Dynamics of the implosion of the dense plasma focus play an essential role in converting electrical energy into the kinetic energy of the current sheath and subsequent production of accelerated electrons, ions, hard X-ray, and neutron emission. This paper presents the analysis of the implosion parameters, such as the implosion velocity and imploding mass, coupled with electrical parameters observed on the PF-1000 facility with a modified electrode system. The first two parameters are based on the 16-frame Mach–Zehnder interferometer, which provides the spatial distribution of electron density in a time sequence. Measurement of the total current, current derivative, and voltage enables us to evaluate the total inductance and kinetic energy driven by the capacitor bank. Then comparing the inductances and kinetic energies evaluated from the interferograms and electrical waveforms can provide more precise information on the current flowing in the imploding sheath. We present a possible way to deal with the fact that only part of the total current flows through the imploding layer. With the supposition that the rest of the current flows close to the insulator, we conclude that roughly 70% of the total current flows through the pinch, which is in good agreement with an input parameter of the Lee model, for example.

1.
B. A.
Remington
,
R. P.
Drake
, and
D. D.
Ryutov
, “
Experimental astrophysics with high power lasers and Z pinches
,”
Rev. Mod. Phys.
78
,
755
(
2006
).
2.
D.
Ryutov
,
M. S.
Derzon
, and
M. K.
Matzen
, “
The physics of fast Z pinches
,”
Rev. Mod. Phys.
72
,
167
(
2000
).
3.
M.
Haines
, “
A review of the dense Z-pinch
,”
Plasma Phys. Controlled Fusion
53
,
093001
(
2011
).
4.
M. A.
Liberman
,
J. S.
De Groot
,
A.
Toor
, and
R. B.
Spielman
,
Physics of High-Density Z-Pinch Plasmas
(
Springer Science & Business Media
,
2012
).
5.
E.
Demina
,
V.
Pimenov
,
S.
Maslyaev
,
M.
Prusakova
,
I.
Sasinivskaya
,
A.
Dubrovsky
,
M.
Scholz
,
M.
Paduch
,
V.
Gribkov
, and
A.
Tartari
, “
Creation of a dense plasma focus device and its application in radiation material sciences for the goals of the mainstream fusion researches
,” IAEA Report No. IAEA-TECDOC--1708 (
2013
).
6.
M.
Krishnan
, “
The dense plasma focus: A versatile dense pinch for diverse applications
,”
IEEE Trans. Plasma Sci.
40
,
3189
3221
(
2012
).
7.
V.
Gribkov
, “
On possible formulation of problems of a dense plasma focus used in material sciences
,”
Nukleonika
45
,
149
153
(
2000
).
8.
M.
Scholz
,
Plasma-Focus and Controlled Nuclear Fusion
(
Institute of Nuclear Physics Polish Academy of Sciences
,
2016
).
9.
J. W.
Mather
, “
Formation of a high-density deuterium plasma focus
,”
Phys. Fluids
8
,
366
377
(
1965
).
10.
J. W.
Mather
and
P. J.
Bottoms
, “
Characteristics of the dense plasma focus discharge
,”
Phys. Fluids
11
,
611
618
(
1968
).
11.
A.
Bernard
,
P.
Cloth
,
H.
Conrads
,
A.
Coudeville
,
G.
Gourlan
,
A.
Jolas
,
C.
Maisonnier
, and
J.
Rager
, “
The dense plasma focus—A high intensity neutron source
,”
Nucl. Instrum. Methods
145
,
191
218
(
1977
).
12.
A.
Bernard
,
H.
Bruzzone
,
P.
Choi
,
H.
Chuaqui
,
V.
Gribkov
,
J.
Herrera
,
K.
Hirano
,
A.
Krejci
,
S.
Lee
,
C.
Luo
,
F.
Mezzetti
,
M.
Sadowski
,
H.
Schmidt
,
K.
Ware
,
C. S.
Wong
, and
V.
Zoita
, “
Scientific status of plasma focus research
,”
J. Moscow Phys. Soc.
8
,
93
170
(
1998
).
13.
J.
