Longitudinal Space Charge Effects-Phase Boundary Equations and Potential Kernels

Technical Report · Fri Jun 26 04:00:00 EDT 1959

DOI:https://doi.org/10.2172/4260839· OSTI ID:4260839

Nielsen, C. E. ^[1]; Sessler, A. M. ^[1]

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1. Midwestern Universities Research Association (MURA), Madison, WI (United States)

An assembly of particles subject only to external fields and long-range interactions may be represented as an incompressible fluid in phase space; it follows that the behavior in the special case described by uniform phase density out to sharp boundaries is completely determined by the boundary motion. For azimuthal particle motion this report gives a derivation of two coupled non-linear first order partial differential equations describing the motion of the phase boundaries when they are single valued functions of coordinate and time. It gives also a derivation of a potential function adequate for representation of the collective-field term in these equations even when charge density varies appreciably in a distance of the order of beam diameter, and it proposes computer programs for their solution. In the appendix certain implications of this potential kernel for the solutions in the small amplitude limit of MURA-441 are discussed; a numerical error in MURA-441 is noted.

• Research Organization: Midwestern Universities Research Association (MURA), Madison, WI (United States)
• Sponsoring Organization: US Atomic Energy Commission (AEC); National Science Foundation (NSF)
• NSA Number: NSA-13-018191
• OSTI ID: 4260839
• Report Number(s): MURA--480
• Country of Publication: United States
• Language: English

Related Subjects

43 PARTICLE ACCELERATORS
CHARGED PARTICLES
COMPUTERS
DENSITY
DIFFERENTIAL EQUATIONS
ELECTRIC CHARGES
ELECTRIC POTENTIAL
ELECTROMAGNETIC FIELDS
EQUATIONS
FLUIDS
INTERACTIONS
MOTION
PROGRAMMING