  The particle motion equation in the Radio Frequency (RF) quadrupole is
derived. The motion equation shows that the general transform matrix of RF
quadrupole with length less than or equal to 0.5b*l (b is the relativistic
velocity of particles and l is wavelength of radio frequency electromagnetic
field) can describe the particle motion in arbitrary long RF quadrupole. By
iterative integration, the general transform matrix of discrete RF quadrupole
is derived from the motion equation. The transform matrix is in form of power
series of focusing parameter B. It shows that for length less than b*l, the
series up to 2nd order of B agrees well with the direct integration results for
B up to 30, while for length less than 0.5b*l, the series up to 1st order is a
good approximation of the real solution for B less than 30 already. The formula
of the transform matrix can be integrated into the linac or beam line design
code to deal with the focusing of the discrete RF quadrupole.
