1 INTRODUCTION
1.1 the energy problem
The present energy scenario and the forecast for the next future reveal an
increasing energy demand [9]. Moreover, the actual global energy supply
is based on fossil fuels for 81%, while just for 13% on different forms of
renewable energy (biomass, hydroelectric, combustible waste, etc). The rest
relies on nuclear fission [5]. Considering the decreasing availability of fossil
resources, the development of alternative and renewable energy sources has
become a crucial challenge. Through a continuous research, new ways have
been explored, solutions have been suggested, and some possible answers
have been found first in nuclear fission, then in investing more in "green en-
ergy". It seems anyway more logical to imagine a future where the energy
demand is sustained by different sources, in order to maintain a stable en-
ergetic and economic system. Energy from sun, wind or similar renewable
resources cannot sustain the whole energy demand, being bound to partic-
ular environmental conditions. Anyway they can be considered a good and
environmentally-friendly alternative to the dependence on main energy re-
sources as, for instance, the current coal, gas or fission power plants. But
now the main challenge is thus to find a new main energy source: hope-
fully long lasting, eco-friendly and inherently safe. A promising candidate
fulfilling these conditions is fusion.
1.2 a possible solution to the increasing
energy demand: fusion
Generally speaking, fusion is a nuclear process in which two light nuclei
merge to form a heavier element. In order to reach a fusion reaction, two
positive charged nuclei have to overcome the mutual Coulomb repulsion.
They have hence to be closer than a distance in the order of 10
-15
m [27].
A vast knowledge about fusion comes from stars, which are the oldest and
biggest fusion "plants" existing. Studying the sun, the proton-proton fusion
chain has been discovered. In this reaction helium is formed out of hydro-
gen, releasing an energy of26.7MeV for each reaction. In the sun, this fusion
process is possible due to the high core density (~10
31particles
m
3
), sustained
by the gravitational force. This is not attainable on earth, since densities in
this range cannot be reached. In order to exploit fusion processes on earth,
the most feasible reaction is employing two hydrogen isotopes, namely deu-
terium and tritium (reaction1). They are used because of their cross section,
which is larger compared to other possible reactions (reactions 2,3,4, see
figure 1).
2
D+
3
T!
4
He+
1
n+17.6MeV (1)
2
D+
2
D!
3
He+
1
n+3.27MeV (2)
1
2 introduction
2
D+
2
D!
3
T +
1
H+4.03MeV (3)
2
D+
3
He!
4
He+
1
H+18.3MeV (4)
Figure 1.: Cross-sections for the reactions D-T, D-D andD-
3
He. The D-D curve is
the sum of the cross sections of the two D-D reaction listed in reactions 2
and 3. [27].
As shown in figure1, the D-T curve has a maximum around a particle en-
ergy of ~100keV . Actually, the mean temperature needed to have a sufficient
number of reactions in a future fusion reactor is 10keV . At this temperature
there are enough high energetic ions lying in the high energy tails of the
Maxwell distribution of the particles which can reach fusion. A concise way
to express the condition needed to achieve fusion is that of the Lawson cri-
teria: temperature (T), density (n) and energy confinement time ( E
) have
to satisfy the relation 5. Figure 2 shows the ignition curve, as function of
triple product parameters. Ignition means a self-sustaining burning plasma
heated without any external system, but just with the energy coming from
fusion reactions.
nT E
>3 10
21
keVs
m
3
(5)
The temperature required is about ten times the core temperature of the
sun: at this temperature atoms are ionized. The state of this hot, ionized gas
is called "plasma": it consists in a globally neutral system of many charged
particles, which is characterized by presenting collective properties (some-
how as a fluid).
Fusion with D-T fuel is very advantageous in terms of energy density:
compared with fossil and fission fuels, it shows its great potential.
fossil fission fusion
10
6
tonne oil 0.8 tonne uranium 0.14 tonne deuterium
Table 1.: Comparison of energy equivalence among different resources [9].
Deuterium is a stable isotope of hydrogen and is widespread in nature
(0,015% of the total hydrogen). Tritium on the contrary, is radioactive and
has a half-life of approximately 12 years. For this reason it does not occur
1.3 thermonuclear fusion by magnetic confinement 3
Figure 2.: The value ofn
E
required to obtain ignition, as a function of temperature
[27].
in nature and it has to be produced directly inside the reactor. Neutrons
coming from the fusion reactions in the plasma will be used to breed tritium
out of lithium (with reactions 6, 7).
