  The solar atmosphere is dominated by loops of magnetic flux which connect the
multi-million-degree corona to the much cooler chromosphere. The temperature
and density structure of quasi-static loops is determined by the continuous
flow of energy from the hot corona to the lower solar atmosphere. Loop scaling
laws provide relationships between global properties of the loop (such as peak
temperature, pressure, and length); they follow from the physical variable
dependencies of various terms in the energy equation, and hence the form of the
loop scaling law provides insight into the key physics that controls the loop
structure. Traditionally, scaling laws have been derived under the assumption
of collision-dominated thermal conduction. Here we examine the impact of
different regimes of thermal conduction -- collision-dominated,
turbulence-dominated, and free-streaming -- on the form of the scaling laws
relating the loop temperature and heating rate to its pressure and half-length.
We show that the scaling laws for turbulence-dominated conduction are
fundamentally different than those for collision-dominated and free-streaming
conduction, inasmuch as the form of the scaling laws now depend primarily on
conditions at the low-temperature, rather than high-temperature, part of the
loop. We also establish regimes in temperature and density space in which each
of the applicable scaling laws prevail.
