Alushta-2010 International Conference-School on Plasma Physics and Controlled Fusion and

PARTICLES
S. Dunets
1
, A. Dobrovolskiy
1
, A. Evsyukov
1
, A. Goncharov
1
, V. Gushenets
2
,
I. Litovko
3
, and E. Oks
2
1
Institute of Physics NAS of Ukraine, 46 pr. Nauki, Kiev 03028, Ukraine;
2
High Current Electronics Institute SD RAS, 4 Akademichesky Ave., Tomsk 634050, Russia;
3
Institute for Nuclear Research NAS of Ukraine, 47 pr. Nauki, Kiev 03028, Ukraine
The configuration of a plasma lens with crossed electric and magnetic fields provides  an
attractive way to maintain a stable plasma discharge at low pressure and create numerous cost
effective, robust construction plasma devices for ion treatment and deposition of exotic
coatings. One of them is a device initially elaborated and designed as a cylindrical plasma
source for ion treatment of cylindrical symmetry parts complicated in shape. In our previous
works it was first proposed as a positive space charge plasma lens based on the principle of
magnetic isolation of electrons for manipulating high current beams of negatively charged
particles [1]. To restrict the influence of the finite magnetic field in the lens volume the
modified magnetic configuration was elaborated and applied. Here we describe new
experimental and theoretical results of the lens development.
Floating potential distributions in the lens with a modified magnetic field under different
anode potentials are investigated. It is shown that reducing the magnetic field at the area of
the lens axis doesn’t change essentially shapes of floating potential distributions in
comparison with our previous measurement of the space charge distribution in the volume of
plasma lens without additional magnetic poles. It is demonstrated experimentally that there is
no noticeable difference between positions of floating potential peaks in the range of anode
potential values as wide as 700-1500 V. It is established that with anode potential growing,
the performance of space charge creation decreases. Radial electric field profiles in the center
of the lens at different anode potentials are complicated shapes. It is noticed that the electric
field magnitude depends weakly upon anode potential at a given pressure in the lens.
Numerical simulations of the lens according to the new improved theoretical model have
been carried out. Angular and energy distributions of ions converging to the axis of the lens
were considered. The transverse magnetic field leading to a momentum aberration of
converging ion beam was taken into account. The qualitative agreement of numerical results
with experimental data is shown.
1. A. Dobrovolskiy, S. Dunets, A. Evsyukov, A. Goncharov, V. Gushenets, I. Litovko, and
E. Oks, Rev. Sci. Instrum. 81, 02B704 (2010).

108
6-11
PHENOMENON OF THE CURRENT CRISIS IN PLASMA ACCELERATORS
WITH DIFFERENT GEOMETRY OF THE IMPENETRABLE ELECTRODES
A.N. Kozlov
Keldysh Institute of Applied Mathematics, RAS, Moscow, Russia
On the basis of the developed two-dimensional two-fluid MHD model it is carried out the
research of the processes near to the continuous impenetrable electrodes in the channels of the
quasi-steady plasma accelerators (QSPA). Now the various modifications of the QSPA (see,
for example, [1-5]) which allow to solve partially the problem of the interaction of the plasma
streams with electrodes are offered and tested. The last experimental development [5] based
on the theoretical analysis [6-7] answers a mode of the ion current transport regime with the
penetrated electrodes at presence of an additional longitudinal magnetic field.
  The continuous impenetrable electrodes use in a lot of cases. The theoretical analysis of
dynamics of the plasma streams across a magnetic field in a vicinity of the equipotential
impenetrable electrode on the basis of the generalized Ohm’s law is presented in [1]. The
account of the Hall effect (
i
e
V
V
≠
) and parameter
e
e
τ
ω
 can lead to a reorganization of the
flow structure. In experiments this phenomenon is shown on the volt-ampere characteristics
and accompanied by erosion of electrodes. Thus the current in system cannot exceed the some
critical value defined by the approximate experimental relation for the given mass flux.
The developed two-fluid MHD model takes into account the Hal effect, the conductivity
tensor of the medium and the dependence of the transport coefficients from
e
e
τ
ω
. The
various modifications of the two-fluid MHD model answer the statement of the various
boundary conditions and have been used earlier for the comparison of the numerical and
analytical models [6], and also for the analysis of the ion current transport regime in QSPA
with an additional longitudinal magnetic field [7]. In the present work it is a question of the
numerical researches of the processes near to the continuous electrodes in the plasma
accelerators with the unique azimuthal component of the magnetic field.
