the energy is presumed to be an additive function of position and velocity. It is shown that energy must be depicted as a function of position and momentum in order to allow for the correct relativistic equations. Accordingly it is argued that not only quantum theory but also special relativity is intrinsically Hamiltonian and requires a description by coordinates and momenta instead of coordinates and velocities. Furthermore it is argued that the usual historical order of the "formulations" of mechanics, from Newtonian via Lagrangian to Hamiltonian mechanics, is illogical and misleading. We suggest that it should be reversed.

arXiv (Cornell University), Jul 16, 2019

We give an exceptionally short derivation of Schrödinger's equation by replacing the idealization... more We give an exceptionally short derivation of Schrödinger's equation by replacing the idealization of a point particle by a density distribution.

arXiv (Cornell University), Oct 12, 2018

When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysi... more When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the Hamiltonian formulation of classical analytical mechanics is based on abstract generalized coordinates and momenta: It is a mathematical rather than a philosophical framework. If the metaphysical assumptions ascribed to classical mechanics are dropped, then there exists a presentation in which little of the purported difference between quantum and classical mechanics remains. This presentation allows to derive the mathematics of relativistic quantum mechanics on the basis of a purely classical Hamiltonian phase space picture. It is shown that a spatio-temporal description is not a condition for but a consequence of objectivity. It requires no postulates. This is achieved by evading spatial notions and assuming nothing but time translation invariance.

The usage of numerical models to study the evolution of particle beams is an essential step in th... more The usage of numerical models to study the evolution of particle beams is an essential step in the design process of particle accelerators. However, uncertainties of input quantities such as beam energy and magnetic field lead to simulation results that do not fully agree with measurements. Hence the machine will behave differently compared to the simulations. In case of cyclotrons such discrepancies affect the overall turn pattern or alter the number of turns. Inaccuracies at the PSI Ring cyclotron that may harm the isochronicity are compensated by 18 trim coils. Trim coils are often absent in simulations or their implementation is simplistic. A realistic trim coil model within the simulation framework OPAL is presented. It was used to match the turn pattern of the PSI Ring. Due to the high-dimensional search space consisting of 48 simulation input parameters and 182 objectives (i.e. turns) simulation and measurement cannot be matched in a straightforward manner. Instead, an evolut...

We describe a precise beam dynamics model of the production set up of the Injector 2 Cyclotron at... more We describe a precise beam dynamics model of the production set up of the Injector 2 Cyclotron at the Paul Scherrer Institut (PSI). Injector 2 is a 72 MeV separate-sector cyclotron producing a high intensity proton beam up to 2.7 mA CW, which is then injected into the 590 MeV Ring Cyclotron. The model includes space charge and is calculated for optimised matched initial conditions. It has been verified with measurements. Based on this model we estimate the limits to the intensity obtainable from Injector 2. The precise beam dynamics model is based on the OPAL (Object Oriented Parallel Accelerator Library) simulation code, a tool for charged-particle optics calculations in large accelerator structures and beam lines including 3D space charge.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2018

In a cyclotron-based proton therapy facility, the energy changes are performed by means of a degr... more In a cyclotron-based proton therapy facility, the energy changes are performed by means of a degrader of variable thickness. The interaction of the proton beam with the degrader creates energy tails and increases the beam emittance. A precise model of the degraded beam properties is important not only to better understand the performance of a facility already in operation, but also to support the development of new proton therapy concepts. The accuracy of the degraded beam properties, in terms of energy spectrum and transverse phase space, is influenced by the approximations in the model of the particle-matter interaction. In this work the model of a graphite degrader has been developed with four Monte Carlo codes: three conventional Monte Carlo codes (FLUKA, GEANT4 and MCNPX) and the multipurpose particle tracking code OPAL equipped with a simplified Monte Carlo routine. From the comparison between the different codes, we can deduce how the accuracy of the degrader model influences the precision of the beam dynamics model of a possible transport line downstream of the degrader.

Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 2018

We investigate limits on the current of the PSI Injector II high intensity separate-sector isochr... more We investigate limits on the current of the PSI Injector II high intensity separate-sector isochronous cyclotron, in its present configuration and after a proposed upgrade. Accelerator Driven Subcritical Reactors, neutron and neutrino experiments, and medical isotope production all benefit from increases in current, even at the ∼ 10% level: the PSI cyclotrons provide relevant experience. As space charge dominates at low beam energy, the injector is critical. Understanding space charge effects and halo formation through detailed numerical modelling gives clues on how to maximise the extracted current. Simulation of a space-charge dominated low energy high intensity (9.5 mA DC) machine, with a complex collimator set up in the central region shaping the bunch, is not trivial. We use the OPAL code, a tool for charged-particle optics calculations in large accelerator structures and beam lines, including 3D space charge. We have a precise model of the present (production) Injector II, operating at 2.2 mA current. A simple model of the proposed future (upgraded) configuration of the cyclotron is also investigated. We estimate intensity limits based on the developed models, supported by fitted scaling laws and measurements. We have been able to perform more detailed analysis of the bunch parameters and halo development than any previous study. Optimisation techniques enable better matching of the simulation setup with Injector II parameters and measurements. We show that in the production configuration the beam current scales to the power of three with the beam size. However, at higher intensities, 4th power scaling is a better fit, setting the limit of approximately 3 mA. Currents of over 5 mA, higher than have been achieved to date, can be produced if the collimation scheme is adjusted.

arXiv (Cornell University), Aug 31, 2020

Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by ... more Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report here about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobi's method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary "decoupling" transformations.

Proceedings of the 3rd J-PARC Symposium (J-PARC2019), 2021

The high intensity proton accelerator (HIPA) at the Paul Scherrer Institut (PSI) delivers a 590 M... more The high intensity proton accelerator (HIPA) at the Paul Scherrer Institut (PSI) delivers a 590 MeV c.w. proton beam with currents of up to 2.4 mA, i.e. 1.4 MW beam power, which is at the forefront of current particle accelerators. The challenge of this high power is to reduce unwanted beam losses and subsequent activation and damage as well as to dissipate the beam power at certain loss points like targets, collimators and beam dumps. Diagnostics and the interlock system have to provide the necessary tools to switch off the beam in case of unwanted beam loss or dangerous tunes. In the cyclotrons, beam losses can efficiently be reduced by increasing the accelerating voltage per turn. This concept was realized by replacing four aluminum cavities by copper cavities in the Ring cyclotron 2008 (s. Fig. 1). Following the same idea, the exchange of two cavities in the Injector II cyclotron (72 MeV) is underway with the aim to reduce beam losses and to increase the reliability. Beam dynamics studies, providing a better understanding of the mechanisms causing beam loss, may result in a further decrease of losses. After the damage of the SINQ Target no. 11 the diagnostics in front of the spallation neutron source SINQ was improved to detect unusual beam conditions in a faster and more reliable way. The talk will focus on the present status of HIPA, its challenges and further projects.

We discuss factors that have potential influence on the space charge induced vortex motion of par... more We discuss factors that have potential influence on the space charge induced vortex motion of particles within high intensity bunches (curling of bunches, Gordon 1969) in isochronous cyclotrons. The influence of the phase slip due to deviations from strict isochronism determines if the bunches of a specific turn are above, below or at "transition", and hence whether stable vortex motion of the bunches is possible at all. Secondly there are possible longitudinal and transverse effects of rf acceleration, the former depending on the bunch phase ("bunching" or "debunching"), the latter depending on the gradient of the accelerating voltage. High accelerating voltages in the first turns call the applicability of adiabatic approximations and analytic methods into question. The influence of the rf acceleration is expected to be significant only at low beam energy, i.e. should have small or even negligible effect beyond the central region of compact machines.

arXiv (Cornell University), Jan 10, 2020

We discuss the key role that Hamiltonian notions play in physics. Five examples are given that il... more We discuss the key role that Hamiltonian notions play in physics. Five examples are given that illustrate the versatility and generality of Hamiltonian notions. The given examples concern the interconnection between quantum mechanics, special relativity and electromagnetism. It will be demonstrated that a derivation of these core concepts of modern physics requires little more than a an abstract classical analysis of linear Hamiltonian theory.

