EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH

Quadrupole

label: QUADRUPOLE,L=real,K1=real,K1S=real,TILT=real, THICK=logical;

• L: The quadrupole length (default: 0 m).
• K1: The normal quadrupole coefficient

  K₁ = 1/(B rho) (ðB_y/ð x).

  The default is 0 m**(-2). A positive normal quadrupole strength implies horizontal focussing of positively charged particles.

• K1S: The skew quadrupole coefficient

  K_1s = 1/(2 B rho) (ðB_x/ð x - ðB_y/ð y)

  where (x,y) is now a coordinate system rotated by -45^o around s with respect to the normal one. The default is 0 m**(-2). A positive skew quadrupole strength implies defocussing (!) of positively charged particles in the (x,s) plane rotated by 45^o around s (particles in this plane have x = y > 0).

• TILT: The roll angle about the longitudinal axis (default: 0 rad, i.e. a normal quadrupole). A positive angle represents a clockwise rotation. A TILT=pi/4 turns a positive normal quadrupole into a negative skew quadrupole.

  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.

• THICK: If this logical flag is set to true the quadrupole will be tracked through as a thick-element, instead of being converted into thin-lenses.

Note also that K₁ and K_1s can be considered as the normal and 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 K₁ with a tilt=0 is equivalent to a positive K_1s with positive tilt=+pi/4.

Example:

QF: QUADRUPOLE,L=1.5,K1=0.001,THICK=1;

Note: Additional attributes can be given to quadrupoles that are useful for PTC and defined in the relevant section

The straight reference system for a quadrupole is a cartesian coordinate system.