# Coherent synchrotron radiation by electrons moving on circular orbits

## Abstract

Here, we study coherent synchrotron radiation by electrons in the Frenet-Serret coordinate system with a constant curvature 1/ρ. Based on the Hamiltonian in the Courant-Synder theory of particle accelerators, we find in general that the transverse force is essentially the Lorentz force but with a substitution of the transverse magnetic field B _{x,y} → (1+x/ρ)B _{x,y}, where x and y are the transverse positions. The curvature term provides us a key to derive the point-charge wakefield explicitly in terms of the incomplete elliptic integrals of the first and second kind, resulting in a steady-state theory of the coherent synchrotron radiation in two-dimensional free space.

- 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

- OSTI Identifier:
- 1363971

- Alternate Identifier(s):
- OSTI ID: 1369392

- Grant/Contract Number:
- AC02-76SF00515

- Resource Type:
- Journal Article: Published Article

- Journal Name:
- Physical Review Accelerators and Beams

- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 6; Journal ID: ISSN 2469-9888

- Publisher:
- American Physical Society (APS)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

### Citation Formats

```
Cai, Yunhai.
```*Coherent synchrotron radiation by electrons moving on circular orbits*. United States: N. p., 2017.
Web. doi:10.1103/PhysRevAccelBeams.20.064402.

```
Cai, Yunhai.
```*Coherent synchrotron radiation by electrons moving on circular orbits*. United States. doi:10.1103/PhysRevAccelBeams.20.064402.

```
Cai, Yunhai. Wed .
"Coherent synchrotron radiation by electrons moving on circular orbits". United States.
doi:10.1103/PhysRevAccelBeams.20.064402.
```

```
@article{osti_1363971,
```

title = {Coherent synchrotron radiation by electrons moving on circular orbits},

author = {Cai, Yunhai},

abstractNote = {Here, we study coherent synchrotron radiation by electrons in the Frenet-Serret coordinate system with a constant curvature 1/ρ. Based on the Hamiltonian in the Courant-Synder theory of particle accelerators, we find in general that the transverse force is essentially the Lorentz force but with a substitution of the transverse magnetic field Bx,y → (1+x/ρ)Bx,y, where x and y are the transverse positions. The curvature term provides us a key to derive the point-charge wakefield explicitly in terms of the incomplete elliptic integrals of the first and second kind, resulting in a steady-state theory of the coherent synchrotron radiation in two-dimensional free space.},

doi = {10.1103/PhysRevAccelBeams.20.064402},

journal = {Physical Review Accelerators and Beams},

number = 6,

volume = 20,

place = {United States},

year = {Wed Jun 14 00:00:00 EDT 2017},

month = {Wed Jun 14 00:00:00 EDT 2017}

}

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Publisher's Version of Record at 10.1103/PhysRevAccelBeams.20.064402

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