  In magnetic confinement fusion devices like tokamaks, it is crucial to
confine the high energy fusion-born helium nuclei ($\alpha$-particles) to
maintain the energy equilibrium of the plasma. However, energetic ions can
excite various instabilities which can lead to their enhanced radial transport.
Consequently, these instabilities may degrade the heating efficiency and they
can also cause harmful power loads on the plasma-facing components of the
device. Therefore, the understanding of these modes is a key issue regarding
future burning plasma experiments.
  One of the main open questions concerning energetic particle (EP) driven
instabilities is the non-linear evolution of the mode structure. In this
thesis, I present my results on the investigation of $\beta$-induced Alfv\'{e}n
eigenmodes (BAEs) and EP-driven geodesic acoustic modes (EGAMs) observed in the
ramp-up phase of off-axis NBI heated plasmas in the ASDEX Upgrade tokamak.
These modes were well visible on several line-of-sights (LOSs) of the soft
X-ray cameras which made it possible to analyse the time evolution of their
spatial structure.
  In order to investigate the radial structure, the mode amplitude has to be
determined on different LOSs. I developed an advanced amplitude reconstruction
method which can handle the rapidly changing mode frequency and the low
signal-to-noise ratio. This method is based on short time Fourier transform
which is widely applied in the thesis, because it is ideal to investigate the
time evolution of transient wave-like phenomena.
  The radial structure analysis showed that in case of the observed downward
chirping BAEs the changes in the radial eigenfunction were smaller than the
uncertainty of the measurement, while in case of rapidly upward chirping EGAMs
the analysis shows shrinkage of the mode structure. These experimental results
are shown to be consistent with the corresponding theory.
