Superdiffusive Stochastic Fermi Acceleration in Space and Energy. (arXiv:1911.07973v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Sioulas_N/0/1/0/all/0/1">Nikos Sioulas</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Isliker_H/0/1/0/all/0/1">Heinz Isliker</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Vlahos_L/0/1/0/all/0/1">Loukas Vlahos</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Koumtzis_A/0/1/0/all/0/1">Argyris Koumtzis</a>, <a href="http://arxiv.org/find/astro-ph/1/au:+Pisokas_T/0/1/0/all/0/1">Theophilos Pisokas</a>
We analyze the transport properties of charged particles (ions and electrons)
interacting with randomly formed magnetic scatterers (e.g. large scale local
“magnetic fluctuations” or “coherent magnetic irregularities” usually
present in strongly turbulent plasmas), using the energization processes
proposed initially by Fermi in 1949. The scatterers are formed by large scale
local fluctuations ($delta B/B approx 1$) and are randomly distributed inside
the unstable magnetic topology. We construct a 3D grid on which a small
fraction of randomly chosen grid points are acting as scatterers. In
particular, we study how a large number of test particles are accelerated and
transported inside a collection of scatterers in a finite volume. Our main
results are: (1) The spatial mean-square displacement $<(Delta r)^2>$ inside
the stochastic Fermi accelerator is superdiffusive, $<(Delta r)^2> sim
t^{a_{r}},$ with $a_r sim 1.2-1.6$, for the high energy electrons with kinetic
energy $(W)$ larger than $1 MeV$, and it is normal ($a_r=1$) for the heated low
energy $(W< 10 keV)$ electrons. (2) The transport properties of the high energy
particles are closely related with the mean-free path that the particles travel
in-between the scatterers ($lambda_{sc}$). The smaller $lambda_{sc}$ is, the
faster the electrons and ions escape from the acceleration volume. (3) The mean
displacement in energy $
the acceleration volume $(a_W=1.5- 2.5)$ for the high energy particles compared
to the thermal low energy particles ($a_W=0.4$), i.e. high energy particles
undergo an enhanced systematic gain in energy.(4) The mean-square displacement
in energy $
for the low energy, heated particles.
We analyze the transport properties of charged particles (ions and electrons)
interacting with randomly formed magnetic scatterers (e.g. large scale local
“magnetic fluctuations” or “coherent magnetic irregularities” usually
present in strongly turbulent plasmas), using the energization processes
proposed initially by Fermi in 1949. The scatterers are formed by large scale
local fluctuations ($delta B/B approx 1$) and are randomly distributed inside
the unstable magnetic topology. We construct a 3D grid on which a small
fraction of randomly chosen grid points are acting as scatterers. In
particular, we study how a large number of test particles are accelerated and
transported inside a collection of scatterers in a finite volume. Our main
results are: (1) The spatial mean-square displacement $<(Delta r)^2>$ inside
the stochastic Fermi accelerator is superdiffusive, $<(Delta r)^2> sim
t^{a_{r}},$ with $a_r sim 1.2-1.6$, for the high energy electrons with kinetic
energy $(W)$ larger than $1 MeV$, and it is normal ($a_r=1$) for the heated low
energy $(W< 10 keV)$ electrons. (2) The transport properties of the high energy
particles are closely related with the mean-free path that the particles travel
in-between the scatterers ($lambda_{sc}$). The smaller $lambda_{sc}$ is, the
faster the electrons and ions escape from the acceleration volume. (3) The mean
displacement in energy $<Delta W> sim t^{a_{W}}$ is strongly enhanced inside
the acceleration volume $(a_W=1.5- 2.5)$ for the high energy particles compared
to the thermal low energy particles ($a_W=0.4$), i.e. high energy particles
undergo an enhanced systematic gain in energy.(4) The mean-square displacement
in energy $<W^2>$ is superdiffusive for the high energy particles and normal
for the low energy, heated particles.
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