Multiple explosions, spherical shocks propagating inside an inhomogeneous
medium or highly turbulent flows will form a large number of discontinuities
moving randomly in space. We study the acceleration of ions and electrons
in such an environment. Our model is applied in solar flares but our
conclusions are independent of the details of mechanism that forms the
shock waves.
We find that fro typical parameters of solar flares, a large number of
ions ($\ge 10^{-2} n_o$, where $n_o$ is the ambient plasma density) with
initial energy 200 keV $\le E_i \le$ 1.2 MeV will be accelerated up to
energies 20 to 60 MeV in less than 5. s. For the same parameters, electrons
with initial energy 20 keV $\le E_i \le$ 200 keV are accelerated up to
5 MeV, in less than 1.5 s. We compared those results with the Fermi
acceleration and found that Fermi process is slower and the energy gained much
smaller.
The energy distribution of accelerated particles escaping the acceleration
volume is of the form $f(E)\approx exp(-E/T_h)$, where $T_{hi}=13 $ MeV
for the ions and $T_{he}= 1$ MeV for the electrons, for typical parameters
(200 shock waves with velocities $2.5\times V_A\le V_s \le 4\times V_A$,
with $V_A= 2.18 10^7 $ cm/s the Alfven velocity, distributed inside a box
with characteristic length $L= 3 10^{10} $ cm). We study numerically the
relation of the acceleration time to the number of shock waves and the
length of the acceleration region. We also estimate that less than
20 % of the total energy of the 200 shock waves goes into acceleration
of particles.
Key words : the Sun : flares - shock waves - acceleration mechanisms.