# Project

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## Precise Simulations of Multi Bunches in High Intensity Cyclotrons

 Applicant Adelmann Andreas 159936 Project funding Paul Scherrer Institut Paul Scherrer Institute - PSI Particle Physics 01.06.2016 - 31.08.2020 241'740.00
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### All Disciplines (2)

Discipline
 Particle Physics
 Mathematics

### Keywords (5)

Beam dynamics; Electrostatics ; Uncertainty quantification; Poisson equation; Adaptive mesh refinement

### Lay Summary (German)

Teilchenbeschleuniger sind nicht mehr aus unserer Gesellschaft wegzudenken. Mehr als 50000Wissenschaftler, Ingenieure und Techniker befassen sich weltweit mit Teilchenbeschleunigern. Dies in den unterschiedlichsten Bereichen: von der Teilchenphysik über Werkstoffkunde bin hin zur Medizin. Darin finden sich zahlreichen und gesellschaftlich relevante Anwendungsgebiete.
Lay summary

Inhalt und Ziel des Forschungsprojekts

Das übergeordnete Ziel dieses Projektes ist es mittels numerischen Modellen berstende Teilchenbeschleuniger zu verbessern und neue optimal zu entwickeln. Im Mittelpunkt steht die Protonenanlage am PSI welche seit etlichen Jahre den Weltrekord in der Stahlintensität innehat.

Wissenschaftlicher und gesellschaftlicher Kontext des Forschungspro-jekts

In dieser Forschungsarbeit soll untersucht werde in wie fern sich adaptive Verfahren zur Lösung von Partiellen Differentialgleichungen, im Gebiet der Beschleunigermodellierung, eigenen. Da bei einer gleichmässige Diskretisierung des Problems meist zu viel Speicher verwendet wird, können relevante Probleme nur mit unzureichender Genauigkeit gelöst werden. Mit der vorgeschlagenen adaptiven Methode soll viel ökonomischer mit dem Speicherplatz umgegangen werden und als Konsequenz kann die Genauigkeit der Rechnung erhöht werden. Dadurch wir ein besseres Verständnis der komplizierten Dynamik in Teilchenbeschleunigern gewonnen welches uns hilft diese effizienter zu entwickeln. Das hat vielfältige Konsequenzen, z.B. Erhöhung der Energieeffizienz, Verringerung der Standzeiten und der Verluste.

 Direct link to Lay Summary Last update: 03.11.2015

Name Institute

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### Publications

Publication
Frey Matthias, Adelmann Andreas (2020), Global sensitivity analysis on numerical solver parameters of Particle-In-Cell models in particle accelerator systems, in Computer Physics Communications, 258, 107577-107577.
Edelen Auralee, Neveu Nicole, Frey Matthias, Huber Yannick, Mayes Christopher, Adelmann Andreas (2020), Machine learning for orders of magnitude speedup in multiobjective optimization of particle accelerator systems, in Phys. Rev. Accel. Beams, 23, 044601-044601.
Frey Matthias, Adelmann Andreas, Locans Uldis (2020), On architecture and performance of adaptive mesh refinement in an electrostatics Particle-In-Cell code, in Computer Physics Communications, 247, 106912-106912.
Frey Matthias, Snuverink Jochem, Baumgarten Christian, Adelmann Andreas (2019), Matching of turn pattern measurements for cyclotrons using multiobjective optimization, in Phys. Rev. Accel. Beams, 22, 064602-064602.
Rizzoglio V., Adelmann A., Baumgarten C., Frey M., Gerbershagen A., Meer D., Schippers J. M. (2017), Evolution of a beam dynamics model for the transport line in a proton therapy facility, in Physical Review Accelerators and Beams, 20(12), 124702-124702.

### Datasets

#### AMR solver data

Author Frey, Matthias https://doi.psi.ch/detail/10.16907%2Ff1285417-f190-4563-a8ee-04ebd9246a21 PSI Peta Byte archive

#### Data of turn pattern matching between measurement and simulation of the PSI Ring Cyclotron

Author Frey, Matthias https://doi.org/10.16907/00b95267-8b8b-48a7-8de6-8da6b9b7bb7d PSI Peta Byte Archive

#### Data of of a global sensitivity study of the PSI Injector 2, PSI Ring Cyclotron, IsoDAR and AWA RF gun

Author Frey , Matthias https://doi.psi.ch/detail/10.16907%2Ffd7d6880-7a0f-4b52-942d-35e23b77d0dc PSi Beta Byte Archive

