First experiments looking at the symmetry of the plasma formation phase of the dense plasma focus using d-dot probes

The Dense Plasma Focus is being considered as the basis of sophisticated technologies such as an energy producing fusion machine, space propulsion for interplanetary and deep space missions and nanomaterial fabrication. However, there are problems with ensuring a reliable and reproducible operation of the device. It does not operate well immediately after the device is exposed to atmosphere and re-evacuated. A series of training shots is required after which the operation stabilizes until the vacuum chamber is opened again. Our previous work on numerical simulation of the formation phase shows that plasma behaviour on hydrodynamic time scales is difficult to predict because of simultaneous presence of many time scales and scale lengths. A systematic understanding of the role of the training shots in the formation process therefore requires a new experimental approach. This paper presents the first experiments looking at the symmetry of the discharge during its formation phase. The new diagnostic uses 3 d-dot probes symmetrically placed outside the squirrel cage cathode looking at the insulator through gaps between cathode rods. First results are presented and discussed.


Introduction
The Dense Plasma Focus [1,2,3] is a versatile, scalable laboratory plasma device.One of its attractive properties is that its neutron yield follows a fourth-power-of-current scaling law.It has been projected as a platform for futuristic advanced technologies such as an energy producing fusion machine [4], space propulsion for interplanetary and deep space missions [5] and nanomaterial fabrication [6].Its operation involves creating an axially symmetric plasma of a working gas such as deuterium or argon carrying a pulsed current of several tens to thousands of kiloamperes.It is accelerated by magnetic forces and focused into a hot and dense plasma that is a source of neutrons, fast ions, fast electrons, hard and soft x-rays and an energetic plasma [2,3].
However, ensuring a reliable and reproducible operation of this device has been a challenge.It does not operate well immediately after the device is exposed to atmosphere and re-evacuated.A series of training shots is required after which the operation stabilizes until the vacuum chamber is opened again.This phenomenon has remained poorly understood in spite of efforts to control it using ultra high vacuum technology [7].
Our previous work [8,9,10] on numerical simulation of the formation phase shows that plasma behavior on hydrodynamic time scales is difficult to predict because of simultaneous presence of many time scales and scale lengths.A systematic understanding of the role of the training shots in the formation process therefore requires a new experimental approach.Proper operation of the plasma focus requires that the plasma be symmetric about the axis.While such symmetry is observed in the radial implosion phase, the conditions that give rise to such symmetry are not understood.It is just an empirical observation that after a few conditioning shots, the insulator becomes capable of creating a plasma that produces a good implosion as seen by a good current derivative singularity.Currently, there is no method of characterizing the effect of conditioning shots on the symmetry of the formation phase.
In this context, this paper presents the first experiments looking at the symmetry of the discharge during its formation phase.The new diagnostic uses 3 d-dot probes symmetrically placed outside the squirrel cage cathode looking at the insulator through gaps between cathode rods.The d-dot probe technique is a standard technique used by electrical engineers for noncontact monitoring of high voltage high current pulsed power installations [11].Conceptually, it is just a floating conductor on which charge is induced by the electric flux being emitted by the charge on the anode.This conductor is connected to the inner core of a coaxial cable terminated in its characteristic impedance at the oscilloscope end.The induced charge flows through the terminating resistance producing a signal equal to the product of the resistance and the current.The plasma focus insulator and the plasma generated over it form a polarizable dielectric medium between the high voltage anode and the floating conductor.The probe signal is therefore sensitive to the presence of the plasma that lies in the path of the electric field lines between the floating tip of the probe and the anode, which might be referred to as the field of observation of the probe.When signals from the three d-dot probes have distinctly different temporal behavior, the plasma evidently is not symmetric.
The next section describes the new technique.Section 3 presents preliminary results.Section 4 concludes the paper with a summary.

