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Proceedings Paper

Structure of singularity in hydrodynamic theory of dense electron and bipolar beams
Author(s): V. A. Syrovoy
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Paper Abstract

The singularity structure is revealed for space-charge-limited (p-regime) and temperature-limited (T-regime) emission in case of relativistic beams in external magnetic field. This structure is described by three-term formula in p-regime: linear combination of two branch points with regular functions of longitudinal coordinate as coefficients. In T-regime the formula consists two terms and one branch point. For T-regime the partial differential equations for regular functions are formulated. It is shown that for axially symmetric flows under p- and T-regime conditions (zero start velocity), Bush's theorem is invalid. The results of regularization for inner and outer tasks in the formation theory of relativistic quasiaxially symmetric three-dimensional beams are given.

Paper Details

Date Published: 31 May 2006
PDF: 6 pages
Proc. SPIE 6278, Seventh Seminar on Problems of Theoretical and Applied Electron and Ion Optics, 627801 (31 May 2006); doi: 10.1117/12.693183
Show Author Affiliations
V. A. Syrovoy, All-Russian Electrotechnical Institute (Russia)


Published in SPIE Proceedings Vol. 6278:
Seventh Seminar on Problems of Theoretical and Applied Electron and Ion Optics
Anatoly M. Filachev, Editor(s)

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