Timekeeping requires practical, continuously operating frequency standards with exceptional long-term stability. JPL mercury linear ion trap standards (LITS) operate continuously with short-term stability to 2.-x10~(-14)/tau~(1/2) and long-term stability limited by remaining sensitivity to the second-order Doppler sift, which varies with ion number fluctuations. In this paper, we report measurements in a 12-pole trap showing a greater than twenty-fold sensitivity reduction to all parameters affecting the Second-order Doppler Shift. This advance should further improve practical ground-based ion standard stability to the 1x10~(-16) level and allow significant engineering simplifications enabling small, high performance flight standards.
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