### Abstract

Space charge effects can be very important for the dynamics of intense particle beams, as they repeatedly pass through nonlinear focusing elements, aiming to maximize the beam's luminosity properties in the storage rings of a high energy accelerator. In the case of hadron beams, whose charge distribution can be considered as "frozen" within a cylindrical core of small radius compared to the beam's dynamical aperture, analytical formulas have been recently derived [C. Benedetti, G. Turchetti, Phys. Lett. A 340 (2005) 461] for the contribution of space charges within first order Hamiltonian perturbation theory. These formulas involve distribution functions which, in general, do not lead to expressions that can be evaluated in closed form. In this Letter, we apply this theory to an example of a charge distribution, whose effect on the dynamics can be derived explicitly and in closed form, both in the case of 2-dimensional as well as 4-dimensional mapping models of hadron beams. We find that, even for very small values of the "perveance" (strength of the space charge effect) the long term stability of the dynamics changes considerably. In the flat beam case, the outer invariant "tori" surrounding the origin disappear, decreasing the size of the beam's dynamical aperture, while beyond a certain threshold the beam is almost entirely lost. Analogous results in mapping models of beams with 2-dimensional cross section demonstrate that in that case also, even for weak tune depressions, orbital diffusion is enhanced and many particles whose motion was bounded now escape to infinity, indicating that space charges can impose significant limitations on the beam's luminosity.

Original language | English |
---|---|

Pages (from-to) | 126-133 |

Number of pages | 8 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 358 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 9 2006 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*358*(2), 126-133. https://doi.org/10.1016/j.physleta.2006.05.011

**Space charges can significantly affect the dynamics of accelerator maps.** / Bountis, Tassos; Skokos, Charalampos.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 358, no. 2, pp. 126-133. https://doi.org/10.1016/j.physleta.2006.05.011

}

TY - JOUR

T1 - Space charges can significantly affect the dynamics of accelerator maps

AU - Bountis, Tassos

AU - Skokos, Charalampos

PY - 2006/8/9

Y1 - 2006/8/9

N2 - Space charge effects can be very important for the dynamics of intense particle beams, as they repeatedly pass through nonlinear focusing elements, aiming to maximize the beam's luminosity properties in the storage rings of a high energy accelerator. In the case of hadron beams, whose charge distribution can be considered as "frozen" within a cylindrical core of small radius compared to the beam's dynamical aperture, analytical formulas have been recently derived [C. Benedetti, G. Turchetti, Phys. Lett. A 340 (2005) 461] for the contribution of space charges within first order Hamiltonian perturbation theory. These formulas involve distribution functions which, in general, do not lead to expressions that can be evaluated in closed form. In this Letter, we apply this theory to an example of a charge distribution, whose effect on the dynamics can be derived explicitly and in closed form, both in the case of 2-dimensional as well as 4-dimensional mapping models of hadron beams. We find that, even for very small values of the "perveance" (strength of the space charge effect) the long term stability of the dynamics changes considerably. In the flat beam case, the outer invariant "tori" surrounding the origin disappear, decreasing the size of the beam's dynamical aperture, while beyond a certain threshold the beam is almost entirely lost. Analogous results in mapping models of beams with 2-dimensional cross section demonstrate that in that case also, even for weak tune depressions, orbital diffusion is enhanced and many particles whose motion was bounded now escape to infinity, indicating that space charges can impose significant limitations on the beam's luminosity.

AB - Space charge effects can be very important for the dynamics of intense particle beams, as they repeatedly pass through nonlinear focusing elements, aiming to maximize the beam's luminosity properties in the storage rings of a high energy accelerator. In the case of hadron beams, whose charge distribution can be considered as "frozen" within a cylindrical core of small radius compared to the beam's dynamical aperture, analytical formulas have been recently derived [C. Benedetti, G. Turchetti, Phys. Lett. A 340 (2005) 461] for the contribution of space charges within first order Hamiltonian perturbation theory. These formulas involve distribution functions which, in general, do not lead to expressions that can be evaluated in closed form. In this Letter, we apply this theory to an example of a charge distribution, whose effect on the dynamics can be derived explicitly and in closed form, both in the case of 2-dimensional as well as 4-dimensional mapping models of hadron beams. We find that, even for very small values of the "perveance" (strength of the space charge effect) the long term stability of the dynamics changes considerably. In the flat beam case, the outer invariant "tori" surrounding the origin disappear, decreasing the size of the beam's dynamical aperture, while beyond a certain threshold the beam is almost entirely lost. Analogous results in mapping models of beams with 2-dimensional cross section demonstrate that in that case also, even for weak tune depressions, orbital diffusion is enhanced and many particles whose motion was bounded now escape to infinity, indicating that space charges can impose significant limitations on the beam's luminosity.

UR - http://www.scopus.com/inward/record.url?scp=33746809550&partnerID=8YFLogxK

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U2 - 10.1016/j.physleta.2006.05.011

DO - 10.1016/j.physleta.2006.05.011

M3 - Article

VL - 358

SP - 126

EP - 133

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 2

ER -