Abstract
The electron cloud effect has been studied by means of detailed simulation codes that typically track the particles' evolution under the influence of the corresponding electromagnetic forces and fields. In this paper we show that, for the RHIC case, the electron cloud can be treated from an abstract point of view as a bunch to bunch evolution using simple maps. Secondly, we show how this treatment yields a useful conclusion, which is otherwise difficult to obtain: for a fixed number of bunches and total beam current in RHIC, it is possible to determine the best way to distribute the bunch pattern around the ring to minimize the electron cloud formation. This application is an example of how maps become a useful tool for exploring the electron cloud evolution in parameter space.
Highlights
II), and secondly we look for a suitable function to follow this evolution
Do existing computer simulations confirm that the electron cloud evolution can be represented by maps? For this purpose, we test this hypothesis using two codes: CSEC and ECLOUD [12], focusing the studies on the RHIC case
After experimental observations in RHIC during Run 3 [17,18,19], it is found that the use of gaps along the bunch train can be useful against the buildup of the electron cloud
Summary
Electric fields present in many vacuum systems may accelerate electrons (produced by field emission, photoemission, residual gas ionization, etc.) towards the wall chamber surface. We consider that, for given beam pipe characteristics (SEY, chamber dimensions, etc.), the electron density after bunch m passes by (referred to as m1) is a function only of the interaction between the bunch and the electron density before bunch m passed by (referred to as m) This is expressed by means of an iterative formalism. The coefficients a and b summarize the EC dependence on the physical parameters This parabolic map is sometimes called the ‘‘logistic’’ difference equation [8], since by introducing the dimensionless variable X b=a, and for a > 0; b < 0, Eq (1) can be expressed as.
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