  Paul traps are ion traps that are widely used in spectroscopic experiments to
confine and stabilize a charged particle within a small region using
oscillating electric fields. The dynamics of the particle inside a Paul trap is
described by Mathieu equations. It has been proposed that such traps can be
used to detect the effects produced by spontaneous collapse of the associated
wavefunction, as described by the model of CSL (Continuous Spontaneous
Localization). This model is a non-linear, stochastic and non-relativistic
modification to the Schr\"{o}dinger equation which predicts an additional
random motion of particles other than environmental effects. In this paper, we
discuss the possibility that such a random motion can throw a particle out of
its stable configuration within the Paul trap. We study the changes in the
stability diagram of a Paul trap in the presence of CSL. We also constrain the
CSL parameter space by assuming the fact that the stability diagram is not
significantly altered. The bounds thus obtained are weaker than those coming
from X-ray emission from Ge slab.
