Abstract
Beam focusing is understood as the result of non-linear motion of a set of particles. As a result of this motion, we have the beam spot on the target. The set has a volume (the phase volume, or emittance). For a given brightness, the phase volume is proportional to the beam current and vice versa. The beam has an envelope surface. All particles of the beam are located inside of this surface, inside of this beam envelope. For the same phase volume (or beam current) the shape of the beam envelope can be different. We say the beam envelope is optimal if the spot size on the target has a minimum value for a given emittance. The essential feature of our optimization is the matrix approach for non-linear beam motion. In this approach we obtain and use analytical expressions for the matrizant (or transfer matrix) and for the envelope matrix. This matrix technique is known as the Matrizant method.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
K.L. Brown, R. Belbeoch, P. Bounin, Rev. Sci. Instr. 35 481 (1964)
A.D. Dymnikov, G.M.Osetinskij, Fiz. Elem. Chastits At. Yadra 20 694 (1989); Sov. J. Part Nucl. 20 293Â (1989)
A. D. Dymnikov, R. Hellborg, Nucl. Instr. Meth. A 330 323 (1993)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Dymnikov, A., Glass, G. (2012). Using a Matrix Approach in Nonlinear Beam Dynamics for Optimizing Beam Spot Size. In: GarcÃa Gómez-Tejedor, G., Fuss, M. (eds) Radiation Damage in Biomolecular Systems. Biological and Medical Physics, Biomedical Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-2564-5_29
Download citation
DOI: https://doi.org/10.1007/978-94-007-2564-5_29
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-2563-8
Online ISBN: 978-94-007-2564-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)