In this monograph the author presents the Canonical Profile
Transport Model or CPTM as a rather general mathematical framework
to simulate plasma discharges.
The description of hot plasmas in a magnetic fusion device is a
very challenging task and many plasma properties still lack a
physical explanation. One important property is plasma
self-organization.
It is very well known from experiments that the radial profile
of the plasma pressure and temperature remains rather unaffected by
changes of the deposited power or plasma density. The
attractiveness of the CPTM is that it includes the effect of
self-organization in the mathematical model without having to recur
to particular physical mechanisms.
The CPTM model contains one dimensional transport equations for
ion and electron temperatures, plasma density and toroidal rotation
velocity. These equations are well established and in fact are
essentially a reformulation the laws of energy, particle and
momentum conservation. But the expressions for the energy and
particle fluxes, including certain critical gradients, are new.
These critical gradients can be determined using the concept of
canonical profiles for the first time formulated in great detail in
the book. This concept represents a totally new approach to the
description of transport in plasmas. Mathematically, the canonical
profiles are formulated as a variational problem. To describe the
temporal evolution of the plasma profiles, the Euler equation
defining the canonical profiles is solved together with the
transport equations at each time step. The author shows that in
this way it is possible to describe very different operational
scenarios in tokamaks (L-Mode, H-Mode, Advanced Modes, Radiating
Improved Modes etc ), using one unique principle.
The author illustrates the application of this principle to the
simulation of plasmas on leading tokamak devices in the world (JET,
MAST, T-10, DIII-D, ASDEX-U, JT-60U). In all cases the small
differences between the calculated profiles for the ion and
electron temperatures and the experimental is rather confirm the
validity of the CPTM. In addition, the model also describes the
temperature and density pedestals in the H-mode and non
steady-state regimes with current and density ramp up. The proposed
model therefore provides a very useful mathematical tool for the
analysis of experimental results and for the prediction of plasma
parameters in future experiments."
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