The corresponding boundary conditions define the character of the interaction of plasma
with a surface of electrodes. The researches have confirmed the theory of the phenomenon of
the current crisis. The formation of a layer near to the anode and the occurrence under the
certain conditions of the current crisis are revealed. The available experimental data defining
the border of occurrence of the critical modes [1] are compared to the results of the numerical
experiments. The analysis of the influence of geometry of the impenetrable electrodes on the
process of formation of the current crisis is carried out.
   The work has been executed at the financial support of RFBR (grant 09-01-12056) and
RAS (program No. 14 of the basic researches of Presidium RAS, the project - 301).
1. A.I. Morozov. Introduction in plasmadynamics. Moscow: Fizmatlit, 2nd issue, 2008.
2. V.I. Tereshin, A.N. Bandura, O.V. Byrka, V.V. Chebotarev, I.E. Garkusha, I. Landman,
V.A. Makhlaj, I.M. Neklyudov, D.G. Solyakov and A.V. Tsarenko.  // Plasma Phys.
Contr. Fusion, 2007, 49, A231.
3. V.G. Belan, S.P. Zolotarev, V.F. Levashov, V.S. Mainashev, A.I. Morozov,
V.L. Podkoviirov and Iu.V. Skvortsov. // Sov. J. Plasma Phys. 1990, 16, p. 96.
4. S.I. Ananin, V.M. Astashinskii, E.A. Kostyukevich, A.A. Man’kovskii and L.Ya. Min’ko.
// Plasma Physics Reports,  1998, 24, p. 936.
5. Kozlov A.N., Drukarenko S.P., Klimov N.S., Moskacheva A.A., Podkovyrov V.L.
// Problems of Atomic Science and Technology. Plasma Physics. 2009. No. 1. P. 92-94.
6. Kozlov A.N. // J. Plasma Physics. 2008. V. 74. No. 2. P. 261-286.
7. Kozlov A.N. // J. Applied Mechanics and Tech. Physics. 2009. V. 50. No. 3. P. 396-405.

109
6-12
RADIATION GAS DYNAMICS OF NEAR-SURFACE LASER PLUMES IN AR
Victor V. Kuzenov
Ishlinsky Institute for Problems in Mechanics RAS,
prosp. Vernadskogo 101, block 1, 119526, Moscow, Russia,
 tel.[phone], e-mail: [e-mail]
Interaction of laser radiation with a metal barrier is numerically studied. The following
general parameters of laser radiation are considered: wavelength is varied in the region 0.3-
10.6 microns, duration of the laser pulses 10
-8
-10
-7
 s, density of the laser radiation is
q <10
10
W/cm
2
. Material of the metallic barrier - Al. An environment was argon. In this case
an interaction of the laser radiation with metallic barrier is accompanied by occurrence of
plasma in pairs a material of the barrier and surrounding gas.
For this reason, numerical simulation model, which is presented in the paper and intended
for interpretation of available experimental data, and also for prediction various
characteristics of the interaction, is constructed on the basis of the equations of multi-species
one-temperature radiative gasdynamics in view of electromagnetic fields and turbulence of
plasma.
Feature of the given model is the account of movement of boundary region dividing a
metallic barrier, laser plasma and surrounding gas. Electromagnetic processes are described
by system of the Maxwell-Ohm equations in plasma with final conductivity. Radiation
transfer is considered within the framework of multi-group approach.
System of equation of the one-temperature radiating magneto-gasdynamics is
supplemented with the equations describing processes of heating and evaporation of metallic
barrier under action of laser radiation and thermal radiation of laser plasma. It consists from
quasi two dimensional equation of heat conductivity in moving system of coordinates (the
wave of evaporation connected to front) in perpendicular direction to surface of the metallic
barrier. The system of the equations also contains kinetic equation for superficial evaporations
of condensed substance within the framework of the Knudsen model.
The numeric solution of this equation system is based on splitting by physical processes
and spatial directions. The solution of splitted equations occurs by the variant of compact
finite-difference scheme of 7-th order, which has been developed. At radiation transfer
equations solution the modified alternative-triangular method has been used. The equations
for magnetic induction are solved by semi-implicit splitting method.
Values of threshold of laser intensity, resulting to "flash" of absorption and formation near
surface laser plasmas are found. It is discovered, that time of a delay of occurrence of plasma
formation near to metallic barrier depends on size of laser radiation focusing, density of a
surrounding gas, and energy of laser radiation.
