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| MOA1MP03 |
A Framework for Maxwell’s Equations in Non-Inertial Frames Based on Differential Forms
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electromagnetic-fields, vacuum |
47 |
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- S. Kurz
Robert Bosch GmbH, Frankfurt
- B. Flemisch, B. Wohlmuth
IANS, Stuttgart
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In many engineering applications the interaction between the electromagnetic field and moving bodies is of great interest. It is natural to use a Lagrangian description, where the unknowns are defined on a mesh which moves and deforms together with the considered objects. What is the correct form of Maxwell’s equations and the material laws under such circumstances? The aim of the present paper is to tackle this question by using the language of differential forms. We first provide a review of the formulations of electrodynamics in terms of vector fields, as well as differential forms in the (1+3)- and four-dimensional setting. In order to keep both Maxwell’s and the constitutive equations as simple as possible, we set up two reference frames. In the natural material frame, the (1+3)-Maxwell’s equations have their simple form, whereas in the co-moving inertial frame, the material laws are canonical. In contrast to existing literature these frames are both retained to benefit from their individual advantages. It remains to construct transformation laws connecting the considered frames. To achieve this, we use a (1+3)-decomposition in terms of general projection operators which do primarily not depend on an underlying metric or on the choice of a spatial coordinate system [1]. The desired transformation laws are established by comparing the different decompositions of an arbitrary p-form with respect to the considered frames. We provide an interpretation in terms of vector fields, and consider the low frequency limit, which is the most relevant case for an implementation into numerical codes. For the description of low frequency electromagnetism, all rigid frames are equivalent. This goes beyond the standard principle of Galilean relativity, where only inertial frames are regarded as equivalent. The proper treatment in the general case is demonstrated by means of an example in rotating coordinates, where the classical paradox by Schiff [2] is resolved.
[1] F. Hehl and Y. Obukhov, Foundations of Classical Electrodynamics. Boston: Birkhäuser, 2003.
[2] L. Schiff, "A question in general relativity," Proc. Nat. Acad. Sci. USA, vol. 25, 1939.
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| TUPPP23 |
Numerical Minimization of Longitudinal Emittance in Linac Structures
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emittance, controls, linac, target |
124 |
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- S. Lange, M. Clemens, L. O. Fichte
Helmut-Schmidt-University, Hamburg
- M. Dohlus, T. Limberg
DESY, Hamburg
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Relativistic electron bunches in linear colliders are characterized by 6D phase spaces. In most linear accelerators, the longitudinal phase space distribution does not interact significantly with the transverse distributions. This assumption allows the use of a 2D design model of the longitudinal phase space. The design of linear colliders is typically based on manipulations in the longitudinal phase space. The two dimensional single bunch tracking code LiTrack (Bane/Emma 2005) allows to simulate bunch-compression up to 3rd order and RF acceleration with wake fields. This code is implemented in Matlab with a graphic user interface front end. In order to improve the ability to simulate a two-stage bunch compression system, which consist of a RF accelerating section, a higher harmonic RF section and a dipole magnet chicane, an extension to the LiTrack code is proposed. An analytical model of this two-stage bunch compression system is defined using the energy and the momentum derivatives up to 3rd order of the system. As a consequence, the energy of the system can now be specified directly, for the simulation criteria the peak current and the symmetry of the charge distributions and be specified via parameters. This extended model allows the definition of bunches with an arbitrary energy, phase space correlation, longitudinal emittance, charge distribution and resulting peak current. A minimal longitudinal emittance is generally considered as a quality factor of the bunch, where the bunch energy, peak current and a symmetric charge distribution are represented as constraints. Under these conditions, a constrained optimization problem is defined to minimize the longitudinal emittance with a predetermined bunch-energy and peak-current with respect to the charge distribution symmetry. For the solution of this problem, LiTrack is extended with a optimization solver based on a SQP formulation to find an optimal bunch corresponding to the newly introduced constraints.
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| TUAPMP03 |
Recent Progress on the MaryLie/IMPACT Beam Dynamics Code
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space-charge, lattice, optics, simulation |
157 |
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- R. D. Ryne, E. W. Bethel, I. V. Pogorelov, J. Qiang, J. M. Shalf, C. Siegerist, M. Venturini
LBNL, Berkeley, California
- D. T. Abell
Tech-X, Boulder, Colorado
- A. Adelmann
PSI, Villigen
- J. F. Amundson, P. Spentzouris
Fermilab, Batavia, Illinois
- A. Dragt
University of Maryland, College Park, Maryland
- C. Mottershead, N. Neri, P. L. Walstrom
LANL, Los Alamos, New Mexico
- V. Samulyak
BNL, Upton, Long Island, New York
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Funding: Supported in part by the US DOE, Office of Science, SciDAC program; Office of High Energy Physics; Office of Advanced Scientific Computing Research
MaryLie/IMPACT (ML/I) is a 3D parallel Particle-In-Cell code that combines the nonlinear optics capabilities of MaryLie 5.0 with the parallel particle-in-cell space-charge capability of IMPACT. In addition to combining the capabilities of these codes, ML/I has a number of powerful features, including a choice of Poisson solvers, a fifth-order rf cavity model, multiple reference particles for rf cavities, a library of soft-edge magnet models, representation of magnet systems in terms of coil stacks with possibly overlapping fields, and wakefield effects. The code allows for map production, map analysis, particle tracking, and 3D envelope tracking, all within a single, coherent user environment. ML/I has a front end that can read both MaryLie input and MAD lattice descriptions. The code can model beams with or without acceleration, and with or without space charge. Developed under a US DOE Scientific Discovery through Advanced Computing (SciDAC) project, ML/I is well suited to large-scale modeling, simulations having been performed with up to 100M macroparticles. ML/I uses the H5Part* library for parallel I/O. The code inherits the powerful fitting/optimizing capabilities of MaryLie, augmented for the new features of ML/I. The combination of soft-edge magnet models, high-order capability, and fitting/optimization, makes it possible to simultaneously remove third-order aberrations while minimizing fifth-order, in systems with overlapping, realistic magnetic fields. Several applications will be presented, including aberration correction in a magnetic lens for radiography, linac and beamline simulations of an e-cooling system for RHIC, design of a matching section across the transition of a superconducting linac, and space-charge tracking in the damping rings of the International Linear Collider.
*ICAP 2006 paper ID 1222, A. Adelmann et al., "H5Part: A Portable High Performance Parallel Data Interface for Electromagnetics Simulations"
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