Mather
, “
15. Dense plasma focus
,” in
Methods in Experimental Physics
(
Elsevier
,
1971
), Vol.
9
, pp.
187
249
.
14.
R. P.
Drake
,
High-Energy-Density Physics: Foundation of Inertial Fusion and Experimental Astrophysics
(
Springer
,
2018
).
15.
V.
Tang
,
M.
Adams
, and
B.
Rusnak
, “
Dense plasma focus Z-pinches for high-gradient particle acceleration
,”
IEEE Trans. Plasma Sci.
38
,
719
727
(
2010
).
16.
A.
Schmidt
,
A.
Link
,
D.
Welch
,
B.
Meehan
,
V.
Tang
,
C.
Halvorson
,
M.
May
, and
E.
Hagen
, “
Fully kinetic simulations of megajoule-scale dense plasma focus
,”
Phys. Plasmas
21
,
102703
(
2014
).
17.
V.
Gribkov
,
B.
Bienkowska
,
M.
Borowiecki
,
A.
Dubrovsky
,
I.
Ivanova-Stanik
,
L.
Karpinski
,
R.
Miklaszewski
,
M.
Paduch
,
M.
Scholz
, and
K.
Tomaszewski
, “
Plasma dynamics in PF-1000 device under full-scale energy storage: I. Pinch dynamics, shock-wave diffraction, and inertial electrode
,”
J. Phys. D: Appl. Phys.
40
,
1977
(
2007
).
18.
T.
Tou
,
S.
Lee
, and
K.
Kwek
, “
Nonperturbing plasma-focus measurements in the run-down phase
,”
IEEE Trans. Plasma Sci.
17
,
311
315
(
1989
).
19.
T.
Oppenlander
,
G.
Pross
,
G.
Decker
, and
M.
Trunk
, “
The plasma focus current in the compression phase
,”
Plasma Phys.
19
,
1075
(
1977
).
20.
S.
Lee
and
S.
Saw
, “
Pinch current limitation effect in plasma focus
,”
Appl. Phys. Lett.
92
,
021503
(
2008
).
21.
S.
Lee
and
A.
Serban
, “
Dimensions and lifetime of the plasma focus pinch
,”
IEEE Trans. Plasma Sci.
24
,
1101
1105
(
1996
).
22.
S.
Lee
, “
Plasma focus radiative model: Review of the lee model code
,”
J. Fusion Energy
33
,
319
335
(
2014
).
23.
S.
Lee
,
S.
Saw
,
L.
Soto
,
S.
Springham
, and
S.
Moo
, “
Numerical experiments on plasma focus neutron yield versus pressure compared with laboratory experiments
,”
Plasma Phys. Controlled Fusion
51
,
075006
(
2009
).
24.
S. H.
Saw
and
S.
Lee
, “
Scaling the plasma focus for fusion energy considerations
,”
Int. J. Energy Res.
35
,
81
88
(
2011
).
25.
E.
Zielinska
,
M.
Paduch
, and
M.
Scholz
, “
Sixteen-frame interferometer for a study of a pinch dynamics in PF-1000 device
,”
Contrib. Plasma Phys.
51
,
279
283
(
2011
).
26.
P.
Kubes
,
M.
Paduch
,
T.
Pisarczyk
,
M.
Scholz
,
T.
Chodukowski
,
D.
Klir
,
J.
Kravarik
,
K.
Rezac
,
I.
Ivanova-Stanik
,
L.
Karpinski
,
K.
Tomaszewski
, and
E.
Zielinska
, “
Interferometric study of pinch phase in plasma-focus discharge at the time of neutron production
,”
IEEE Trans. Plasma Sci.
37
,
2191
2196
(
2009
).
27.
P.
Kubes
,
M.
Paduch
,
T.
Pisarczyk
,
M.
Scholz
,
D.
Klir
,
J.
Kravarik
,
K.
Rezac
,
T.
Chodukowski
,
I.
Ivanova-Stanik
,
L.
Karpinski
,
E.
Zielinska
,
K.
Tomaszewski
, and
M. J.
Sadowski
, “
Transformation of the pinched column at a period of the neutron production
,”
IEEE Trans. Plasma Sci.