6
Li+
1
n!T +
4
He+4.8MeV (6)
7
Li+
1
n!T +
4
He+n-2.5MeV (7)
However, lithium supplies, unlike deuterium ones, could in principle rep-
resent a limit [8]. This depends on future demands and on possible new
developments of new extraction processes, as for instance obtaining Li from
the seawater. Anyway, by now, lithium supplies do not represent a crucial
issue. Future fusion plants can also be considered inherently safe: given the
strict constraints to maintain burning plasma, any accident in the reactor
will lead to a stop in the reaction chain, on the contrary to fission plants.
But due to the difficult conditions to reach ignition, the track to commercial
fusion plants is still long.
1.3 thermonuclear fusion by magnetic con-
finement
At the moment, two mechanisms to achieve fusion processes are being
studied. The Inertial Confinement Fusion (ICF) approach intends to reach
a very high density and temperature of a Deuterium-Tritium target using
high power lasers, causing an implosion. The other way, which is topic of
this thesis, is the magnetic confinement of the plasma, the most advanced
concept to achieve fusion.
As plasma consists of an ionized gas, it is possible confine it in a device
with strong magnetic fields without direct contact to any material surface.
When a magnetic field is present, the Lorentz force imposes to the particles
4 introduction
Figure 3.: Helically twisted field lines and flux surfaces in a tokamak
a circular motion around the field lines ("gyro-motion"). In this way the par-
ticles are strictly confined to the magnetic field. Anyway, with this kind of
confinement, the particles can move freely along the magnetic field line (e.g.
due to an electric field). In a linear magnetic field setup (e.g. a magnetic
bottle configuration), the particles are lost at the ends, therefore a closed
configuration for the magnetic field lines has been chosen, and the devices
are currently shaped as a torus. The torus is enclosed by coils, in order
to generate a confining toroidal magnetic field. However this field is not
enough: to prevent the loss of the plasma to the wall due to drift effects, the
magnetic field configuration is set to be helically twisted. A poloidal com-
ponent is therefore added, so the main particle trajectory becomes helical,
keeping most of the plasma in the central part of the torus. The magnetic
fields generate nested surfaces characterized by constant magnetic flux and
pressure ("flux surfaces"), as shown in figure 3. The pressure increases per-
pendicularly to the flux surfaces confining the hot plasma in the centre of
the torus. In the core region at the centre of the torus, it is thus possible to
fulfill the conditions necessary to heat the plasma up to about 10keV with
a density in the order of 10
20particles
m
3
, as required by the triple product
equation 5. Since this value of density is lower than that in the atmosphere
of a factor10
6
, plasma is consequently contained in a vacuum vessel.
Among magnetic confined devices, three main configurations can be dis-
tinguished: tokamak, reversed field pinch (RFP , figure 4a) and stellarator
(figure 4b). The first two create the poloidal magnetic field with induced
plasma current, the latter uses complex shaping of the magnetic field coils
to generate directly helical twisted magnetic field lines. The tokamak con-
figuration, subject of this thesis, will be briefly presented in the following
section.
1.4 tokamaks 5
(a) Reversed field pinch (RFP) (b) Stellarator
Figure 4.: Representations of helical plasma configurations in RFP (quasi-single he-
licity (QSH) regime in RFX-mod, Padova [22]) and stellarator (Wendel-
stein 7-X, Greifswald [20]). These are alternative magnetic configurations
to tokamak.
1.4 tokamaks
Figure 5.: General design of a tokamak. The plasma column is in yellow, while the
magnetic field coils are shown in red (toroidal field) and green (vertical
field). A vertical field is necessary to control the position of the plasma
column. In the centre of the torus the transformator coil is illustrated,
which is needed to generate the plasma current.
