Newly obtained results on hot and dense deuterium and deuterium-neon plasma compression in a z-pinch electrical discharge configuration are presented. The investigated plasma was generated and compressed using 269 high-current discharges in a medium-sized (dense) plasma focus device. The experimental chamber of the device was filled with deuterium and deuterium-neon gas mixtures under constant total mass/density conditions. Magnetic and electric probes, beryllium neutron activation counter, and high-speed four-frame vacuum ultraviolet/soft x-ray pinhole camera were used to study the plasma dynamics and radiation emission. The results obtained experimentally for the first time confirmed clearly a decrease in the minimum radius of plasma columns with an increase in initial neon fraction. Simultaneously, a decrease in the total neutron emission from deuteron fusion was found. The observed plasma/discharge evolution revealed that the classical description of plasma-focus discharges can be approximately correct up to the moment of maximum compression. Including, existence of quasi-equilibrium plasma compression is probable. It is also possible that the homogeneity of plasma columns during the slow compression phase and maximum compression moment increases with the increase in initial neon fraction. The effect of higher stabilization (repeatability) of discharges was confirmed, for higher initial neon fractions. The dependency of the total neutron emission yield on the parameters describing the full discharge dynamics and the maximum discharge voltage was confirmed. The existence of this type of dependency, for a minimum pinch radius is also possible. In contrast, there was little dependency to the total discharge current parameters measured in the collector area.

High-current discharges in dense plasma focus and z-pinch systems operating with mixtures of deuterium (or deuterium-tritium) and heavier noble gas have potential to increase maximum plasma compression, and thus increase the occurrence of fusion reactions (Vikhrev, 1978; Haines, 1982). It is widely believed that in the plasma focus, beam-target is the dominant mechanism while thermonuclear fusion is negligible (Jäger and Herold, 1987; Bernard , 1998; Gribkov , 2007; Lee and Saw, 2008a; and Auluck , 2021). On the other hand, simulations (Narkis , 2021) suggest that transition from the beam-target to thermonuclear fusion may be possible for discharges in mega-ampere plasma foci operating with mixtures of deuterium and noble gas krypton.

The added heavier gas increases total x-ray emission from the plasma pinch, enhances radiative cooling and thus reduce the Pease-Braginskii current. This facilitates radiative compression at sub-MA pinch currents (Shearer, 1976; Pereira and Davis, 1988). The Pease-Braginskii current is a necessary but not sufficient condition for radiative compression. A second condition is that the characteristic energy depletion time must be of the order of the pinch stability time or smaller. This conditions are fulfilled in heavier noble gases (Lee , 2016; Marciniak , 2022). These two conditions may also be met with sufficiently high doping levels of deuterium with a heavier noble gas (Marciniak , 2022). On the other hand, other calculations suggest that significant plasma radiative compression may not be realized due to instabilities, thermodynamic non-balance and nonuniformity of plasma column (Pereira and Davis, 1988; Liberman ., 1999; Haines, 2011). In a recent publication (Marciniak , 2022), experimental discharges in a medium-sized plasma focus operating with deuterium (D2) and deuterium-argon (D2 + Ar) gas mixtures were analyzed. The experiments sought to clarify conditions for plasma radiative compression. The analysis was based on the measured waveforms of total discharge current using the 5-phase Lee model code (Lee, 2014). Based on calculations, with pinch current higher than 200–300 kA with significant fraction of neon (Ne) in the mixture, the basic conditions for plasma radiative compression should be fulfilled. However, the power of radiation emission is connected with fraction of mass swept into plasma pinch. Experiments indicate that efficient mass sweeping of heavier noble gas and compression of this mass into pinch, may be problematic in plasma focus devices (Marciniak , 2022).

Attention has also been paid to the existence of so-called hot-spots, within the plasma pinch column. These hot-spots can also be subjected to plasma radiative compression (Pereira and Davis, 1988; Koshelev and Pereira, 1991; and Liberman ., 1999). Hot-spots have been observed in different z-pinch devices operating with pure noble gases and with mixtures of these with deuterium. It was suggested that hot-spot occur possibly only in gases having atomic number higher or equal to 18 (Lebert , 1995). Some of the models used in the computer simulations showed very good agreement with the experimental results regarding the evolution of hot-spots—e.g., Hebach (1993). It was suggested that high-density hot-spots can be local centers of radiative compression, can appear when ions are accelerated and may contribute significantly to the occurring nuclear fusion.