JINST, 2023

One of the decisive issues in the design and operation of cyclotrons is the choice of the beam ex... more One of the decisive issues in the design and operation of cyclotrons is the choice of the
beam extraction method. Typical methods are extraction by electrostatic extractors and by stripping.
The former method requires DC high voltage electrodes which are notorious for high-voltage breakdowns. The latter method requires beams of atomic or molecular ions which are notorious for rest gas and Lorentz stripping. Here we discuss the conditions to be met such that a beam will leave the magnetic field of an isochronous cyclotron purely by fast acceleration.

Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei d... more Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei der Erstellung dieser Arbeit, ebenso bei Dr. G. Court, Dr. U. Stoesslein und M. Henoch für die vielen Anregungen und Diskussionen. Bei den Mitarbeitern und dem Direktorium des DESY bedanke ich mich für die Möglichkeit, diese Arbeit durchführen zu können. Allen Mitgliedern des HERMES Experiments danke ich für die freundliche Aufnahme in der HERMES Kollaboration und die herzliche und produktive Zusammenarbeit. Allen am Targetaufbau und Betrieb beteiligten Personen, insbesondere auch in den am Target beteiligten Instituten und ihren Werkstätten, die ich hier weder vollständig aufzählen noch angemessen würdigen kann, spreche ich meinen herzlichen Dank für ihre Beiträge aus. Besonders genannt seien Dr. J. Stenger und Dr. C. Grosshauser für ihren Beitrag am Aufbau des Target Gas Analysators, B.

Paul Scherrer Institute extends its proton therapy facility PROSCAN by a third gantry. It is deli... more Paul Scherrer Institute extends its proton therapy facility PROSCAN by a third gantry. It is delivered by Varian Medical Systems (VMS) as part of a joint research project. Gantry 3 is equipped with a cone beam CT and allows 360 degrees of rotation while occupying a 10.5 m diameter. The integration of a gantry into the existing PSI system typically being designed for a complete Varian system is a challenging project, since also the certification is to be maintained. Especially the interfaces between the PROSCAN control system and the one of Gantry 3 have been a major development. Gantry 3 is designed to deliver proton beam of up to 8 nA with an accuracy better than a mm, while having a high level of over-current protection. This comprises a new current monitoring unit, several levels of interlock controllers and a beam energy dependent intensity compensation concept. One challenge concerns the specified layer switching time of 200 ms, required to reduce the treatment time to enable f...

The High Intensity Proton Accelerator Facility at PSI routinely produces a proton beam with up to... more The High Intensity Proton Accelerator Facility at PSI routinely produces a proton beam with up to 1.4 MW power at a kinetic energy of 590 MeV. The beam is used to generate neutrons in spallation targets, and pions in meson production targets. The pions decay into muons and neutrinos. Pions and muons are used for condensed matter and particle physics research at the intensity frontier. This section presents the main physics and technology concepts utilized in the facility. It includes beam dynamics and the control of beam losses and activation, power conversion, efficiency aspects, and performance figures, including the availability of the facility.

Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices... more Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report here about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobi's method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary ``decoupling'' transformations.

Physical Review Accelerators and Beams

The usage of numerical models to study the evolution of particle beams is an essential step in th... more The usage of numerical models to study the evolution of particle beams is an essential step in the design process of particle accelerators. However, uncertainties of input quantities such as beam energy and magnetic field lead to simulation results that do not fully agree with measurements, hence the final machine will behave slightly differently than the simulations. In case of cyclotrons such discrepancies affect the overall turn pattern or may even alter the number of turns in the machine. Inaccuracies at the PSI Ring cyclotron facility that may harm the isochronism are compensated by additional magnetic fields provided by 18 trim coils. These are often absent from simulations or their implementation is very simplistic. In this paper a newly developed realistic trim coil model within the particle accelerator framework OPAL is presented that was used to match the turn pattern of the PSI Ring cyclotron. Due to the high-dimensional search space consisting of 48 design variables (simulation input parameters) and 182 objectives (i.e. turns) simulation and measurement cannot be matched in a straightforward manner. Instead, an evolutionary multi-objective optimization with a population size of more than 8000 individuals per generation together with a local search approach were applied that reduced the maximum absolute error to 4.5 mm over all 182 turns.

Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei d... more Stewart und T. Wise bedanke ich mich für die hervorragende Zusammenarbeit und Unterstützung bei der Erstellung dieser Arbeit, ebenso bei Dr. G. Court, Dr. U. Stoesslein und M. Henoch für die vielen Anregungen und Diskussionen. Bei den Mitarbeitern und dem Direktorium des DESY bedanke ich mich für die Möglichkeit, diese Arbeit durchführen zu können. Allen Mitgliedern des HERMES Experiments danke ich für die freundliche Aufnahme in der HERMES Kollaboration und die herzliche und produktive Zusammenarbeit. Allen am Targetaufbau und Betrieb beteiligten Personen, insbesondere auch in den am Target beteiligten Instituten und ihren Werkstätten, die ich hier weder vollständig aufzählen noch angemessen würdigen kann, spreche ich meinen herzlichen Dank für ihre Beiträge aus. Besonders genannt seien Dr. J. Stenger und Dr. C. Grosshauser für ihren Beitrag am Aufbau des Target Gas Analysators, B.

Double-spin asymmetries in the cross section of ρ 0 and φ production at intermediate energies.

It is demonstrated that energy conservation allows for a ``heuristic'' derivation of Newtonia... more It is demonstrated that energy conservation allows for a ``heuristic'' derivation
of Newtonian mechanics, if the energy is presumed to be an additive function of
position and velocity. It is shown that energy must be depicted as a function of
position and momentum in order to allow for the correct relativistic equations.
Accordingly it is argued that not only quantum theory but also special
relativity is intrinsically Hamiltonian and requires a description by
coordinates and momenta instead of coordinates and velocities.

Furthermore it is argued that the usual historical order of the ``formulations''
of mechanics, from Newtonian via Lagrangian to Hamiltonian mechanics, is illogical and
misleading. Therefore it should be reversed.

We discuss the key role that Hamiltonian notions play in physics. Five examples are given that il... more We discuss the key role that Hamiltonian notions play in physics. Five examples are given that illustrate the versatility and generality of Hamiltonian notions. The given examples concern the interconnection between quantum mechanics, special relativity and electromagnetism. We demonstrate that a derivation of these core concepts of modern physics requires little more than a proper formulation in terms of classical Hamiltonian theory.

Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by ... more Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report here about the generalization of these elementary rotations towards canonical transformations acting in Hamiltonian phase spaces. This generalization allows to use Jacobi's method in order to compute eigenvalues and eigenvectors of Hamiltonian (and skew-Hamiltonian) matrices with either purely real or purely imaginary eigenvalues by successive elementary "decoupling" transformations. The real importance of Einstein's work was that he introduced Lorentz transformations as something fundamental in physics-P.A.M. Dirac [1]

We discuss the key role that Hamiltonian notions could play in physics. Five examples are given t... more We discuss the key role that Hamiltonian notions could play in physics. Five examples are given that illustrate the underestimated versatility and almost magical generality of Hamiltonian notions. The given examples concern the interconnection between quantum mechanics, special relativity and electromagnetism. We demonstrate that a derivation of these core concepts of modern physics requires little more than a proper formulation in terms of classical Hamiltonian theory.

We give an exceptionally short derivation of Schroedinger's equation by replacing the idealizatio... more We give an exceptionally short derivation of Schroedinger's equation by replacing the idealization of a point particle by a density distribution.

When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysi... more When compared to quantum mechanics, classical mechanics is often depicted in a specific metaphysical flavour: spatio-temporal realism or a Newtonian "background" is presented as an intrinsic fundamental classical presumption. However, the Hamiltonian formulation of classical analytical mechanics is based on abstract generalized coordinates and momenta: It is a mathematical rather than a philosophical framework. If the metaphysical assumptions ascribed to classical mechanics are dropped, then there exists a presentation in which little of the purported difference between quantum and classical mechanics remains. This presentation allows to derive the mathematics of relativistic quantum mechanics on the basis of a purely classical Hamiltonian phase space picture. It is shown that a spatio-temporal description is not a condition for but a consequence of objectivity. It requires no postulates. This is achieved by evading spatial notions and assuming nothing but time translation invariance.