High-frequency behavior of the longitudinal impedance for a cavity of general shape

Journal Article · Mon May 01 04:00:00 EDT 1989 · Phys. Rev. D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.39.2773· OSTI ID:6080950

Gluckstern, R L

An ultrarelativistic beam bunch traveling along the axis of an azimuthally symmetric cavity of general shape connected to a beam pipe generates wake fields. An integral equation is derived for the longitudinal electric component of these wake fields at the beam-pipe radius. The kernel for this equation is approximated at high frequency for several different cavity shapes and the resulting integral equation is solved for the electric field at the beam-pipe radius. The longitudinal coupling impedance is obtained and shown to vary inversely as the square root of the frequency, in agreement with recent results obtained by others using different approximation techniques. The results are also shown to depend only on the axial extent of the cavity at the beam-pipe radius, but otherwise are independent of cavity shape for four different cavity geometries. In addition, the results are shown to be in agreement with the analytic properties of the coupling impedance as a function of complex frequency required by causality for an ultrarelativistic beam.

• Research Organization: Physics Department, University of Maryland, College Park, Maryland 20742
• OSTI ID: 6080950
• Journal Information: Phys. Rev. D; (United States), Journal Name: Phys. Rev. D; (United States) Vol. 39:9; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
430200* -- Particle Accelerators-- Beam Dynamics
Field Calculations
& Ion Optics
ACCELERATORS
BEAM BUNCHING
BEAM DYNAMICS
CAVITIES
COUPLINGS
DIFFRACTION MODELS
ELECTRIC FIELDS
ELECTRIC IMPEDANCE
ENERGY RANGE
EQUATIONS
IMPEDANCE
INTEGRAL EQUATIONS
MATHEMATICAL MODELS
PARTICLE MODELS
RELATIVISTIC RANGE
WAKEFIELD ACCELERATORS