the ions follow the evolution of the perturbation and about one half of them become poloidally local

1
Modelling of energetic ions behaviour in the n1
kink distorted central core of the JET tokamak A.
Perona1, S. D. Pinches2, S. E. Sharapov2 and F.
Porcelli1 1Burning Plasma Research Group,
Politecnico di Torino, 10129 Torino,
Italy 2Euratom/UKAEA Fusion Association, Culham
Science Centre, Abingdon, Oxfordshire OX14 3DB,
UK
The aim of this work is to investigate the
behaviour of energetic ions in the presence of an
n1 kink distortion of the plasma core in the
Joint European Torus (JET). To achieve this aim,
the particle-following HAGIS (Hamiltonian GuIding
System) code 1 will be used. In order to
investigate fast ion orbit effects in such a
kinked magnetic topology, the HAGIS code has been
extended to produce Poincaré plots for both the
magnetic field lines and the drift orbits of the
fast ions. The changes in the orbit topology are
investigated both for a static kink and for a
perturbation whose amplitude is exponentially
growing in time. Three characteristic types of
unperturbed orbits, all initially localized
inside the q1 magnetic surface, are considered
trapped banana orbits arising from Ion Cyclotron
Resonance Heating (ICRH) passing ions (i. e.
ions circulating in the poloidal and toroidal
coordinates) and orbits close to the stagnation
point. Conclusions in the case of the static
kink, the stagnation and passing orbits show the
most significant distortions, whilst the trapped
ions are much less sensitive to the presence of
the mode. For the growing perturbation, the
banana orbits are insensitive to the changes in
the perturbed magnetic topology. In this case,
all passing ions retain their circulating feature
in the toroidal coordinate, but about one half of
them become poloidally localized , so that they
no longer circulate around the displaced
magnetic axis.
Magnetic field lines in HAGIS
Scenario
The equations for the magnetic field lines have a
Hamiltonian structure 2. In the
coordinates
In order to model the magnetic island, which
is the dominant perturbation, we use the
perturbed internal kink profile supplied by the
linear MHD stability code CASTOR 3, which uses
the information on the equilibrium (for JET
discharge 60195 t11.0) provided by HELENA 4
and solves the ideal MHD equations linearized
around a static axisymmetric equilibrium. Eight
additional poloidal harmonics, driven by the
dominant kink perturbation because of the
toroidal coupling, are taken into account.
Although an ideal MHD perturbation is used, a
characteristic island-type structure of the
magnetic field appears.
The surfaces inside q1 present a shift
determined by the kink and related to the
amplitude by the relation
The q1 unperturbed surface
The internal kink mode perturbed fluid velocity
r?Vr(s).
The q1.014 surface perturbed by a mn1 kink of
amplitude
The q2 unperturbed surface
The q2 surface perturbed by a m2, n1 kink of
amplitude
Passing ions
The orbits of deeply passing ions
depend on the way the final amplitude of the
perturbation is reached. We have considered here
the orbits of energetic ions (500 KeV) observed
for a period comparable to the duration of a
sawtooth crash .
Exponential growth of the amplitude

Static kink the ions
remain in the region where their initial position
is located and retain their circulating feature
in the toroidal coordinate.
the ions follow the evolution of the perturbation
and about one half of them become poloidally
localized if they cross the region of the
island while the amplitude has reached a
threshold value ,
otherwise they do not invert the poloidal
direction of their trajectory.

Ions orbits
Poincaré plot of the q1 unperturbed surface
Poincaré plot of the q1 perturbed surface
Trapped ions
Stagnation orbits
We have considered the banana orbits of ions that
arise due to on-axis ICRH heating. The banana
orbits are much less affected than the passing
ions neither by a static kink 6, 7, nor an
exponentially growing perturbation, even when the
ions toroidal orbit frequency is comparable with
the frequency of the mode, as shown in the
Poincaré plots on the right.
The stagnation orbit is strongly affected by the
kink. It is characterized by the fact that its
poloidal and radial coordinates change very
slightly with time in the unperturbed case 5.
Here we show a zoom of the unperturbed trajectory
(left) and of the same ion affected by the
perturbation (right) in the presence of a static
kink. Both orbits remain inside the q1 perturbed
surface.
growing perturbation
static kink
ACKNOWLEDGEMENTS One of the authors (A. P.) would
like to thank UKAEA for providing support for her
stay in UK. The work was performed under the
European Fusion Development Agreement and was
partly funded by Euratom and the UK Engineering
and Physical Sciences Research Council.
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