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Magnet Strength

Magnet strengths are frequently specified in terms of a series expansion. For normal multipoles and $y=0$, the expansion is [2]

\begin{displaymath}
B_y(x,0)= \sum_{n=0}^\infty \frac{B_n x^n}{n!},
\end{displaymath} (6)

where $B_0$ is the dipole, $B_1$ is the quadrupole, etc. In general,
\begin{displaymath}
B_n = \left(\frac{\partial^n B_y}{\partial x^n}\right)_{x=y=0}.
\end{displaymath} (7)

For electrons, the deflection from a thin element is
\begin{displaymath}
\theta(x,y=0) = \frac{1}{H} \int B(x,y=0) dl,
\end{displaymath} (8)

where $H = B\rho = -p/e$ is the beam rigidity and $p=m_e c \beta\gamma$ is the momentum. The geometric strengths $K_n$ are defined as
\begin{displaymath}
K_n = \frac{B_n}{H}.
\end{displaymath} (9)

By convention in elegant, a positive $K_n$ value deflects a particle at $x>0$ toward $x=0$. E.g., a positive $K_1$ value indicates a horizontally focusing quadrupole.



Robert Soliday 2014-03-21