# Curvature-Induced Bunch Self-Interaction for an Energy-Chirped Bunch in Magnetic Bends

## Abstract

Within the realm of classical electrodynamics, the curvature-induced bunch collective interaction in magnetic bends can be studied using effective forces in the canonical formulation of the coherent synchrotron radiation (CSR) effect. As an application of this canonical formulation, in this paper, for an electron distribution moving ultrarelativistically in a bending system, the dynamics of the particles in the distribution is derived from the Hamiltonian of the particles in terms of the bunch internal coordinates. The consequent Vlasov equation manifests explicitly how the phase-space distribution is perturbed by the effective CSR forces. In particular, we study the impact of an initial linear energy chirp of the bunch on the behavior of the effective longitudinal CSR force, which arises due to the modification of the retardation relation as a result of the energy-chirping- induced longitudinal-horizontal correlation of the bunch distribution (bunch tilt) in dispersive regions. Our study demonstrates clearly the time delay (or retardation) of the behavior of the effective longitudinal CSR force on a bunch in responding to the change of the bunch length in a magnetic bend. Our result also shows that the effective longitudinal CSR force for a bunch under full compression can have sensitive dependence on the transversemore »

- Authors:

- Publication Date:

- Research Org.:
- Thomas Jefferson National Accelerator Facility, Newport News, VA

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 922266

- Report Number(s):
- JLAB-ACP-07-773; DOE/OR/23177-0285

TRN: US0801114

- DOE Contract Number:
- AC05-06OR23177

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Phys. Rev. ST Accel. Beams; Journal Volume: 11

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 43 PARTICLE ACCELERATORS; BENDING; BOLTZMANN-VLASOV EQUATION; COMPRESSION; DISTRIBUTION; ELECTRODYNAMICS; ELECTRONS; HAMILTONIANS; MODIFICATIONS; PHASE SPACE; SYNCHROTRON RADIATION; TEST PARTICLES; TIME DELAY

### Citation Formats

```
Li, Rui.
```*Curvature-Induced Bunch Self-Interaction for an Energy-Chirped Bunch in Magnetic Bends*. United States: N. p., 2008.
Web. doi:10.1103/PhysRevSTAB.11.024401.

```
Li, Rui.
```*Curvature-Induced Bunch Self-Interaction for an Energy-Chirped Bunch in Magnetic Bends*. United States. doi:10.1103/PhysRevSTAB.11.024401.

```
Li, Rui. Fri .
"Curvature-Induced Bunch Self-Interaction for an Energy-Chirped Bunch in Magnetic Bends". United States. doi:10.1103/PhysRevSTAB.11.024401. https://www.osti.gov/servlets/purl/922266.
```

```
@article{osti_922266,
```

title = {Curvature-Induced Bunch Self-Interaction for an Energy-Chirped Bunch in Magnetic Bends},

author = {Li, Rui},

abstractNote = {Within the realm of classical electrodynamics, the curvature-induced bunch collective interaction in magnetic bends can be studied using effective forces in the canonical formulation of the coherent synchrotron radiation (CSR) effect. As an application of this canonical formulation, in this paper, for an electron distribution moving ultrarelativistically in a bending system, the dynamics of the particles in the distribution is derived from the Hamiltonian of the particles in terms of the bunch internal coordinates. The consequent Vlasov equation manifests explicitly how the phase-space distribution is perturbed by the effective CSR forces. In particular, we study the impact of an initial linear energy chirp of the bunch on the behavior of the effective longitudinal CSR force, which arises due to the modification of the retardation relation as a result of the energy-chirping- induced longitudinal-horizontal correlation of the bunch distribution (bunch tilt) in dispersive regions. Our study demonstrates clearly the time delay (or retardation) of the behavior of the effective longitudinal CSR force on a bunch in responding to the change of the bunch length in a magnetic bend. Our result also shows that the effective longitudinal CSR force for a bunch under full compression can have sensitive dependence on the transverse position of the test particle in the bunch for certain parameter regimes.},

doi = {10.1103/PhysRevSTAB.11.024401},

journal = {Phys. Rev. ST Accel. Beams},

number = ,

volume = 11,

place = {United States},

year = {Fri Feb 01 00:00:00 EST 2008},

month = {Fri Feb 01 00:00:00 EST 2008}

}