Transcript Nonlinear Alfven waves in dusty astrophysical plasmas

The University of Sydney
Plasma Kinetics around a Dust Grain
in an Ion Flow
N F Cramer and S V Vladimirov,
School of Physics, University of Sydney,
S A Maiorov,
General Physics Institute, Moscow
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The dust structures in a low-temperature weakly ionized
plasma have attracted considerable recent attention
associated with colloidal crystals, as well as with other selforganized formations such as dust clouds, ``drops", ``voids",
etc.
In a typical laboratory discharge, dust particles are negatively
charged and usually levitate in the sheath or pre-sheath
region under the balance of gravitational, electrostatic (due to
the sheath electric field) and plasma (such as the ion drag)
forces.
The ion flow provides not only a direct (dragging) influence,
but is also responsible for the generation of associated
collective plasma processes which can strongly affect the
vertical arrangement of dust grains.
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Three-dimensional dust lattices
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Dust charging
 Micrometer sized particles embedded in a plasma acquire a
charge; if the main charging mechanism is due to plasma
currents then dust grains are charged negatively
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 The effect of the wake behind each grain in the Mach cone
(Vladimirov and Nambu, 1995; Vladimirov and Ishihara 1996-1998)
M=1.5
ion
elec t rode
----------->
15
----------->
flow
----------->
to the

D 0
----------->
electrode
----------->
15
5
0
Z/D
-25
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The kinetics of plasma particles around a stationary dust
grain in the presence of an ion flow is studied using a 3dimensional molecular dynamics simulation method.
The model is self-consistent, involving the dynamics of
plasma electrons and ions as well as charging of the dust
grain.
The effect of ion focusing is investigated as a function of
the ion flow velocity.
Distributions of electron and ion number densities, and
electrostatic plasma potential are obtained.
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The method includes consideration of the time evolution of
N charged and N
the system consisting of Ni positively
e
negatively charged particles confined in a region
0<x<Lx, 0<y<Ly, 0<z<Lz.
i
There is a macroscopic absorbing grain (“dust particle") of
radius R with infinite mass and an initial (negative) charge
Q=-Zde, where -e is the electron charge.
The dust grain is placed at x=x0, y=y0, and z=z0.
The walls bounding the simulation region are elastic for
electrons.
For ions, they are elastic in the y and z directions, i.e. at
y=(0,Ly) and z=(0,Lz).
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The ions are introduced in the system at the plane x=0 as a
uniform flow with the Mach number M=V0/cs and the
temperature Ti, where cs is the ion-acoustic sound speed.
At x=Lx the ions are removed from the system.
The paths of the ions and electrons are determined through
numerical integration of the equations of motion, with all
particles interacting via the Coulomb force.
For the characteristic lengths we have Lx/4=Ly=Lz=10hx, with
the characteristic grid step hx=4hy=4hz=1.077mm.
Other initial values are summarized in Table 1.
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For the given values, the characteristic lengths in the plasma
are: electron Debye length rDe=5.256mm, ion Debye length
rDi=0.831mm, and the Landau length for scattering of the ions
on the dust particle by the angle p/2 is rL=0.6/M2mm.
TA BLE
M ac r o p a r t i cl e
I on s
E l ect r o n s
C h arge
¡ 10 0 0 e
e
¡ e
M a ss
1
N u m b er
1
10000
9000
T em p er a t u r e
n/ a
0 .0 2 5eV
1eV
4m
T A B L E I . T h e i n t i a l v a l u es f or t h e d u st g r ai n a n d p l a sm a p ar t i cl es. m
m a ss, m
e
= 9: 1 1 ¢1 0 2 8 g i s t h e el ect r on m a ss, e = 4 :8 ¢1 0 ¡
10
100m
p
p
= 18 4 2m
e
e
is t h e p r ot on
st at co u l i s t h e ( a b so l u t e) el ect r o n ch a r g e.
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The total simulation time of the computed physical processes is
3.36 x 10-9 s which is approximately half the oscillation period of
plasma ions oscillating with the ion plasma frequency.
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Fig 1: Contour plots of the ion density, for three values of the speed of the ion
flow (one is subsonic with M2=0.6, and two supersonic, with M2=1.2 and
M2=2.4). A strong ion focus is formed at the distance of a fraction of the 11
electron Debye length behind the dust grain.
Fig. 2: surface plot of
the ion density.The
maximum value of the
density at the ion focus
is almost independent
of the flow velocity,
whereas the
characteristic distance
of the ion focus from
the dust grain
increases with
increasing flow
velocity.
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This characteristic spacing corresponds to an ion focus effect in
the near zone of the dust grain, which is a purely kinetic effect
not associated with the collective wake field formation.
The oscillating wake field which is formed in the wave zone
behind the grain cannot form for the considered simulation time
(half of the period of the ion oscillations).
Another kinetic effect seen from Figs. 1 and 2 is the appearance
of precursors in front of the dust grain, which can be attributed to
those ions reflected backwards within the radius (around the x
axis) of order of the Landau length.
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Fig. 3: Surface plot of the plasma
electrostatic potential
(in Volts). The parts where the
potential becomes positive, thus
forming an attractive region for
negatively charged particles,
can be seen behind the grain.
The potential well behind the
dust grain deepens, and the
characteristic distance of the
potential minimum increases with
the increase of the flow velocity.
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Conclusions
MD calculations show plasma kinetics around a charged
macroscopic body (dust grain) in the presence of an ion flow
involves a strong ion focusing behind the grain.
The most important for the processes involved is the ion timescale; the kinetics of the electrons follows a Boltzmann
distribution with good agreement. To save computer time,
future MD simulations can assume that the ions and the dust are
immersed in an electron background which obeys a Boltzmann
distribution.
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