In addition to plasma radiative compression, it was shown theoretically that in plasma pinches of gases and mixtures, the compressibility of the plasma changes depending on its specific heat ratio (Potter, 1978; Haines, 2011; and Lee, 2014, 2016). The specific heat ratio is related to the number of degrees of freedom of plasma particles. Adding a high atomic number noble gas increases the number of degrees of freedom of the gas ensemble due to the continuing ionization. This reduces the specific heat ratio and increases the compressibility. The result is a smaller pinch radius. This may enhance nuclear fusion (Saw , 2014; Lee, 2016).

Other phenomena or effects have been postulated and/or observed during studies on plasma-focus discharges in pure noble gases or in gas mixtures in reference to discharges in pure deuterium. One should mention possible changes in: the initial break-down and plasma/current sheath formation (Goudarzi , 2005; Veloso , 2014), thickness and curvature of the current sheath, sweeping of the mass of gases through the plasma sheath (Marciniak , 2022), plasma outflow from pinch (Marciniak , 2022), current flow through the plasma sheath (Marciniak , 2022), stability/repeatability of discharges (Bailey , 1982; Marciniak , 2022), stability of the plasma column (Bailey , 1982), plasma distribution in a column (Bailey , 1982), emission of x-rays (Pereira and Davis, 1988; Liberman ., 1999), and emission of neutrons from the nuclear fusion reactions (Veloso , 2014; Hahn , 2020). The probable appearance of ion separation effect in the accelerating or imploding plasma sheath composed of a gas mixture should also be mentioned (Commisso and Kunze, 1975; Weingarten , 2001; and Haines, 2011). Especially interesting effect that has only been observed during selected experiments is the increase in total fusion neutron emission when doping deuterium with a heavier noble gases (Yap , 2005; Verma , 2008; Bures , 2009; Bures , 2010; Talaei and Sadat Kiai, 2010; Mohammadi , 2011; Talebitaher , 2016; and Hahn , 2020). This effect may be due to the phenomena mentioned above—especially plasma radiative compression, increase in the plasma compressibility, and/or formation of hot-spots.

In this article, the authors present the results of their research obtained from experiments using a medium-sized plasma focus device, whose experimental chamber was filled with pure deuterium or a selected mixture of deuterium and neon under constant total mass conditions. The authors focus on the description of the observed plasma/discharge evolution, its characteristics, determination of changes in plasma/discharge parameters and determination of impact of plasma/discharge parameters on total deuteron–deuteron (D–D) fusion occurrence. A possible explanation of the obtained results is given.

All experiments within the frame of this work were carried out using a medium-sized plasma focus system, which is called PF-24 (Marciniak , 2016; Auluck , 2021)—see Fig. 1. The capacitor bank of PF-24 consists of 24 condensers connected in parallel, where each condenser is trigger by an individual spark-gap. The battery total capacitance is 116 μF and charging voltage used is 17 kV. This results in 16.8 kJ of total energy storage in the bank. All condensers are connected to the device's collector via a large number of transmission cables. The electrodes inside the experimental chamber of PF-24 have the Mather type layout. The anode consists of a single copper rod. The rod is about 17.8 cm long inside the chamber and has diameter equal to 6.2 cm. The rod is partially hollow. The diameter of hole in the anode is about 1.6 cm and diameter of larger hollow step of 0.7 cm depth is about 3.2 cm—shape of the anode is presented in Fig. 2. The cathode of PF-24 consists of 16 rods made of stainless steel. The rods are placed on the circumference of the circle with the anode as the center—squirrel cage (Fig. 2). The diameter of the circle is 11 cm. The length of each rod inside the chamber is about 17.8 cm and diameter is 1.2 cm. The anode and cathode are divided by a ceramic insulator (Al2O3) sleeve at the bottom part of the anode (part connected to the collector). The length of the anode covered by the insulator inside the chamber is about 4.4 cm. The PF-24 operates in static filling gas mode (no gas puffing during discharge).

FIG. 1.

The PF-24 plasma focus device, along with diagnostic systems used, operating in the Institute of Nuclear Physics in Krakow, Poland.

FIG. 1.