Complication of radiative gas dynamic processes are observed at density of laser radiation
~10
6
 – 10
10
 W/cm
2
 . Waves of absorption of the laser radiation, moving from a place of
breakdown towards to radiation of the laser are observed. Thus, there is shielding of
illuminated surfaces of a metallic barrier, a reduction of temperature of a material, that in
some cases is accompanied by the termination of evaporation. As a whole, the mode of
evaporation in this case has pulsing character. The detailed analysis of laws of formation and
scattering of plasma formation will be submitted in the paper.
Acknowledgements
Work is executed within the framework of the basic researches program of Russian Academy
of Science and RFBR (Russia) – Consortium EINSTEIN (Italy) Grant 09-08-92422-KE-a

110
6-13
EFFECT OF AN EXPLOSIVE ELECTRON EMISSION
ON MAGNETIZED SHEATH BETWEEN PLASMA AND ISOLATED WALL
O.Yu. Kravchenko, G.I. Levada, I.S. Maruschak, T.E. Lisitchenko
Taras Shevchenko Kyiv University, Volodymyrska str., 64, 01601, Kyiv, Ukraine
Plasma is separated from plasma reactors walls by a space charge sheath (Langmuir–Debye
sheath) because of the mobility difference between ions and electrons. The phenomena in
sheath play a considerable role in the various plasma technologies of solid surfaces processing
and controlled thermonuclear power production. Due to essentially nonlinear character of the
sheath it seems actually to study its properties by means of computer modeling.
One of the most interesting phenomena bound with sheath is formation of an unipolar arc.
According to modern representations unipolar arcs lead to corrupting of walls. Particularly,
an unipolar arc is the emission source of heavy ions which are sources of the enhanced
Bremsstrahlung radiation losses of energy.
Essential for this kind of discharges is that one electrode serves both as cathode and anode.
The cathode is the region of explosive electron emission, the anode is ringlike area
surrounding the cathode. Explosive electron emission can appear on some cathode surface
defects caused by enhanced electric fields near them, then complement by thermal and
secondary electron emission. In some conditions, that should be determined, the return flow
of electrons appears around emitting spot. This return flow closes the current loop of the
unipolar arc.
A two-dimensional model of magnetized sheath is considered. One edge of modeling area is a
wall with the floating potential. The ion flow with directed Bohm velocity is defined from
opposite edge. The area between edges is filled with argon. The secondary electron emission
with its coefficient
γ
is taken into account.
High-density electron flow injection is defined from central small area of wall to take into
consideration the explosive electron emission.
Simulations were made by means of Particle-in-Cell method and Monte-Carlo method to take
into account following reactions caused by electron and ion impact in our code:
-
elastic electron-neutral collisions
Ar + e
–
→
Ar + e
–
;
-
elastic ion-neutral collisions
r + Ar
+
→
r + Ar
+
;
-
ionization
Ar + e
–
→
 Ar
+
 + 2e
–
;
-
neutral excitation by electron heat
Ar + e
–
→
 Ar* + e
–
;
-
charge exchange between ions and atoms 
r +  r
+
→
r
+
 +  r.
Following parameters were used: electron and ion densities
15
3
,
10
e i
n
m
−
=
, electron temperature
2,5 eV
e
T
=
, ion temperature
0, 04 eV
i
T
=
, explosive emission current density
em
j
  =
10
3
-10
5
/m
2
, magnetic induction is chosen within
0.01 0.2
÷
tesla, the angle of the magnetic
field to the wall was
8
θ =
o
. According to suggested approach, the sheath modification caused
by explosive emission has been obtained. There are an potential  minimum formation near the
wall. It seems like the potential profile in vacuum diode with thermo- or auto-electron
emission. This means electric field diversion in the region of emission. It leads to return flow
of electrons around emitting spot.
When current density of explosive emission reaches j = 10
5
A/
2
, the return current to wall
has the same order as the direct current. On the basis of this result we can determine the
ignition of the unipolar arc. It is shown that the magnetic field increasing reduces the reverse
flow of electrons on the wall, thereby preventing the development of unipolar arc.

