We present here the detailed measurements of radial distribution of the magnetic field in a gas-puff z-pinch plasma at the final stages of the implosion phase and at stagnation. While the measurements are chordal, the radial distribution of different charge states was utilized to measure the magnetic field locally for certain radii, so that unlike chordal measurements in general, the magnetic field radial distribution was obtained with no need for the Abel inversion of the data. The distribution was measured using the Zeeman effect via a novel spectroscopic technique, at several axial locations, and demonstrates striking features such as the peak field remaining at a radius much larger than the stagnation radius at all times. Furthermore, while the distribution observed is sometimes monotonic with respect to the radius, it is often not, a behavior that can be linked to 2D features in the plasma column resulting from the Rayleigh–Taylor instability. The current flowing through the stagnating plasma was found to be a small fraction of the total current, resulting in clearly insufficient magnetic pressure to balance the plasma pressure at stagnation. The magnetic field data, taken over several axial positions, are used to obtain the true inductance in the imploding plasma for the first time; it is found that the data cannot explain the current turnover at stagnation. A simulation with the MACH2-Tabular Collisional-Radiative Equilibrium magnetohydrodynamics code in the rz plane shows that the peak of the magnetic field pinches to a much smaller radius than is observed in the spectroscopic data. Furthermore, the depth of the computed current turnover at stagnation is smaller than the measured one. The two observed features of a radially extended magnetic field at stagnation together with a deep current turnover are a challenge to match in simulations. Various calculations and estimates of the inductive and resistive load voltages are examined to ascertain if they are responsible for the observed current notch. The results demonstrate that the knowledge of the true inductance in the driven load requires such magnetic-field-distribution measurements and that imaging data or electrical measurements are insufficient.

1.
D. D.
Ryutov
,
M. S.
Derzon
, and
M. K.
Matzen
, “
The physics of fast Z pinches
,”
Rev. Mod. Phys.
72
,
167
223
(
2000
).
2.
J. L.
Giuliani
and
R. J.
Commisso
, “
A review of the gas-puff Z-pinch as an x-ray and neutron source
,”
IEEE Trans. Plasma Sci.
43
,
2385
2453
(
2015
).
3.
R.
Doron
,
D.
Mikitchuk
,
C.
Stollberg
,
G.
Rosenzweig
,
E.
Stambulchik
,
E.
Kroupp
,
Y.
Maron
, and
D. A.
Hammer
, “
Determination of magnetic fields based on the Zeeman effect in regimes inaccessible by Zeeman-splitting spectroscopy
,”
High Energy Density Phys.
10
,
56
60
(
2014
).
4.
G.
Davara
,
L.
Gregorian
,
E.
Kroupp
, and
Y.
Maron
, “
Spectroscopic determination of the magnetic-field distribution in an imploding plasma
,”
Phys. Plasmas
5
,
1068
1075
(
1998
).
5.
G.
Rosenzweig
,
E.
Kroupp
,
A.
Fisher
, and
Y.
Maron
, “
Measurements of the spatial magnetic field distribution in a z-pinch plasma throughout the stagnation process
,”
J. Instrum.
12
,
P09004
(
2017
).
6.
G. S.
Sarkisov
,
B.
Etlicher
,
V. V.
Yan'kov
,
S.
Attelan
,
C.
Rouille
, and
A. S.
Shikanov
, “
Structure of the magnetic fields in Z-pinches
,”
J. Exp. Theor. Phys.
81
,
743
752
(
1995
), http://www.jetp.ac.ru/cgi-bin/e/index/e/81/4/p743?a=list.
7.
V.
Munzar
,
D.
Klir
,
J.
Cikhardt
,
B.
Cikhardtova
,
J.
Kravarik
,
P.
Kubes
, and
K.
Rezac
, “
Investigation of magnetic fields in Z-pinches via multi-MeV proton deflectometry
,”
IEEE Trans. Plasma Sci.
46
,
3891
3900
(
2018
).
8.
F. C.
Jahoda
,
F. L.
Ribe
, and
G. A.
Sawyer
, “
Zeeman-effect magnetic field measurement of a high-temperature plasma
,”
Phys. Rev.
131
,
24
29
(
1963
).
9.
N. J.
Peacock
and
B. A.
Norton
, “
Measurement of megagauss magnetic fields in a plasma focus device
,”
Phys. Rev. A
11
,
2142
2146
(
1975
).
10.
R. P.
Golingo
,
U.
