# Calculation of wakefields in 2D rectangular structures

## Abstract

We consider the calculation of electromagnetic fields generated by an electron bunch passing through a vacuum chamber structure that, in general, consists of an entry pipe, followed by some kind of transition or cavity, and ending in an exit pipe. We limit our study to structures having rectangular cross section, where the height can vary as function of longitudinal coordinate but the width and side walls remain fixed. For such structures, we derive a Fourier representation of the wake potentials through one-dimensional functions. A new numerical approach for calculating the wakes in such structures is proposed and implemented in the computer code echo(2d). The computation resource requirements for this approach are moderate and comparable to those for finding the wakes in 2D rotationally symmetric structures. Finally, we present numerical examples obtained with the new numerical code.

- Authors:

- Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany)
- 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:
- 1224110

- Alternate Identifier(s):
- OSTI ID: 1213171

- Report Number(s):
- SLAC-PUB-16353

Journal ID: ISSN 1098-4402; PRABFM; arXiv:1508.00066

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Published Article

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

- Additional Journal Information:
- Journal Volume: 18; Journal Issue: 10; Journal ID: ISSN 1098-4402

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCPHY; ECHO(2D)

### Citation Formats

```
Zagorodnov, I., Bane, K. L. F., and Stupakov, G. Calculation of wakefields in 2D rectangular structures. United States: N. p., 2015.
Web. doi:10.1103/PhysRevSTAB.18.104401.
```

```
Zagorodnov, I., Bane, K. L. F., & Stupakov, G. Calculation of wakefields in 2D rectangular structures. United States. doi:10.1103/PhysRevSTAB.18.104401.
```

```
Zagorodnov, I., Bane, K. L. F., and Stupakov, G. Mon .
"Calculation of wakefields in 2D rectangular structures". United States. doi:10.1103/PhysRevSTAB.18.104401.
```

```
@article{osti_1224110,
```

title = {Calculation of wakefields in 2D rectangular structures},

author = {Zagorodnov, I. and Bane, K. L. F. and Stupakov, G.},

abstractNote = {We consider the calculation of electromagnetic fields generated by an electron bunch passing through a vacuum chamber structure that, in general, consists of an entry pipe, followed by some kind of transition or cavity, and ending in an exit pipe. We limit our study to structures having rectangular cross section, where the height can vary as function of longitudinal coordinate but the width and side walls remain fixed. For such structures, we derive a Fourier representation of the wake potentials through one-dimensional functions. A new numerical approach for calculating the wakes in such structures is proposed and implemented in the computer code echo(2d). The computation resource requirements for this approach are moderate and comparable to those for finding the wakes in 2D rotationally symmetric structures. Finally, we present numerical examples obtained with the new numerical code.},

doi = {10.1103/PhysRevSTAB.18.104401},

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

number = 10,

volume = 18,

place = {United States},

year = {2015},

month = {10}

}

DOI: 10.1103/PhysRevSTAB.18.104401

*Citation information provided by*

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Works referenced in this record:

##
Impedance calculations of nonaxisymmetric transitions using the optical approximation

journal, July 2007

- Bane, K. L. F.; Stupakov, G.; Zagorodnov, I.
- Physical Review Special Topics - Accelerators and Beams, Vol. 10, Issue 7

##
Long-time numerical computation of electromagnetic fields in the vicinity of a relativistic source

journal, November 2003

- Zagorodnov, Igor; Schuhmann, Rolf; Weiland, Thomas
- Journal of Computational Physics, Vol. 191, Issue 2

##
Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media

journal, May 1966

- Kane Yee,
- IEEE Transactions on Antennas and Propagation, Vol. 14, Issue 3

##
Coupling impedance of beam pipes of general cross section

journal, January 1993

- Gluckstern, Robert L.; van Zeijts, Johannes; Zotter, Bruno
- Physical Review E, Vol. 47, Issue 1

##
Electromagnetic wake fields and beam stability in slab-symmetric dielectric structures

journal, December 1997

- Tremaine, A.; Rosenzweig, J.; Schoessow, P.
- Physical Review E, Vol. 56, Issue 6

##
Indirect methods for wake potential integration

journal, October 2006

- Zagorodnov, Igor
- Physical Review Special Topics - Accelerators and Beams, Vol. 9, Issue 10

##
Three-dimensional electromagnetic relativistic particle-in-cell code VLPL (Virtual Laser Plasma Lab)

journal, April 1999

- Pukhov, A.
- Journal of Plasma Physics, Vol. 61, Issue 3

##
Maxwell's Equations for Structures with Symmetries

journal, July 2002

- Weiland, Thomas; Zagorodnov, Igor
- Journal of Computational Physics, Vol. 180, Issue 1

##
TE/TM field solver for particle beam simulations without numerical Cherenkov radiation

journal, April 2005

- Zagorodnov, Igor; Weiland, Thomas
- Physical Review Special Topics - Accelerators and Beams, Vol. 8, Issue 4

##
Some Considerations Concerning the Transverse Deflection of Charged Particles in Radio‐Frequency Fields

journal, November 1956

- Panofsky, W. K. H.; Wenzel, W. A.
- Review of Scientific Instruments, Vol. 27, Issue 11

##
Hybrid TE-TM scheme for time domain numerical calculations of wakefields in structures with walls of finite conductivity

journal, May 2012

- Tsakanian, Andranik; Dohlus, Martin; Zagorodnov, Igor
- Physical Review Special Topics - Accelerators and Beams, Vol. 15, Issue 5

##
A uniformly stable conformal FDTD-method in Cartesian grids

journal, January 2003

- Zagorodnov, I. A.; Schuhmann, R.; Weiland, T.
- International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 16, Issue 2

##
Corrugated pipe as a beam dechirper

journal, October 2012

- Bane, K. L. F.; Stupakov, G.
- Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 690

##
TBCI and URMEL - New Computer Codes for Wake Field and Cavity Mode Calculations

journal, August 1983

- Weiland, T.
- IEEE Transactions on Nuclear Science, Vol. 30, Issue 4

##
Experimental Demonstration of Energy-Chirp Control in Relativistic Electron Bunches Using a Corrugated Pipe

journal, January 2014

- Emma, P.; Venturini, M.; Bane, K. L. F.
- Physical Review Letters, Vol. 112, Issue 3

Works referencing / citing this record:

##
Accelerator beam dynamics at the European X-ray Free Electron Laser

journal, February 2019

- Zagorodnov, Igor; Dohlus, Martin; Tomin, Sergey
- Physical Review Accelerators and Beams, Vol. 22, Issue 2