### Scientific events

#### Active participation

Title Type of contribution Title of article or contribution Date Place Persons involved
 SIAM Conference on Par- allel Processing for Scien- tific Computing (PP20) Talk given at a conference Hardware Architecture In- dependent Adaptive Mesh Refinement Solver using Trilinos 14.02.2020 Seattle, United States of America Adelmann Andreas; Frey Matthias;
 International Workshop on Fixed Field alternating gradient Accelerators (FFA’19 Talk given at a conference Adaptive mesh refinement Poisson solver for neigh- bouring bunch simulations 22.11.2019 Villigen, Switzerland Frey Matthias; Adelmann Andreas;
 NES PhD Day Poster Machine Learning to En- able Orders of Magni- tude Speedup in Multi- Objective Optimization of Particle Accelerator Sys- tems (3rd year PhD poster prize) 23.05.2019 Villigen, Switzerland Frey Matthias;
 13th International Com- putational Accelera- tor Physics Conference (ICAP’18) Talk given at a conference Trimcoil Optimisation us- ing Multi-ob jective Opti- misation Techniques and HPC 23.10.2018 Key West, United States of America Adelmann Andreas; Frey Matthias;
 13th International Com- putational Accelera- tor Physics Conference (ICAP’18) Talk given at a conference Computer Architecture In- dependent Adaptive Geo- metric Multigrid Solver for AMR-PIC 21.10.2018 Key West, United States of America Adelmann Andreas; Frey Matthias;
 Invitarion to Sandia National Laboratories Individual talk Computer Architecture In- dependent Adaptive Geo- metric Multigrid Solver for AMR-PIC 17.10.2018 Albuquerque, United States of America Frey Matthias;
 Platform for Advanced Scientific Computing (PASC18) Poster Performance and Imple- mentation of a Geometric Multigrid Solver with Trili- nos (CSM17) 03.07.2018 Basel, Switzerland Adelmann Andreas; Frey Matthias;
 10th International Work- shop on Parallel Matrix Al- gorithms and Applications (PMAA’18) Talk given at a conference Performance and Imple- mentation of a Geometric Multigrid Solver with Trili- nos 27.06.2018 Zurich, Switzerland Frey Matthias;
 NES PhD Day Talk given at a conference Performance and Implementation of a Geometric Multigrid Solver with Trilinos 24.05.2018 Villigen, Switzerland Frey Matthias;

### Awards

Title Year
 3rd year PSI PhD poster prize 2019

### Abstract

Intensive research has been conducted into how to deliver high intensity beams with low particle losses/halo over several decades. This is an important problem for spallation neutron sources, nuclear waste transmutation, neutrino physics, proton radiography and isotope production. It is essential to understand the nonlinear space charge effects on beam dynamics in all high intensity accelerators, in particular, the world record 1.4 MW proton cyclotron facility at PSI. The main two questions driving research are, 1. To what extent do neighboring bunches affect the halo formation in cyclotrons? 2. How do uncertainties propagate in the model, and influence results?Particle-Mesh based particle-in-cell (PIC) is the method of choice used in macro-particle simulation for different types of accelerators and beam lines. In most of the state-of-the-art models, the associated time dependent partial differential equations are solved on regular grids. This fact hinders the development of applications by the large memory requirements of regular grids and the prohibitive time to solution. A well known remedy to this problem is to adapt the grid to the solution. The grid should be fine where the solution varies much and can be coarse at other places. Block-structured Adaptive Mesh Refinement (AMR) technique will take into account both particles and fields and combine them for the quantitative and efficient evaluation of the effects of space charge in the neighboring bunch region. In the case of the PSI Ring Cyclotron this would enable, for the first time, start-to-end simulations allowing a detailed characterization of the 6D phase space at every location in the machine, with required resolution better than $10^{-4}$ to $10^{-5}$ of the total intensity. In all high intensity hadron accelerators, minimizing losses are of primary concern. From a mathematical point of view, this sort of problems are ill posed and embedded in a high dimensional space of parameters. From the simulation point of view, in order to fight the curse of dimensionality, an accurate sensitivity analysis is needed. With the help of uncertainty quantification we will determine a minimal set of, physics and numeric related parameters, and in turn provides us with a solvable model, that allows precise prediction of losses. The importance of each input parameter and the uncertainty in outputs due to the uncertainty in the input parameters will be quantified using sensitivity analysis and forward uncertainty propagation respectively. One way of achieving this, is the usage of polynomial chaos expansion (PCE). PCE of quantity of interest such as current will be constructed using the non-intrusive spectral projection method. Both of the method must be carefully developed and benchmarked. For this purpose, we will use existing data from the PSI proton cyclotron facility and can use dedicated beam time, which is available within the ongoing high intensity upgrade. Adaptive mesh refinement strategies and quantifying the uncertainty in space charge computation will enable precise and efficient multi bunch simulations in high intensity cyclotrons. This work will contribute to the further development of the PSI high intensity proton accelerator upgrade program and also play a part in new projects such as DAE$\delta$ALUS/IsoDAR, requiring multimegawatt cyclotrons.
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