General Multipoles

A MULTIPOLE is thin lens of arbitrary order, including a dipole:

label:MULTIPOLE,TYPE=string,APERTURE=real-vector,L=real,
      KNORMAL=real-vector,KSKEW=real-vector;

L

The multipole length (default: 0 m). A thin multipole is defined by setting the length to zero.

KN

A real vector, containing the normal multipole coefficients. A component is positive, if $B_y$ is positive on the positive $x$-axis.

KS

A real vector, containing the skew multipole coefficients. A component is negative, if $B_x$ is positive on the positive $x$-axis.

The multipole coefficients are defined as $K_{n} = \frac{1}{B \rho}\frac{\partial^n B_y}{\partial x^n}$. (default: $0 \mathrm{m}^{-n}$). The order $n$ is unlimited, but all components up to the maximum must be given, even if zero. The number of poles of each component is ($2 n + 2$). The most important error components of fully symmetric quadrupoles are: KNORMAL[5], the 12-pole, and KNORMAL[9], the twenty-pole. Superposition of many multipole components is permitted. The reference system for a multipole is a Cartesian coordinate system.

Example:

M27:MULTIPOLE,L=1,KNORMAL[3]=0.0001,KSKEW[2]=0.0001;

A multipole with no dipole component has no effect on the reference orbit, i.e. the reference system at its exit is the same as at its entrance. If it includes a dipole component, it has the same effect on the reference orbit as a SBEND with the same length and deflection angle KNORMAL[0]*L.