The PF-24 plasma focus device, along with diagnostic systems used, operating in the Institute of Nuclear Physics in Krakow, Poland.

Close modal
FIG. 2.

Interior of the experimental chamber of plasma focus PF-24 device. After performing all 269 discharges no significant deformation of the electrodes was stated.

FIG. 2.

Interior of the experimental chamber of plasma focus PF-24 device. After performing all 269 discharges no significant deformation of the electrodes was stated.

Close modal

The following diagnostic systems were used during all experiments conducted (Fig. 1):

  • Magnetic probe registering signal of total discharge current (Rogowski coil)—I. Placed in the collector area of PF-24—wound on the conductive plate to which transmission cables are connected on one side, and on the other is connected to the anode (winding around the back part of the anode). Waveform registered using 350 MHz digital phosphorus oscilloscope with 1 point per ns (minimum statistical error). Calibration constant equal to 26.4 kA/V.

  • Magnetic probe registering signal of derivative of total discharge current over time (magnetic coil)—dI/dt. Placed in the collector area of PF-24—wound on the conductive plate to which transmission cables are connected on one side, and on the other is connected to the anode (winding around the back part of the anode). Waveform registered using 350 MHz digital phosphorus oscilloscope with 1 point per ns (minimum statistical error).

  • Electric probe registering signal of discharge voltage (resistive voltage divider)—U. Placed in the collector area of PF-24—connected to the back of the anode. Waveform registered using 350 MHz digital phosphorus oscilloscope with 1 point per ns (minimum statistical error). Calibration constant equal to about 1 kV/V.

  • Two magnetic probes placed along the anode inside the experimental chamber—see Fig. 2. Used to register signal coming from changes in the magnetic field generated by traveling plasma sheath. Waveform registered using 500 MHz digital phosphorus oscilloscope with 1 point per ns (minimum statistical error). Distance between two probes along the z axis is equal to about 5.3 cm.

  • Beryllium neutron activation counter placed above the experimental chamber at a fixed position (Talebitaher , 2011; Bieńkowska , 2014; and Marciniak , 2016). The detector consists of a beryllium target and a gas proportional counter. The utilized nuclear reactions are: 9Be(n,α)6He and 6He → 6Li + β + ν ¯ e. The counter is fully calibrated and calibration constant is equal to 2.00(±0.04) × 105 n/discharge (Bieńkowska , 2014; Marciniak , 2016).

  • High-speed 4-frame vacuum-ultraviolet/soft x-ray camera (VUV/SXR) pinhole camera (Tomaszewski , 2003; Marciniak , 2016). System used to register 2-dimensional images of plasma evolution close to the anode end—2-dimensional 4-frame images of plasma emissivity in VUV and SXR radiation. Energy of registered radiation is between about 10 eV and 6.2 keV. The system uses an open microchannel plate device (MCP) and a CCD camera sensitive to visible light. The MCP constitutes primary image detector, amplifier and signal converter to visible light. The MCP consists of 4 triangular sectors, electrically separated. Each sector corresponds to a single camera frame. The time delay of each frame is adjusted by the length of the cable used to transmit the triggering pulse. During all experiments position of the camera was always central in reference to the face of the anode. Used pinholes had diameters: 150 μm (frame #1), 50 μm (frame #2), 50 μm (frame #3) and 150 μm (frame #4). Frame #1 and #2 were registered at the same time. Frame #3 and #4 were registered at the same time. So, the number of independent time frames was 2. Delay between independent time frames was 14 ns. Time of exposure of a single frame is 1–2 ns. Frame #1 and #4 were covered with 7 μm thick Be filter—registration only of SXR above about 670 eV (assuming 10% cut-off). Total number of pixels used in the final image detector is 2048 × 2048. Size of a single pixel is about 43 μm. Spatial resolution of an image is around 215 μm. The camera is vacuum-tightly connected to the experimental chamber—maintained vacuum in the body of the camera during operation is not worse than 10−5–10−4 mbar (shutter between the camera body and the PF-24 experimental chamber opened only during a discharge).

The registered data with diagnostic systems were used to determine various plasma and discharge parameters and provide qualitative description. Below, the list of parameters and their method of determination is presented. Each discharge (individual experiment) mentioned in this article was thoroughly analyzed in the same manner described below (as long as the relevant data were available).

