The inductance of imploding cylindrical wire array z-pinches has been determined from measurements of load voltage and current. A thorough analysis method is presented that explains how the load voltage of interest is found from raw signals obtained using a resistive voltage divider. This method is applied to voltage data obtained during z-pinch experiments carried out on the MAGPIE facility (1.4 MA, 240 ns rise-time) in order to calculate the load inductance and thereafter the radial trajectory of the effective current sheath during the snowplough implosion. Voltage and current are monitored very close to the load, allowing these calculations to be carried out without the need for circuit modelling. Measurements give a convergence ratio for the current of between 3.1 and 5.7 at stagnation of the pinch.

1.
V. V.
Aleksandrov
,
A. G.
Alekseev
,
V. N.
Amosov
,
M. M.
Basko
,
G. S.
Volkov
,
E. V.
Grabovskii
,
A. V.
Krasilnikov
,
G. M.
Oleinik
,
I. N.
Rastyagaev
,
P. V.
Sasorov
,
A. A.
Samokhin
,
V. P.
Smirnov
, and
I. N.
Frolov
, “
Experimental and numerical studies of plasma production in the initial stage of implosion of a cylindrical wire array
,”
Plasma Phys. Rep.
29
,
1034
1040
(
2003
).
2.
E. M.
Waisman
,
M. E.
Cuneo
,
W. A.
Stygar
,
R. W.
Lemke
,
K. W.
Struve
, and
T. C.
Wagoner
, “
Wire array implosion characteristics from determination of load inductance on the z pulsed-power accelerator
,”
Phys. Plasmas
11
(
5
),
2009
2013
(
2004
).
3.
V. V.
Aleksandrov
,
E. V.
Grabovskii
,
K. N.
Mitrofanov
,
G. M.
Oleinik
,
V. P.
Smirnov
,
P. V.
Sasorov
, and
I. N.
Frolov
, “
Relation between the electric parameters of a z-pinch discharge and plasma production in the load during the implosion of a cylindrical wire array
,”
Plasma Phys. Rep.
30
,
568
581
(
2004
).
4.
M. E.
Cuneo
,
E. M.
Waisman
,
S. V.
Lebedev
,
J. P.
Chittenden
,
W. A.
Stygar
,
G. A.
Chandler
,
R. A.
Vesey
,
E. P.
Yu
,
T. J.
Nash
,
D. E.
Bliss
,
G. S.
Sarkisov
,
T. C.
Wagoner
,
G. R.
Bennett
,
D. B.
Sinars
,
J. L.
Porter
,
W. W.
Simpson
,
L. E.
Ruggles
,
D. F.
Wenger
,
C. J.
Garasi
,
B. V.
Oliver
,
R. A.
Aragon
,
W. E.
Fowler
,
M. C.
Hettrick
,
G. C.
Idzorek
,
D.
Johnson
,
K.
Keller
,
S. E.
Lazier
,
J. S.
McGurn
,
T. A.
Mehlhorn
,
T.
Moore
,
D. S.
Nielsen
,
J.
Pyle
,
S.
Speas
,
K. W.
Struve
, and
J. A.
Torres
, “
Characteristics and scaling of tungsten-wire-array z-pinch implosion dynamics at 20 ma
,”
Phys. Rev. E
71
,
046406
(
2005
).
5.
E. M.
Waisman
,
M. E.
Cuneo
,
R. W.
Lemke
,
D. B.
Sinars
, and
W. A.
Stygar
, “
Lower bounds for the kinetic energy and resistance of wire array z pinches on the z pulsed-power accelerator
,”
Phys. Plasmas
15
(
4
),
042702
(
2008
).
6.
C. A.
Jennings
,
M. E.
Cuneo
,
E. M.
Waisman
,
D. B.
Sinars
,
D. J.
Ampleford
,
G. R.
Bennett
,
W. A.
Stygar
, and
J. P.
Chittenden
, “
Simulations of the implosion and stagnation of compact wire arrays
,”
Phys. Plasmas
17
(
9
),
092703
(
2010
).
7.
D. P.
Murphy
,
R. J.
Allen
,
B. V.
Weber
,
R. J.
Commisso
,
J. P.
Apruzese
,
D. G.
Phipps
, and
D.
