Download coulomb energy of a solitary dust grain in dusty plasma

Annual Moscow Workshop “Physics of Nonideal Plasma”
(PNP’2003)
(2-3 December 2003, Moscow, Presidium RAS)
ABSTRACTS
SESSION D
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1
COULOMB ENERGY OF A SOLITARY DUST GRAIN IN DUSTY PLASMA
A.F. Pal’, A.N. Starostin, A.V. Filippov
SRC RF TRINITI
Numerical simulation results of formation process of solitary dust grain charge and
occurrence of plasma space charge near the dust grain in the argon plasma created by
an external ionization source are reported. Electron and ion currents to the dust grain
are described in the diffuse-drift approximation. The dust grain charging model used
in numerical simulations consists of discontinuity equations for electron and ion
densities, electron energy balance equation for electron temperature and Poisson
equation for the self-consistent electric field strength. The effective boundary
conditions for ion and electron densities and electron temperature are used. The
external ionization rate is mainly equal to 1.51017 cm-3s-1 and the external uniform
electric field strength has a range of values from 0 to 1600 V/cm. Argon density is
varied around 2.51019 cm-3. The dependence of the Coulomb energy of the grainplasma complex on task parameters such as the external electric field strength, the
gas ionization rate and the argon atom density is studied. It is shown that the
interaction energy of the dust grain with the plasma space charge is considerably
higher than the interaction energy of the dust grain with another one and than the dust
thermal energy as well.
2
THE INTERACTION POTENTIAL OF TWO CHARGED DUST PARTICLES AND ITS
APPLICATION FOR CALCULATION OF DUST CRYSTAL CHARACTERISTICS.
D.N. Gerasimov, O.A. Sinkevich
(MPEI)
The brief analysis of analytical and numerical results of works [1 - 7]), studying interaction of two
charged dust particle in plasma s, is given. Is shown, The received in [1] the analytical formula, that
describes electrostatic interaction of two charged dust particles in plasmas, is convenient for a
various analytical estimations and for numerical experiment. Earlier in our work [1], the analytical
expression for the potential of interaction of two charged dust particles in partly ionized gas was
received. Received potential takes into account influence not only interactions of dust particles but
also influence of electron and ion clouds that are surrounding particles. The obtained potential
essentially differs from the well-known Debye - Yukawa potential
U(r) = U0[2(1 + Xs + Xs2 )s-1 - exp(xs)]exp(-s)
(1)
Here U0 = 3 kTNDs2xs2 = qs2/80rD, xs = rd /rD is dimensionless radius of a dust, rD is the Debye
radius, s = r/rD is the dimensionless distance between centers of dusts, ND = (4/3) rD3 n0 is number
of particles in Debye’s sphere, qs is the charge of a dust, s is the surface electrical potential of a
dust. As it is clear from a fig. 1 the interaction potential of dust particles depends on radius of
particles and their charge. Potential (1) is not monotonous, has a minimum, which situation depends
on dimensionless radius of a dust xs = rd /rD. Taking into account, that xs << 1, we have for the
location of the potential energy minimum smin  1 + 3. (2)
The potential well depth is
Umin/kT = U(smin) /kT  (U0/kT) [(3-1)/ (1 + 3)] exp-(1+ 3).
The presence of the potential well depth testifies to an opportunity of formation in plasmas of the
bound state for two particles carrying an identical electrical charge. The plasma non - ideality is
 = qs2/0rD kT = 8(1 + 3) (3 - 1)-1 exp(1 + 3) > 1400. (3)
It is possible using our potential to calculate many characteristics plasma dust crystal. So, we could
find the boundary of the crystal formation using the Vlasov criterion


-(4nd/kBT)
U(s)s2ds = 1
(4)
xc
From (4) we could find the next conditions for the charged dust crystal formation
(e Zd rd)2 nd = 20kBT/3.
