Differential energy loss for a particle in a square pulse of charge traveling between infinite conducting plates
In a recent paper by Papiernik et al., the problem of including the beam-induced fields in a cavity to determine the steady-state bunch shape was studied. In order to understand how the fields felt by a particle in the beam are generated, the authors have rederived these fields from a slightly different approach and have concentrated on obtaining the physical picture of the fields. In a previous note, we calculated the electromagnetic fields in a cavity produced by an ultra-relativistic point charge. The cavity was approximated by two infinite conducting plates and the particle was assumed to travel with the speed of light c. It was found that a particle q/sub 2/ following at a finite distance behind another particle q/sub 1/ will not see any fields produced by q/sub 1/ until q/sub 1/ has left the cavity, and, when doing so, has sent (accelerating) delta-function fields backwards toward the oncoming q/sub 2/. In this case, q/sub 2/ always gains energy from the fields generated by q/sub 1/, and as the distance between q/sub 1/ and q/sub 2/ decreases to zero, the energy gain goes to positive infinity. At first glance, this appears to contradict the results of Ref. 1; however, if q/sub 1/ is exactly on top of q/sub 2/, then q/sub 2/ will travel across the cavity together with the (decelerating) delta-function field of q/sub 1/. Due to this charge, q/sub 2/ loses an infinite amount of energy. In the following treatment, we attempt to clarify this confusion. 2 refs., 3 figs.
- Research Organization:
- Stanford Linear Accelerator Center, Menlo Park, CA (USA)
- DOE Contract Number:
- AC03-76SF00515
- OSTI ID:
- 6955680
- Report Number(s):
- SLAC-PEP-NOTE-119; ON: DE88014850; TRN: 88-030405
- Resource Relation:
- Other Information: Portions of this document are illegible in microfiche products
- Country of Publication:
- United States
- Language:
- English
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71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
BEAM BUNCHING
ENERGY LOSSES
POINT CHARGE
FIELD EQUATIONS
CAVITIES
ELECTRIC CONDUCTORS
ELECTROMAGNETIC FIELDS
BEAM DYNAMICS
ELECTRIC CHARGES
EQUATIONS
LOSSES
430200* - Particle Accelerators- Beam Dynamics
Field Calculations
& Ion Optics
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics