2born (2born) wrote,

Еще об электрических изображениях

Real and image fields of an ultra relativistic bunch: https://arxiv.org/abs/1810.12109

We derive analytical expressions for external fields of a charged relativistic bunch with a circular and an elliptical cross section. The particle density in the bunch is assumed to be uniform as well as non-uniform. At distances far apart from the bunch, the field reduces to the relativistic modified Coulomb form for a point-like charge and at small distances the expressions reproduce the external fields of a continuous beam. In an ultra relativistic limit the longitudinal components of the internal and external electric fields of the bunch are strongly suppressed by the Lorentz factor. If the bunch is surrounded by conducting surfaces, the bunch self-fields are modified. Image fields generated by a bunch between two parallel conducting plates are studied in detail. Exact summation of electric and magnetic image fields allows the infinite series to be represented in terms of elementary trigonometric functions. The new expressions for modified fields are applied to study image forces acting on the bunch constituents and the bunch as a whole and calculated in the framework of the linear theory the coherent and incoherent tune shifts for an arbitrary bunch displacement from the midplane. Moreover, the developed method allows to generalize the Laslett image coefficients ε1, ε2, ξ1, ξ2 to the case of an arbitrary bunch offset between parallel conducting plates and magnet poles, and reveal relationships between these coefficients.
Tags: наука, разгребая arXiv'ы

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