  We propose speeding up a single ion heat pump based on a tapered ion trap. If
a trapped ion is excited in an oscillatory motion axially the radial degrees of
freedom are cyclically expanded and compressed such that heat can be pumped
between two reservoirs coupled to the ion at the turning points of oscillation.
Through the use of invariant-based inverse engineering we can speed up the
process without sacrificing the efficiency of each heat pump cycle. This
additional control can be supplied with additional control electrodes or it can
be encoded into the geometry of the radial trapping electrodes. We present
novel insight how speed up can be achieved through the use of inverted harmonic
potentials and verified the stability of such trapping conditions.
