xmpl3d71, simple ion trap.
A simple design, intended only as a demonstration. A cylinder that has a sinusiodal potential is sandwiched between grounded plates.
A simulation of an ideal quadrupole ion trap is given in test3d20.
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 quickly. The conditions have been chosen to trap ions that have an atomic mass in the region of 105.
12 rays are started, all with the same energy (1eV), position and direction, but with different masses and starting times:
mass starting time
95 0 not trapped
105 0 trapped
115 0 not trapped
105 tau/4 trapped
105 tau/2 trapped
105 3*tau/4 not trapped
The period is tau = 0.001ms and the applied voltage is
V_appl = U + V*sin(2*pi*t/tau),
where U = 125, V = 500.
Using the results output for potentials we can deduce that the potential distribution is approximately
phi(r,z) = 97.01 - 2.359E4*V_appl*(r^2 - 2*z^2)
where r and z are in metres here. In fact the potential distribution has the quadrupole form (r^2 - 2*z^2) only near the origin. Higher order terms are significant over most of the
region occupied by the trapped ions. Therefore for a mass 105AU the parameters a and q defined by Dawson (Quadrupole Mass Spectrometry, P. H. Dawson, Elsevier, Amsterdam 1976) are approximately
a = 0.545, q = 1.090,
which is a point inside the stability diagram shown in Fig. 2.30(b) of Dawson.
No attempt has been made here to narrow the range of masses that are trapped nor to investigate the behaviour of the trap in more detail. In fact it would not be possible to obtain a very narrow mass range because the field is too 'impure'. Electrodes with hyberbolic shapes are needed for a purer field -see test3d20.