TU Darmstadt, Darmstadt
TEMF, TU Darmstadt, Darmstadt
The problem of self-consistent simulations of short relativistic particle bunches in long accelerator structures exhibits a pronounced multi-scale character. The adequate resolution of the THz space charge fields excited by short ultra-relativistic bunches requires mesh spacings in the micrometer range. On the other hand, the discretization of complete accelerator sections using such fine meshes results in a vast number of degrees of freedom. Due to the spatial concentration of the particles and the excited space charge fields, the application of time-adaptive mesh refinement is an emerging idea. We reported on the implementation of time-adaptive mesh refinement for the Finite Integration Technique (FIT)*. Based on this work, we implemented an hp-adaptive discontinuous Galerkin (DG) code. The twofold refinement mechanisms of the hp-adaptive DG method offer maximum modeling freedom. We present details of the h- and p-adaptations for the DG method on Cartesian grids. Special emphasis is put on the stability and efficiency of the adaptation techniques.
TEMF, TU Darmstadt, Darmstadt
KU Leuven, Kortrijk
Numerical simulations are frequently used in the design, optimization and commissioning phase of accelerator components. Strict requirements on the accuracy as well as the complex structure of such devices lead to challenges regarding the numerical simulations in 3D. In order to capture all relevant details of the geometry and possibly strongly localized electromagnetic effects, large numerical models are often unavoidable. The use of parallelization strategies in combination with higher-order finite-element methods offers a possibility to account for the large numerical models while maintaining moderate simulation times as well as high accuracy. Using this approach, the magnetic properties of the SIS100 magnets designated to operate within the Facility of Antiproton and Ion Research (FAIR) at the GSI Helmholtzzentrum für Schwerionenforschung GmbH (GSI) in Darmstadt, are calculated. Results for eddy-current losses under time-varying operating conditions as well as field quality considerations are reported.
KU Leuven, Kortrijk
TEMF, TU Darmstadt, Darmstadt
The modeling of eddy-current phenomena in superconductive accelerator magnets is challenging because the large differences in geometrical dimensions (skin depth vs. magnet size) and time constants (ramping time vs. relaxation time). The paper addresses modeling issues as e.g. the ferromagnetic saturation of the iron yoke, the eddy-current losses in the yoke end parts, the eddy-current losses in the beam tube and possible eddy-current losses in the windings. Heavy saturation, small skin depths and small time constants render simulations of this kind to be challenging. The simulation approach is used in combination with an optimization procedure involving both continuous and integer-valued parameters.
TEMF, TU Darmstadt, Darmstadt
The Vlasov equation describes the evolution of a particle density under the effects of electromagnetic fields. It is derived from the fact that the volume occupied by a given number of particles in the 6D phase space remains constant when only long-range interaction as for example Coulomb forces are relevant and other particle collisions can be neglected. Because this is the case for typical charged particle beams in accelerators, the Vlasov equation can be used to describe their evolution within the whole beam line. This equation is a partial differential equation in 6D and thus it is very expensive to solve it via classical methods. A more efficient approach consists in representing the particle distribution function by a discrete set of characteristic moments. For each moment a time evolution equation can be stated. These ordinary differential equations can then be evaluated efficiently by means of time integration methods if all considered forces and a proper initial condition are known. The beam dynamics simulation tool V-Code implemented at TEMF utilizes this approach. In this paper the numerical model, main features and designated use cases of the V-Code will be presented.