So what does this have to do with fractals and chaos?
N.N. Bogolubov was a Russian fusion scientist
who is thought of as the father of the Tokamak.
He was also a noted fractal -chaos mathematician.
Current American projects from the Russian school at Princeton:
http://w3.pppl.gov/gradprogram/Misc/research.html
Nonadiabatic Ponderomotive Barriers
Ilya Dodin: (graduated 2005)
Ponderomotive barriers are regions of localized electromagnetic field
oscillating at a high frequency. Depending on the type of particles
(electrons, ions, clusters, molecules, or atoms) and the parameters of
the field, such barriers can either attract or repel particles, acting
essentially like effective potentials. Outside the parameter domain
where ponderomotive barriers behave in this simple ("adiabatic")
fa****on, the particle behavior is generally considered hard to control,
and, as we show, resembles the motion of a quantum object in a
conservative field.
We have found that even these, "nonadiabatic" ponderomotive barriers can
produce robust and easily controllable operations on plasma particles.
In fact, employing the nonadiabatic regime allows additional flexibility
for manipulating particles by means of electromagnetic fields, as
compared to conventional attraction and repulsion. For example, the new
techniques include a possibility of selective separation and cooling of
plasma species (somewhat similar to that in atomic physics) and even
formation of one-way walls, which can repel particles from one side but
transmit those from another side, hence providing a novel and highly
efficient current drive mechanism. All of these effects can be practiced
on particles of virtually any type, from electrons to molecules or even
atoms for they originate from the fundamental properties of
ponderomotive interactions.
The purpose of our ongoing, mainly analytical research is to develop a
general understanding of single-particle nonadiabatic dynamics in
intense high-frequency fields and apply this knowledge for suggesting
new advanced applications of ponderomotive barriers for plasma science
and technology.
( picture here is of a kind of Henon map ( second kind))
Advisor: Nathaniel J. Fisch
Bifurcation Analysis and the Onset of Drift-wave Turbulence
Roman Kolesnikov (graduated 2006)
The subject of anomalous energy losses in tokamaks has been studied
since almost the very beginning of fusion research. It is now believed
that in discharges dominated by ion heating the principal mechanism for
anomalous ion heat losses is the nonlinear generation of the
ion-temperature-gradient-driven (ITG) mode. Recently considerable
attention has been given to the role of zonal flows (linearly stable and
modes), nonlinearly driven by ITG fluctuations, in the self-consistent
regulation of the ITG saturation and trans****t level.
It is found that in a regime just above linear threshold (of temperature
gradient~ ) without collisions, strong zonal flows are excited that
completely suppress the turbulence. That regime is called the Dimits
up****ft.
I apply a bifurcation theory to study the onset of drift waves/ITG modes
and sheared convective cells, including zonal flows. Bifurcation theory
is a systematic procedure that obtains the qualitative changes in the
behavior of solutions of nonlinear equations as a parameter (like~ ) is
varied in the regime near linear threshold.
A reactive fluid model is used for the investigation of the first and
second bifurcations in a temperature-gradient-driven system with
toroidal effects and parallel dynamics. The systematic analysis involves
the calculation of center manifolds and normal forms for a system of
infinite-dimensional partial differential equations. The results are
used to study aspects of the Dimits up****ft regime as a function of
temperature gradient~ and collisionality parameter .
Advisor: John A. Krommes
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