QCD plasma instabilities appear to play an important role in the
equilibration of quark-gluon plasmas in heavy-ion collisions in the theoretical
limit of weak coupling (i.e. asymptotically high energy). It is important to
understand what non-linear physics eventually stops the exponential growth of
unstable modes. It is already known that the initial growth of plasma
instabilities in QCD closely parallels that in QED. However, once the unstable
modes of the gauge-fields grow large enough for non-Abelian interactions
between them to become important, one might guess that the dynamics of QCD
plasma instabilities and QED plasma instabilities become very different. In
this paper, we give suggestive arguments that non-Abelian self-interactions
between the unstable modes are ineffective at stopping instability growth, and
that the growing non-Abelian gauge fields become approximately Abelian after a
certain stage in their growth. This in turn suggests that understanding the
development of QCD plasma instabilities in the non-linear regime may have close
parallels to similar processes in traditional plasma physics. We conjecture
that the physics of collisionless plasma instabilities in SU(2) and SU(3) gauge
theory becomes equivalent, respectively, to (i) traditional plasma physics,
which is U(1) gauge theory, and (ii) plasma physics of U(1)x U(1) gauge theory.Comment: 36 pages; 15 figures [minor changes made to text, and new figure
added, to reflect published version