A brief description of the azimuthally staggered multiple d-dot probe technique
The University of Sofia plasma focus laboratory operates a 3 kJ Mather type device (20 µF, 40 kV) with a hollow copper anode of 2 cm diameter and 14.5 cm length.The squirrel cage cathode is made of six copper rods (0.8 cm diameter, 16 cm length) fixed on a brass cathode base plate on a circle with a 3.5 cm radius.Figure 1 shows the schematic of the experiment, which includes some features not relevant to this paper.The d-dot probes are shown at the bottom.The vacuum chamber has 15.5 cm inner diameter and 35 cm height and is made of stainless steel.Operations with air, argon or deuterium are possible.The diagnostics facilities consist of discharge current and current derivative using Rogowski belt / pick up coils, soft x-ray emission using PIN diodes, hard x-ray emission using scintillator / photomultiplier probe, thermoluminescent dosimeters (TLDs) for radiation dose measurements.Two 4 channel Tektronix oscilloscopes (TDS 3034C, TDS 2004B) are available for recording waveforms.Operation at 16 to 19 kV and 0.8 to 1.2 Torr of argon is normally found to be convenient in exploratory shots.
The d-dot probe is made from a flanged BNC female panel mount connector with solder cup.(See the left image on figure 2).An acrylic disc of 7 mm diameter with a 2.5 mm diameter hole and 3 mm thickness is placed and glued with epoxy over the solder cup such that its tip just protrudes out of the disc.A copper foil of 7 mm diameter is soldered to the solder cup while being supported on the acrylic disc.Three such detectors are fitted on a plastic tube that fits snugly outside the cathode such that they look at the middle of the insulator from 3 directions at 120 • separation (see right image on figure between the squirrel cage cathode rods.While the three hand-made and manually assembled d-dot probes cannot be expected to be exactly identical, they cannot be radically different either.Hence, any qualitative differences in their signals must be attributed to existence of asymmetry of the plasma that lies in the path of the electric field lines between the floating tip of the probe and the anode unless there are reasons to believe that the probe has a systemic defect.

Experimental results
Preliminary results of the experiment are presented and discussed below.We display two series of 3 consecutive shots, in which one shot has a discernible current derivative dip and propose our tentative interpretation of the data.
Shot #16 has a small but distinct current derivative singularity at ∼ 3 µs but the preceding and succeeding shots just have a slight deviation from a sinusoidal waveform at the position of the dip.activity in front of it or a malfunction in the detection system such as could happen due to an imperfect contact between the cable and the probe.In shot #16, the signals from d-dot-2 and d-dot-3 have a flat portion between 2 µs and 3.8 µs.The occurrence of the dip at 3 µs suggests that a proper sheath was formed and detached from the insulator and accelerated in the rundown region away from the insulator.The flat portion of the d-dot-2 and d-dot-3 signals therefore suggests that the probes functioned as expected, registering absence of the plasma in their zone of observation.This would imply that the d-dot-1 probe has a systemic defect and therefore must be ignored until the defect is located and rectified.
If this interpretation is accepted, one could identify the zone between the start of current and the start of the flat portion (at 2 µs) in Shot #16 as the plasma formation phase.Then the noticeable qualitative difference between the d-dot-2 and d-dot-3 probe signals in the formation phase of Shot #16 must be ascribed to asymmetry in plasma.
The parts of the d-dot-2 and d-dot-3 signals after the end of flat portion at 3.8 µs have a similar structure at least up to 12 µs.This can be interpreted as the back flow of the post-pinch plasma into the inter electrode gap.
This reading of the data is supported by similar observations in the triplet of consecutive shots #45, 46 and 47.We emphasize that our interpretation is tentative, based on the first results.However, the following points are clearly established: • When there is a distinct current derivative dip, at least two d-dot probes show a flat signal that begins ∼ 0.5 − 0.8 ns before the dip and lasts ∼ 0.5 − 0.8 ns after the dip.This supports the basic premise underlying our experiment that the d-dot probes are sensitive to the presence of plasma in their zone of observation.• Even when a small but distinct current derivative dip is observed, the plasma in the formation zone suffers from azimuthal asymmetry.• The back-flow of the post-pinch plasma in the zone near the insulator can be observed in the d-dot signals.

Conclusions
The Dense Plasma Focus has considerable potential for applications in diverse technologies.However, unreliable operation is a major hurdle in its realization.This unreliability is manifested in the need for a series of conditioning shots after exposure of the chamber to ambient atmosphere.This aspect is not understood since there is no interpretable diagnostic for the proper formation of a symmetric plasma in the initial phase.This paper proposes a new diagnostic that is sensitive to the symmetry of plasma formation.It utilizes three d-dot probes placed symmetrically between the rods of the squirrel cage cathode looking at the electric flux being emitted by the anode.The insulator and the plasma formed over it form a polarizable dielectric in the path of the electric field lines between the floating tip of the probe and the anode.Any asymmetry in this dielectric is reflected in qualitatively different behavior of the d-dot signals.
Our first results, from a very limited series of shots, validate this basic premise of our diagnostic and indicate the direction of further improvements of the technique.

Figure 1 :
Figure 1: Schematic of the experiment.

Figure 2 :
Figure 2: Left image: flanged BNC female panel mount connector with solder cup.(image of Pomona 2451 BNC from the internet).Right image: mounting of the d-dot probes 120 • apart on a plastic tube outside the cathode.