  We present a trajectory dynamically tracing compensation method to smooth the
spatial fluctuation of the static magnetic field (C-field) that provides a
quantization axis in the fountain clock. The C-field coil current is
point-to-point adjusted in accordance to the atoms experienced magnetic field
along the flight trajectory. A homogeneous field with a 0.2 nT uncertainty is
realized compared to 5 nT under the static magnetic field with constant current
during the Ramsey interrogation. The corresponding uncertainty associated with
the second-order Zeeman shift that we calculate is improved by one order of
magnitude. The technique provides an alternative method to improve the magnetic
field uniformity particularly for large-scale equipment that is difficult to
machine with magnetic shielding. Our method is simple, robust, and essentially
important in frequency evaluations concerning the dominant uncertainty
contribution due to the quadratic Zeeman shift.
