Coronal plumes are bright magnetic funnels found in quiet regions (QRs) and coronal holes (CHs). They extend high into the solar corona and last from hours to days. The heating processes of plumes involve dynamics of the magnetic field at their base, but the processes themselves remain mysterious. Recent observations suggest that plume heating is a consequence of magnetic flux cancellation and/or convergence at the plume base. These studies suggest that the base flux in plumes is of mixed polarity, either obvious or hidden in SDO HMI data, but do not quantify it. To investigate the magnetic origins of plume heating, we select ten unipolar network flux concentrations, four in CHs, four in QRs, and two that do not form a plume, and track plume luminosity in SDO AIA 171 A images along with the base flux in SDO HMI magnetograms, over each flux concentrations lifetime. We find that plume heating is triggered when convergence of the base flux surpasses a field strength of 200 to 600 G. The luminosity of both QR and CH plumes respond similarly to the field in the plume base, suggesting that the two have a common formation mechanism. Our examples of non-plume-forming flux concentrations, reaching field strengths of 200 G for a similar number of pixels as for a couple of our plumes, suggest that a critical field might be necessary to form a plume but is not sufficient for it, thus, advocating for other mechanisms, e.g. flux cancellation due to hidden opposite-polarity field, at play.