An improved model of the fringing fields of a quadrupole mass filter

The fringing field region of a quadrupole mass filter is modelled using an iterative finite difference technique to solve Laplace's equation for the electrostatic potential. The results are used to formulate an expression f(z) such that the electrostatic potential of the fringing field, F(x, y, z, t) may be written in the form F(x, y, z, t) = f(z) φ(x, y, t), where φ(x, y, t) is the hyperbolic field of the quadrupole. The function f(z) is expressed in the form f(z) = 1 - exp {- az - bz²}), where a and b are constants and z is in units of r_O, where 2r_O is the spacing of the quadrupole rods. The effect of the distance from the quandrupole rods to the end plate of the quadrupole mass filter, d on f(z) is investigated and the results presented show that for d < 0.125 r_O the function f(z) does not alter significantly.