  We investigate the free magnetic energy and relative magnetic helicity
budgets of solar quiet regions. Using a novel non-linear force-free method
requiring single solar vector magnetograms we calculate the instantaneous free
magnetic energy and relative magnetic helicity budgets in 55 quiet-Sun vector
magnetograms. As in a previous work on active regions, we construct here for
the first time the (free) energy-(relative) helicity diagram of quiet-Sun
regions. We find that quiet-Sun regions have no dominant sense of helicity and
show monotonic correlations a) between free magnetic energy/relative helicity
and magnetic network area and, consequently, b) between free magnetic energy
and helicity. Free magnetic energy budgets of quiet-Sun regions represent a
rather continuous extension of respective active-region budgets towards lower
values, but the corresponding helicity transition is discontinuous due to the
incoherence of the helicity sense contrary to active regions. We further
estimate the instantaneous free magnetic-energy and relative magnetic-helicity
budgets of the entire quiet Sun, as well as the respective budgets over an
entire solar cycle. Derived instantaneous free magnetic energy budgets and, to
a lesser extent, relative magnetic helicity budgets over the entire quiet Sun
are comparable to the respective budgets of a sizeable active region, while
total budgets within a solar cycle are found higher than previously reported.
Free-energy budgets are comparable to the energy needed to power fine-scale
structures residing at the network, such as mottles and spicules.
