1.
L. Chen and C. Z. Cheng, Phys. Fluids 23, 2242-2249 (November 1980):
A
fundamental work on micro-instabilities in toroidal
systems which maintains the freshness of its message despite it is limited to
linear analyses. At the time when drift waves became a hot topic in fusion
research, it has only gradually become clear that toroidal
plasmas are very peculiar in character and very different from plasma slabs due
to magnetic drifts and curvature. This work sets a turning point in every
sense: because it is the first detailed and complete numerical and analytical
study to demonstrate the peculiar features of drift waves in a torus; and because it uses asymptotic techniques to
actually calculate the parallel mode structure, on which a great deal of the
wave stability and propagation properties depend. Essentially, this work shows
that the potential well which a drift wave experiences while propagating along
a magnetic field line may cause locally bound states to exists, which do not
have a slab equivalent. These states have typically weaker damping (shear
damping) than the "slab-like" states which still exist, and they are
called "toroidicity-induced" since they are
peculiar to toroidal systems.
2.
L. Chen, Z. Lin, and R. White, Phys. of Plasmas 7, 3129 (2000):
This work
is highly innovative since it introduces a rigorous treatment of the
spontaneous generation of zonal flows in toroidal
plasmas, based on the assumption that the coherent interaction of micro-turbulence
and zonal flows is the dominant non-linear interaction, which determines the
non-linear behavior of the system on the shortest non-linear time-scale. In
this sense, the non-linear dynamical system is solvable due to the existence of
a hierarchy among non-linear interactions. This is the case, e.g., of the Ion
Temperature Gradient (ITG) driven turbulence. In fact, the coherent 4-wave
modulation interaction model, presented here, is capable of reproducing and
explaining results of 3D gyrokinetic PIC simulations
of ITG turbulence as far as zonal flow growth rate and most unstable wavelength
are concerned. In the local limit, the
model is equivalent to the logistic map and the nonlinear system exhibits
period doubling bifurcations and, eventually, transition to chaos. The fixed
point attractors of the dynamical system have a scaling with ion collisionality that allows explaining the collisionality dependence of ITG turbulent transport.
Another important aspect of this work is that it sets the basis for subsequent
research which successfully explained turbulent transport scaling with the
system size as well as the radial (direction of magnetic flux gradient)
spreading of turbulence in toroidal systems.