On the horizontal shape of an electron bunch

Technical Report · Fri Aug 01 00:00:00 EDT 1975

OSTI ID:6955656

Chao, A W

Effects upon longitudianl bunch shape due to linear and non-linear potentials can be calculated by finding the stationary solution to the Fokker-Planck equation for the particle distribution function. Under certain conditions, this method can be used to find the transverse bunch shape; i.e., whenever the stationary distribution function can be written as exp (..sigma.. ..sigma.. a/sub ij/X/sub i/X/sub j/ with X/sub i/ the particle coordinates (x, /dot x/, y, /dot y/) and a/sub ij/some constants. As an illustration of this technique in one dimension, the well-known horizontal bunch shape due to quantum excitation is recalculated in this note. 4 refs.

• Research Organization: Stanford Linear Accelerator Center, Menlo Park, CA (USA)
• DOE Contract Number: AC03-76SF00515
• OSTI ID: 6955656
• Report Number(s): SLAC-PEP-NOTE-129; ON: DE88014677
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200 -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
430300* -- Particle Accelerators-- Auxiliaries & Components
657002 -- Theoretical & Mathematical Physics-- Classical & Quantum Mechanics
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BEAM BENDING MAGNETS
BEAM BUNCHING
BEAM DYNAMICS
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
ELECTRICAL EQUIPMENT
ELECTROMAGNETS
EQUATIONS
EQUATIONS OF MOTION
EQUIPMENT
FOKKER-PLANCK EQUATION
FUNCTIONS
HAMILTONIANS
MAGNETS
MATHEMATICAL OPERATORS
PARTIAL DIFFERENTIAL EQUATIONS
PEP STORAGE RINGS
QUANTUM OPERATORS
STORAGE RINGS