Numerical Methods of Accelerator Physics

MSc lecture at TU Darmstadt, etit, TEMF by Adrian Oeftiger in 2022/23.

Twelveth part of a jupyter notebook lecture series, held on 27.01.2023.

Find the rendered HTML slides here.

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Run online

Run this notebook talk online, interactively on mybinder.org:

The lecture.ipynb notebook will work out-of-the-box.

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Run on TU Darmstadt jupyterhub

If you have a TU ID, access the local TU Darmstadt jupyterhub using your TU ID.

A possible way to upload and run this lecture repository is the following:

1. Open a terminal by clicking on the top right "New" -> "Terminal".

2. A new tab opens with a terminal, click into the black area and enter (copy&pasting):

wget https://github.com/aoeftiger/TUDa-NMAP-12/archive/refs/heads/main.zip
unzip main.zip
cd TUDa-NMAP-12-main

3. You have downloaded, unzipped and entered the lecture repository. As a last step, install the dependencies:

export TMPDIR="`pwd`"
pip install -r requirements_noversions.txt --prefix="`pwd`"/requirements

Close the terminal tab and open the lecture.ipynb notebook inside the repository directory on the jupyterhub main page.

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Run locally

The notebook can of course also be run on your local computer using your own jupyter notebook server. Install such an environment e.g. via the extensive Anaconda distribution, the minimalistic Miniconda distribution or the extremely fast Mamba package manager. (The order indicates preference by simplicity in installation and usage.)

You may find all required packages in the requirements.txt file.

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Overview Lecture Series

1. Lecture 01: basic concepts (accelerators, time scales, modelling a pendulum)
2. Lecture 02: basic concepts (rms emittance, emittance preservation & filamentation, discrete frequency analysis & NAFF)
3. Lecture 03: basic concepts (chaos and early indicators, numerical artefacts)
4. Lecture 04: longitudinal beam dynamics (acceleration with rf cavities, longitudinal tracking equations)
5. Lecture 05: longitudinal beam dynamics (Monte-Carlo technique, synchrotron Hamiltonian, phase space initialisation)
6. Lecture 06: longitudinal beam dynamics (simulating transition crossing, equilibrium distributions, emittance growth)
7. Lecture 07: transverse beam dynamics (dipole / quadrupole / sextupole magnetic fields, betatron matrices)
8. Lecture 08: transverse beam dynamics (Hill differential equation, Floquet theory, optics, off-momentum particles)
9. Lecture 09: longitudinal tomography
10. Lecture 10: closed orbit correction (local and global)
11. Lecture 11: reinforcement learning (Q-learning, actor-critic methods)
12. Lecture 12: collective effects (space charge, lambda-prime model, microwave instability)
13. Lecture 13: summary
14. Lecture 14: Bayesian optimisation