U.S. Particle Accelerator School

Iron Bound Magnets course

Sponsoring University:

Old Dominion University


Iron Bound Magnets


Jack Tanabe, ret. SLAC and Mau Lopes, Fermilab

Purpose and Audience
The course is intended for magnet engineers and scientists interested in the design, engineering, fabrication, measurement, installation and alignment of electromagnets for low and medium energy accelerators and beam transport lines. The course is suitable for both the last year undergraduates and all graduate students in physics and engineering as well as those planning careers in the field of particle accelerators or those participating in magnet design and manufacture. The material concentrates on practices resulting in high-quality magnets, especially for synchrotron light sources and collider accelerators requiring the use of high-performance magnets required to achieve beam lifetimes measured in tens of hours. The course covers the design, fabrication and assembly practices as well as reviewing the mathematical basis for the computation of two and three dimensional fields. A section of this course exploits the mathematics of magnetic fields to describe one of many means used to measure and characterize the performance of fabricated magnets.

It is the responsibility of the student to ensure that he or she meets the course prerequisites or has equivalent experience.

One objective of this course is to familiarize the student with accelerator electromagnets, the mathematical concepts used to define the physics requirements for accelerator and beam transport magnets and to characterize their performance. Fabrication and assembly techniques used to construct magnets satisfying these requirements are described. Another objective is to familiarize the magnet designer with power supply and hydraulic infrastructure constraints typical of most accelerator facilities and to provide algorithms which can be used to ensure that magnet designs will conform to these constraints. Good fabrication and assembly practices as well as means of component and assembly testing during magnet manufacture to ensure long magnet service life and personnel safety are discussed. A final objective is to introduce often overlooked areas of magnet design; fiducialization, installation, alignment and mechanical stability.

Instructional Method
Two lectures per day will be presented for a period of 4½ days. Homework will be assigned during the afternoon sessions. The completed homework will be handed in and the solutions reviewed during the following morning sessions. The graded homework will be available on the following day. Some of the homework will be taken from problem sets at the ends of the chapters in the course text. One of the afternoon sessions and up to two evening sessions will be scheduled to work in the computer lab performing two dimensional magnet calculations using Poisson.

Course Content
The course will cover all aspects of magnet design, fabrication and measurements. Solution of Laplace’s equation using two forms of the function of a complex variable and numerical solution of Poisson’s two dimensional magnet will be used to describe the ideal magnetic fields as well as the error spectrum. Means of writing files for POISSON, the two dimensional magnetic analysis program will be presented. The two dimensional concepts will be generalized to three dimensional field integrals. Stoke’s theorem will be used to develop formulae required to compute the coil excitation to generate the required field in the magnet gap as well as the excitation to drive the field through the permeable material which ultimately shapes the field.
The first part of the course will include design tools to ensure good field quality including pole width criteria to ensure uniform fields in dipoles. Magnetic measurement techniques and means for reducing the data to evaluate multipole errors will be covered with detailed specific examples from SPEAR3, the ALS, the Canadian Light Source and the Australian Light Source. Error analyses including rules to estimate errors due to pole placement and excitation will be presented by using tables. Conformal mapping will be extensively discussed as a tool to simplify design of high quality quadrupoles by extending the dipole criteria. Hydraulic computations are reviewed for dissipating the heat generated by the electrical excitation of magnet coils. Laboratory work will consist of performing two dimensional magnet calculations using Poisson.

Reading Requirements
(to be provided by the USPAS) “Iron Dominated Electromagnets - Design, Fabrication, Assembly and Measurements”, World Scientific (2005) by Jack T. Tanabe. The students should familiarize themselves with the mathematics of complex variables using both Cartesian and polar coordinate and concepts of conformal mapping.

Credit Requirements
Students will be evaluated based on performance as follows: final exam (40 % of final grade), homework assignments (40% of final grade) computer/lab sessions (20% of final grade).

IU/USPAS course number P671