# Storage Rings for Precision Physics Applications

*\(~~~~~\) — Measuring \(g\)-2 of the Muon*

*David Rubin*^{1}, Diktys Stratakis^{2}, and Mike Syphers^{3}

^{1}, Diktys Stratakis

^{2}, and Mike Syphers

^{3}

*last update: 31 Jan 2019*

**Winter 2019 USPAS Session**

*U.S. Particle Accelerator School*

*January 21 - February 1, 2019, in Knoxville, TN.*

**Team:**

- David Rubin,
*Cornell University* - Diktys Stratakis,
*Fermi National Accelerator Laboratory* - Michael Syphers,
*Northern Illinois University and Fermilab*

**Purpose and Audience**

Precision magnetic storage rings are being used in experiments to measure properties of fundamental particles, such as the measurement of the anomalous magnetic moment of the muon and searches for non-zero electric dipole moments. The most recent iteration of this particular measurement technique is taking place at Fermilab today using a 1.45 T magnet with integrated field fluctuations less that 1 ppm. This course will use the Muon g-2 experimental apparatus and beam delivery system at Fermilab as its model to introduce and discuss the basic accelerator and beam physics issues inherent in such systems and the interplay of beam physics and high energy physics in the measurement of fundamental particle properties.

**Prerequisites**

*Credit-seeking students:* Students should have completed intermediate level courses in mechanics and electromagnetism and be proficient in basic relativistic mechanics. Knowledge of elementary aspects of accelerator physics such as transfer matrices and lattice functions is useful, however any required elementary accelerator physics will be presented or reviewed during the course.

*Audit-only students:* Courses in College Physics and first year Calculus.

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

**Objectives**

The analysis of the experimental data taken to determine the anomalous magnetic moment of the muon relies very heavily on detailed knowledge and understanding of the properties of the incoming particle beam and of the resulting beam motion once in the ring, providing a unique interplay between high energy physics and beam dynamics. Upon completion of this course, the students are expected to understand the basic workings of accelerators and their components, basic principles and definitions of beam dynamics, and will be able to interpret and analyze beam measurements in terms of fundamental beam properties and dynamical motion.

**Instructional Method**

This course primarily includes a series of lectures with additional sessions dedicated to computer calculations/simulations to provide insights into basic accelerator physics as related to the production, transport and storage of charged particles including particle decay and spin manipulation. Problem sets will be assigned which will be expected to be completed outside of scheduled class sessions.

The class will make use of the USPAS Computer Lab on Wednesday and Thursday mornings.

**Course Content**

Topics to be presented in the course include

Introduction and Review of Basics – the magnetic dipole moment, basic accelerator physics, hardware overview

Muon Beam Production and Transport – targeting and beam delivery, instrumentation, phase space measurements, final rate estimates, beam polarization

Storage Ring Particle Dynamics – injection issues, equilibrium distributions, loss rates

Commissioning, beam and ring measurements, sources of systematic errors

Future Prospects – polarization measurements, wedge cooling, muon EDM search, future EDM storage rings

**Reading Requirements**

*An Introduction to the Physics of Particle Accelerators*, 2nd Edition, World Scientific (2008) by M. Conte and W. W. MacKay; ISBN-13: 978-9812779601. This texbook will be provided to the student by the USPAS. The flow of the course will not follow the text directly, but material and sections of the textbook will be relevant to the course, in particular Chapters 2-4, 10, 13 and 14. (Conte and MacKay 2008).Muon (g-2) Technical Design Report, J. Grange, et al., https://arxiv.org/abs/1501.06858 (2015).

*Additional suggested reading:*

*An Introduction to the Physics of High Energy Accelerators*, Wiley Publishers (1993) by D.A. Edwards and M.J. Syphers; ISBN-13: 978-0471551638. (If the student’s institution has an agreement with Wiley Publishers, it may be possible to download this text from http://onlinelibrary.wiley.com/book/10.1002/9783527617272 ). (Edwards and Syphers 1993).For a refresher on introductory accelerator and beam physics, see the notes from the USPAS 2018 Fundamentals course.

**Grading Policy**

Students will be evaluated on homework assignments (75%) and a group project (25%).

**Homework Problems**

Problems will be drawn from the list provided in **Homework Problems**. Each daily assignment will contain 3 to 5 problems to be solved. Homework is due before 9:00 a.m each due date.