# A generic formulation for emittance and lattice function evolution for non-Hamiltonian systems with stochastic effects

## Abstract

I describe a generic formulation for the evolution of emittances and lattice functions under arbitrary, possibly non-Hamiltonian, linear equations of motion. The average effect of stochastic processes, which would include ionization interactions and synchrotron radiation, is also included. I first compute the evolution of the covariance matrix, then the evolution of emittances and lattice functions from that. I examine the particular case of a cylindrically symmetric system, which is of particular interest for ionization cooling.

- Authors:

- Brookhaven National Lab. (BNL), Upton, NY (United States). Collider-Accelerator Dept.

- Publication Date:

- Research Org.:
- Brookhaven National Laboratory (BNL)

- Sponsoring Org.:
- USDOE Office of Science (SC), Nuclear Physics (NP) (SC-26)

- OSTI Identifier:
- 1188272

- Report Number(s):
- BNL-107127-2015-CP

R&D Project: KBCH139; KB0202011

- DOE Contract Number:
- DE-SC00112704

- Resource Type:
- Conference

- Resource Relation:
- Conference: 6th International Particle Accelerator Conference (IPAC’15); Richmond, VA; 20150503 through 20150508

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS

### Citation Formats

```
Berg, J. S.
```*A generic formulation for emittance and lattice function evolution for non-Hamiltonian systems with stochastic effects*. United States: N. p., 2015.
Web.

```
Berg, J. S.
```*A generic formulation for emittance and lattice function evolution for non-Hamiltonian systems with stochastic effects*. United States.

```
Berg, J. S. Sun .
"A generic formulation for emittance and lattice function evolution for non-Hamiltonian systems with stochastic effects". United States. https://www.osti.gov/servlets/purl/1188272.
```

```
@article{osti_1188272,
```

title = {A generic formulation for emittance and lattice function evolution for non-Hamiltonian systems with stochastic effects},

author = {Berg, J. S.},

abstractNote = {I describe a generic formulation for the evolution of emittances and lattice functions under arbitrary, possibly non-Hamiltonian, linear equations of motion. The average effect of stochastic processes, which would include ionization interactions and synchrotron radiation, is also included. I first compute the evolution of the covariance matrix, then the evolution of emittances and lattice functions from that. I examine the particular case of a cylindrically symmetric system, which is of particular interest for ionization cooling.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2015},

month = {5}

}

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