M: Thin Multipole / Axially symmetric multipole (radial focusing)

Parameter Description Argument Order Argument Name Units Default Value
1 m 0.0
Integrated Strength 2 s_m kG/cm**(m-1) 0.0
Tilt 3 Tilt[deg] degrees 0.0

The letter "M" (or "m") denotes a thin (zero length) multipole. The first parameter is the multipole harmonic order (m=1 - quadrupole, m=2 - sextupole, ...). The second parameter is the integrated multipole strength in kG/cm**(m-1). The third parameter is the roll angle (tilt) of the multipole in degrees in the local beam frame. The rotation axis is tangential to the beam trajectory. For tilt=0 the coordinate dependence of the horizontal and vertical magnetic kicks is given by the following equations: $$ \begin{eqnarray} \Delta\theta_x & = & - \frac{B_mL}{B\rho} \frac{r^m}{m!} \cos mq \\ \Delta\theta_y & = & \frac{B_mL}{B\rho} \frac{r^m}{m!} \sin mq \end{eqnarray} $$ where $r$ and $q$ are polar coordinates with $x = r \cos q$ and $y = r \sin q$ . First order focusing $(m=1)$ is taken into account in all calculations; in particular, it affects the linear Twiss functions. Second order focusing (m=2) is taken into account for chromaticity calculations. Multipoles of higher orders affect particle tracking only (see Tools|Trajectory, Tools|Type trajectory). If the multipole parameter is set to a negative value, the element is interpreted as axially symmetric; in that case the kicks experienced by the particle case are as follows $$ \begin{eqnarray} \Delta\theta_x & = & - \frac{B_m L}{B\rho} \frac{r^m}{m!} \\ \Delta\theta_y & = & \frac{B_m L}{B\rho} \frac{r^m}{m!} \end{eqnarray} $$ This may be used to describe nonlinear focusing in axially symmetric elements such as a lithium lens or a solenoid. Note that the tilt parameter does not have any effect if the element describes radial focusing. Linear axially symmetric multipoles $(m=-1)$ are taken into account in all calculations. Higher order multipoles $(m < -1)$ are taken into account only for particle tracking (see Tools|Trajectory, Tools|Type trajectory).

Example: 
m21		Order:m=3  Bm*L[kG/cm**(m-1)]=0.01  Tilt[deg]=0
m          	Order:m=10   Bm*L[kG/cm**(m-1)]=0.01   Tilt[deg]=45
maxi         	Order:m=-4   Bm*L[kG/cm**(m-1)]=0.21