In Fig. 3, exemplary waveforms of I, dI/dt, and U are presented. The registered waveforms were used to determine a set of various parameters—the method of determination of parameters is presented in Fig. 3. The determined parameters are maximum discharge current—Imax, current at the dI/dt minimum (current value in the center of dI/dt jump)—Ip, current at the first dI/dt minimum (if many minima)—Ip1, time to the beginning of radial compression (approximated time to the beginning of current drop)—tc, time to global dI/dt minimum (time to the center of dI/dt jump)—tp, time to the first dI/dt minimum (if many minima)—tp1, average axial velocity—vz = (lalins/2)/tc (la is the total length of the anode inside the experimental chamber and lins is the length of insulator ring inside the experimental chamber), maximum discharge voltage—Umax, and time to maximum discharge voltage—tUmax. In the rest of this article, tp1 parameter was always taken as the t = 0 ns point, for each analyzed discharge—tp1 determined for each investigated discharge in this work independently.

FIG. 3.

Registered waveforms of (a) total discharge current (I), (b) derivative of total discharge current over time (dI/dt) and (c) discharge voltage (U) in the collector area of the PF-24 device during discharge #20090901 in D2 [p0 = 2.80(±0.01) mbar and U0 = 17 kV]. All 3 waveforms have the same time base, as presented. Marked parameters are: Imax—maximum discharge current, Ip1—discharge current at the first dI/dt minimum, Ip—discharge current at the dI/dt minimum, Umax—maximum discharge voltage, tc—time to the beginning of radial compression, tp1—time to the first dI/dt minimum, tp—time to the dI/dt minimum, and tUmax—time to the maximum discharge voltage.

FIG. 3.

Registered waveforms of (a) total discharge current (I), (b) derivative of total discharge current over time (dI/dt) and (c) discharge voltage (U) in the collector area of the PF-24 device during discharge #20090901 in D2 [p0 = 2.80(±0.01) mbar and U0 = 17 kV]. All 3 waveforms have the same time base, as presented. Marked parameters are: Imax—maximum discharge current, Ip1—discharge current at the first dI/dt minimum, Ip—discharge current at the dI/dt minimum, Umax—maximum discharge voltage, tc—time to the beginning of radial compression, tp1—time to the first dI/dt minimum, tp—time to the dI/dt minimum, and tUmax—time to the maximum discharge voltage.

Close modal

In Fig. 4, exemplary waveforms of signals from magnetic probes placed in the experimental chamber are presented. Using the obtained waveforms, average axial velocity between two points was determined (see Fig. 4)—vz(Δt) = la12/(t2 – t1). The la12 is the distance between center of probe #1 and probe #2, and t1 and t2 are times which correspond to the moment of registration of the highest and smallest signal from probe: #1 and #2, respectively. Probe #2 [waveform presented in Fig. 4(b)] is placed closer to the end of the anode.

FIG. 4.

Registered waveforms during discharge #20090901 in D2 by the magnetic probe (a) #1 and (b) #2 placed in the experimental chamber of the PF-24 device along the anode (probes placed at different distances with respect to the z axis). Both waveforms have the same time base, as presented. Parameter t1 stands for time to the highest signal jump at the probe #1 and parameter t2 stands for time to the smallest signal jump at the probe #2, and Δt = t2t1.

FIG. 4.

Registered waveforms during discharge #20090901 in D2 by the magnetic probe (a) #1 and (b) #2 placed in the experimental chamber of the PF-24 device along the anode (probes placed at different distances with respect to the z axis). Both waveforms have the same time base, as presented. Parameter t1 stands for time to the highest signal jump at the probe #1 and parameter t2 stands for time to the smallest signal jump at the probe #2, and Δt = t2t1.

Close modal

The total D-D fusion neutron emission yield (Yn) was determined simply by multiplying the registered number of counts by the calibration constant.

