# A Thin Lens Model for Charged-Particle RF Accelerating Gaps

## Abstract

Presented is a thin-lens model for an RF accelerating gap that considers general axial fields without energy dependence or other a priori assumptions. Both the cosine and sine transit time factors (i.e., Fourier transforms) are required plus two additional functions; the Hilbert transforms the transit-time factors. The combination yields a complex-valued Hamiltonian rotating in the complex plane with synchronous phase. Using Hamiltonians the phase and energy gains are computed independently in the pre-gap and post-gap regions then aligned using the asymptotic values of wave number. Derivations of these results are outlined, examples are shown, and simulations with the model are presented.

- Authors:

- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Publication Date:

- Research Org.:
- Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1408581

- Report Number(s):
- ORNL/TM-2017/395

- DOE Contract Number:
- AC05-00OR22725

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Allen, Christopher K.
```*A Thin Lens Model for Charged-Particle RF Accelerating Gaps*. United States: N. p., 2017.
Web. doi:10.2172/1408581.

```
Allen, Christopher K.
```*A Thin Lens Model for Charged-Particle RF Accelerating Gaps*. United States. doi:10.2172/1408581.

```
Allen, Christopher K. Sat .
"A Thin Lens Model for Charged-Particle RF Accelerating Gaps". United States.
doi:10.2172/1408581. https://www.osti.gov/servlets/purl/1408581.
```

```
@article{osti_1408581,
```

title = {A Thin Lens Model for Charged-Particle RF Accelerating Gaps},

author = {Allen, Christopher K.},

abstractNote = {Presented is a thin-lens model for an RF accelerating gap that considers general axial fields without energy dependence or other a priori assumptions. Both the cosine and sine transit time factors (i.e., Fourier transforms) are required plus two additional functions; the Hilbert transforms the transit-time factors. The combination yields a complex-valued Hamiltonian rotating in the complex plane with synchronous phase. Using Hamiltonians the phase and energy gains are computed independently in the pre-gap and post-gap regions then aligned using the asymptotic values of wave number. Derivations of these results are outlined, examples are shown, and simulations with the model are presented.},

doi = {10.2172/1408581},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sat Jul 01 00:00:00 EDT 2017},

month = {Sat Jul 01 00:00:00 EDT 2017}

}

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