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Three-dimensional end model.  

Three-dimensional end model.  

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SIS100 is the world's second fast ramped synchrotron using superconducting magnets. The foreseen high current operation requires a sound understanding of the field homogeneity next to a field parametrization which allows investigating if the existing inhomogeneity introduces transverse oscillations on the particle beam. The SIS100 dipole magnets ar...

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... The permeability of each charge of the used iron was measured and the lamination was sorted to equalize the magnetic properties of all yokes as good as possible. The distortion of the magnetic end fields at both sides of the yoke was optimized by a so-called Rogowski profile which was designed by simulations regarding a suppression of undesirable multipole terms [7]. The outer shell welding was established with a laser technique which is lowering the heat input and the tension on the yoke. ...
... During the R&D phase of the heavy ion synchrotron SIS100 these problems had to be tackled as the beam uses considerable area of the elliptic vacuum chamber. This led to the development of elliptic cylindric multipoles [1][2][3]. ...
... The appropriate multipoles were derived using local toroidal coordinates and the technique of R-separation, as these give simpler solutions, as the global toroidal ones (see e.g. [4,5]), and are easier to interpret [2,6]. The solution was then further extended to elliptic toroidal multipoles [7]. ...
... Any non-negative integer power is such a complex regular solution of Eqs. (2) or (3). The reference radius R Ref is inserted to render all the solutions dimensionless and of similar magnitude. ...
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Recent progress in particle accelerator tracking has shown that the field representation is one of the major limits of the prediction accuracy especially for machines, whose aperture is fully filled by the beam and thus higher the artefacts created by higher order modes have to be thoroughly understood. The standard tool for field presentation today are cylindrical circular multipoles due to their straight forward correspondence to the Cartesian coordinates. In this paper we extend the standard approach to other coordinate systems, show how these can be measured next to their realisation in measuring the SIS100 Magnets for the FAIR project.
Chapter
For many problems an adapted coordinate system allows reducing the number of dimensions if chosen appropriately. A familiar example is the use of the polar coordinate system, which simplifies any circular problem independent of the polar angle. Here coordinate systems are presented, which are commonly known but have not been frequently applied for describing the fields of accelerator magnets.
Chapter
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