The images registered using the 4-frame VUV/SXR pinhole camera (4-frame images) were used to obtain information about plasma pinch evolution—maximum compression moment time position in reference to the first dI/dt minimum, stability or instability, uniformity or nonuniformity (including presence of internal structures), VUV and SXR emission from compressed plasma and scenario of a discharge evolution. Moreover, registered 4-frame images were used to determine two plasma parameters: minimum radius of a plasma pinch in shape similar to a column (rpmin)—radius at the maximum compression moment (radius approximately at the beginning of stagnation), and radial velocity of current/plasma sheath (CS) collapse or plasma pinch compression between two frames—vr(Δrp) = (rp1rp2)/tr12, where tr12 is the time between independent frames of the camera, rp1 is the pinch radius at time t3 and rp2 is the pinch radius at time t3 + tr12. The calculations were made on the assumption of symmetry—symmetrical CS moving with the same velocity from each direction along the y axis toward the z axis. The rp1 and rp2 values were determined based on the plots of profile of plasma emissivity along the y axis, for a selected distance on the z axis (distance “d” over the surface of the anode—see Figs. 5 and 6) for which tangent of the surface of compressing plasma sheath is (most) parallel to the z axis—see Fig. 5. In the plotted profiles of plasma emissivity along the y axis, distance at the bottom of peak was used—usually 10%–20% of total height of the investigated peak over the background level was taken (depending on the height above which the radiation peak began to rise rapidly)—see Fig. 6. A similar procedure was applied for the determination of rpmin, wherein only the frames presenting the maximum compression moment (or very close) were used in the analysis. Additionally, for the more precise determination of rpmin value, many profiles along the y axis, at different distances along the z axis, were plotted in the space occupied by a well-compressed plasma column (ROI—“region of interest”—see Fig. 7) and rpmin value was determined for each plotted profile independently. The average value of rpmin was calculated using all plotted profiles for a given discharge: rpmin = (rpmin_1 + rpmin_2 + ⋯ + rpmin_n)/n (n is the total number of plotted profiles).

FIG. 5.

Presentation of the analysis of the 4-frame image, obtained during discharge #20100803 in 85.8%D2 + 14.2%Ne gas mixture (in relation to the total mass) in the PF-24 plasma focus device [p0 = 2.51(±0.01) mbar and U0 = 17 kV], in order to determine the value of radial velocity of compression between two frames—vr(Δrp). Parameter “d” is the distance from the anode face along the z axis—at this distance profile 1 and profile 2 were plotted along the y axis. Frames #1 and #2 were recorded at the same time—18(±10) ns before tp1. Frame #3 and #4 were recorded at the same time and 14 ns later in reference to frame #1 and #2.

FIG. 5.

Presentation of the analysis of the 4-frame image, obtained during discharge #20100803 in 85.8%D2 + 14.2%Ne gas mixture (in relation to the total mass) in the PF-24 plasma focus device [p0 = 2.51(±0.01) mbar and U0 = 17 kV], in order to determine the value of radial velocity of compression between two frames—vr(Δrp). Parameter “d” is the distance from the anode face along the z axis—at this distance profile 1 and profile 2 were plotted along the y axis. Frames #1 and #2 were recorded at the same time—18(±10) ns before tp1. Frame #3 and #4 were recorded at the same time and 14 ns later in reference to frame #1 and #2.

Close modal
FIG. 6.

Plot of the single plasma VUV/SXR emissivity profile along the y axis—profile 2 from Fig. 5, at the distance “d” over the surface of the anode. The r_p2 length is the radius of the plasma pinch (rp2) at distance “d.”

FIG. 6.

Plot of the single plasma VUV/SXR emissivity profile along the y axis—profile 2 from Fig. 5, at the distance “d” over the surface of the anode. The r_p2 length is the radius of the plasma pinch (rp2) at distance “d.”

Close modal
FIG. 7.

Presentation of the analysis of the 4-frame image, obtained during discharge #20100803 in 85.8%D2 + 14.2%Ne gas mixture (in relation to the total mass) in the PF-24 device, in order to determine the value of minimum plasma column radius—rpmin. Frames #1 and #2 were recorded at the same time—18(±10) ns before tp1. Frames #3 and #4 were recorded at the same time and 14 ns later in reference to frames #1 and #2.

FIG. 7.

Presentation of the analysis of the 4-frame image, obtained during discharge #20100803 in 85.8%D2 + 14.2%Ne gas mixture (in relation to the total mass) in the PF-24 device, in order to determine the value of minimum plasma column radius—rpmin. Frames #1 and #2 were recorded at the same time—18(±10) ns before tp1. Frames #3 and #4 were recorded at the same time and 14 ns later in reference to frames #1 and #2.