(5)
The condition (5) connects the charge of a dust particle, its radius, the density of dust particles, and
temperature of plasma. The formula (5) for the boundary of the dust crystal formation differs from
known Lindemann’s criterion. From (5) the next scaling between a charge of dust and their average
size is following
Zd = С rd 1\2 , С = 20kBT/3e.
(6)
We used the results, following from received criterion, for the finding condition of the crystal
formation in the atmospheric discharges [3-5]. Naturally, the obtained interaction potential of
charged dust particles (1) requires experimental check. Other kind of checking can be obtained from
the numerical calculations of behavior of charged dust particles in plasmas. Various mechanisms of
charged dust particles interaction were numerically investigated using the Vlasov equations in [6].
These numerical experiments have also confirmed similar non - monotonous changing of the
potential of interaction of charged dust particle in plasma. The dependence of total force of
interaction of two charged particles in plasma that was obtained in [6] is presented in a fig. 2. From
fig. 2 also follows an opportunity of the bound state formation for two particles carrying an identical
electrical charge in plasmas. Later, appearance of a minimum of potential energy of interaction of
two similarly charged dust particles was received in work [7]. The author of [7] was starting from
similar physical behavior of two charged particles interaction in plasma. His result was presented
2
3
without the reference to our works [1- 6], published early in the domestic and foreign editions. In [7]
the following expression for the energy of interaction of two dust particles is received.
U(r) = (q1q2/0r) (1 - r/2rD) exp(-r/rD). (6)
The form of this potential is represented in a fig. 3. The position of the potential energy minimum,
that was following from the formula (6), within small parameter representing the attitude of radius of
a dust to Debye’s radius does not reflect influence of the dust sizes. Despite of some distinction in
representation of potential of interaction of two charged dust particles in plasma that are given by
formulas (1) and (6), the location of the minimum energy of interaction completely coincides with
(2).
REFERENSES
1.D.N. Gerasimov, O.A. Sinkevich. Formation of Ordered Structures in Thermal Dusty Plasma.
High Temperature 1999, Vol. 37, No 6, pp. 823-827.
2.D.N. Gerasimov, V.V. Chinnov, O.A. Sinkevich. Periodical strustures in Thermal Dusty Plasmas.
Journal of Technical Physics, Special Issue, Polish Academy of Science, 2000, Vol. 41, No 1,
pp. 593 - 595.
3.D.N. Gerasimov, O.A. Sinkevich Formation of Periodical Structures in Thermal Dusty Plasmas.
Bulletin of the American Physical Society, Program of the 42nd Annual Meeting of the Division
of Plasma Physics and 10th Int. Conf. on Plasma Physics. October 23-27, 2000, Quebec City,
Quebec, Canada, Vol. 45, No 10, pp. 124- 126.
4.V.V.Glazkov, D.N. Gerasimov, O.A. Sinkevich. Lightning Initiation by Laser Radiation in an
Atmosphere. Bulletin of the American Physical Society, Program of the 2000 Gaseous
Electronics Conference, October 24-27, 2000, Houston, TX, Report LR1.002 41).
5.V.V.Glazkov, D.N. Gerasimov, O.A. Sinkevich. The Dust Plasma Crystal and Lightning Initiation
in the Atmosphere. Proc. XXV Int. Conf. on Phenomena in Ionized Gases (ICPIG), July 17-27,
2001, Nagoye, Japan, Vol. 3, p.79.
6.Л.В. Иньков. Численное моделирование кинетических процессов в пылевой плазме.
Диссертация канд.ф.-м.н., 2003, МФТИ.
7.A.S.Ivanov. Polarization’s interaction and bound states of like charged particles in plasma.
PhysicsLetters, 2001, Vol.A290, P. 304–308.
4
LONG-RANGE INTERACTION OF CHARGED PARTICLES
OF CONDENSED PHASE IN THE THERMAL PLASMA
V.I.Vishnyakov, G.S.Dragan
Mechnikov Odessa national university
<[email protected]>
Thermal plasma is characterized by that its components have identical temperature. Ionization
equilibrium in thermal plasma is achieved due to collisions of gas particles. Therefore the thermal
plasma containing particles of a condensed phase (a smoky plasma) essentially differs from dusty
plasma. The potential distribution in plasma is featured by a Poisson equation
  4
(1)
The problem of assignment of boundary conditions for equation (1) surveyed by Einstein in paper
[1]. It was shown, that the potential is necessary for digitizing from some value  0 , which is the
trivial solution of the equation (1).
