Test3d20.dat, 20th 'test' file for CPO3D

Superseded in Oct 2012 by test3d34, which uses the option for users equations.

For information on the option for users equations, see users equations.

The ends of the cones that comprise the grounded end caps follow the equation

r^2 - 2*z^2 = -r0^2

while the ring electrodes follow

r^2 - 2*z^2 = +r0^2

where r0 = 4mm.

The voltage applied to the ring electrode is

V_appl = U + V*sin(2*pi*t/tau),

where U = 55, V = 204.5, tau = 0.001ms.

These conditions have been chosen to trap ions that have an atomic mass in the region of 100.

(A simple ion trap in which the electrodes are cylinders and discs is given in xmpl3d71.)

The 'mesh' method of ray tracing is used -therefore the first few rays are traced slowly while a mesh of points is built up to save field values, but after that the remaining rays are traced more quickly.

20 rays are started, all with the same energy (0.1eV) and all starting at the origin. Four of the rays correspond to mass 98 and another four to mass 102 and all of these fail to be trapped. The other 12 rays correspond to mass 100 and 7 of them are trapped for at least 20ms.

Using the results output for potentials we can deduce that the potential distribution is approximately

phi(r,z) = 22.9635 - 3.1048*10^4*V_appl*(r^2 - 2*z^2)

where r and z are in metres here. (Theoretically the constant should 10^6/32 = 3.125*10^4, so the error is 0.6%, which would be reduced with more cones and more segments.)

Therefore for a mass 100AU the parameters a and q defined by Dawson (Quadrupole Mass Spectrometry, P. H. Dawson, Elsevier, Amsterdam 1976) are

a = 0.663, q = 1.232,

which is a point very near to the extreme corner of the stability diagram shown in Fig. 2.30(b) of Dawson.

The results obtained here are therefore consistent with the theoretical results given by Dawson.