Experimental and numerical study of the pinch dynamics in the PF-1000 device
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| Дата: | 2002 |
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2002
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| Цитувати: | Experimental and numerical study of the pinch dynamics in the PF-1000 device / M. Scholz, B. Bieńkowska, I. Ivanova-Stanik, A. Kasperczuk, R. Miklaszewski, M. Paduch, T. Pisarczyk, W. Stępniewski, K. Tomaszewski, P. Kubes, J. Kravarik // Вопросы атомной науки и техники. — 2002. — № 5. — С. 72-76. — Бібліогр.: 8 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1860195394943713280 |
|---|---|
| author | Scholz, M. Bieńkowska, B. Ivanova-Stanik, I. Kasperczuk, A. Miklaszewski, R. Paduch, M. Pisarczyk, T. Stępniewski, W. Tomaszewski, K. Kubes, P. Kravarik, J. |
| author_facet | Scholz, M. Bieńkowska, B. Ivanova-Stanik, I. Kasperczuk, A. Miklaszewski, R. Paduch, M. Pisarczyk, T. Stępniewski, W. Tomaszewski, K. Kubes, P. Kravarik, J. |
| citation_txt | Experimental and numerical study of the pinch dynamics in the PF-1000 device / M. Scholz, B. Bieńkowska, I. Ivanova-Stanik, A. Kasperczuk, R. Miklaszewski, M. Paduch, T. Pisarczyk, W. Stępniewski, K. Tomaszewski, P. Kubes, J. Kravarik // Вопросы атомной науки и техники. — 2002. — № 5. — С. 72-76. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| first_indexed | 2025-12-07T18:08:29Z |
| format | Article |
| fulltext |
PLASMA DYNAMICS AND PLASMA-WALL INTERACTION
EXPERIMENTAL AND NUMERICAL STUDY
OF THE PINCH DYNAMICS IN THE PF-1000 DEVICE
M. Scholz1), B. Bieńkowska1), I. Ivanova-Stanik1), A. Kasperczuk1), R. Miklaszewski1),
M. Paduch1), T. Pisarczyk1), W. Stępniewski1), K. Tomaszewski1), P. Kubes2), J. Kravarik2)
1) Institute of Plasma Physics and Laser Microfusion,
Hery 23, 00-908 Warsaw, P.O.Box 49, Poland;
2) Czech Technical University, Prague, Czech Republic
PACS: 52.58.Lq
1. INTRODUCTION
Plasma Focus devices belong to the family of the
dynamic Z-pinch, where the dense and hot plasma is
created. The plasma is formed by the discharge of a
capacitor bank and the dynamics of the current sheet has
two successive different phases: a long time scale phase
(several microseconds) from breakdown to maximum
compression during which the current sheet is formed and
pushed by the Lorentz force; a short time phase (in the
few tens of ns time scale) during which the pinch is
created and disrupted by instabilities.
The fame of the PF has been based on the fact
that it was the very intense neutron-producing device. The
scaling laws for the neutron yields formulated at the
beginning of the plasma focus investigations were very
promising for these devices. Later investigations however
carried out on bigger devices suggested that there is a
certain condenser energy limit above which the scaling
law is not valid. Hence the essential problem to be
resolved in PF research has always been to discover the
physics, which dominates the configuration, a question
closely related to the neutron production mechanism and
plasma dynamics.
In this paper, experimental and numerical
investigations of last phase of plasma sheet dynamics in
large scale PF are presented.
The physical model for numerical simulations is
based on the set of non-ideal MHD equations in the two-
fluid approximation with coupled equation of ionization
kinetics. To study the evolution of the plasma an optical
frame camera with exposure time of 1 ns were employed.
On the basis of the plasma imager the dynamics of the
plasma sheet evolution and plasma dimension were
determined.
The experimental observations from large-scale
PF-1000 machines are compared with numerical
calculations of plasma evolution for parameters of PF-
1000. Therefore, the main aim of the experiments was to
determine operational regimes of the PF-1000 facility, in
which the maximum neutron emission occurs, and to
define characteristic features of the last phase of plasma
evolution.
