  Velocity of a deeply non-relativistic particle can change during its
acceleration inside an RF cavity significantly enough to cause a deviation of
the energy gain from a linear model. This paper derives formulae for
corrections to the energy gain in a two-gap RF cavity calculated by taking into
account this velocity change in the next approximation. Then, the results are
compared with direct particle tracking of an HWR cavity used at the PIP2IT test
accelerator. The formulae significantly extend the range of parameters where
analytical calculations work with a good accuracy. The approach is applied to
two aspects of cavity phasing.
