  Magnetic bions---stable bound states of monopoles and twisted
("Kaluza-Klein") monopoles, carrying two units of magnetic charge---have been
shown to be the leading cause of confinement and mass gap in four-dimensional
gauge theories with massless adjoint fermions compactified on R**{1,2} x S**1,
at least at small S**1. In this paper, we study in detail the bion mechanism
and the scales involved for an SU(2) gauge group, using traditional QCD
instanton methods. We represent the vacuum functional as the partition function
of a bion-anti-bion plasma and obtain the next-to-leading dependence of the
mass gap on the S**1 size L at fixed strong-coupling scale Lambda. We find
that, at small Lambda x L, the mass gap is an increasing function of L for
theories with four massless adjoint Weyl fermions, a case left undetermined by
the previous leading-order analysis, and comment on the approach to R**4.
