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| MOA1MP02 |
Geometry of Electromagnetism and its Implications in Field and Wave Analysis
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electromagnetic-fields, background |
42 |
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- L. Kettunen, A. Tarhasaari
TUT, Tampere
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Electromagnetism has a strong geometrical structure which, however, is hidden when the theory is examined in terms of classical vector analysis. Consequently a more powerful framework of algebraic topology and differential geometry is needed to view the subject. Recently, the geometric view has become rather popular among the community of computational electromagnetism, but still it has been asked, whether the more generic view truly enables one to develop new tools applicable to pragmatic field and wave analysis which could not be discovered otherwise. In other words, is the investment needed to study the new subject justified by the advantages brought by the more accurate viewpoint? Such a question is, evidently, not trivial to answer. Not because the larger framework did not have clear advantages, but rather for it takes a considerable effort to understand the difference between the "old" and "new" approach. Second, the advantages tend to be rather generic in the sense, that the geometric viewpoint tends to be more useful in building a software system to solve electromagnetic boundary value problems instead of in finding some handy techniques to solve certain specific problems. This paper makes an attempt to highlight some keypoints of the geometric nature of electromagnetism and to explain which way the geometric viewpoint is known to be useful in numerical analysis of electromagnetic field and wave problems. We start from the basics of electromagnetism and end up with more specific questions related to computing.
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| TUPPP29 |
Charge Conservation for Split-Operator Methods in Beam Dynamics Simulations
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simulation, electron, space-charge, electromagnetic-fields |
140 |
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- T. Lau, E. Gjonaj, T. Weiland
TEMF, Darmstadt
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Funding: DFG (1239/22-3) and DESY Hamburg
For devices in which the bunch dimensions are much smaller than the dimensions of the structure the numerical field solution is typically hampered by spurious oscillations. The reason for this oscillations is the large numerical dispersion error of conventional schemes along the beam axis. Recently, several numerical schemes have been proposed which apply operator splitting to optimize and under certain circumstances eliminate the dispersion error in the direction of the bunch motion. However, in comparison to the standard Yee scheme the methods based on operator splitting do not conserve the standard discrete Gauss law. This contribution is dedicated to the construction of conserved discrete Gauss laws and conservative current interpolation for some of the split operator methods. Finally, the application of the methods in a PIC simulations is shown.
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| THMPMP02 |
Adaptive 2-D Vlasov Simulation of Particle Beams
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simulation, heavy-ion, emittance, lattice |
310 |
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- E. Sonnendrucker, M. Gutnic, O. Hoenen, G. Latu, M. Mehrenberger, E. Violard
IRMA, Strasbourg
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In order to address the noise problems occuring in Particle-In-Cell (PIC) simulations of intense particle beams, we have been investigating numerical methods based on the solution of the Vlasov equation on a grid of phase-space. However, especially for high intensity beam simulations in periodic or alternating gradient focusing fields, where particles are localized in phase space, adaptive strategies are required to get computationally efficient codes based on this method. To this aim, we have been developing fully adaptive techniques based on interpolating wavelets where the computational grid is changed at each time step according to the variations of the distribution function of the particles. Up to now we only had an adaptive axisymmetric code. In this talk, we are going to present a new adaptive code solving the paraxial Vlasov equation on the full 4D transverse phase space, which can handle real two-dimensional problems like alternating gradient focusing. In order to develop this code efficiently, we introduce a hierarchical sparse data structure, which enabled us not only to reduce considerably the computation time but also the required memory. All computations and diagnostics are performed on the sparse data structure so that the complexity becomes proportional to the number of points needed to describe the particle distribution function.
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