38
,
672
679
(
2009
).
28.
P.
Kubes
,
D.
Klir
,
J.
Kravarik
,
K.
Rezac
,
J.
Kortanek
,
V.
Krauz
,
K.
Mitrofanov
,
M.
Paduch
,
M.
Scholz
,
T.
Pisarczyk
,
T.
Chodukowski
,
Z.
Kalinowska
,
L.
Karpinski
, and
E.
Zielinska
, “
Scenario of pinch evolution in a plasma focus discharge
,”
Plasma Phys. Controlled Fusion
55
,
035011
(
2013
).
29.
P.
Kubes
,
V.
Krauz
,
K.
Mitrofanov
,
M.
Paduch
,
M.
Scholz
,
T.
Piszarzcyk
,
T.
Chodukowski
,
Z.
Kalinowska
,
L.
Karpinski
,
D.
Klir
,
J.
Kortanek
,
E.
Zielinska
,
J.
Kravarik
, and
K.
Rezac
, “
Correlation of magnetic probe and neutron signals with interferometry figures on the plasma focus discharge
,”
Plasma Phys. Controlled Fusion
54
,
105023
(
2012
).
30.
V.
Krauz
,
K.
Mitrofanov
,
M.
Scholz
,
M.
Paduch
,
L.
Karpinski
,
E.
Zielinska
, and
P.
Kubes
, “
Experimental study of the structure of the plasma-current sheath on the PF-1000 facility
,”
Plasma Phys. Controlled Fusion
54
,
025010
(
2012
).
31.
K.
Mitrofanov
,
V.
Krauz
,
P.
Kubes
,
M.
Scholz
,
M.
Paduch
, and
E.
Zielinska
, “
Study of the fine structure of the plasma current sheath and magnetic fields in the axial region of the PF-1000 facility
,”
Plasma Phys. Rep.
40
,
623
639
(
2014
).
32.
S.
Auluck
, “
On the representation of dense plasma focus as a circuit element
,”
Phys. Plasmas
28
,
030703
(
2021
).
33.
R. D.
McBride
,
W. A.
Stygar
,
M. E.
Cuneo
,
D. B.
Sinars
,
M. G.
Mazarakis
,
J. J.
Leckbee
,
M. E.
Savage
,
B. T.
Hutsel
,
J. D.
Douglass
,
M. L.
Kiefer
,
B. V.
Oliver
,
G. R.
Laity
,
M. R.
Gomez
,
D. A.
Yager-Elorriaga
,
S. G.
Patel
,
B. M.
Kovalchuk
,
A. A.
Kim
,
P. A.
Gourdain
,
S. N.
Bland
,
S.
Portillo
,
S. C.
Bott-Suzuki
,
F. N.
Beg
,
Y.
Maron
,
R. B.
Spielman
,
D. V.
Rose
,
D. R.
Welch
,
J. C.
Zier
,
J. W.
Schumer
,
J. B.
Greenly
,
A. M.
Covington
,
A. M.
Steiner
,
P. C.
Campbell
,
S. M.
Miller
,
J. M.
Woolstrum
,
N. B.
Ramey
,
A. P.
Shah
,
B. J.
Sporer
,
N. M.
Jordan
,
Y. Y.
Lau
, and
R. M.
Gilgenbach
, “
A primer on pulsed power and linear transformer drivers for high energy density physics applications
,”
IEEE Trans. Plasma Sci.
46
,
3928
3967
(
2018
).
34.
J.
Kortanek
and
P.
Kubes
, “
Calculation of the inductance of plasma column at PF-1000 device with assumed current distribution
,”
Acta Polytech.
53
,
185
188
(
2013
).
35.
P.
Kubes
,
D.
Klir
,
J.
Kravarik
,
K.
Rezac
,
M.
Paduch
,
T.
Pisarczyk
,
M.
Scholz
,
T.
Chodukowski
,
B.
Bienkowska
,
I.
Ivanova-Stanik
,
L.
Karpinski
,
M. J.
Sadowski
,
K.
Tomaszewski
, and
E.
Zielinska
, “
Energy transformations in column of plasma-focus discharges with megaampere currents
,”
IEEE Trans. Plasma Sci.