For the single particle, which is taking place in equilibrium with a gas phase, the density of
charge in the equation (1) is set as a Boltzmann distribution law, and the potential is digitized from
potential of plasma
(2)
 pl  kT / 2e  ln( ni / ne ) .
Here we guess, that somewhere in volume of plasma the requirement is implemented (r  )  0 and
in a neighbourhood of point r* there are some values of electron n e* and ions n i* number densities.
All solutions of the Poisson-Boltzmann equation should be symmetrical concerning direct (2).
The Potential of plasma is interlinked linearly with parameter of non-equilibrium:
  e pl
(3)
Nonequilibrium ionization at surface of the condensed particle is corollary of equilibrium on
boundary a particle - plasma and does not depend on presence of other particles and distance
between them. However a gradient  , if it exists, may render essential influence on the processes
happening in plasma.
We radiate from that standing, that local perturbations in plasma are not spread to all volume,
and damp in accordance with removal from the disturbing particle. Then the perturbation of
ionization equilibrium called by processes on phase boundary a particle - plasma should damp in
accordance with removal from particle.
However the parameter of non-equilibrium is interlinked linearly with potential of plasma. We
shall note, that all properties of the trivial solution of a Poisson equation any function being the
solution of Laplace equation   0 has. That is in neighbourhood of some particle of radius a ,
stimulating the surface potential of plasma  pls , the potential distribution of plasma may look like:
 pl (r )   pls a / r ,
(4)
Thus everywhere where measured value of potential does not differ from value  pl , plasma
remains electroneutral:
ne ( pl )  ni ( pl ) .
(5)
Spatial inhomogeneity of potential of plasma and parameter of non-equilibrium of plasma may
cause long-range interaction of the condensed charged particles.
1. A. Einstein, in: “Albert Einstein and gravitation theory”, Moscow, Mir (1979) p. 287
5
LARGE-AMPLITUDE AND SHOCK WAVES
IN A DC GLOW DISCHARGE COMPLEX PLASMA
V.E. Fortov, O.F. Petrov, V.I. Molotkov, V.M. Torchinsky, M.Y.Poustylnik, A.G.
Khrapak, V.N. Naumkin, A.V. Chernyshov
IHED RAS
A large-amplitude wave with two humps of dust density, separated by a dip was
generated. To excite the wave in the dc glow discharge dusty plasma a gas-dynamic
impact was used. The structure obtained had several interesting properties such as
strong compression of dust in the humps, supersonic dust particles in the rarefaction
zone, reconstruction of the initial dust configuration after the passing of the wave.
The velocity of the perturbation is of the order of the dust-acoustic velocity. The
peculiarities of the phenomenon observed are discussed. The mechanism of
generation and propagation for such kind of perturbation is proposed.
In other experiments a jump of dust density propagating through the dusty
plasma structure with the supersonic speed has been observed. To excite the
disturbance an impulse of axial magnetic field has been applied to the dusty plasma
structure formed in a dc glow discharge striation. This impulse resulted in the
dynamical stretching. During the reconstruction of the structure a ramp-shaped
perturbation of dust density appeared. The perturbation was steepening and formed
possibly into a dust-acoustic shock. The observations are presented and discussed.