2. THE APPARATUS
The large scale PF-1000 facility consists of
following main units:
• the condenser bank and pulsed electrical power
circuit with a collector and low-inductance cables.
• the mechanical vacuum and gas system consist of the
vacuum chamber, coaxial electrodes and gas handling
system.
The electrical energy is transferred to a collector
and electrodes by means of low-inductance cables. The
vacuum chamber, which surrounds the electrodes, has a
large volume (1400 mm in diameter and 2500 mm in
length). Two coaxial electrodes are shown on Fig. 1. The
outer electrode (cathode) consists of 24 stainless steel
rods with 32 mm in diameter. The outer electrode (OE)
and copper center electrode (CE) radii are 200 and 115.5
mm respectively with CE length of 600 mm. The
cylindrical alumina insulator sits on the CE and the main
part of the insulator extends 113 mm along the CE into
the vacuum chamber. The insulator prescribes the shape
of the initial current sheet between the CE and the back
plate of the OE.
Fig. 1. Geometry of the electrodes of the PF-1000 device
The condenser bank of capacitance 1332 µF was
charged to voltage ranging between 20-40 kV, which
corresponded to discharge energies ranging from 266 kJ
to 1064 kJ. During the described experiment the
condenser bank was charged to 33 kV. The total energy
stored in the bank was 725 kJ, while the maximum
discharge current reached the value of 1.7 MA.
3. EXPERIMENTAL ARRANGEMENT
The scheme of the experimental set-up is shown
on Fig. 1. To study the evolution of the plasma, a three
frame optical camera with exposure time of about 1 ns
was employed (see Fig. 2). In the case of the optical
camera, image converters are used as a fast shutter and
light amplifier. This camera allows capturing a frame
plasma images with spatial resolution of 0.4 mm.
The delay between subsequent frames is in the
range of 10 or 20 ns. An interference filter (λmax = 593
nm, FWHM = 6 nm) was put into the optical path of the
72 Problems of Atomic Science and Technology. 2002. № 5. Series: Plasma Physics (8). P. 72-76
passive optical diagnostic subsystem. Its spectral position
enabled to record only continuous radiation.
Fig. 2. Scheme of the passive optical system
In addition the following diagnostics were used:
• dI/dt probe for registration of the discharge current
derivative (after performance of a numerical integral
procedure). It was mounted inside of the PF-1000
collector;
• P-I-N diode for registration of the soft X-ray
emission from the plasma column. This emission was
observed by 230 µm pinhole in front of the diode.
This diode was blocked by a 10 µm Be foil, therefore
the diode sensitivity covered the range of 0.8 ÷ 10
keV;
• silver activation counters for estimation of the
neutron yield; only the side-on counter reading was
taken into account).
The soft X-ray signal detected by the P-I-N diode
was used for synchronization purposes and determination
of the temporal relation between the maximum
compression of the plasma and frame images recorded by
means of optical diagnostics. The special electrical and
optical synchronization arrangement allowed
synchronizing the optical diagnostics and the PF
phenomenon with a temporary precision of 5 ns.
4. EXPERIMENTAL RESULTS
An investigation of the PF-1000 facility was
carried out in the deuterium pressure range of 1 ÷ 5 Torr
and a discharge energy level exceeding to 1 MJ. The
obtained result have been successively published [1 – 4]
and they can be summarized as follows:
1. PF-1000 facility can be operated with a regular and
reproducible neutron emission (of the order of 1010 ÷
1011 neutron/shot);
2. It was found that for each filling pressure value (p)
neutron yield (Yn) increases initially as a function of
the charging voltage (V0) up to maximum and after
that it decreases with a further increase in V0.
3. Two (or three) neutron pulses about 2 µs apart were
observed in most of the discharges.
It is therefore of considerable importance to
investigate the connection between the various
mechanisms responsible for the neutron production and
formation of PF radially collapsing sheet, the quality of
the sheet velocity and the resulting pinch plasma as well
as the stability and break-up of this pinch.