Close modal

For the determination of well-compressed area of a plasma column also frame #1 and/or #4 were used, reveling areas which emitted SXR radiation (ROI—see Fig. 7). In general, for the approximate determination of the minimum plasma column radius (selection of the images presenting the maximum compression moment and ROI), following data were taken into account: the time position of registered image in reference to the first dI/dt minimum, the observed moment of evolution of plasma pinch, the shape of the plasma pinch, and the emission of VUV and SXR radiation from the area of plasma pinch.

The total number of 269 experimental discharges were performed in the PF-24 device operated with D2 and (1 − x)D2 + xNe gas mixtures under constant, initial, total mass of gas or gases between the electrodes [m0 = 0.37(±0.02) mg], and constant, initial, total density of gas or gases inside the experimental chamber [ρ0 = 0.46(±0.03) μg/cm3]. From the 269 discharges,

  • 79 discharges in 100%D2+0%Ne (discharges in D2) at ⟨p0⟩ = 2.84(±0.03) mbar.

  • 54 discharges in 96.8%D2 + 3.2%Ne mixture (x—pressure/volume fraction) and in 85.8%D2 + 14.2%Ne (x—mass/density fraction) at ⟨p0⟩ = 2.51(±0.03) mbar.

  • 39 discharges in 93.2%D2 + 6.8%Ne mixture (x—pressure/volume fraction) and in 73.2%D2 + 26.8%Ne (x—mass/density fraction) at ⟨p0⟩ = 2.23(±0.02) mbar.

  • 39 discharges in 88.6%D2 + 11.4%Ne mixture (x—pressure/volume fraction) and in 60.8%D2 + 39.2%Ne (x—mass/density fraction) at ⟨p0⟩ = 1.92(±0.02) mbar.

  • 35 discharges in 83.4%D2 + 16.6%Ne mixture (x—pressure/volume fraction) and in 50.1%D2 + 49.9%Ne (x—mass/density fraction) at ⟨p0⟩ = 1.69(±0.02) mbar.

  • 23 discharges in 72.0%D2 + 28.0%Ne mixture (x—pressure/volume fraction) and in 33.9%D2 + 66.1%Ne (x—mass/density fraction) at ⟨p0⟩ = 1.32(±0.02) mbar.

Above, ⟨x⟩ represents the average value of fraction of pressure/volume of Ne in a given mixture or the average value of fraction of mass/density of Ne in a given mixture, while ⟨p0⟩ is the average value of total initial pressure of gas or gas mixture inside the experimental chamber. So, the discharges were performed for 0%, 3.2(±0.3)%, 6.8(±0.3)%, 11.4(±0.5)%, 16.6(±0.6)%, and 28.0(±0.7)% of Ne, with respect to the total initial pressure/volume of the gas or gas mixture, and for 0%, 14.2(±1.8)%, 26.8(±1.9)%, 39.2(±2.1)%, 49.9(±1.9)%, and 66.1(±1.9)% of Ne, with respect to the total initial mass/density of the gas or gas mixture between the electrodes. The uncertainties of x and p0 were determined based on the fluctuations of initial pressure values measured with a pressure gauge just before a discharge (presented uncertainties are average values of errors). Filling the experimental chamber with Ne was always done first and no mechanical mixing of D2 and Ne was used before a discharge. In the rest of the article, only percentages relative to the total mass will be used.

The percentage compositions of the gas mixtures were selected based on the initial simulations performed using the Lee model code (Lee, 2014; Akel , 2019; and Marciniak , 2022) (computational results not presented in this article) and to maintain a constant total mass corresponding to the initial mass of deuterium at the initial pressure of 2.84(±0.03) mbar. Under these conditions the initial pressure and mass of D2 gradually decreased and Ne gradually increased with x, simultaneously. The pressure of D2 equal to about 2.84 mbar and corresponding density of 0.46 μg/cm3 are below the optimum initial pressure and density for the total D-D fusion neutron emission (verified experimentally with discharges at different initial D2 pressures). So, cumulatively, the experiments were performed under sub-optimal conditions for the total D-D fusion occurrence, for the PF-24 device. On the other hand, due to the wide spread of the device's operating parameters, some of the single discharges could have also occur at optimal and above-optimal conditions. During the experiments, discharges were always performed in a series of 4–6 times with initial base pressures of 10−6 mbar.

