# Three dimensional analysis of longitudinal plasma oscillations in a thermal relativistic electron beam: Application to an initial value problem

## Abstract

In this paper, we study the initial value problem of longitudinal plasma oscillations in a relativistic electron beam. Our analysis is based on the formalism developed in Marinelli et al.[Phys. Plasmas 18, 103105 (2011)]. We study the evolution of an arbitrary six-dimensional phase-space perturbation under the effect of longitudinal space-charge forces, with the inclusion of three-dimensional effects due to the finite size of the beam, transverse betatron motion, and longitudinal thermal motion induced by both energy-spread and transverse emittance. We expand the phase-space perturbation in a series of eigenmodes of a Schroedinger-like equation, corresponding to a set of propagating space-charge waves. We develop a general formalism, which we use to find explicit expressions for the evolution of an initial perturbation coupled to the fundamental plasma eigenmode. This work has important applications in the theory of space-charge instabilities in high brightness electron beams and control of shot-noise in seeded free-electron lasers. We discuss the application of the present theory to a specific experimental scenario corresponding to a shot-noise suppression scheme at optical wavelengths.

- Authors:

- Particle Beam Physics Laboratory, Department of Physics and Astronomy, University of California Los Angeles, Los Angeles, California 90095 (United States)
- (Italy)
- SLAC National Accelerator Laboratory, Menlo Park, California 94025 (United States)

- Publication Date:

- OSTI Identifier:
- 22072487

- Resource Type:
- Journal Article

- Journal Name:
- Physics of Plasmas

- Additional Journal Information:
- Journal Volume: 19; Journal Issue: 6; Other Information: (c) 2012 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1070-664X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; BEAM EMITTANCE; BETATRONS; DISTURBANCES; ELECTRON BEAMS; FREE ELECTRON LASERS; MATHEMATICAL EVOLUTION; PHASE SPACE; PLASMA WAVES; RELATIVISTIC RANGE; SCHROEDINGER EQUATION; SPACE CHARGE; THREE-DIMENSIONAL CALCULATIONS; WAVELENGTHS

### Citation Formats

```
Marinelli, Agostino, Universita degli Studi di Roma La Sapienza, Via Antonio Scarpa 14, Rome 00161, Hemsing, Erik, and Rosenzweig, James B.
```*Three dimensional analysis of longitudinal plasma oscillations in a thermal relativistic electron beam: Application to an initial value problem*. United States: N. p., 2012.
Web. doi:10.1063/1.4714639.

```
Marinelli, Agostino, Universita degli Studi di Roma La Sapienza, Via Antonio Scarpa 14, Rome 00161, Hemsing, Erik, & Rosenzweig, James B.
```*Three dimensional analysis of longitudinal plasma oscillations in a thermal relativistic electron beam: Application to an initial value problem*. United States. doi:10.1063/1.4714639.

```
Marinelli, Agostino, Universita degli Studi di Roma La Sapienza, Via Antonio Scarpa 14, Rome 00161, Hemsing, Erik, and Rosenzweig, James B. Fri .
"Three dimensional analysis of longitudinal plasma oscillations in a thermal relativistic electron beam: Application to an initial value problem". United States. doi:10.1063/1.4714639.
```

```
@article{osti_22072487,
```

title = {Three dimensional analysis of longitudinal plasma oscillations in a thermal relativistic electron beam: Application to an initial value problem},

author = {Marinelli, Agostino and Universita degli Studi di Roma La Sapienza, Via Antonio Scarpa 14, Rome 00161 and Hemsing, Erik and Rosenzweig, James B.},

abstractNote = {In this paper, we study the initial value problem of longitudinal plasma oscillations in a relativistic electron beam. Our analysis is based on the formalism developed in Marinelli et al.[Phys. Plasmas 18, 103105 (2011)]. We study the evolution of an arbitrary six-dimensional phase-space perturbation under the effect of longitudinal space-charge forces, with the inclusion of three-dimensional effects due to the finite size of the beam, transverse betatron motion, and longitudinal thermal motion induced by both energy-spread and transverse emittance. We expand the phase-space perturbation in a series of eigenmodes of a Schroedinger-like equation, corresponding to a set of propagating space-charge waves. We develop a general formalism, which we use to find explicit expressions for the evolution of an initial perturbation coupled to the fundamental plasma eigenmode. This work has important applications in the theory of space-charge instabilities in high brightness electron beams and control of shot-noise in seeded free-electron lasers. We discuss the application of the present theory to a specific experimental scenario corresponding to a shot-noise suppression scheme at optical wavelengths.},

doi = {10.1063/1.4714639},

journal = {Physics of Plasmas},

issn = {1070-664X},

number = 6,

volume = 19,

place = {United States},

year = {2012},

month = {6}

}