The tokamak (from toroidal’naya kamera s magnitnymi katushkami -
toroidal chamber with magnetic coils) design represents the most advanced
fusion concept. Figure 5 shows a sketch of the tokamak design. It is the
most used and studied configuration, and, at the moment, the most promis-
ing one for next step fusion reactors. With this configuration, parameters
needed for fusion have been reached, but not all at the same time for a
sufficient duration to obtain energy gain. The largest operating tokamaks
are JET in Oxford (GB), DIII-D in San Diego (USA) and ASDEX Upgrade
in Garching (DE). In the tokamak configuration, magnetic fields consist of
an externally applied toroidal field and a poloidal field which is induced
by a toroidal current flowing through the plasma. The plasma current is
generated using a voltage ramp in a central solenoid, causing a change of
magnetic flux in the central gap of the torus. That solenoid acts as the
primary winding of a transformer with the plasma itself acting as the sec-
ondary. Plasma is a conductor, and presents a resistance which varies with
the temperature. The plasma current can therefore be used to heat the
plasma ("ohmical heating"): as described by the Joule’s law, a current flow-
6 introduction
ing through a conductor generates heat. However, due to the decreasing
plasma resistivity with temperature, plasma cannot be heated only ohmi-
cally. For this reason it is necessary to add external heating systems, such as
neutral beam injection system (NBI) or heating with electromagnetic waves.
The NBI system uses neutral particle beams injected in the plasma at high
energy, which release energy by scattering with plasma. The other system is
based on heating plasma particles using electromagnetic waves at particular
resonance frequencies connected to particles gyro-motion.
Current tokamak experiments are not sufficiently large to provide energy
gain with fusion. On the way to commercial fusion reactors, the next step
is the ITER experiment [19] (see figure 6), under construction in Cadarache
(FR). This will be the largest tokamak in the world. It has been designed to
demonstrate the feasibility of a high-gain fusion reactor, with long lasting
burning plasma and with effective power production, conditions achievable
just with a larger experiment like ITER. It is supported by a worldwide
collaboration among China, EU, India, Japan, Korea, Russia and USA. The
next step after ITER is supposed to be DEMO (DEMOnstration Power Plant),
the prototype of a commercial fusion reactor. According to the planned
timetable (subject to change), ITER first plasma will be created in 2019 and
DEMO first phase of operation will start from 2030 [25].
Figure 6.: ITER tokamak design. Artist’s drawing of the entire ITER device (ITER
Final Design Report.(2001). Vienna:IAEA).
1.5 the asdex upgrade tokamak (aug)
The present work has been performed at the Max-Planck-Institut für Plasma-
physik (IPP) in Garching (Germany), where ASDEX Upgrade tokamak (Axially
Symmetric Divertor EXperiment) is operated. ASDEX Upgrade, briefly
AUG, went into operation in 1991. It is the largest German fusion exper-
iment in operation and, in an international comparison, it is a large sized
1.5 the asdex upgrade tokamak (aug) 7
Figure 7.: The ASDEX Upgrade tokamak (AUG). The orange part is the supporting
structure. Surrounding the vacuum vessel (light blue), one can see the
toroidal coils (light orange) and the poloidal coils (purple).
Experiment parameters AUG(maximum) AUG(typical) ITER
Major plasma radius 1.6m 1.6m 6.2m
Magnetic field 3.9T 2.6T 5.3T
Plasma current 2MA 1.2MA 15MA
Heating power 30MW 620MW 73MW
Temperature 10
8
K 10
8
K >1.5 10
8
K
Table 2.: Parameters of AUG (maximum and typical ones) compared with ITER ones.
Magnetic field value is referred to the magnetic axis.
tokamak. It is one of the leading fusion experiments worldwide (figure 7
and table 2 for further information).
As indicated in the name, AUG is an experiment in divertor configuration.
This implies additional coils in order to create a null-point or X-point in the
magnetic field (there its value is zero) at the bottom or at the top of the
plasma. Figure 8 shows a poloidal section of the torus. This configuration
causes the onset of a last closed magnetic flux surface, called "separatrix"
or LCFS-from last closed flux surface-, which separates the confined plasma
from the "scrape-off layer" (SOL), the region in which plasma is in direct
contact with the wall. Every flux surface is labeled with a normalized radial
coordinate, called poloidal ( pol
). This coordinate, depending on the
magnetic fields in the plasma, is zero in the centre at the magnetic axis
(see figure 8) and 1 at the LCFS. The magnetic configuration is determined
during the discharge by reconstruction from magnetic probes [23]. Poloidal
coordinate is calculated as following:
pol
=
r
- a
s
- a
(8)
where is the magnetic flux, a
is the magnetic flux on the magnetic axis
and s
at the separatrix.
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