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Register a new userA Formula of the Electron Cloud Linear Map Coefficient in a Strong Dipole
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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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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.
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.
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.
Electron cloud can lead to a fast instability in intense proton and positron beams in circular accelerators. In the Fermilab Recycler the electron cloud is confined within its combined function magnets. We show that the field of combined function magnets traps the electron cloud, present the results of analytical estimates of trapping, and compare them to numerical simulations of electron cloud formation. The electron cloud is located at the beam center and up to 1% of the particles can be trapped by the magnetic field. Since the process of electron cloud build-up is exponential, once trapped this amount of electrons significantly increases the density of the cloud on the next revolution. In a Recycler combined function dipole this multi-turn accumulation allows the electron cloud reaching final intensities orders of magnitude greater than in a pure dipole. The multi-turn build-up can be stopped by injection of a clearing bunch of $10^{10}$ p at any position in the ring.
The creation of an electron space charge in a dipole magnetic trap and the subsequent injection of positrons has been experimentally demonstrated. Positrons (5eV) were magnetically guided from their source and injected into the trapping field generated by a permanent magnet (0.6T at the poles) using a cross field E $times$ B drift, requiring tailored electrostatic and magnetic fields. The electron cloud is created by thermionic emission from a tungsten filament. The maximum space charge potential of the electron cloud reaches -42V, which is consistent with an average electron density of ($4 pm 2$) $times 10^{12}$ $text{m}^{-3}$ and a Debye length of ($2 pm 1$) $text{cm}$. We demonstrate that the presence of this space potential does not hamper efficient positron injection. Understanding the effects of the negative space charge on the injection and confinement of positrons represents an important intermediate step towards the production of a confined electron-positron pair plasma.
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