6
Low Frequency Tensor of Dielectric Permittivity of Dusty Plasma
With Account of Dipole Moments of Granules
V.Mal’nev1, Eu. Martys2
1
2
Physics Department, Kiev National University, Kiev, Ukraine,
Radio Physics Department, Kiev National University, Kiev, Ukraine,
mail:[email protected]
According to many reports on physical properties of dusty plasmas, the granules may
carry a comparatively large negative electric charge q that could reach up to 103 charges of
electrons In many cases the granules cannot be treated as spherical particles. They could be
modeled rather as elongated ellipsoids or even needles. The corresponding electric dipole
moments of the granules are of the order of d  qL (L is a length of an elongated particle)
[1]. For L ~ 1 we obtain that a dipole of the granule could reach d~104D. These dipoles
rotate with a thermal frequency  T  T / J (T is a temperature of granules that is equal to
the temperature of ions or a buffer gas, J is a moment of inertia the granule J  ML2, M is a
mass of the granule). Taking the granule mass M ~ 10-11 - 10-12g we obtain that T ~102-103
Hz. It is worth noting that there is a report even about T ~ 104 Hz [2].
In this communication we present the results of calculation of the low frequency
part of the tensor of dielectric permittivity of the dusty plasma consisting of charged
granules with dipole moments. We have calculated the tensor of polarizability of a system
of rigid rotators in an alternating electric field by using the methods of quantum mechanics.
The tensor of dielectric permittivity associated with the rotational motion of the granulerotators could be obtained in the classical limit because a difference between the rotation
levels E   2 l (l  1) / 2 J is always very small in comparison with a temperature T.
The tensor of dielectric permittivity under consideration contains an imaginary part
that results in appearance of a special type of the Landau damping that does not depend on a
wave vector and takes the form  ~ exp(  2 /  T2 ) . This type of the Landau damping was
firstly discussed in [3] where the tensor of dielectric permittivity of the electron – ion
plasma with polar molecules as a neutral component has been obtained.
The above mentioned Landau damping results in a considerable absorption of the
low frequency electromagnetic radiation near the frequency T. It may also suppress the
allowed vibrations of the dusty plasma that are close to T. From the other hand, this
mechanism of damping may be inverted and utilized for amplifying of the low frequency
vibrations in the dusty plasma. It could be realized with the help of an external source of
energy that creates a nonequilibrium population of the rotation levels or when a temperature
of rotation of the granules becomes higher than a temperature of their translation motion.
REFERENCES
1. D.D. Tskhakaya, P.K. Shukla, N.L. Tsintsadze, Electrodynamics and dispersion properties of a
magnetized plasma containing elongated and rotating dust grains, Zhur. Exper. Teor. Fiz., 120,
340 (2001).
2. P.K. Shukla, A.A. Mamum, Introduction to Dusty Plasma Physics, IoP Publishing, London,
2002.
3. Solomon.Mulugeta and V. Malnev, Thermodynamic properties and waves in a dipole plasma, J.
Plasma Phys, 39, 475 (1988).
7
Magnetic Susceptibility of Dusty Plasma with Ferromagnetic Granules
V.Mal’nev1, Eu. Martysh2
1
Physics Department, Kiev National University, Kiev, Ukraine, e-mail:[email protected]
2
Radio Physics Department, Kiev National University, Kiev, Ukraine, email:[email protected]
In this report we consider the low frequency dispersion properties of the dusty plasma
with ferromagnetic negatively charged granules. We assume that typical sizes of the
granules are small enough to treat them as one-domain ferromagnetic particles. All granules
are identical spheres possessing a constant magnetic dipole moment dB and a moment of
inertia J. (Such a system could created in laboratory by imposing of a constant magnetic
field to the plasma with ferromagnetic granules). A mention about the experimental study of
this type of dusty plasma is given in [1]. The collective properties of the electron-ion plasma
with the neutral component consisting of paramagnetic atoms were considered in [2].
The magnetic dipoles execute the rotational heat motion with an angular frequency T.
Calculating the magnetization of the unit volume of the gas of dusty particles it is possible
to get expressions of magnetic permittivity as a function of frequency  (). The results are
similar to those that have been obtained for a gas of the electric polar molecules while
calculating the tensor of dielectric permittivity. In the limit  << T , we get an expression
for the Langevin magnetization. At  >> T , it is necessary to take into account a
dispersion of the magnetization associated with the rotation of the magnetic moments of
granules. The imaginary part of magnetization even in the collisionless approach results in
the rotation Landau damping.