Mosher
, “
Time-resolved voltage measurements of z-pinch radiation sources with a vacuum voltmeter
,”
Rev. Sci. Instrum.
79
(
10
),
10E306
(
2008
).
8.
A. J.
Harvey-Thompson
,
S. V.
Lebedev
,
S. N.
Bland
,
J. P.
Chittenden
,
G. N.
Hall
,
A.
Marocchino
,
F.
Suzuki-Vidal
,
S. C.
Bott
,
J. B. A.
Palmer
, and
C.
Ning
, “
Quantitative analysis of plasma ablation using inverse wire array z pinches
,”
Phys. Plasmas
16
(
2
),
022701
(
2009
).
9.
F.
Suzuki-Vidal
,
S. V.
Lebedev
,
S. N.
Bland
,
G. N.
Hall
,
G.
Swadling
,
A. J.
Harvey-Thompson
,
J. P.
Chittenden
,
A.
Marocchino
,
A.
Ciardi
,
A.
Frank
,
E. G.
Blackman
, and
S. C.
Bott
, “
Generation of episodic magnetically driven plasma jets in a radial foil z-pinch
,”
Phys. Plasmas
17
(
11
),
112708
(
2010
).
10.
I. H.
Mitchell
,
J. M.
Bayley
,
J. P.
Chittenden
,
J. F.
Worley
,
A. E.
Dangor
,
M. G.
Haines
, and
P.
Choi
, “
A high impedance mega-ampere generator for fiber z-pinch experiments
,”
Rev. Sci. Instrum.
67
(
4
),
1533
1541
(
1996
).
11.
D. G.
Pellinen
and
M. S.
Di Capua
, “
Two-megavolt divider for pulsed high voltages in vacuum
,”
Rev. Sci. Instrum.
51
(
1
),
70
73
(
1980
).
12.
G. F.
Swadling
, “
An experimental investigation of the azimuthal structures formed during the ablation phase of wire array z-pinches
,” Ph.D. dissertation (
Imperial College
, London,
2012
).
13.
F. S.
Felber
and
N.
Rostoker
, “
Kink and displacement instabilities in imploding wire arrays
,”
Phys. Fluids
24
(
6
),
1049
1055
(
1981
).
14.
A. L.
Velikovich
,
I. V.
Sokolov
, and
A. A.
Esaulov
, “
Perfectly conducting incompressible fluid model of a wire array implosion
,”
Phys. Plasmas
9
(
4
),
1366
1380
(
2002
).
15.
S. V.
Lebedev
,
F. N.
Beg
,
S. N.
Bland
,
J. P.
Chittenden
,
A. E.
Dangor
,
M. G.
Haines
,
K. H.
Kwek
,
S. A.
Pikuz
, and
T. A.
Shelkovenko
, “
Effect of discrete wires on the implosion dynamics of wire array z pinches
,”
Phys. Plasmas
8
,
3734
3747
(
2001
).
16.
J.
Greenly
,
M.
Martin
,
I.
Blesener
,
D.
Chalenski
,
P.
Knapp
, and
R.
McBride
, “
The role of flux advection in the development of the ablation streams and precursors of wire array z-pinches
,”
AIP Conf. Proc.
1088
(
1
),
53
56
(
2009
).
17.
M. R.
Martin
,
C. E.
Seyler
, and
J. B.
Greenly
, “
The role of magnetic field in the transition to streaming ablation in wire arrays
,”
Phys. Plasmas
17
(
5
),
052706
(
2010
).
18.
V. V.
Aleksandrov
,
V. A.
Barsuk
,
E. V.
Grabovski
,
A. N.
Gritsuk
,
G. G.
Zukakishvili
,
S. F.
Medovshchikov
,
K. N.
Mitrofanov
,
G. M.
Oleinik
, and
P. V.
Sasorov
, “
Studies of penetration of the magnetic field into electrically imploded loads in the angara-5-1 facility
,”
Plasma Phys. Rep.
35
,
200
221
(
2009
).
19.
A. J.
Harvey-Thompson
,
S. V.
Lebedev
,
S.
Patankar
,
S. N.
Bland
,
G.
Burdiak
,
J. P.
Chittenden
,
A.
Colaitis
,
P.