Shumlak
, and
D. J. D.
Hartog
, “
Note: Zeeman splitting measurements in a high-temperature plasma
,”
Rev. Sci. Instrum.
81
,
126104
(
2010
).
11.
M. R.
Gomez
,
S. B.
Hansen
,
K. J.
Peterson
,
D. E.
Bliss
,
A. L.
Carlson
,
D. C.
Lamppa
,
D. G.
Schroen
, and
G. A.
Rochau
, “
Magnetic field measurements via visible spectroscopy on the Z machine
,”
Rev. Sci. Instrum.
85
,
11E609
(
2014
).
12.
J. T.
Banasek
,
J. T.
Engelbrecht
,
S. A.
Pikuz
,
T. A.
Shelkovenko
, and
D. A.
Hammer
, “
Measuring 20–100 T B-fields using Zeeman splitting of sodium emission lines on a 500 kA pulsed power machine
,”
Rev. Sci. Instrum.
87
,
11D407
(
2016
).
13.
G.
Rosenzweig
, “
Investigation of the magnetic field distribution and the fundamental properties of an imploding plasma, near and during stagnation
,” Ph.D. thesis (
Feinberg Graduate School
, WIS,
2015
).
14.
E.
Stambulchik
,
K.
Tsigutkin
, and
Y.
Maron
, “
Spectroscopic method for measuring plasma magnetic fields having arbitrary distribution of direction and amplitude
,”
Phys. Rev. Lett.
98
,
225001
(
2007
).
15.
E.
Kroupp
,
D.
Osin
,
A.
Starobinets
,
V.
Fisher
,
V.
Bernshtam
,
L.
Weingarten
,
Y.
Maron
,
I.
Uschmann
,
E.
Förster
,
A.
Fisher
,
M. E.
Cuneo
,
C.
Deeney
, and
J. L.
Giuliani
, “
Ion temperature and hydrodynamic-energy measurements in a Z-pinch plasma at stagnation
,”
Phys. Rev. Lett.
107
,
105001
(
2011
).
16.
L.
Gregorian
,
V.
Bernshtam
,
E.
Kroupp
,
G.
Davara
, and
Y.
Maron
, “
Use of emission-line intensities for a self-consistent determination of the particle densities in a transient plasma
,”
Phys. Rev. E
67
,
016404
(
2003
).
17.
L.
Gregorian
,
E.
Kroupp
,
G.
Davara
,
V. I.
Fisher
,
A.
Starobinets
,
V. A.
Bernshtam
,
A.
Fisher
, and
Y.
Maron
, “
Electron density and ionization dynamics in an imploding z-pinch plasma
,”
Phys. Plasmas
12
,
092704
(
2005
).
18.
L.
Gregorian
,
E.
Kroupp
,
G.
Davara
,
A.
Starobinets
,
V. I.
Fisher
,
V. A.
Bernshtam
,
Y. V.
Ralchenko
, and
Y.
Maron
, “
Electron-temperature and energy-flow history in an imploding plasma
,”
Phys. Rev. E
71
,
056402
(
2005
).
19.
D.
Osin
,
E.
Kroupp
,
A.
Starobinets
,
G.
Rosenzweig
,
D.
Alumot
,
Y.
Maron
,
A.
Fisher
,
E.
Yu
,
J. L.
Giuliani
, and
C.
Deeney
, “
Evolution of MHD instabilities in plasma imploding under magnetic field
,”
IEEE Trans. Plasma Sci.
39
,
2392
2393
(
2011
).
20.
J. L.
Giuliani
,
J. W.
Thornhill
,
E.
Kroupp
,
D.
Osin
,
Y.
Maron
,
A.
Dasgupta
,
J. P.
Apruzese
,
A. L.
Velikovich
,
Y. K.
Chong
,
A.
Starobinets
,
V.
Fisher
,
Y.
Zarnitsky
,
V.
Bernshtam
,
A.
Fisher
,
T. A.
Mehlhorn
, and
C.
Deeney
, “
Effective versus ion thermal temperatures in the Weizmann Ne z-pinch: Modeling and stagnation physics
,”
Phys. Plasmas
21
,
031209
(
2014
).
21.
T. J. M.
Boyd
and
J. J.
Sanderson
,
The Physics of Plasmas
(
Cambridge University Press
,
2003
).
22.
J. D.
Huba
,
NRL Plasma Formulary Supported by the Office of Naval Research
(
Naval Research Laboratory
,
Washington, DC
,
2018
).
23.
I. E.
Ochs
,
C.