111
6-14
CHARACTERISTICS OF PLASMA STREAMS AND OPTIMIZATION OF
OPERATIONAL REGIMES FOR MAGNETOPLASMA COMPRESSOR
A.N. Bandura, O.V. Byrka, A.A. Chuvilo
*
, I.E.Garkusha, M.S. Ladygina, A.K. Marchenko,
D.G. Solyakov, D.V. Yeliseyev
NSC  Kharkov Institute of Physics and Technology , Institute of Plasma Physics
61108, Akademicheskaya Str. 1, Kharkov, Ukraine;
*V.N. Karazin Kharkov National University, Svobody sq.4, Kharkov, Ukraine
Spatial and time distributions of plasma stream density as well as plasma pressure
distributions are able to provide detailed information about dynamics of plasma stream and,
therefore, there are important characteristics of magnetoplasma compressor (MPC) from the
point of view optimization of MPC operation regimes.
In these studies, several local movable piezoelectric detectors were designed and
manufactured for plasma pressure measurements with necessary spatial and temporal
resolution. All detectors were calibrated for absolute measurements of plasma pressure at
different distances from the MPC output [1]. It was obtained that plasma pressure in the
compression region is achieved 22-25 bar that indicates efficiency of MPC as dense plasma
source. On the base of plasma pressure measurements several important plasma parameters,
e.g. plasma stream velocity and plasma temperature were estimated. It was found that average
plasma temperature in dense plasma stream, generated by MPC is in the range of 20-40 eV.
Results of energy density measurements in MPC plasma streams are presented also.
Radial distributions of energy density were obtained using set of small movable calorimeters.
In near axis region the energy density value achieves 40 J/cm
2
. Effective diameter of high-
energy plasma stream was estimated. Also, performed analysis of current and voltage
waveforms and energy measurements in plasma in different distances from MPC output have
shown that about 30% of discharge energy in MPC converts to the energy of generated
plasma stream.
Spectroscopy measurements of electron density in plasma stream generated by MPC are
discussed. In particular, effects that can influence on accuracy of plasma density
measurements by broadening spectral lines are analyzed. It was demonstrated that most
important one is self-absorption of spectral lines. In the case of known optical thickness, the
real value of electron density can be calculated with accounting self-absorption using the
method described in [2]. In present paper, estimations of plasma thickness were made and
resulting electron density was calculated. Radial distribution plasma density was
reconstructed for particular MPC operation mode using Abel inversion procedure, i.e.
azimuthal symmetry of plasma stream was presupposed. As was found the maximum value of
plasma density in compression region achieved 10
18
 cm
-3
.
[1] A.N. Bandura et al. Application of Piezodetectors for Diagnostics of Pulsed and Quasi-
Steady-State Plasma Streams. Physica Scripta (73) (2006) pp. 84-88
[2] Ya. F. Volkov et al. Plasma parameters measurements in quasi-stationary plasma
accelerator using the spectral lines with accounting self-absorption.”, Sov. J. Appl. Spectros.,
v. 56, N3, 451-455, 1992.

112
6-15
INFLUENCE OF HYDROGEN AND HELIUM PLASMA STREAMS EXPOSURES
ON MODIFICATION OF TUNGSTEN STRUCTURE UNDER POWERFUL
TRANSIENT LOADS
V.A. Makhlaj
1
, I.E. Garkusha
1
, I. Landman
2
, S.V. Malykhin
3
, A.T. Pugachev
3
, O.V. Byrka
1
,
S.I. Lebedev
1
, P.B. Shevchuk
1
, V.I. Tereshin
1
1
Institute of Plasma Physics of the NSC KIPT, 61108 Kharkov, Ukraine
2
Karlsruhe Institute of Technology (KIT), IHM, 76344 Karlsruhe, Germany
3
Kharkov Polytechnic Institute, NTU, 61002, Kharkov, Ukraine
One of important issues that need to be studied experimentally in the ITER simulation
conditions is behavior of divertor materials under the helium ions bombardment during multi-
pulsed repetitive ELM-like plasma loads, which are below/close to the melting threshold. The
effects of helium ions impact (blistering, flaking), helium dynamics in surface layers, its
influence on cracking development in tungsten (helium retention in microcracks volume) are
still actual topics. This paper presents the results of comparative studies of W targets response
to the plasma exposures at QSPA Kh-50 facility and pulsed plasma gun PPA, which were
performed with various number of hydrogen and helium plasma pulses. Plasma loads were
chosen either below the melting threshold or providing conditions of pronounced melting.