De Grouchy
,
H. W.
Doyle
,
G. N.
Hall
,
E.
Khoory
,
M.
Hohenberger
,
L.
Pickworth
,
F.
Suzuki-Vidal
,
R. A.
Smith
,
J.
Skidmore
,
L.
Suttle
, and
G. F.
Swadling
, “
Optical Thomson scattering measurements of plasma parameters in the ablation stage of wire array z pinches
,”
Phys. Rev. Lett.
108
,
145002
(
2012
).
20.
S. C.
Bott
,
S. V.
Lebedev
,
D. J.
Ampleford
,
S. N.
Bland
,
J. P.
Chittenden
,
A.
Ciardi
,
M. G.
Haines
,
C.
Jennings
,
M.
Sherlock
,
G.
Hall
,
J.
Rapley
,
F. N.
Beg
, and
J.
Palmer
, “
Dynamics of cylindrically converging precursor plasma flow in wire-array z-pinch experiments
,”
Phys. Rev. E
74
,
046403
(
2006
).
21.
S. N.
Bland
,
D. J.
Ampleford
,
S. C.
Bott
,
A.
Guite
,
G. N.
Hall
,
S. M.
Hardy
,
S. V.
Lebedev
,
P.
Shardlow
,
A.
Harvey-Thompson
,
F.
Suzuki
, and
K. H.
Kwek
, “
Use of faraday probing to estimate current distribution in wire array z pinches
,”
Rev. Sci. Instrum.
77
(
10
),
10E315
(
2006
).
22.
S. V.
Lebedev
,
D. J.
Ampleford
,
S. N.
Bland
,
S. C.
Bott
,
J. P.
Chittenden
,
J.
Goyer
,
C.
Jennings
,
M. G.
Haines
,
G. N.
Hall
,
D. A.
Hammer
,
J. B. A.
Palmer
,
S. A.
Pikuz
,
T. A.
Shelkovenko
, and
T.
Christoudias
, “
Physics of wire array z-pinch implosions: Experiments at imperial college
,”
Plasma Phys. Controlled Fusion
47
(
5A
),
A91
(
2005
).
23.
J. P.
Chittenden
,
S. V.
Lebedev
,
B. V.
Oliver
,
E. P.
Yu
, and
M. E.
Cuneo
, “
Equilibrium flow structures and scaling of implosion trajectories in wire array z pinches
,”
Phys. Plasmas
11
(
3
),
1118
1127
(
2004
).
24.
S. V.
Lebedev
,
F. N.
Beg
,
S. N.
Bland
,
J. P.
Chittenden
,
A. E.
Dangor
, and
M. G.
Haines
, “
Snowplow-like behavior in the implosion phase of wire array z pinches
,”
Phys. Plasmas
9
(
5
),
2293
2301
(
2002
).
25.
G. N.
Hall
,
S. A.
Pikuz
,
T. A.
Shelkovenko
,
S. N.
Bland
,
S. V.
Lebedev
,
D. J.
Ampleford
,
J. B. A.
Palmer
,
S. C.
Bott
,
J.
Rapley
,
J. P.
Chittenden
, and
J. P.
Apruzese
, “
Structure of stagnated plasma in aluminum wire array z pinches
,”
Phys. Plasmas
13
(
8
),
082701
(
2006
).
26.
G. N.
Hall
,
J. P.
Chittenden
,
S. N.
Bland
,
S. V.
Lebedev
,
S. C.
Bott
,
C.
Jennings
,
J. B. A.
Palmer
, and
F.
Suzuki-Vidal
, “
Modifying wire-array z-pinch ablation structure using coiled arrays
,”
Phys. Rev. Lett.
100
,
065003
(
2008
).
27.
A. J.
Harvey-Thompson
,
S. V.
Lebedev
,
G.
Burdiak
,
E. M.
Waisman
,
G. N.
Hall
,
F.
Suzuki-Vidal
,
S. N.
Bland
,
J. P.
Chittenden
,
P.
De Grouchy
,
E.
Khoory
,
L.
Pickworth
,
J.
Skidmore
, and
G.
Swadling
, “
Suppression of the ablation phase in wire array z pinches using a tailored current prepulse
,”
Phys. Rev. Lett.
106
,
205002
(
2011
).
You do not currently have access to this content.