U.S. Particle Accelerator School
U.S. Particle Accelerator School
Education in Beam Physics and Accelerator Technology

Vibrational Aspects of Accelerators

Sponsoring University:

Northern Illinois University

Course Name:

Vibrational Aspects of Accelerators


Michael McGee, Warren Schappert and Jeremiah Holzbauer, Fermilab

Purpose and Audience
The purpose of this course is to introduce the students to the physics and technology of vibrational analysis for different aspects of particle beam accelerators. This course is suitable for physics and engineering graduate students or students from other fields considering accelerator physics as a possible career. This course also can provide a broader background to scientists and engineers working in the field of accelerator technology.

The student must have practical or classroom knowledge of dynamics and vibration theory.  Knowledge of matrices and some familiarity with ANSYS (a finite element approach) and MATLAB simulation programs are very helpful.

It is the responsibility of the student to ensure that they meet the course prerequisites or have equivalent experience.

On completion of this course, the students are expected to understand the effects of ground motion, cultural and technical noise regarding the stability of particle accelerators and their components.  Furthermore, they will be able to apply basic engineering principles in regards to vibrational stability and deploy measurement equipment to properly characterize accelerator component response to the environment in order to design accelerator component supporting structures. 

Instructional Method
This course includes a series of lectures during the morning sessions, followed by afternoon laboratory sessions which will introduce students to computer (MATLAB) simulations and data analysis. Also, the students will be exposed to hands-on experience of ground motion and accelerator component measurement using geophones, accelerators and seismometers.  These measurements consider exercises to understand accelerator component stability for components such as radio-frequency cavities.  Some discussion involving Finite Element Analysis (FEA) approach to accelerator component structural support using ANSYS will also be included.  Problem sets will be assigned which will be expected to be completed outside of the scheduled class sessions. Two instructors will be available at all times.

Course Content
The course will include lectures on Dynamic Systems and Vibration Theory and Control for accelerators focusing on the study of mechanical support design and stability of critical accelerator beamline and storage ring elements. We will cover the process of developing a model from the equation of motion to examine energy dissipation through viscous damping in a linear system and also consider the dynamical matrix method to solve eignvalue problems.  Furthermore, we will investigate techniques of acceleration (piezo device) and motion (seismic device) measurement, DAQ systems and data analysis in the time and frequency domains.  This will involve integrated displacement and power spectra measurements. 

Reading Requirements
“Vibration Simulation Using MATLAB and ANSYS,” Chapman & Hall/CRC (2001) by M. Hatch (provided by the USPAS).  Also as a reference, “Handbook of Accelerator Physics and Engineering,” 2nd Edition, Sections 5.13 and 5.14, World Scientific Publishing Co. (2002) edited by A. W. Chao and M. Tigner (not provided by the USPAS).  Additional materials and lecture notes will be provided by the instructors.

Credit Requirements
Students will be evaluated based on performance: final exam (approximately 20% of final grade), homework assignments (approximately 50% of final grade) and computer/lab sessions (approximately 30% of final grade).

Northern Illinois University course number:
PHYS 790D - Special Topics in Physics - Beam Physics
Indiana University course number: Physics 671 "Advanced Topics in Accelerator Physics"
Michigan State University course number: PHY 963
MIT course number: 8.790 "Accelerator Physics"