  A novel Penning trap tower consisting of five compensated cylindrical Penning
traps is developed for the PENTATRAP mass spectrometer at the
Max-Planck-Institut f\"ur Kernphysik in Heidelberg, Germany. An analytical
expression for the electrostatic potential inside the trap tower is derived to
calculate standard Penning trap properties like the compensation of
anharmonicities and an orthogonal geometry of the trap electrodes. Since the
PENTATRAP project described in the preceding article aims for ultra
high-precision mass-ratio measurements of highly charged ions up to uranium,
systematic effects for highly charged ions inside the trap tower are considered
for the design process as well. Finally, a limit due to remaining anharmonic
shifts at large amplitudes is estimated for the resulting geometry, which is
important for phase-sensitive measurements of the reduced cyclotron frequency
of the ions.
