Algorithm for Computation of Electromagnetic Fields of An Accelerated Short Bunch Inside a Rectangular Chamber
We discuss the feasibility of an application of an implicit finite-difference approximation to calculate the fields of a relativistic bunch moving with no restriction inside a vacuum chamber. We assume that a bunch trajectory is not straight but is inside a vacuum chamber or its branch. The bunch can be deflected by the fields of bending magnets. The bunch can be short enough to produce coherent synchrotron radiation (CSR). Accelerator physicists believe that electromagnetic phenomena of charged beams are governed by Maxwell's equations together with Newton's equations for particle dynamics. To understand the behavior of the beams and radiated fields we just need to find a solution to these equations for the case, which can fully describe the real accelerator environment. So, at first we make a model, which contains all the necessary components, but at the same time can be easily 'inserts' into the equations. Sometimes, it is possible to find analytical solutions, but usually they are only work for one-dimensional cases and rarer for two-dimension cases. To find a solution in general we may transform the equations into a equivalent finite-difference form and solve them using computers. We can find a lot of finite-difference schemes, which approximate Maxwell's equations since the first one that was published in 1966. Most of them are so called explicit schemes. That means that the value of the field at the new time step is calculated only by the field values at the previous time step. Stability conditions for these schemes do not allow a time step to be greater than or equal to a space (mesh) step. This limitation brings an additional troublesome effect for short wavelengths compared a mesh step. We state that this effect works like a frequency dispersion media, which is 'hidden' in the finite-difference equation.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 992888
- Report Number(s):
- SLAC-PUB-14241; TRN: US1007916
- Journal Information:
- Conf.Proc.C100523:TUPEB028,2010, Conference: 1st International Particle Accelerator Conference: IPAC'10, 23-28 May 2010, Kyoto, Japan
- Country of Publication:
- United States
- Language:
- English
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