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# On the propagation of electrodynamic waves along a wire by A. Sommerfeld

## Abstract

This is a translation of a classic paper of Arnold Sommerfeld published in 1899. It reflected the first rigorous theory of waves traveling on a resistive wire of finite radius. General solutions inside and outside the wire are written in terms of Bessel functions, and the boundary condition at the surface is well approximated by a transcendental equation. A detailed analysis of the equation demonstrates that surface waves are supported, which decay exponentially with the radial distance from the wire. The propagation velocity, less than c, and the longitudinal damping rate are related to the material properties of the wire. An historical overview of related work, on surface waves and open waveguides, is given by the translator.

- Authors:

- SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of New Mexico, Albuquerque, NM (United States)

- Publication Date:

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

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1547380

- Grant/Contract Number:
- AC02-76SF00515; AC03-76SF00515

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Electromagnetics

- Additional Journal Information:
- Journal Volume: 39; Journal Issue: 5; Journal ID: ISSN 0272-6343

- Publisher:
- Taylor & Francis

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Surface waves; Sommerfeld-Goubau; wire waves; open waveguide

### Citation Formats

```
Warnock, Robert. On the propagation of electrodynamic waves along a wire by A. Sommerfeld. United States: N. p., 2019.
Web. doi:10.1080/02726343.2019.1619235.
```

```
Warnock, Robert. On the propagation of electrodynamic waves along a wire by A. Sommerfeld. United States. doi:10.1080/02726343.2019.1619235.
```

```
Warnock, Robert. Wed .
"On the propagation of electrodynamic waves along a wire by A. Sommerfeld". United States. doi:10.1080/02726343.2019.1619235.
```

```
@article{osti_1547380,
```

title = {On the propagation of electrodynamic waves along a wire by A. Sommerfeld},

author = {Warnock, Robert},

abstractNote = {This is a translation of a classic paper of Arnold Sommerfeld published in 1899. It reflected the first rigorous theory of waves traveling on a resistive wire of finite radius. General solutions inside and outside the wire are written in terms of Bessel functions, and the boundary condition at the surface is well approximated by a transcendental equation. A detailed analysis of the equation demonstrates that surface waves are supported, which decay exponentially with the radial distance from the wire. The propagation velocity, less than c, and the longitudinal damping rate are related to the material properties of the wire. An historical overview of related work, on surface waves and open waveguides, is given by the translator.},

doi = {10.1080/02726343.2019.1619235},

journal = {Electromagnetics},

number = 5,

volume = 39,

place = {United States},

year = {2019},

month = {6}

}

Works referenced in this record:

##
Über elektromagnetische Drahtwellen

journal, January 1909

- Hondros, D.
- Annalen der Physik, Vol. 335, Issue 15

##
The Theory of Anomalous Diffraction Gratings and of Quasi-Stationary Waves on Metallic Surfaces (Sommerfeld’s Waves)

journal, January 1941

- Fano, U.
- Journal of the Optical Society of America, Vol. 31, Issue 3

##
Surface Waves and Their Application to Transmission Lines

journal, November 1950

- Goubau, Georg
- Journal of Applied Physics, Vol. 21, Issue 11

##
Elektromagnetische Wellen an dielektrischen Drähten

journal, January 1910

- Hondros, D.; Debye, P.
- Annalen der Physik, Vol. 337, Issue 8

##
Metal wires for terahertz wave guiding

journal, November 2004

- Wang, Kanglin; Mittleman, Daniel M.
- Nature, Vol. 432, Issue 7015

##
Über die Ausbreitung der Wellen in der drahtlosen Telegraphie

journal, January 1909

- Sommerfeld, A.
- Annalen der Physik, Vol. 333, Issue 4

##
Elektromagnetische Wellen an einem Draht mit isolierender zylindrischer Hülle

journal, January 1907

- Harms, F.
- Annalen der Physik, Vol. 328, Issue 6