Test3d34.dat, 34th 'test' file for CPO3D

Electrodes defined by users equations, replaces test3d20.

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

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

while the ring electrodes follow

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

where r0 = 4mm.

The caps have been simulated in 3 parts, to avoid long, this triangles at or near the centre.

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 'direct' method of ray tracing is used here, but with more rays the 'mesh' method would be more appropriate.

24 rays are started, all with the same energy (0.1eV) and all starting at the origin. The first 4 rays correspond to masses 96 and 104 and none is trapped. The next 8 correspond to masses 98 and 102 and only 2 of these are trapped in the given maximum time of 20ms. The other 12 rays correspond to mass 100 and 5 of them are trapped for at least 20ms. So this performance is not exactly as expected, but is in the right ball-park.

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

V(r,z) = 27.5038 - 3.1226*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 0.1%)

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.