A sequence of frame camera pictures of
discharges carried out in deuterium filling gas (p = 3
Torr), are shown on Fig. 3. The images were taken at
different times during the implosion (Fig. 3a), minimum
radius (Fig. 3b) and post pinch instability phase (Fig. 3c).
The anode is on the left side of the pictures.
a)
-0.178 µs -0.168 µs -0.148 µs
-0.079 µs -0.069 µs -0.049 µs
b)
-0.005 µs 0.005 µs 0.025 µs
c)
0.057 µs 0.067 µs 0.087 µs
0.107 µs 0.117 µs 0.137 µs
0.139 µs 0.149 µs 0.169 µs
Fig. 3. A set of frame camera pictures of pinching
dynamics (PF-1000 results in 2002: a) implosion phase;
b) minimum radius phase; c) post pinch phase
73
A
B
C
In the images a strong surface of plasma sheet
perturbations can be found. These surface perturbations
could be traced back to that appearing early on in the
sheet during the radial compression. This perturbation
remains more or less frozen in until radial compression
and tends not to destroy the integrity of the collapsing
column. The upper part of the collapsing sheet has a low
radial velocity of compression. These perturbations have
a ring like shape around the surface of the plasma column
as is shown in Fig. 3a. The trajectory of characteristics
points (maximum or minimum) of the perturbations is
approximately perpendicular to the axis of the electrodes.
The pinch column tends to develop into multiple
necking as the pinch evolves. An example is shown in
Fig. 3b. The necking develops at different z along the
pinch column, each pushing plasma material away from
the neck. The occurrence of two such regions would
produce a jet like expansion of plasma at the junction
between the two regions. This can be seen referring to the
positions marked A, B and C on a picture on Fig. 3.
A and B mark the positions of the two collapsing
and than necking regions while C clearly develops into a
great scale perturbation. It has a clear border and an
amplitude reaching size of 5 cm. This type of perturbation
is stable and its lifetime is about 1 µs. The large-scale
perturbation appears about 8 cm from the anode.
The period of the plasma column creation lasts
about 200 ns. After this time a plasma column of about 12
cm in length should exist. So long time of plasma column
creation results in a disruption of the earliest created part
(see mark A) of the plasma column before the creation
process of the whole pinch is finished. As a rule the
minimum radius (rmin) of plasma column in any cross
section is 0.7 cm.
In the PF scheme one relies on the development
of self-consistent phenomena occurring after maximum
compression during the cylindrical re-expansion of the
plasma column. Anomalous microscopic effect are
probably responsible for particle heating while
instabilities create a favorable situation for the onset of
relaxation processes of the magnetized plasma, which
lead to the formation of a sheet plasma configuration (the
great plasma perturbations).
Its lifetime exceeds by an order of magnitude the
transit time of reacting particles. In such a case the
efficiency of energy transfer from the source of the
magnetic energy stored in the system, as the distribution
of current densities in the plasma column, are of
paramount importance.
5. NUMERICAL MODEL
In order to address the questions of the sheet
dynamics we developed a two-dimensional, two fluid,
non-ideal MHD code. This code is based on the modified
Dyachenko-Jach code [5], which includes kinetic of
ionization. With this model it is possible to simulate the
main features of the compression and expansion phase of
the PF.
The magnetohydrodynamics equations in this
code are described in detail elsewhere [6-8]. They are
solved for six unknown variables namely the mass density
ρ, The radial and axial moments ρvr and ρvz, the ion and
electron temperatures Tc and Te and the azimuthal
magnetic field Bϕ. All other quantities follow from these
variables. Transport coefficients are given by Braginski,
therefore we obtain the following system of equations:
u
dt
d ⋅∇−= ρρ
Bj
c
p
dt
ud
×+Π∇+− ∇= 1ρ
ionizie
e
eee
e
ve QQjR
en
qup
dt
dTc −−⋅+⋅∇−⋅∇− ∇= −
1ρ
ieiii
i
vi Qquup
dt
dTc −+⋅∇−∇⋅Π+⋅∇−= ρ
( )
×+−∇+××∇= Bj
en
Rp
en
cBu
dt
dB
e
e
e
1
Bcj
×∇=
π4
where:
∇⋅+
∂
∂≡ u
tdt
d
( )zr uuu ,0,=
( )0,,0 ϕBB =
( )zr jjj ,0,=
ie ppp +=
ortΠ+Π=Π
i
neiee −− += ννν
niiii −− += ννν .
