MULTIPOLE: General Thin Multipole

label:   MULTIPOLE,LRAD=real,TILT=real,
         KNL:={..,..,..}, KSL:={..,..,..};

• LRAD: A fictitious length, which was originally just used to compute synchrotron radiation effects.
  A non-zero LRAD in conjunction with the OPTION thin_foc set to a true logical value takes into account of the weak focussing of bending magnets.
• TILT: The roll angle about the longitudinal axis (default: 0 rad). A positive angle represents a clockwise rotation of the multipole element.

  Please note that contrary to MAD8 one has to specify the desired TILT angle, otherwise it is taken as 0 rad. We believe that the MAD8 concept of having individual TILT values for each component and on top with default values led to considerable confusion and allowed for excessive and unphysical freedom. Instead, in MAD-X the KNL/KSL components can be considered as the normal or skew multipole components of the magnet on the bench, while the TILT attribute can be considered as an tilt alignment error in the machine.

• KNL: The normal multipole coefficients from order zero to the maximum; the parameters are positional, therefore zeros must be filled in for components that do not exist. Example of a thin-lens sextupole:

  ms:multipole, knl:={0, 0, k2l};
  

• KSL: The skew multipole coefficients from order zero to the maximum; the parameters are positional, therefore zeros must be filled in for components that do not exist. Example of a thin-lens skew octupole:

  ms:multipole, ksl:={0, 0, 0, k3sl};
  

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 dipole with zero length and deflection angle K0L, being the first component of KNL above.