Stollberg
,
E.
Kroupp
,
Y.
Maron
,
A.
Fruchtman
,
E. J.
Kolmes
,
M. E.
Mlodik
, and
N.
Fisch
, “
Current channel evolution in ideal Z pinch for general velocity profiles
,”
Phys. Plasmas
26
,
122706
(
2019
).
24.
Y.
Maron
,
A.
Starobinets
,
V. I.
Fisher
,
E.
Kroupp
,
D.
Osin
,
A.
Fisher
,
C.
Deeney
,
C. A.
Coverdale
,
P. D.
Lepell
,
E. P.
Yu
,
C.
Jennings
,
M. E.
Cuneo
,
M. C.
Herrmann
,
J. L.
Porter
,
T. A.
Mehlhorn
, and
J. P.
Apruzese
, “
Pressure and energy balance of stagnating plasmas in z-pinch experiments: Implications to current flow at stagnation
,”
Phys. Rev. Lett.
111
,
035001
(
2013
).
25.
S. I.
Braginskii
, “
Transport processes in a plasma
,”
Rev. Plasma Phys.
1
,
205
(
1965
), https://ui.adsabs.harvard.edu/abs/1965RvPP....1..205B.
26.
P.-A.
Gourdain
,
M. B.
Adams
,
J. R.
Davies
, and
C. E.
Seyler
, “
Axial magnetic field injection in magnetized liner inertial fusion
,”
Phys. Plasmas
24
,
102712
(
2017
).
27.
J. W.
Thornhill
,
J. L.
Giuliani
,
Y. K.
Chong
,
A.
Dasgupta
, and
J. P.
Apruzese
, “
Improved non-local radiation coupling for MACH2-TCRE
,” in
2012 Abstracts IEEE International Conference on Plasma Science
(
2012
), p.
2C
3
.
28.
A. L.
Velikovich
,
J. L.
Giuliani
,
S. T.
Zalesak
,
J. W.
Thornhill
, and
T. A.
Gardiner
, “
Exact self-similar solutions for the magnetized Noh Z pinch problem
,”
Phys. Plasmas
19
,
012707
(
2012
).
29.
J.
Apruzese
and
J.
Giuliani
, “
Multi-dimensional radiation transport for modeling axisymmetric Z pinches: Ray tracing compared to Monte Carlo solutions for a two-level atom
,”
J. Quant. Spectrosc. Radiat. Transfer
111
,
134
143
(
2010
).
30.
J.
Thornhill
,
J.
Giuliani
,
Y.
Chong
,
A.
Velikovich
,
A.
Dasgupta
,
J.
Apruzese
,
B.
Jones
,
D.
Ampleford
,
C.
Coverdale
,
C.
Jennings
,
E.
Waisman
,
D.
Lamppa
,
J.
McKenney
,
M.
Cuneo
,
M.
Krishnan
,
P.
Coleman
,
R.
Madden
, and
K.
Elliott
, “
Two-dimensional radiation MHD modeling assessment of designs for argon gas puff distributions for future experiments on the refurbished Z machine
,”
High Energy Density Phys.
8
,
197
208
(
2012
).
31.
V.
Tangri
,
A. J.
Harvey-Thompson
,
J. L.
Giuliani
,
J. W.
Thornhill
,
A. L.
Velikovich
,
J. P.
Apruzese
,
N. D.
Ouart
,
A.
Dasgupta
,
B.
Jones
, and
C. A.
Jennings
, “
Simulations of Ar gas-puff Z-pinch radiation sources with double shells and central jets on the Z generator
,”
Phys. Plasmas
23
,
101201
(
2016
).
32.
G.
Rosenzweig
, “
Determining the density distribution of a gas injected through a multi-nozzle system for plasma implosion experiments
,” Master's thesis (
Feinberg Graduate School
, WIS,
2007
).
33.
A. L.
Velikovich
,
J.
Davis
,
J. W.
Thornhill
,
J. L.
Giuliani
,
L. I.
Rudakov
, and
C.
Deeney
, “
Model of enhanced energy deposition in a Z-pinch plasma
,”
Phys. Plasmas
7
,
3265
3277
(
2000
).
34.
M. G.
Haines
, “
Viscous heating at stagnation in Z-pinches
,”
AIP Conf. Proc.
1088
,
57
(
2009
).
35.
Y.
Raizer
,
V.
Kisin
, and
J.
Allen
,
Gas Discharge Physics
(
Springer Berlin Heidelberg
,
1997
).
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