  Since its commissioning in 1977, the U-120M cyclotron has been equipped with
one pair of harmonic coils dedicated to establishing optimal beam quality at
low accelerating radii. In 2022, the cyclotron was upgraded and a second pair
of harmonic coils was added. The new harmonic coils are positioned at a radius
of approximately 50\,cm corresponding to the outermost beam orbit, where they
were installed to ensure efficient extraction of positively accelerated ions
from the cyclotron in the newly developed extraction system. This article
describes in detail the design of the new harmonic coils, their installation in
the accelerator vacuum chamber, and their use in the extraction process.
Furthermore, the design of a new extraction system using the precession and
linear integer resonance extraction methods is presented and a comparison of
the basic properties of these two methods is given. Finally, an evaluation of
their advantages and limitations concerning their possible use in the cyclotron
and an estimation of the efficiency of the new extraction system is made.
