# A LEAKY WAVE APPROACH TO CERENKOV AND SMITH-PURCELL RADIATION

## Abstract

>The effect of the interaction between a linearized modulated electron beam of finite thickness and the electromagnetic field is investigated for Cherenkov and SmithPurcell radiation under self-consistent conditions. The eigenwavenumbers of the space-charge waves are calculated for a sheet beam in free space and for a similar beam passing between two plane-parallel plates. This calculation leads to a denumerably infinite set of eigenpropagation wavenumbers for both the fast and slow waves. These wavenumbers are real for both cases. The beam in free space calculation can be made the starting point of a linear perturbation procedure for the Cherenkov effect. The perturbation consists of the introduction of two semi-infinite dielectric regions; through the gap of these the sheet beam of finite thickness passes, The eigenwavenumbers must be complex for this case, if Cherenkov radiation is present. It is shown that the fast and slow waves behave differently and that only the fast space-charge waves contribute to radiation. The fast space-charge waves are leaky waves; thus this radiation is a leaky-wave phenomenon. The slow waves do not leak, but are attenuated transversely. A similar calculation has been carried out for the case of a small-signal modulated sheet beam passing between two plane-parallel,more »

- Authors:

- Publication Date:

- Research Org.:
- Originating Research Org. not identified

- OSTI Identifier:
- 4743147

- NSA Number:
- NSA-17-017081

- Resource Type:
- Thesis/Dissertation

- Resource Relation:
- Other Information: Thesis. Orig. Receipt Date: 31-DEC-63

- Country of Publication:
- Country unknown/Code not available

- Language:
- English

- Subject:
- PHYSICS; ABSORPTION; CHERENKOV RADIATION; DIELECTRICS; DIFFERENTIAL EQUATIONS; ELECTRODES; ELECTROMAGNETIC FIELDS; ELECTRON BEAMS; FIELD THEORY; FREQUENCY; INTERACTIONS; MATHEMATICS; MODULATION; NUMERICALS; PERTURBATION THEORY; PLATES; QUANTUM MECHANICS; SHEETS; THICKNESS

### Citation Formats

```
Palocz, I.
```*A LEAKY WAVE APPROACH TO CERENKOV AND SMITH-PURCELL RADIATION*. Country unknown/Code not available: N. p., 1962.
Web.

```
Palocz, I.
```*A LEAKY WAVE APPROACH TO CERENKOV AND SMITH-PURCELL RADIATION*. Country unknown/Code not available.

```
Palocz, I. Mon .
"A LEAKY WAVE APPROACH TO CERENKOV AND SMITH-PURCELL RADIATION". Country unknown/Code not available.
```

```
@article{osti_4743147,
```

title = {A LEAKY WAVE APPROACH TO CERENKOV AND SMITH-PURCELL RADIATION},

author = {Palocz, I},

abstractNote = {>The effect of the interaction between a linearized modulated electron beam of finite thickness and the electromagnetic field is investigated for Cherenkov and SmithPurcell radiation under self-consistent conditions. The eigenwavenumbers of the space-charge waves are calculated for a sheet beam in free space and for a similar beam passing between two plane-parallel plates. This calculation leads to a denumerably infinite set of eigenpropagation wavenumbers for both the fast and slow waves. These wavenumbers are real for both cases. The beam in free space calculation can be made the starting point of a linear perturbation procedure for the Cherenkov effect. The perturbation consists of the introduction of two semi-infinite dielectric regions; through the gap of these the sheet beam of finite thickness passes, The eigenwavenumbers must be complex for this case, if Cherenkov radiation is present. It is shown that the fast and slow waves behave differently and that only the fast space-charge waves contribute to radiation. The fast space-charge waves are leaky waves; thus this radiation is a leaky-wave phenomenon. The slow waves do not leak, but are attenuated transversely. A similar calculation has been carried out for the case of a small-signal modulated sheet beam passing between two plane-parallel, zero- thickness, perfectly conducting transmission gratings, i.e., an example of the Smith-Purcell effect. In contrast to the previous case, space harmonics arise due to the periodicity of the grating. Only these space harmonics may radiate if the gratings are located in vacuum For this case the far-field behavior of the gratings must first be evaluated by solving the integral equation for one grating in free space under multimode conditions. Then, knowing the eigenwavenumbers for the beam between two conducting plates, the boundary perturbations (the replacement of the plates by gratings) can be taken into account by a linear perturbation calculation. The propagation wavenumbers are also complex for the perturbed case, and only the fast waves contribute to radiation. The possibility of backward waves is also shown. The analytical results, which are presented in graphical form, take into account the finite thickness and the space-charge characteristics of the beam. Oissertation Abst., Vol 23, No. 7)},

doi = {},

url = {https://www.osti.gov/biblio/4743147},
journal = {},

number = ,

volume = ,

place = {Country unknown/Code not available},

year = {1962},

month = {1}

}