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Register a new userE-cloud Map Formalism: an Analytical Expression for Quadratic Coefficient
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The evolution of the electron density during electron cloud formation can be reproduced using a bunch-to-bunch iterative map formalism. The reliability of this formalism has been proved for RHIC [1] and LHC [2]. The linear coefficient has a good theoretical framework, while quadratic coefficient has been proved only by fitting the results of compute-intensive electron cloud simulations. In this communication we derive an analytic expression for the quadratic map coefficient. The comparison of the theoretical estimate with the simulations results shows a good agreement for a wide range of bunch population.
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The Electron Cloud is an undesirable physical phenomenon which might produce single and multi-bunch instability, tune shift, increase of pressure ultimately limiting the performance of particle accelerators. We report our results on the analytical study of the electron dynamics.
Electron cloud effects have recognized as as one of the most serious bottleneck for reaching design performances in presently running and proposed future storage rings. The analysis of these effects is usually performed with very time consuming simulation codes. An alternative analytic approach, based on a cubic map model for the bunch-to-bunch evolution of the electron cloud density, could be useful to determine regions in parameters space compatible with safe machine operations. In this communication we derive a simple approximate formula relating the linear coefficient in the electron cloud density map to the parameters relevant for the electron cloud evolution with particular reference to the LHC dipoles.
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Wide field-of-view (FOV) optics are widely used in various imaging, display, and sensing applications. While conventional wide FOV optics rely on cascading multiple elements to suppress coma and other aberrations, it has recently been demonstrated that diffraction-limited, near-180 degree FOV operation can be achieved with a single-piece flat fisheye lens designed via iterative numerical optimization [Nano Lett. 20, 7429(2020)]. Here we derive an analytical solution to enable computationally efficient design of flat wide FOV lenses based on metasurfaces or diffractive optical elements (DOEs). Leveraging this analytical approach, we further quantified trade-offs between optical performance and design parameters in wide FOV metalenses.
The Electron Cloud, an undesirable physical phenomena in the accelerators, develops quickly as photons striking the vacuum chamberwall knock out electrons that are then accelerated by the beam, gain energy, and strike the chamber again, producing more electrons. The interaction between the electron cloud and a beam leads to the electron cloud effects such as single- and multi-bunch instability, tune shift, increase of pressure and particularly can limit the ability of recently build or planned accelerators to reach their design parameters. We report a principal results about the analytical study to understanding a such dynamics of electrons.
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