40
,
481
486
(
2012
).
36.
V.
Gribkov
, “
Physical processes taking place in dense plasma focus devices at the interaction of hot plasma and fast ion streams with materials under test
,”
Plasma Phys. Controlled Fusion
57
,
065010
(
2015
).
37.
H.
Schmidt
,
T.
Pisarczyk
, and
T.
Chodukowski
, “
Density distributions during the neutron-producing phase of the plasma focus poseidon
,”
IEEE Trans. Plasma Sci.
40
,
3265
3272
(
2012
).
38.
H.
Herold
,
A.
Jerzykiewicz
,
M.
Sadowski
, and
H.
Schmidt
, “
Comparative analysis of large plasma focus experiments performed at IPF, Stuttgart, and IPJ, Świerk
,”
Nucl. Fusion
29
,
1255
(
1989
).
39.
P.
Hariharan
,
Basics of Interferometry
(
Elsevier
,
2010
).
40.
S.
Harilal
and
M.
Tillack
, “
Laser plasma density measurements using interferometry
,” in
Fusion Division, Center for Energy Research
(
University of California
,
2004
).
41.
S.
Jackson
and
U.
Shumlak
, “
Abel inversion of a holographic interferogram for determination of the density profile of a sheared-flow Z pinch
,”
Rev. Sci. Instrum.
77
,
083502
(
2006
).
42.
A.
Tarifeno-Saldivia
,
C.
Pavez
,
J.
Moreno
, and
L.
Soto
, “
Dynamics and density measurements in a small plasma focus of tens-of-joules-emitting neutrons
,”
IEEE Trans. Plasma Sci.
39
,
756
760
(
2010
).
43.
B.
Cikhardtova
, “
High density plasma experimental diagnostics
,”
Doctoral thesis
(Czech Technical University, Prague,
2019
).
44.
M. I.
Pergament
,
Methods of Experimental Physics
(
CRC Press
,
2014
).
45.
M.
Kalal
and
K.
Nugent
, “
Abel inversion using fast fourier transforms
,”
Appl. Opt.
27
,
1956
1959
(
1988
).
46.
I.
Kochetkov
,
T.
Pisarczyk
,
M.
Kalal
,
T.
Chodukowski
,
A.
Zaras-Szydlowska
,
Z.
Rusiniak
,
R.
Dudzak
,
J.
Dostal
,
M.
Krupka
, and
P.
Korneev
, “
Complex interferometry of magnetized plasma: Accuracy and limitations
,” e-print arXiv:2103.01076 (
2021
).
47.
P.
Tomassini
and
A.
Giulietti
, “
A generalization of abel inversion to non-axisymmetric density distribution
,”
Opt. Commun.
199
,
143
148
(
2001
).
48.
I. H.
Hutchinson
, “
Principles of plasma diagnostics
,”
Plasma Phys. Controlled Fusion
44
,
2603
(
2002
).
49.
A.
Kasperczuk
and
T.
Pisarczyk
, “
Application of automated interferometric system for investigation of the behaviour of a laser-produced plasma in strong external magnetic fields
,”
Opt. Appl.
31
,
571
598
(
2001
).
50.
L.
Akter
,
G. S.
Rakib
,
M. R.
Haque
,
M.
Malek
,
M. M. H.
Prodhan
, and
M. K.
Islam
, “
Study of axial and radial phase plasma dynamics as a function of the variation of gas using lee model code
,” in
2018 International Conference on Innovation in Engineering and Technology (ICIET)
(
IEEE
,
2018
), pp.
1
3
.
51.
M.
Milanese
and
J.
Pouzo
, “
Critical analysis of plasma focus design based on the implications of an upper pressure limit
,”
Nucl. Fusion
25
,
840
(
1985
).
52.
S.
Czekaj
,
A.
Kasperczuk
,
R.
Miklaszewski
,
M.
Paduch
,
T.
Pisarczyk
, and
Z.
Wereszczynski
, “
Diagnostic method for the magnetic field measurement in the plasma focus device
,”
Plasma Phys. Controlled Fusion
31
,
587
(
1989
).
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