We also considered the behavior of the magnetization of the gas of ferromagnetic granules
in the external homogeneous constant field. In this case, the magnetic moments of granules
are oriented along the magnetic field in accordance with the Langevin formula. They
execute a precession motion along this field with the angular velocity T . It is necessary to
note that there is one more allowed frequency appears in the granule subsystem that is
connected with vibrations of magnetic moments of granules in the constant magnetic field
 B  d B B0 / J (B0 is the external magnetic field).
The corresponding expressions of the magnetic permittivity tensor are presented in the
report. It is interesting that charged elongated ferromagnetic particles possess magnetic and
electric dipole moments at the same time. At the special set of parameters of the dusty
plasma with ferromagnetic granules it is possible to meet conditions for realization of
negative dielectric and magnetic permittivities (<0 and <0) simultaneously. An
experimental realization of this situation is mentioned in [3].
REFERENCES
1. V.I. Molotkov, M.Yu. Pustyl’nik, V.M. Torchinskii, and V.E. Fortov, Plasma of DC current
corona with dusty particles: selforganization and peculiarities of behavior, Proceedings of the
Conference on Plasma Chemistry, Ivanovo, Russia, v.1, pp 51-54.,( 2002).
2. W. Bantikassegn and V.N. Mal’nev, Waves in a paramagnetic plasma, J. Plasma Phys, 45, 125
(1991).
3. D. Smith, W.J. Padilla, D.C. Vier,e.a., Composite Medium with Simultaneouasly Negative
Permeability and Permittivity, Phys. Rev. Lett. V.84,#18 pp. 4184-4187 (2000).
8
ON A POSSIBILITY OF REALIZATION OF DUST PLASMA CRYSTAL
WITH FREE BOUNDARIES.
I.I. Klimovskii, V.A. Sinel’shchikov
Institute for High Energy Density, RAS, Moscow, Russia
On the basis of the analysis of literary data the conditions on the radius rp of dust particles,
on the interparticle distance Lp, on relation between the electron and ion concentrations, averaged
on interparticle volume, on the coupling parameter are formulated, at which realization the
formation of a dust plasma crystal with free boundaries, not subject to influence of external forces,
is possible. Such crystal can be formed as a result of an attraction between the Debye atoms
consisting from a dust particle and a cloud of electrons and ions, shielding its field. Assuming that
the lengths of free path of electrons and ions are much greater than the ion Debye length, and the
charging of dust particles occurs by plasma electrons, the plasma parameters (concentrations of dust
particles, electrons and ions, the particle charge) satisfying to the formulated conditions were
calculated. The calculations were fulfilled for isothermal plasma at temperature T = 500K for a
range of dust particle radiuses from 0.1 up to 25 microns. The opportunity of transition of Debye
dusty plasma consisting from Debye atoms to Coulomb dusty plasma at increase of the particle
charge is discussed. It is suggested that an abrupt increase of a particle charge results in the
explosion of Debye plasma.
For experimental realization of dust plasma Debye crystals, i.e. crystals formed by Debye
atoms, it is proposed to use photoionized plasma, in which an alkaline metal vapour is ionized by
ultraviolet (UV) of radiation. It is analyzed the opportunity of creation of such plasma at the
expense of ionization of Cs vapour by UV-radiation of XeCl-excilamp. For isothermal plasma with
temperature 500 K the range of pressures of He, Ne, Ar and Cs vapour, corresponding to conditions
of formation of Debye plasma crystal received in analytical and numerical accounts, are
determined. According to results of calculations and estimations, at change of radius of dusty
particles from 25 up to 0,1 microns the limiting allowable pressure of buffer gas grows
approximately from 102 up to 104 Pa, and the limiting allowable concentration of Cs atoms - from
1015 up to 1017 sm-3. At nCs = 1015 sm-3 the necessary intensity of UV-radiation is increased from 102
up to 106 W/sm2.
9