dorsal/arxiv
View SchemaSpace Charges Can Significantly Affect the Dynamics of Accelerator Maps
| Authors | T. Bountis, Ch. Skokos |
|---|---|
| Categories | |
| ArXiv ID | physics/0605084 |
| URL | https://arxiv.org/abs/physics/0605084 |
| DOI | 10.1016/j.physleta.2006.05.011 |
| Journal | Phys.Lett.A358:126-133,2006 |
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 \cite{BenTurc} 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 paper, 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.
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"abstract": "Space charge effects can be very important for the dynamics of intense\nparticle beams, as they repeatedly pass through nonlinear focusing elements,\naiming to maximize the beam\u0027s luminosity properties in the storage rings of a\nhigh energy accelerator. In the case of hadron beams, whose charge distribution\ncan be considered as \"frozen\" within a cylindrical core of small radius\ncompared to the beam\u0027s dynamical aperture, analytical formulas have been\nrecently derived \\cite{BenTurc} for the contribution of space charges within\nfirst order Hamiltonian perturbation theory. These formulas involve\ndistribution functions which, in general, do not lead to expressions that can\nbe evaluated in closed form. In this paper, we apply this theory to an example\nof a charge distribution, whose effect on the dynamics can be derived\nexplicitly and in closed form, both in the case of 2--dimensional as well as\n4--dimensional mapping models of hadron beams. We find that, even for very\nsmall values of the \"perveance\" (strength of the space charge effect) the long\nterm stability of the dynamics changes considerably. In the flat beam case, the\nouter invariant \"tori\" surrounding the origin disappear, decreasing the size of\nthe beam\u0027s dynamical aperture, while beyond a certain threshold the beam is\nalmost entirely lost. Analogous results in mapping models of beams with\n2-dimensional cross section demonstrate that in that case also, even for weak\ntune depressions, orbital diffusion is enhanced and many particles whose motion\nwas bounded now escape to infinity, indicating that space charges can impose\nsignificant limitations on the beam\u0027s luminosity.",
"arxiv_id": "physics/0605084",
"authors": [
"T. Bountis",
"Ch. Skokos"
],
"categories": [
"physics.acc-ph",
"nlin.CD"
],
"doi": "10.1016/j.physleta.2006.05.011",
"journal_ref": "Phys.Lett.A358:126-133,2006",
"title": "Space Charges Can Significantly Affect the Dynamics of Accelerator Maps",
"url": "https://arxiv.org/abs/physics/0605084"
},
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