Most of these equations are self-explanatory. It
should be noted that in the energy equations, the
convective and advective terms contain the velocities of
the species under consideration. Also anomalous
resistivity caused by.
Apart from the ion velocity u , – or ambipolar –
plasma velocity, we also need the electron velocity:
e
jmuu i
e ρ
−= .
In equation for electron temperature we included Joule
heating, energy exchange with ions and ionization.
Equation for ion temperature contains the exchange
between ions and electrons.
74
z0 z
Rh
Rin
Rout
Rm
∆ z
Fig. 4. Initial conditions of numerical calculations: Rin =
12 cm, Rout = 18 cm, Rh = 1.5 cm (hole radius), Rm = 24
cm, z = 18 cm, z0 = 6 cm, ∆z = 0.9 cm (current sheet
thickness)
-20
-15
-10
-5
0
5
10
15
20
cm
t = -0.130 µ s
0
25
50
75
100
125
150
175
200
225
250
275
eV
-20
-15
-10
-5
0
5
10
15
20
cm
t = -0.030 µ s
0
25
50
75
100
125
150
175
200
225
250
275
eV
75
-20
-15
-10
-5
0
5
10
15
20
cm
t = 0.0 µ s
0
25
50
75
100
125
150
175
200
225
250
275
eV
Luminosity Particle density Ion temperature
Fig. 5. A set of calculated spatial distributions of the plasma luminosity, particle density and ion temperature for three
time steps
A different treatment is necessary for the
inelastic processes. We consider electron impact
ionization from the ground state radiative recombination
and three body Auger recombination.
Since ionization and recombination are
extremely strong functions of electron temperature and
density respectively, it is not possible to solve the
resulting equation:
( ) 3
B3
2
0 eeree
e nnSnnn
dt
dn
βα −−⋅−= .
within the algorithm for the MHD equations because
numerical stability would require very small time step.
There were boundary conditions of a typical nature:
• on the pinch surface:
0=⋅ iqn , 0=⋅ eqn ,
p
rr cr
IB
p
2=
= ,
( ) 0=−⋅ nIpn ,
• on the electrode:
0=nu ,
0=
∂
∂
n
Te , 0=
∂
∂
n
Ti ,
• on the axis:
0=ru ,
0=ϕB ,
0=
∂
∂
r
Te , 0=
∂
∂
r
Ti .
We have started the two-fluid calculations with
formed current sheet, which parameters were as follows:
the current sheet thickness ∆z = 0.9 cm, the temperature is
assumed to be 5 eV. The current sheet has started 6 cm
before the end of the electrodes (Fig4). The initial current
through the sheet was chosen (from experiment) equal to
1.7 MA. Subsequently, the current is determined by the
magnetic flux conservation:
const=⋅ IL .
The filling pressure D2 was 3 Torr with 0.1%
homogeneously ionized deuterium plasma and initial
temperature of the deuterium plasma was equal to 0.5 eV.
Fig. 5 shows the calculated spatial distributions
of the plasma luminosity, density and ion temperature for
three time steps. The square marked on the pictures is the
area observed by the frame camera in our experiment.
Our calculations clearly show the instabilities
that take place in a plasma focus device and give
qualitative information about their temporal evolution
(see Fig. 5). The appearance of RT instabilities on the
plasma sheet is detected during the radial collapse phase.
These perturbations do not grow significantly during the
radial compression stage and they are apparently frozen in
the plasma sheet. The initial perturbations on the plasma
sheet lead to the growth of strong perturbations at pinch
time. Multiple necking is observed on the much tightly
pinched dense plasma column. This is in line with the
frame camera observations on PF-1000 device.
