An ‘electrostatic bathtub potential’ is defined and analytical expressions for the time period and
amplitude of charged particles in this potential are obtained and compared with simulations. These
kinds of potentials are encountered in linear electrostatic ion traps, where the potential along the
axis appears like a bathtub. Ion traps are used in basic physics research and mass spectrometry to
store ions; these stored ions make oscillatory motion within the confined volume of the trap.
Usually these traps are designed and studied using ion optical software, but in this work the
bathtub potential is reproduced by making two simple modifications to the harmonic oscillator
potential. The addition of a linear ‘ k 1 | x |’ potential makes the simple harmonic potential curve
steeper with a sharper turn at the origin, while the introduction of a finite-length zero potential
region at the centre reproduces the flat region of the bathtub curve. This whole exercise o…