The pulsed plasma accelerator PPA generates plasma streams with ion energy up to
2 keV, plasma density (2-20) × 10
15
 cm
-3
, a maximum specific power of about 10 MW/cm
2
and plasma energy density varied in the range of (5-40) J/cm
2
. The plasma stream duration
was 3-6
µ
s. Both, helium and hydrogen were used as working gases.
The main plasma parameters of QSPA hydrogen plasma streams are as follows: the ion
energy is about 0.4 keV, the maximum plasma pressure is 3.2 bar (time averaged pressure
during the pulse is 1.6-1.7 bar) and the plasma stream diameter is 0.18 m. The plasma pulse
shape is triangular with pulse duration of 0.25 ms. The surface energy load measured with a
calorimeter was chosen either 0.45 MJ/m
2
, which is below the melting threshold, or
0.75 MJ/m
2
, which resulted in pronounced melting.
X-ray diffraction (XRD) has been used to study the micro-structural evolution of exposed
W targets of several grades: sintered, rolled etc. XRD
ϑ
-2
ϑ
 scans were performed using a
monochromatic K
α
 line of Cu anode radiation. Analysis of diffraction peaks intensity,
profiles, and their angular positions was applied to evaluate the texture, the coherent
scattering zone size, the macro-strain and the lattice parameters. Surface observations with
optical microscopy and SEM were performed also.
It is shown that uniform tensile stresses are created in thin surface layer of tungsten target
in result of plasma exposure. Main residual stresses are caused by first plasma pulses. For
regimes with melting, residual stresses are mainly attributed to re-solidification of melt layer.
Non uniform changes of both stress-free lattice spacing and half-width of diffraction
maximum are observed under heat loads above the tungsten melting threshold. This result can
be explained by introducing light impurities into the melt layer structure. Differences in
evolution of tungsten substructure after exposures with helium and hydrogen plasma streams
are discussed.

113
6-16
TWO-DIMENSIONAL SIMULATION OF DYNAMIC DUST CLOUDS
IN THE PLASMA BOUNDARY NEAR THE WALL
O.Yu. Kravchenko,  I.S. Maruschak, G.I. Levada
Taras Shevchenko Kyiv University, Volodymirs ka Str. 64, 01601 Kyiv, Ukraine
Studies of levitation and dynamics of charged dust grains are of significant interest in
space and low-temperature laboratory plasma discharges [1]. Charged dust particularly also
appear at tokamak edges as natural contaminants arising from the plasma interaction with
divertor plates, plasma limiters and blankets [2]. Due to their heavy masses and tendency to
form self-organized structures  the dust particles affect waves, instabilities and transport
processes. Recent laboratory experiments [3] have conclusively demonstrated the motions of
charged dust clouds near negatively biased electrodes in low temperature dusty plasma
discharges. In a dusty plasma sheath the dust grains execute bouncing motions, which are
repeatedly away and towards the electrode.
In this article, we investigate the behavior of a dust cloud in the field of the plasma sheath.
Specifically, we determine the place of a dust cloud localization, viz. the distance from the
wall, and also discuss the form of the cloud. We assume that the dynamics of a dust cloud is
significantly influenced by the sheath electric force and gravity, and that the wall has a
negative potential and is absolutely absorbing.
We consider the wall region of two-dimensional dusty plasma model, wherein the plasma
is contaminated by dust charged grains. Plasma consist of electrons, ions and dust particles
with densities
e
n ,
i
n ,
d
n . At initial time electron and ions are distributed uniformly in space.
Dust grains acquire a charge and influence the potential of the electric field
ϕ
, which is
described by Poisson equation. The movement of dust particles and ions is governed by
hydrodynamics equations, electrons are assumed to be in thermal equilibrium.  It is assumed
that the forces on the dust consist of electrostatic, gravity and ion drag forces.
The spatial distributions of parameters were obtained at various initial densities and radii
of dust grains at different times.
Results show that peaks of the dust density are formed in space of the dust cloud and dust
particles perform the oscillations along radial axis. Moreover, dust cloud is compressed along
axial axis and it is formed thin layer under the wall. It is shown that ion density is increased in
the dust cloud and has peaks on the boundaries of dust cloud.  Dust clouds modify potential
spatial profiles thus that minimum of electric potential is appeared near the dust cloud
boundary from the direction of plasma. This potential drop is accelerate ions toward the dust
cloud and it is potential barrier for negative dust particles.
  This work was supported by joint NASU-RFFR grant.
1. T. Nitter, O. Havnes, F. Melandsø // J. Geophys. Res. -1998. –V.101. –P. 6605.
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