EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Octupole

label: OCTUPOLE,L=real,K3=real,K3S=real,TILT=real;

• L: The octupole length (default: 0 m).
• K3: The normal octupole coefficient

  K₃ = 1/(B rho) (ð³B_y/ðx³).

  (default: 0 m**(-4)).

• K3S: The skew octupole coefficient

  K_3S = 1/(2 B rho) (ð³B_x/ðx³ - ð³B_y/ðy³).

  where (x,y) is now a coordinate system rotated by -22.5^o around s with respect to the normal one. (default: 0 m**(-4)). A positive skew octupole strength implies defocussing (!) of positively charged particles in the (x,s) plane rotated by 22.5^o around s (particles in this plane have x > 0, y > 0).

• TILT: The roll angle about the longitudinal axis (default: 0 rad, i.e. a normal octupole). A positive angle represents a clockwise rotation. A TILT=pi/8 turns a positive normal octupole into a negative skew octupole.

  Please note that contrary to MAD8 one has to specify the desired TILT angle, otherwise it is taken as 0 rad. This was needed to avoid the confusion in MAD8 about the actual meaning of the TILT attribute for various elements.

Note also that K₃/K_3s can be considered as the normal or skew quadrupole components of the magnet on the bench, while the TILT attribute can be considered as an tilt alignment error in the machine. In fact, a positive K₃ with a tilt=0 is equivalent to a positive K_3s with positive tilt=+pi/8.

Example:

O3: OCTUPOLE,L=0.3,K3=0.543;