Structure of singularity in hydrodynamic theory of dense electron and bipolar beams

V. A. Syrovoy

doi:10.1117/12.693183

31 May 2006 Structure of singularity in hydrodynamic theory of dense electron and bipolar beams

V. A. Syrovoy

Proceedings Volume 6278, Seventh Seminar on Problems of Theoretical and Applied Electron and Ion Optics; 627801 (2006) https://doi.org/10.1117/12.693183
Event: Seventh Seminar on Problems of Theoretical and Applied Electron and Ion Optics, 2005, Moscow, Russian Federation

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.

Citation Download Citation

V. A. Syrovoy "Structure of singularity in hydrodynamic theory of dense electron and bipolar beams", Proc. SPIE 6278, Seventh Seminar on Problems of Theoretical and Applied Electron and Ion Optics, 627801 (31 May 2006); https://doi.org/10.1117/12.693183

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