# Mathematical and Numerical Methods for Non-linear Beam Dynamics

@article{Herr2016MathematicalAN, title={Mathematical and Numerical Methods for Non-linear Beam Dynamics}, author={Werner Herr}, journal={arXiv: Accelerator Physics}, year={2016}, pages={157-198} }

Non-linear effects in accelerator physics are important for both successful operation of accelerators and during the design stage. Since both of these aspects are closely related, they will be treated together in this overview. Some of the most important aspects are well described by methods established in other areas of physics and mathematics. The treatment will be focused on the problems in accelerators used for particle physics experiments. Although the main emphasis will be on accelerator…

## 8 Citations

### Non-linear Dynamics model for the ESS Linac Simulator

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- 2015

The ESS Proton Linac will run a beam with 62.5 mA of current. In the first meters of the accelerator, the nonlinear space-charge force dominates the dynamics of the beam. The Drift Tube Linac, the…

### Introduction to Landau Damping

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The mechanism of Landau damping is observed in various systems from plasma oscillations to accelerators. Despite its widespread use, some confusion has been created, partly because of the different…

### INCOHERENT ELECTRON CLOUD EFFECTS IN THE LARGE HADRON COLLIDER

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During the operation of the Large Hadron Collider in 2018, the majority of physics data was collected with a beam energy of 6.5 TeV, a bunch spacing of 25 ns and with V-functions in the high…

### Direct Vlasov solvers

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In these proceedings we will describe the theory and practical steps required to build Vlasov solvers such as those commonly used to compute coherent instabilities in synchrotrons. Thanks to a…

### Landau damping in the transverse plane

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In these proceedings we sketch a general theory for Landau damping in the transverse plane, in the particular case of beam-coupling impedance with linear (octupolar) detuning as the source of tune…

### Transfer Lines

- Physics
- 2018

Transfer lines are used to connect accelerators or deliver beam to fixed target experiments. In the following sections the design steps of a transfer line are introduced, starting from…

### Manipulation of transverse emittances in circular accelerators by crossing nonlinear 2D resonances

- PhysicsThe European Physical Journal Plus
- 2022

Controlling nonlinear effects in the transverse dynamics of charged particle beams in circular accelerators opens new possibilities for controlling some of the beam properties. Beam splitting by…

### Beam-Beam Effects

- Physics
- 2014

One of the most severe limitations in high-intensity particle colliders is the beam-beam interaction, i.e. the perturbation of the beams as they cross the opposing beams. This introduction to…

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