CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
SHOCK WAVES IN DUSTY PLASMAST
J.E.Hammerberg, T.C.Germann and B.L.Holian
Los Alamos National Laboratory, Los Alamos, NM 87545
Abstract. It will soon become possible to create confined dusty plasmas in microgravity environments
with particle numbers approaching 106. Very high plasma F's are possible, F>103. Characteristic time
and length scales for these systems are of the order 100 msec and 500 |Lim. Consequently the possibility
now exists for observing microscopic dynamics in real time. We present molecular dynamics simulations of such a confined system under shock loading and discuss the nature of the microscopic deformations
densed matter (1,3,4), particularly for single crystals. Some of the behavior is apparently generic,
depending more on crystalline structure than on the
detailed nature of the atomic interaction potential, at
least for close-packed structures. Most of these simulations have been for pairwise additive potentials
such as Morse and Lennard-Jones interactions but
more sophisticated many body interaction potentials
such as embedded atom method potentials have
been studied as well.
Another class of potentials which has not been
studied as much in the above context is the moderate
range screened potentials such as Debye-Huckel or
Yukawa potentials. This class is of interest in the
study of complex plasmas exemplified by dusty
plasmas (5-7). These systems are composed of Jim
sized grains in a neutralizing background of ions
and electrons. Negative grain charges in excess of
104 are readily attainable and the dominant component of the grain-grain interaction potential is a
screened Coulomb interaction with a Debye length
of order 500 jLim. In terrestrial experiments a trap
potential due to combined electric and gravitational
potentials leads to trapped configurations which are
non-uniform in the field direction, resulting in nonuniform densities in this direction. A variety of equi-
INTRODUCTION
The microscopic deformations which are
responsible for plastic flow in shocked crystals are
complex (1). The temporal evolution of defect distributions which define the nonequilibrium steady
state behind a shock wave in a metal are exceedingly
difficult to observe, due in part to the short characteristic time scales for metals.These time scales,
which are of the order of an optical phonon period,
i.e. 10"12 sec, require dynamic experiments of great
precision. Dynamic X-ray diffraction may provide
some information, particularly on shock induced
phase transitions (2).More traditional plate impact
experiments which measure macroscopic wave profiles constrain microscopic and mesoscopic constitutive models but cannot provide definitive
information concerning the detailed microscopic
mechanisms of plastic deformation. Recovered samples provide final state information; however, questions of release wave kinetics confound that picture.
In recent years large scale nonequilibrium
molecular dynamics (NEMD) simulations have provided a window to the short time (nsec) and small
length scale (0.1 Jim) behavior in shocked con359
or defining a dimensionless distance x=r/!0 and a
dimensionless inverse screening length P=cclo>
librium configurations and properties have been analyzed (8,9). Typical plasma parameters for the dust
grains result in a Coulomb parameter (the ratio of
1 -Px
V(x) = 60ie
Z.2e2
potential to kinetic energy), T =
ak
BTd
, greater
We measure energy in units of
than 103, i.e. in the crystalline regime of the
screened Coulomb phase diagram (10). Here a is the
Wigner Seitz radius for the charged dust particles,
n-
d
1= : 47Ca3
5
> Zd e is the dust charge, and Td is
time in units of
the dust temperature. While the potential of interaction also contains symmetry breaking ion-streaming
wake terms which lead to more complex crystal
structures in terrestrial experiments (11), spacebased experiments offer the possibility of realizing
uniform configurations of 105 or more grains with
interactions approaching a screened Coulomb interaction (12-14). Moreover, in the strongly coupled
phases, fluid or crystalline, the effective period of
oscillation for a grain is of order 0.1 sec or more
with length scales of order 500 |Lim. Thus it is possible, in principle, to observe using optical means the
detailed kinetics both of phase transformations and
nonlinear dynamical processes such as dislocation
dynamics and shock processes. Furthermore, system
sizes are of the scale realizable in large-scale
NEMD simulations. In the following we present
some results of NEMD simulations for shock waves
in a crystalline Yukawa plasma to indicate some of
the behavior and structural dynamics occurring
behind a shock front in these systems.
e0 = —;—
and
°~
We have used the SPaSM NEMD code developed at Los Alamos by Lomdahl and collaborators
(15,16) and use the geometry described by Holian
and Lomdahl (3), i.e. a perfect bcc crystal at an initial temperature T0 moves with a uniform velocity Up toward a stationary piston which constitutes a
specularly reflecting boundary. A shock moves away
from the piston with velocity us-up. We apply periodic boundary conditions in the directions transverse to the shock direction and constrain the free
end of the sample (the first five layers) to move with
velocity -up. The boundary conditions we impose
correspond to plain strain boundary conditions. For
the simulations we report here we consider a velocity (the piston velocity) to be directed along the
<100> direction of the bcc lattice.
