  Using full three-dimensional magnetohydrodynamic numerical simulations, we
study the effects of magnetic field sigmoidity or helicity on the properties of
the fundamental kink oscillation of solar coronal loops. Our model consists of
a single denser coronal loop, embedded in a plasma with dipolar force-free
magnetic field with a constant alpha-parameter. For the loop with no
sigmoidity, we find that the numerically determined oscillation period of the
fundamental kink mode matches the theoretical period calculated using WKB
theory. In contrast, with increasing sigmoidity of the loop, the actual period
is increasingly smaller than the one estimated by WKB theory. Translated
through coronal seismology, increasing sigmoidity results in magnetic field
estimates which are increasingly shifting towards higher values, and even
surpassing the average value for the highest alpha value considered.
Nevertheless, the estimated range of the coronal magnetic field value lies
within the mimimal/maximal limits, proving the robustness coronal seismology.
We propose that the discrepancy in the estimations of the absolute value of the
force-free magnetic field could be exploited seismologically to determine the
free energy of coronal loops, if averages of the internal magnetic field and
density can be reliably estimated by other methods.
