EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Sextupole

label: SEXTUPOLE,L=real,K2=real,K2S=real,TILT=real;

• L: The sextupole length (default: 0 m).
• K2: The normal sextupole coefficient

  K₂ = 1/(B rho) (ð²B_y/ð x²).

  (default: 0 m**(-3)).

• K2S: The skew sextupole coefficient

  K_2S = 1/(2 B rho) (ð²B_x/ð x² - ð²B_y/ð y²).

  where (x,y) is now a coordinate system rotated by -30^o around s with respect to the normal one. (default: 0 m**(-3)). A positive skew sextupole strength implies defocussing (!) of positively charged particles in the (x,s) plane rotated by 30^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 sextupole). A positive angle represents a clockwise rotation. A TILT=pi/6 turns a positive normal sextupole into a negative skew sextupole.

  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 K₂/K_2s can be considered as the normal or skew sextupole 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 K₂ with a tilt=0 is equivalent to a positive K_2s with positive tilt=+pi/6.

Example:

S: SEXTUPOLE,L=0.4,K2=0.00134;