Data from I, dI/dt and U probes, magnetic probes placed along the anode, and from the Be neutron counter were obtained practically for all 269 discharges. Data from 4-frame VUV/SXR pinhole camera were recorded in only 65% of the discharges due to synchronization difficulties.

From the time-resolved 4-frame images, the scheme plasma pinch evolution was determined—see Fig. 8. The evolution can be described with six phases:
FIG. 8.

Sequence of six 4-frame images registered during six different discharges in D2, presenting general scheme of a plasma/discharge evolution in a medium-sized plasma focus. Frames #1 and #2 of the image recorded: (a) 31(±3) ns before, (b) 27(±3) ns before, (c) 17(±3) ns before, (d) 9(±3) ns after, (e) 14(±3) ns after, and (f) 33(±3) ns after, the first dI/dt minimum (tp1). Frames #3 and #4 were recorded 14 ns later. The number of a discharge is given in bottom left corner of each 4-frame image.

FIG. 8.

Sequence of six 4-frame images registered during six different discharges in D2, presenting general scheme of a plasma/discharge evolution in a medium-sized plasma focus. Frames #1 and #2 of the image recorded: (a) 31(±3) ns before, (b) 27(±3) ns before, (c) 17(±3) ns before, (d) 9(±3) ns after, (e) 14(±3) ns after, and (f) 33(±3) ns after, the first dI/dt minimum (tp1). Frames #3 and #4 were recorded 14 ns later. The number of a discharge is given in bottom left corner of each 4-frame image.

Close modal
  1. Fast compression of CS. Fast compression with average speeds up to tens of cm/μs. Radial compression of CS accelerates, until the beginning of next phase. See Fig. 8(a) (all frames) and 8(b) (frames #1 and #2).

  2. Slow compression of plasma pinch—plasma pinch is formed in shape similar to a column. Relatively slow compression with strong radiation emission from the entire volume of formed plasma pinch. Radial compression systematically slows down due to internal plasma pressure increase. See Figs. 8(b) (frames #3 and #4) and 8(c) (frames #1 and #2).

  3. Maximum compression moment. Compression of plasma column is stopped—beginning of the stagnation with increased SXR emission. See Fig. 8(c) (frame #3 and #4).

  4. Early instability phase—instabilities start to dominate plasma pinch evolution. Nanoseconds after reaching maximum compression, plasma pinch starts to change its internal structure. Profiles of emissivity quickly change along the z axis—plasma temperature and density must also change. Plasma column often slightly increases its diameter. Regions which emit larger amounts of VUV/SXR radiation appear. These regions usually are spherical-like (Lerner , 2012; Kubes , 2013; and Kubes , 2016). The described behavior could be accompanied by magnetic field line reconnection, turbulence growth and micro-instabilities/micro-turbulence (Liberman ., 1999; Haines, 2011; Lerner , 2012; Kubes , 2013; Kubes , 2016; and Auluck , 2021). This could lead to anomalous resistivity and heating consistent with the observed extended current drop. Significant acceleration of ions is expected starting from this phase. See Figs. 8(d) (all frames) and 8(e) (frame #1 and #2).

  5. Instability and post-compression phase—MHD instabilities start to develop along the z axis and deform the plasma column (phase 4 and 5 partially overlap each other on a time scale as well as phase 5 and 6). These developments lead to single or multiple post-compressions. At this point plasma pinches can have very different shapes even for practically identical discharges. See Figs. 8(d) (frames #3 and #4), 8(e) (all frames), and 8(f) (frames #1 and #2).

  6. Disruption and expansion phase. Disruptions appear along the length of plasma pinch where post-compressions took place. They can appear all simultaneously or one after another in different parts of the pinch. Moreover, during the disruptions, some intensely emitting hot-spots are observed. Thereafter, the residual plasma expands and cools down. See Fig. 8(f) (frames #3 and #4).

Figure 8 shows six 4-frame images from various discharges in D2. The presented series of images shows the described general plasma/discharge evolution scheme. Found 6-phase scheme is consistent with previously published results (Bernard , 1998; Auluck , 2021). However, the details of each discharge differ in relative timings with reference to the current dip, in size and in evolution of late phases of plasma pinch compression. During some discharges, already in the fast CS compression phase, magneto Rayleigh–Taylor-like (R-T) instabilities and some deformations/asymmetries [see Fig. 9(c)] of compressing plasma are visible and plasma outflow is possible. However, these instabilities do not develop over time as compression progresses—until the instability phases. The impact of magneto R–T-like instabilities appears to be suppressed–see Fig. 9(b). So, it appears possible for a pinch to exist in mechanical equilibrium of pressures, or even some thermodynamic equilibrium.

