label: QUADRUPOLE,L=real,K1=real,K1S=real,TILT=real;A QUADRUPOLE has four real attributes:
K1 = 1/(B rho) (ðBy/ð x).
The default is 0 m**(-2). A positive normal quadrupole strength implies horizontal focussing of positively charged particles.
K1s = 1/(2 B rho) (ðBx/ð x - ðBy/ð y)
where (x,y) is now a coordinate system rotated by -45o 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 45o around s (particles in this plane have x = y > 0).
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 K1/K1s 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 K1 with a tilt=0 is equivalent to a positive K1s with positive tilt=+pi/4.
Example:
QF: QUADRUPOLE,L=1.5,K1=0.001;The straight reference system for a quadrupole is a cartesian coordinate system.
hansg, frs, August 28, 2003