| Paper |
Title |
Other Keywords |
Page |
| MOM1MP03 |
Resonance Driving Term Experiments: An Overview
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resonance, betatron, sextupole, lattice |
22 |
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- R. Bartolini
Diamond, Oxfordshire
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The frequency analysis of the betatron motion is a valuable tool for the characterization of the linear and non-linear motion of a particle beam in a storage ring. In recent years, several experiments have shown that resonance driving terms can be successfully measured from the spectral decomposition of the turn-by-turn BPM data. The information on the driving terms can be used to correct unwanted resonances, to localize strong non-linear perturbations and provides a valuable tool for the construction of the non-linear model of the real accelerator. In this paper we introduce briefly the theory, the computational tools and we give a review of the resonance driving terms experiments performed on different circular machines.
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Slides
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| MOM2IS01 |
A Highly Accurate 3-D Magnetic Field Solver
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ion |
28 |
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- S. L. Manikonda, M. Berz, K. Makino
MSU, East Lansing, Michigan
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We present a new high precision parallel three dimensional magnetic field solver. This tool decomposes the problem of solving the Poisson equation into the problem of solving the Laplace equation and finding the magnetic field due to an arbitrary current distribution. The underlying theory to find solutions to both these problems using Differential Algebraic methods is developed, resulting in a local field expansion that can be computed to arbitrary order. Using the remainder differential algebraic approach, it is also possible to obtain fully rigorous and sharp estimates for the approximation errors. The method provides a natural multipole decomposition of the field which is required for the computation of transfer maps, and also allows obtaining very accurate finite element representations with very small numbers of cells. The method has the unique advantage of always producing purely Maxwellian fields, and naturally connects to high order DA-based map integration tools. We demonstrate the utility of this field solver for the design and analysis of novel combined function multipole with elliptic cross section that can simplify the correction of aberrations in large acceptance fragment separators for radioactive ion accelerators.
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Slides
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| WEPPP21 |
Efficient Time Integration for Beam Dynamics Simulations Based on the Moment Method
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simulation, emittance, beam-transport, space-charge |
224 |
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- W. Ackermann, T. Weiland
TEMF, Darmstadt
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Funding: This work was partially funded by EUROFEL (RIDS-011935) and DESY Hamburg.
The moment method model has been proven to be a valuable tool for numerical simulations of a charged particle beam transport both in accelerator design studies and in optimization of the operating parameters for an already existing beam line. On the basis of the Vlasov equation which describes a collision-less kinetic approach, the time evolution of such integral quantities like the mean or rms dimensions, the mean or rms kinetic momenta, and the total energy or energy spread for a bunched beam can be described by a set of first order non-autonomous ordinary differential equations. Application of a proper time integrator to such a system of ordinary differential equations enables then to determine the time evolution of all involved ensemble parameter under consistent initial conditions. From the vast amount of available time integration methods different versions have to be implemented and evaluated to select a proper algorithm. The computational efficiency in terms of effort and accuracy serves as a selection criterion. Among possible candidates of suited time integrators for the given set of moment equations are the explicit Runge-Kutta methods, the implicit theta methods, and the linear implicit Rosenbrock methods. Various algorithms have been implemented and tested under real-world conditions. In the paper the evaluation process is documented.
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| WESEPP02 |
COSY INFINITY
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229 |
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- M. Berz, K. Makino
MSU, East Lansing, Michigan
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Funding: DOE, NSF
We will demonstrate the code COSY INFINITY Version 9. Besides the known feature of computations of high order Taylor transfer maps based on differential algebras, the latest version has many new features, many of them using algorithms only possible with differential algebras and Taylor models. Aside from conventional beam dynamics design and optimization tools, we will focus on new features, including rigorous global optimization, computation of remainder bounds for high order maps, minimal symplectic tracking in the EXPO framework, and the ability to integrate high-order maps through user-specified fields. Specific applications will focus on maps of absorbers, wedges, and novel non-cylindrical multipole elements.
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