# Using surface impedance for calculating wakefields in flat geometry

## Abstract

Beginning with Maxwell's equations and assuming only that the wall interaction can be approximated by a surface impedance, we derive formulas for the generalized longitudinal and transverse impedance in flat geometry, from which the wakefields can also be obtained. From the generalized impedances, by taking the proper limits, we obtain the normal longitudinal, dipole, and quad impedances in flat geometry. These equations can be applied to any surface impedance, such as the known dc, ac, and anomalous skin models of wall resistance, a model of wall roughness, or one for a pipe with small, periodic corrugations. We show that, for the particular case of dc wall resistance, the longitudinal impedance obtained here agrees with a known result in the literature, a result that was derived from a very general formula by Henke and Napoly. As an example, we apply our results to representative beam and machine parameters in the undulator region of LCLS-II and estimate the impact of the transverse wakes on the machine performance.

- Authors:

- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Publication Date:

- Research Org.:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

- OSTI Identifier:
- 1180057

- Alternate Identifier(s):
- OSTI ID: 1168986

- Report Number(s):
- SLAC-PUB-16203

Journal ID: ISSN 1098-4402; PRABFM

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review Special Topics. Accelerators and Beams

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 3; Journal ID: ISSN 1098-4402

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; free electron lasers (FELs); flat geometry; longitudinal impedance; transverse impedance; particle trajectories

### Citation Formats

```
Bane, Karl, and Stupakov, Gennady.
```*Using surface impedance for calculating wakefields in flat geometry*. United States: N. p., 2015.
Web. doi:10.1103/PhysRevSTAB.18.034401.

```
Bane, Karl, & Stupakov, Gennady.
```*Using surface impedance for calculating wakefields in flat geometry*. United States. doi:10.1103/PhysRevSTAB.18.034401.

```
Bane, Karl, and Stupakov, Gennady. Wed .
"Using surface impedance for calculating wakefields in flat geometry". United States.
doi:10.1103/PhysRevSTAB.18.034401.
```

```
@article{osti_1180057,
```

title = {Using surface impedance for calculating wakefields in flat geometry},

author = {Bane, Karl and Stupakov, Gennady},

abstractNote = {Beginning with Maxwell's equations and assuming only that the wall interaction can be approximated by a surface impedance, we derive formulas for the generalized longitudinal and transverse impedance in flat geometry, from which the wakefields can also be obtained. From the generalized impedances, by taking the proper limits, we obtain the normal longitudinal, dipole, and quad impedances in flat geometry. These equations can be applied to any surface impedance, such as the known dc, ac, and anomalous skin models of wall resistance, a model of wall roughness, or one for a pipe with small, periodic corrugations. We show that, for the particular case of dc wall resistance, the longitudinal impedance obtained here agrees with a known result in the literature, a result that was derived from a very general formula by Henke and Napoly. As an example, we apply our results to representative beam and machine parameters in the undulator region of LCLS-II and estimate the impact of the transverse wakes on the machine performance.},

doi = {10.1103/PhysRevSTAB.18.034401},

journal = {Physical Review Special Topics. Accelerators and Beams},

number = 3,

volume = 18,

place = {United States},

year = {Wed Mar 18 00:00:00 EDT 2015},

month = {Wed Mar 18 00:00:00 EDT 2015}

}

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