76
6. CONCLUSIONS
1. Preliminary results agree qualitatively and
quantitatively with experimental results.
2. The velocity computed for the run down phase is
lower than the measured one: vz exp = 8 · 106 cm/s;
vz com = 6.8 · 106 cm/s.
3. Qualitative agreement of experimentally observed
pinch dynamics and structures with numerical
modeling of the pinch phase.
4. Specific features of PF-1000 phenomena:
independent radial dynamics in separate two or three
pinches positioned one after another along the axis.
5. Stable plasma radiating structures on axis situated in-
between of two pinching sequences of a pinch.
REFERENCES
[1] M. Scholz, L. Karpinski, M. Paduch et al./ Proc. 27th
IEEE Int. Conf. Plasma Science, COPS 2000, New
Orelan, USA. 1C 09:94.
[2] M. Scholz, L. Karpinski, M. Paduch et al.//
Nukleonika. (46). (supplement), 2001, p.35.
[3] A. Szydlowski, M. Scholz, M. Paduch et al.//
Nukleonika. (46). (supplement), 2001,p. 61.
[4] M. Scholz, R. Miklaszewski, M. Paduch et al.// IEEE
Trans on Plasma Science (30). 2002, p.476.
[5] K. Jach et al.// Comput. Assisted Mech. Eng. Sci. (2),
1995, p.2.
[6] D. E. Potter// Phys. Fluids (21), 1971, p. 1911
[7] V. P. Dyachenko, V. S. Imshennik// Sov. Phys. JETP
(29), 1969, p.947.
[8] S. Maxon, J. Eddleman// Phys. Fluids (21). 1978,
p.1856.
77
1. INTRODUCTION
2. THE APPARATUS
3. EXPERIMENTAL ARRANGEMENT
Fig. 2. Scheme of the passive optical system
4. EXPERIMENTAL RESULTS
5. NUMERICAL MODEL
6. CONCLUSIONS
REFERENCES
|
| id | nasplib_isofts_kiev_ua-123456789-77886 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T18:08:29Z |
| publishDate | 2002 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Scholz, M. Bieńkowska, B. Ivanova-Stanik, I. Kasperczuk, A. Miklaszewski, R. Paduch, M. Pisarczyk, T. Stępniewski, W. Tomaszewski, K. Kubes, P. Kravarik, J. 2015-03-08T21:05:57Z 2015-03-08T21:05:57Z 2002 Experimental and numerical study of the pinch dynamics in the PF-1000 device / M. Scholz, B. Bieńkowska, I. Ivanova-Stanik, A. Kasperczuk, R. Miklaszewski, M. Paduch, T. Pisarczyk, W. Stępniewski, K. Tomaszewski, P. Kubes, J. Kravarik // Вопросы атомной науки и техники. — 2002. — № 5. — С. 72-76. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.58.Lq https://nasplib.isofts.kiev.ua/handle/123456789/77886 en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Plasma dynamics and plasma-wall interaction Experimental and numerical study of the pinch dynamics in the PF-1000 device Article published earlier |
| spellingShingle | Experimental and numerical study of the pinch dynamics in the PF-1000 device Scholz, M. Bieńkowska, B. Ivanova-Stanik, I. Kasperczuk, A. Miklaszewski, R. Paduch, M. Pisarczyk, T. Stępniewski, W. Tomaszewski, K. Kubes, P. Kravarik, J. Plasma dynamics and plasma-wall interaction |
| title | Experimental and numerical study of the pinch dynamics in the PF-1000 device |
| title_full | Experimental and numerical study of the pinch dynamics in the PF-1000 device |
| title_fullStr | Experimental and numerical study of the pinch dynamics in the PF-1000 device |
| title_full_unstemmed | Experimental and numerical study of the pinch dynamics in the PF-1000 device |
| title_short | Experimental and numerical study of the pinch dynamics in the PF-1000 device |
| title_sort | experimental and numerical study of the pinch dynamics in the pf-1000 device |
| topic | Plasma dynamics and plasma-wall interaction |
| topic_facet | Plasma dynamics and plasma-wall interaction |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/77886 |
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