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\ttmdump{\make_cover_page{TRI-BN-10-xx} {R. Baartman} {Magnetic BPM feedthrus} {These feedthrus are magnetic and can result in steering of the electron beam. The allowed proximity to the electron beam was determined.} {Feb., 2011}}
%%ttm:\title{TRI-BN-10-01: Bunch Dynamics ...}
%%ttm:\author{R. Baartman}
%%ttm:\date{July,2010}
%%ttm:\section*{Abstract} The differential equations...
\section{Measurements}
Marco Marchetto made measurements near the feedthrus. For distances far from the feedthru, it will act as an isolated dipole with a field falloff $\propto 1/r^3$, $r$ being the distance to the centre of the feedthru. I fitted his farthest measurement to this to come to a dipole strength of
\[S=6.6\,\mu\mbox{T}(3.5\,\mbox{cm})^3=0.17\,\mbox{Gauss-in}^3\]
This is for a fully magnetized case.
\section{Proximity calculation}
The effect on the beam is the integral of the field along an axis. If $r_c$ is the distance to the beam axis,
\[\int Bds=\frac{2S}{r_c^2}\]
At a distance of 1 inch, $\int Bds=0.34$\,G-in. This will have the ffect of kicking the beam 0.4\,mrad; enough effect that some steerers may have to be ``tweaked''. At a distance of 2 inches, the kick would be 0.1\,mrad. This will have no noticeable effect on the beam, as the beam rms divergence is roughly 5\,mrad.
So 1\,inch distance may cause slight inconvenience, but 2\,inch distance would be fine.
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