RESULTS AND DISCUSSION
We have taken an initial point in the Yukawa
phase diagram with T=1354 and (3=3.0 (aa0=1.477).
This is a bcc state close to the bcc-fcc phase boundary. We considered a series of piston velocities, up
from 0.1 to 1.0. System sizes ranged from 16x16x80
to 64x64x128 cubic bcc unit cells. Above the velocity, Up = 0.5, the final shocked state was molten with
no evidence of long range order. For smaller piston
velocities a defective bcc configuration resulted.
Figure 1 shows particle positions in two contiguous
(100) planes located 1/4 of the distance from the
fixed boundary at a time well after the shock wave
has passed and before there is any influence from
the reflection from the opposite surface. At the lowest piston velocities the response is purely elastic,
SHOCK SIMULATIONS FOR A YUKAWA
PLASMA
We consider initial states for a Yukawa potential system in the bcc portion of the phase diagram.
The equilibrium phase diagram may be found in
(10). Our initial configuration has a cubic lattice
constant IQ with density 2/10 and we write the interparticle potential as
2 2
360
*
• • * * * * »i
*
•
up=0.2
•
*
•
•
•
•
•
•
•
»
i
•;
up=0.3
....i._.^..i-._.^...^...-r._...^...
„..._,......_....
t .• . • . . • » • * • . * » . • ! % • t ,*
•••**•• *•*»•!••* * • * % * « • *
• % • • • % « • % • • « , • • * * • \ * %
i * t»* • • » » • * • • % , » * • * * • * % «
». * » , * , • i % * %;« *. % *
*».•*•* * » ^ * » » l * » f i
Up=0.4
up=0.5
FIGURE 1. Views along the <100> direction of two (100) planes located at a distance of 30 planes from the stationary end at times t= 30 IQ.
System size: 16x16x80 cubic unit cells.
followed at higher velocities by a transition to a
steady plastic wave as evidenced by the dislocation
structures seen in Fig. 1. Finally, the shock temperature is sufficiently high to induce melting at temperatures consistent with the phase diagram of
Hamaguchi et al. (10). One of the remarkable
aspects of propagation along <100> is seen in Fig. 2.
The steady wave profile is preceeded by a solitonlike wave train with compressive distortions involv-
ing approximately three lattice planes. A similar
structure has been observed in fee Lennard-Jones
systems for shock propagation along the <110>
direction (4). Another striking feature is the apparent patterning seen for up=0.4 which may be a signature of stacking fault nucleation similar to that
seen in (3,4) for fee Lennard-Jones systems. The
shock dynamics described above ought to be
directly observable in experimental high F dusty
361
FIGURE 2.Side view of the shocked Yukawa plasma at t=30to for up=0.30. Sample size=32x32x96 cubic unit cells. Particles are colored by
potential energy with blue corresponding to 0.6 and red to 0.95.
T.Morfill, G.E. et al., "Plasma crystals-a review", in
Advances in Dusty Plasmas, edited by P.K.
Shukla et al., World Scientific, 1997, pp. 99-142.
S.Pieper, J.B., Goree, J., and Quinn, R.A., Phys.
Rev. E54, 5636-5640 (1996).
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(1996).
10.Hamaguchi, S. et al., Phys. Rev. E56, 4671-4682
(1997).
1 l.Hammerberg, J.E. et al., IEEE Trans. Plasma Sci.
29, 247-255 (2001).
12.Morfill, G.E. et al., "Plasma crystals and liquid
plasmas", in Physics of Dusty Plasmas, edited by
M. Horanyi et al., AIP Conference Proceedings
446, New York, 1998, pp. 184-198.
13.Morfill, G.E. et al., Phys. Rev. Lett. 83, 15981601 (1999).
14.Zuzic, M. et al Phys. Rev. Lett. 85,4064-4067
(2000).
15.Lomdahl, P.S. et al., Proc. Supercomputing 93,
IEEE Computer Society Press, 1993, p. 520.
16.Beazley, D.M. and Lomdahl, PS., Comput. Phys.
11,230(1997).
t Work performed under auspices of U.S. DOE at
LANL under contract W-7405-Eng-36
plasmas provided sufficiently large numbers of
grains can be confined so that edge effects can be
controlled for in finite size systems. Such systems
are expected to be produced under microgravity
conditions. The rich dynamic structure indicated
here will, we hope, provide impetus for experiments
in dusty plasmas under nonequilibrium forcing.
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