JavaScript is disabled for your browser. Some features of this site may not work without it.
Three-dimensional peeling-ballooning theory in magnetic fusion devices
Other title:
Three-dimensional ideal linear peeling ballooning theory in magnetic fusion devices 3D ideal linear peeling ballooning theory in magnetic fusion devices
Department/Institute:
Universidad Carlos III de Madrid. Departamento de Física
Degree:
Programa Oficial de Doctorado en Plasmas y Fusión Nuclear
Issued date:
2016-12
Defense date:
2016-12-16
Committee:
Presidente: Nicolas Joost Lopes Cardozo.- Secretario: Eduardo Antonio Ahedo Galilea.- Secretario: Carlos Hidalgo Vera
Sponsor:
This research was sponsored in part by DGICYT (Dirección General de Investigaciones Científicas y Tecnológicas) of Spain under Project No. ENE2012-38620-C02-02 and Project. No.
ENE2015-68265, and also in part by EUROFUSION-WP14-EDU and through FUSENET mobility funding.
Project:
Gobierno de España. ENE2012-38620-C02-02 Gobierno de España. ENE2015-68265
Rights:
Atribución-NoComercial-SinDerivadas 3.0 España
Abstract:
Nuclear fusion is the fundamental process that generates
heat and light in the stars but it is also a promising
potential candidate for the generation of energy by man.
However, where in the center of stars the combination of extreme
temperatures with extrNuclear fusion is the fundamental process that generates
heat and light in the stars but it is also a promising
potential candidate for the generation of energy by man.
However, where in the center of stars the combination of extreme
temperatures with extreme pressure is what drives light elements
close enough together for them to fuse and release part of their
combined mass as energy, on earth only extreme temperatures
can be employed. Matter at these temperatures exists in the state
of plasma, where the atoms are stripped clean of their electrons.
In the resulting physical system the presence of long term electromechanical
forces between the charged particles can lead to
violent collective behavior. Therefore, the general question of
confining hot plasma in a stable way is crucial in order to achieve
fusion. One strategy of doing this is by employing powerful magnetic
fields to guide the charged particles around a toroidal configuration.
This work is about a class of instabilities that these
configurations are susceptible to, called high-n instabilities.
High-n instabilities are instabilities that have strong localization
around the magnetic field lines that confine the plasma, and
they have previously been identified as possible culprits for some
significant processes that occur in magnetic configurations, such
as the periodic release of energy through Edge-Localized Modes
(ELMs), or even the complete loss of confinement during disruptions,
during which a large amount of energy is released to the
reactor walls, damaging them.
However, whereas much work has been performed in this
field, the analysis of high-n instabilities in realistic 3-D geometries,
including the effects of the deformation of the plasma edge,
has not yet been done yet in a systematic and dedicated manner.
Therefore, in the first part of this work a suitable theoretical
framework is developed. Here, the simplification can be made
that only modes pertaining to the same field line couple, through
their high-n nature. This reduces the dimensionality of the problem
by one, but at the same time does not pose any limitations on
the 3-D aspects of the instabilities.
One of the results of the theory is a system of coupled ordinary
differential equations that can be solved for an eigenvalue,
the sign of which determines whether the mode formed by the
corresponding eigenvector is unstable or not. The solution of
these equations, however, is something that has to be done using
numerical techniques, so to this end the numerical code PB3D
is developed. This stands for Peeling-Ballooning in 3-D, two
modes that are described well through high-n theory. PB3D can
treat the stability of various equilibrium codes such a VMEC and
HELENA in a modular way, is parallelized making use of the
message-passing interface (MPI) and is optimized for speed. The
code is verified making use of physical criteria and by comparisons
with two other, well-established numerical codes that have
ranges of applicability bordering on that of PB3D. The first one,
MISHKA, is a general-n stability code for axisymmetric equilibria,
whereas the second one, COBRA, can treat general 3-D cases,
but only in the n→ ∞ limit, with a static edge.
The successful introduction of PB3D paves the way for a multitude
of potential applications concerning 3-D edge effects. It
can be investigated, for example, how many previous findings
concerning peeling-ballooning modes in axisymmetric configurations
change or not when 3-D effects are introduced. The
theory of high-n stability of axisymmetric equilibria, for example,
in the past has shed light on the dynamics of ELMs, and how
this changes by including 3-D effects is a topic of interest. This is
true even more so as recently the relevance of ELM control has
risen due to the potentially dangerous behavior of ELMs in the
next generation nuclear fusion reactors. A strategy for controlling
them also intrinsically relies on applying 3-D resonant magnetic perturbations. The study of these effects with PB3D is planned in
the near future in the ITER Organization.
Before that, in this work, as a first concrete application, the
modification of the stability of the pedestal of a High-confinement
plasma equilibrium configuration by a toroidal field ripple is considered.
These so-called H-mode configurations are characterized
by a steep pressure gradient near the plasma edge, called the
pedestal, which increases the temperature and pressure attainable
in the core. Therefore, they are often seen as vital in order to
achieve fusion. In practice, however, a degradation of the pedestal
size is often observed, due to 3-D modifications of the equilibrium,
such as the periodic ripple in the toroidal magnetic field
due to the discreteness of the toroidal field coils. It was observed
here that the application of a toroidal ripple in the shape of the
poloidal cross section in the order of a percent, lead to a substantial
decrease in the highest possible pedestal pressure, in the order
of 30-40%. This substantiates good qualitative agreement with
experimental results, where degradations of similar magnitude
were observed.[+][-]