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An unnoticed property of the cylindrical relativistic Brillouin flow
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13.It is assumed that the slow wave structure of a magnetron at the anode has no effect on the particle orbit and on the Brillouin flow, and the inner radius of the vane tip is taken to be the anode radius (b) of the equivalent smooth bore magnetron (Fig. 1). It is these slow wave structures that allow βph < 1 in Eq. (2).
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21.The general solution to A(r) contains a term C/r in the right hand side of Eq. (5), where C is an arbitrary constant. This term does not contribute to the magnetic field by Eq. (7). We set C = 0 upon setting A(a) = 0. The arbitrariness in A is also removed upon specification of the total magnetic flux within the gap.
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