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Coupling Physics and Geometrica
Author

Bruno Autin
Organization: MathSoft Overseas
Conference

2006 Wolfram Technology Conference
Conference location

Champaign IL
Description

The geometry application Geometrica can be coupled to scientific programs to produce in an integrated way diagrams that are hard to obtain with any other method. The example is taken in the field of high-energy physics and more especially of particle accelerators. These machines are composed of a variety of elements. The magnetic elements determine the shape of the machine and the transverse contour of the particle beam. The radio-frequency cavities act on the particle energy and on the longitudinal structure of the beam. Among the characteristics of those elements are geometric parameters. The magnetic poles are parallel for a dipole, hyperbolic for a quadrupole, and cubic for a sextupole, whereas the electric field is most often axisymmetric in an RF cavity. The specification of the magnetic field and of the length of a dipole determine the angle of rotation of the beam at given particle momentum. The physics part of the program consists basically in the determination of the particle orbits and of the beam shape. The geometry part uses the basic parameters and the physics results to generate exactly the layout of an accelerator and, in first approximation, the shape of its elements. The method applied here to a special instrument, a particle accelerator, is actually very general since, in most machines, systems, or buildings, shape, and function are correlated.
Subjects

*Mathematica Technology > Application Packages > Applications from Independent Developers > Geometrica
*Mathematics > Geometry
*Science > Physics
Keywords

Geometerica, physics, particle accelerators, beam optics
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CouplingPhysics.nb (3.2 MB) - Mathematica Notebook [for Mathematica 5.2]