One of the main research interests of the Plasma Astrophysics
Group is the problem of transport, acceleration
and radiation of high energy particles (electrons and
ions) in Astrophysics. Our goal is to estimate the
energy distribution function of
energetic particles as well as the corresponding radiation
emitted in a variety of
astrophysical systems such as the Sun, the
extragalactic radio sources (jets and hot spots), the AGN's
and the Supernovae.

So far work has been done on solar flares and
extragalactic radio sources, using coherent
(E-fields and waves) and stochastic acceleration
mechanisms (Fermi acceleration and multiple shock acceleration).
Numerical methods (particle simulation codes)
and analytical approach (solutions of the Fokker - Planck
equation) gave results for the particle distribution
in remarkable agreement with the observations.
Recently we have started the investigation of acceleration and
transport of the energetic
particles in strong turbulent flows, which are very common in
Astrophysics.

We study the spatiotemporal evolution of solar and stellar active regions and investigate the
statistical properties of solar and stellar flares.We model the evolution of an active region
using an idea developed initially for complex dynamically systems, namely the concept of Self-
Organised Criticality (SOC). The Self-Organisation of certain types of dynamical systems,
results in the formation of fractal structures and the appearance of Self-Similarity is well
known. Only recently it was argued that certain types of spatially extended dynamical systems
can naturally evolve into a state in which the system is marginally stable against a disturbance.
In the SOC state, a single perturbation can ignite cascades of events of all sizes with a scale-
invariant behaviour, thus providing a connection between nonlinear dynamics and the
emergence of Self-Similarity. Self-similar behaviour leads to the emergence of power laws in
the events' size frequency distribution. Well-defined power laws are obtained by the observed
peak-luminosity frequency distribution of flares. Using a "Three-Dimensional Sandpile Model"
embedded in a cellular automaton, we have reproduced the observed frequency distribution of
solar hard X-ray bursts. Furthermore, we have developed a model, which seems to reproduce
better small events and obeys to a frequency distribution with a much steeper power cut-off.
We stress that these weak events correspond to the presently unobserved nanoflares, which,
due to the steep power rollover, may account for coronal heating in typical main-sequence
(Sun-like) stars.

We demonstrate that adding extended instability criteria to 3D critical-slope sand-pile models
has the effect of considerably enhancing the self-organised critical state displayed by these
models. We present two extended models, an isotropic one which shows much shorter and
much more frequent energy bursts. We illuminate the multifractal nature of the self-organised
critical state in both extended models by finding a nontrivial spectrum of generalised
correlation dimensions from the time series and by showing that the power-law regions of the
distribution functions for different lattice sizes show a scaling behaviour which is ruled by a
generalised multifractal scaling transformation. Recently we
have investigate the effect of a non-constant (power-law) loading
mechanism on SOC.

We also emphasise that a competition process as well as a feedback mechanism are essential
features of, and possibly necessary conditions for self-organised criticality. Our conclusions are
based on a simple one-dimensional feedback-controlled competition model as well as on
existing sandpile cellular automata. We argue that self-organised criticality can be divided into
two main classes: in the one class there is a perfect symmetry between the two competing
tendencies, and the distribution functions associated with both tendencies show power-law
behaviour. In the other case, there is an asymmetry between the competing tendencies and the
power laws in the distribution functions associated with one tendency are replaced by
exponential ones, while the power-law behaviour in the distribution functions associated with
the other tendency remains. A too strong feedback destroys the self-organised critical state: all
power laws are replaced by exponential ones.

The evolution of active regions is an inherently complex phenomenon. Magnetic fields generated in the base of convection zone follow a chaotic evolution before reaching the surface. Turbulent convection zone splits the magnetic field in fibers (which are the magnetohydrodynamic equivalent for the fluid eddies). The statistical description of the evolution of fibers and the rate of emergence on the solar surface is rather difficult, unless computer simulation is introduced. We use a competition probabilistic model for the formation of magnetic patterns in the stellar surface. We construct a one and two dimensional grid and load initially a small percentage of grid points with magnetic field (we call them A(active)) whereas the rest remain not active (N, unmagnetised). We follow the evolution of magnetised cells in many timesteps. In each timestep a) every A can turn its neighbouring N?s into A?s with a given probability and b) every A can be turned into N with another probability which depends on the numbers of N?s in its nearest neighbourhood. Studying this process numerically in one and two dimensions we found power laws for the number of clusters of active (magnetised) cells versus their size and we calculated the fractal dimension of the patterns formed. Our results are compared with solar observations.