U.S. Particle Accelerator School

Iron Dominated Electromagnet Design course

Sponsoring University:

Cornell University


Iron Dominated Electromagnet Design


Jack Tanabe, retired LBNL

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.

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. The final afternoon will be reserved for the final examination.

Course Content
The course will cover the solution of Laplace’s equation using two forms of the function of a complex variable and Poisson’s two dimensional magnet equations using a two dimensional computer code. Mathematical concepts will be used to describe the ideal magnetic fields as well as the error spectrum. 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. Hydraulic computations are reviewed for dissipating the heat generated by the electrical excitation of magnet coils. Mathematical concepts will be used to visualize the field and design pole contours which satisfy the demanding field quality specified for high performance accelerators. Conformal mapping will be extensively discussed as a tool to simplify design of high quality quadrupoles and sextupoles using principles used for dipole design. Laboratory work will consist of performing two dimensional magnet calculations using Poisson. Mechanical fabrication and assembly practices to assure high field quality are reviewed.

Reading Requirements
(to be provided by the USPAS) “Iron Dominated Electromagnets - Design, Fabrication, Assembly and Measurements”, by Jack Tanabe is presently being prepared for publication. Reading from this volume will be assigned during the class. A CD including Power Point slides intended for use during the lectures will also be available. Computers in the computer lab can be used to review these CD’s after the lectures. 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).