  We introduce and derive the Fourier-enhanced 3D electrostatic field solver of
the gyrokinetic full-f PIC code PICLS. The solver makes use of a Fourier
representation in one periodic direction of the domain to make the solving of
the system easily parallelizable and thus save run time. The presented solver
is then verified using two different approaches of manufactured solutions. The
test setup used for this effort is a pinch geometry with ITG-like electric
potential, containing one non-periodic and two periodic directions, one of
which will be discrete Fourier transformed. The results of these tests show
that in all three dimensions the L2-error decreases with a constant rate close
to the ideal prediction, depending on the degree of the chosen basis functions.
