  In the QCD evolution of transverse momentum dependent parton distribution and
fragmentation functions, the Collins-Soper evolution kernel includes both a
perturbative short-distance contribution as well as a large-distance
non-perturbative, but strongly universal, contribution. In the past, global
fits, based mainly on larger $Q$ Drell-Yan-like processes, have found
substantial contributions from non-perturbative regions in the Collins-Soper
evolution kernel. In this article, we investigate semi-inclusive deep inelastic
scattering measurements in the region of relatively small $Q$, of the order of
a few GeV, where sensitivity to non-perturbative transverse momentum dependence
may become more important or even dominate the evolution. Using recently
available deep inelastic scattering data from the COMPASS experiment, we
provide estimates of the regions of coordinate space that dominate in TMD
processes when the hard scale is of the order of only a few GeV. We find that
distance scales that are much larger than those commonly probed in large $Q$
measurements become important, suggesting that the details of non-perturbative
effects in TMD evolution are especially significant in the region of
intermediate $Q$. We highlight the strongly universal nature of the
non-perturbative component of evolution, and its potential to be tightly
constrained by fits from a wide variety of observables that include both large
and moderate $Q$. On this basis, we recommend detailed treatments of the
non-perturbative component of the Collins-Soper evolution kernel for future TMD
studies.
