Skip to main content
Menu
Navigation
Research
Arrow
Research Areas
Accelerator Systems
Advanced Computing
Advanced Manufacturing
Artificial Intelligence
Autonomous Discovery
Biology
Chemistry
Critical Materials
Electric Grid
Energy Storage
Fusion
Infrastructure Resilience
Materials Science and Engineering
Microelectronics
Mobility and Transportation
Nanoscience
Nuclear
Particle and Nuclear Physics
Quantum
Water
X-ray Science
More Research Areas >
Research Resources
Argonne Researchers
National User Facilities
Research Facilities
Research Highlights
Scientific Publications
Advancing U.S. Energy Leadership
Lab Divisions
Arrow
Research Directorates and Divisions
Advanced Energy Technologies
AET
Arrow
Applied Materials
AMD
Energy Systems and Infrastructure Assessment
ESIA
Transportation and Power Systems
TAPS
Computing, Environment and Life Sciences
CELS
Arrow
Biosciences
BIO
Computational Science
CPS
Data Science and Learning
DSL
Environmental Science
EVS
Mathematics and Computer Science
MCS
Nuclear Technologies and National Security
NTNS
Arrow
Chemical and Fuel Cycle Technologies
CFCT
Decision and Infrastructure Sciences
DIS
Experimental Operations and Facilities
EOF
Nuclear Science and Engineering
NSE
Strategic Security Sciences
SSS
Photon Sciences
PSC
Arrow
APS Accelerator Systems
ASD
APS Engineering Support
AES
X-Ray Science
XSD
Physical Sciences and Engineering
PSE
Arrow
Chemical Sciences and Engineering
CSE
High Energy Physics
HEP
Materials Science
MSD
Nanoscience and Technology
NST
Physics
PHY
Partner With Us
Arrow
Partner With Us
Available Technologies
Collaborative Partnerships
Contracts and Agreements
Discovery to Impact
Economic Impact
Procurement
More About Partnerships >
National User Facilities
Become a User
Advanced Photon Source
APS
Argonne Leadership Computing Facility
ALCF
Argonne Tandem Linac Accelerator System
ATLAS
Atmospheric Radiation Measurement User Facility
ARM
Center for Nanoscale Materials
CNM
Intermediate Voltage Electron Microscope
IVEM
More About Facilities >
Connect
Arrow
Engage with Us
Educational Programs
OutLoud Lecture Series
Take a Tour of Argonne
Newsletters and Bulletins
Social Media
Facebook
Instagram
LinkedIn
Threads
X
YouTube
All Argonne Social Media >
Careers
News
Events
Staff Directory
About
Argonne National Laboratory Homepage
Search
Search
Search
Search Context
Argonne National Laboratory
Argonne Researchers
Collaborative Research
National User Facilities
Research Facilities
Research Organizations
Scientific Publications
Publication
Formulae for tune shift and beta beat due to perturbations in circular accelerators.
Authors
Wang, Chun-xi