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\begin{opening}
\title{PARTICLE ACCELERATION IN THE HELIOSPHERE}
\author{Loukas Vlahos}
\institute{Department of Physics\\
University of Thessaloniki,\\
54006 Thessaloniki, GREECE}
\runningtitle{Particle Acceleration in the Heliosphere}
\end{opening}
\begin{document}

The heliosphere could be divided in three major acceleration
Laboratories, the solar surface (Laboratory 1), 
the interplanetary medium (Laboratory 2) and Earth and Planetary
magnetospheres (Laboratory 3). Our understanding of the 
acceleration  
process depends strongly on the nature of the drivers and the
energy dissipation process. The energy gain by a particle 
with velocity $\vec{v}$ is
$\Delta E(t) = \int \vec{E}(\vec{r}, t) \cdot 
\vec{v}(\vec{r}, t) d\vec{r}$,
where $\vec{E}(\vec{r}, t)$  is the variation of the 
electric field in space and time. 
All three Laboratories mentioned above share a common 
characteristic, the drivers and the
energy dissipation processes are closely connected to fully 
developed MHD turbulence.
We can show that our understanding of particle acceleration 
depends strongly 
on the interaction of particles with fields resulting from
fully developed MHD turbulence.

The following processes have been used 
for the study of particle
acceleration in the heliosphere: (1) Neutral sheets and
turbulent neutral sheets, (2) Shock and turbulent shocks, 
(3) Double layer $E$-field and randomly distributed 
$E$-fields, (4) Small amplitude MHD waves. It is obvious that
the turbulent nature of the fields has been added 
to neutral sheets,
shocks, $E$-fields to enhance the efficiency of the acceleration
process. 

The standard diffusion equation used for particle 
acceleration process is

\begin{equation}
{\partial f \over {\partial t}} = {\partial \over {\partial p}}
D_{\rm pp} {\partial f \over {\partial p}}
\end{equation}
where $f$ is  the velocity distribution function, $p$ is the
momentum and $D_{\rm pp}$ is the diffusion coefficient
in the momentum space 

\begin{equation}
D_{\rm pp} \sim (\delta B /B)^2
\end{equation}
where ($\delta B/B$) are the field fluctuations.
Eq.~(1)  is applicable only when  
$(\delta B/B)$ are much smaller than one.

It is obvious that Eq.~(1) cannot handle fluctuation 
when $(\delta B/B) >> 1$. Current theories on fully 
developed MHD
turbulence have emphasised the role played by strong 
intermittent structures where $(\delta B/B)>>1$ inside the
turbulent flow. These coherent
nonlinear structures play a major role on particle 
acceleration. The
diffusion coefficient in such a turbulent environment 
is very different from the one shown in Eq.~(2). 
Inside fully developed turbulence, coherent structures
like neutral sheets, shocks, randomly placed $E$-fields
appear naturally. A new generation of particle acceleration 
mechanisms will be developed in the 
near future where a collection of
structures will appear inside  the turbulent flow.

We outline the approach used for particle acceleration in
the Laboratories mentioned above:

$\bullet$ The study of particle acceleration inside the 
solar atmosphere is based on the non-linear fields developed
during (1) the formation and evolution of active regions, 
(2) the formation and
interaction of magnetic discontinuities, 
(3) MHD waves inside magnetic
discontinuities and a collection of strong $E$-fields.

The driver for the formation and evolution of an 
active region is the turbulent
convection zone. A spectrum of magnetic flux tubes 
raised above the solar surface. A part of the flux tube 
is still inside the convection zone. The turbulent 
convection zone forms stochastic magnetic fields inside 
the active region. A large number of neutral sheets and
shock waves are spontaneously formed. 
The study of the energy gain by
electrons and protons inside a complex active region driven by 
the turbulent convection zone has produced a number 
of interesting results.

$\bullet$ In the Interplanetary medium, the
driver is the fast hydrodynamic flow. Formation of a series of
interplanetary shocks and the turbulent fields around the shock
play a crucial role
on particle acceleration. Stochastic magnetic field lines return
many times in the surface of the shock and dramatically 
enhance the shock-particle interaction.

$\bullet$ In the rotating Magnetosphere 
the driver is the turbulent solar wind.
Several unique structures  are formed (1) the turbulent Bow
shock, (2) Random $E$-fields inside the Aurora, 
(3) Radiation belts and the (4) turbulent
neutral sheets at the tail. Here again a collection of 
non-linear discontinuities accelerate the particles.

Our main points are:

\begin{itemize}

\item[$\bullet$] Turbulent motion dominates the acceleration
of particles in the  heliosphere. Organised
forms inside fully developed turbulence cause many 
energetic phenomena, e.g.
flares, interplanetary shocks, Auroras, Bow shocks, 
magnetospheric tail etc.

\item[$\bullet$] Structures like shocks, neutral sheets, 
double layers, large amplitude
waves propagating inside turbulent media are 
common in the heliosphere.

\item[$\bullet$] These structures have an intermittent 
behaviour and are part of the energy
release process.

\item[$\bullet$] The new generation of accelerators will 
include a variety of non-linear structures e.g. ensembles 
of shocks, neutral sheets, collection
of double layers and waves, so we believe that the 
developments and understanding of MHD turbulence will go hand by hand with
the development of new acceleration processes in the heliosphere.

\end{itemize}


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