  In many of the high-precision optical frequency standards with trapped atoms
or ions that are under development to date, the AC Stark shift induced by
thermal radiation leads to a major contribution to the systematic uncertainty.
We present an analysis of the inhomogeneous thermal environment experienced by
ions in various types of ion traps. Finite element models which allow the
determination of the temperature of the trap structure and the temperature of
the radiation were developed for 5 ion trap designs, including operational
traps at PTB and NPL and further optimized designs. Models were refined based
on comparison with infrared camera measurement until an agreement of better
than 10% of the measured temperature rise at critical test points was reached.
The effective temperature rises of the radiation seen by the ion range from 0.8
K to 2.1 K at standard working conditions. The corresponding fractional
frequency shift uncertainties resulting from the uncertainty in temperature are
in the 10-18 range for optical clocks based on the Sr+ and Yb+ E2 transitions,
and even lower for Yb+ E3, In+ and Al+. Issues critical for heating of the trap
structure and its predictability were identified and design recommendations
developed.