FIG. 9.

Six 4-frame images registered during six different discharges in (100%% − x)D2 + xNe mixtures presenting properties of plasma/discharge evolution in a medium-sized plasma focus. Discharge with Ne fraction (x) equal to: (a) 26.8%, (b) 39.2%, (c) 49.9%, (d) 66.1%, (e) 39.2%, and (f) 49.9%. Frames #1 and #2 of the image recorded: (a) 55(±3) ns before, (b) 38(±3) ns before, (c) 2(±3) ns before, (d) 39(±3) ns before, (e) 52(±3) ns after, and (f) 61(±3) ns before, the first dI/dt minimum (tp1). Frames #3 and #4 were recorded 14 ns later. The number of a discharge is given in bottom left corner of each 4-frame image.

FIG. 9.

Six 4-frame images registered during six different discharges in (100%% − x)D2 + xNe mixtures presenting properties of plasma/discharge evolution in a medium-sized plasma focus. Discharge with Ne fraction (x) equal to: (a) 26.8%, (b) 39.2%, (c) 49.9%, (d) 66.1%, (e) 39.2%, and (f) 49.9%. Frames #1 and #2 of the image recorded: (a) 55(±3) ns before, (b) 38(±3) ns before, (c) 2(±3) ns before, (d) 39(±3) ns before, (e) 52(±3) ns after, and (f) 61(±3) ns before, the first dI/dt minimum (tp1). Frames #3 and #4 were recorded 14 ns later. The number of a discharge is given in bottom left corner of each 4-frame image.

Close modal

At maximum compression, the emissivity profiles along the y axis have a parabolic-like shape—see Figs. 7, 8(c), 9(b), and 9(c). This can mean that electron and ion density profiles have also a parabolic-like shape with quasi-equilibrium. During discharges, usually at least two dI/dt minima were registered. The time of the maximum compression was often nanoseconds before or after the first dI/dt minimum. The voltage spike was almost always 20–30 after the first dI/dt minimum.

In Fig. 8, only the discharges in D2 were presented. However, presented scheme generally applies to vast majority of discharges carried out in each type of gas mixture (as well as the description above). At the same time, the discharges in the gas mixtures differed a little from the discharges in D2 as well as among themselves. For 14.2%–49.9% of Ne, more VUV/SXR radiation was emitted during the compression phases. The emission areas are often longer in comparison with discharges in D2—see Figs. 9(a) and 9(b). Longer pinches may be the result of enhanced radial compression (Marciniak , 2022) and/or changes in plasma sheath curvature and higher end axial velocity. The emissivity profiles at maximum compression were more uniform—see Fig. 9(b). This indicates more uniform and stable plasma compression (Bailey , 1982; Bailey , 1986). On the other hand, for 39.2% of Ne, some small number of the registered discharges became less uniform at maximum compression. For 49.9% of Ne this effect increased. For 66.1% of Ne, greater differences between emissivity profiles along the z axis are observed, with possible presence of filamentation or division into layers of current sheath. Also, the shape of entire plasma pinches became more deformed. More VUV/SXR radiation was emitted from smaller, well-compressed, inner area, while less radiation was emitted from bigger, surrounding and not so well-compressed area—see Fig. 9(d). This indicates significant problems with sweeping of the mass of ionized gases and compression of this mass into pinch for higher Ne fraction. The final phases of plasma pinch evolution appear to be more complex compared to discharges in D2—during phases 4, 5, and 6, plasma forms into more complicated shapes. This was particularly noticeable for discharges with Ne content of 39.2% and above—see Fig. 9(e). Finally, for the discharges in D2 and in gas mixtures with 14.2%–49.9% of Ne, maximum compression often coincided with the dI/dt minimum to within ±10 ns. This close coincidence occurred 85% of cases for D2 and in increasingly lesser percentage of cases as the percentage of Ne increased (85%–70%). For the remaining 15% (15%–30%) of discharges, the moment of maximum compression was earlier than 10 ns in reference to tp1. For discharges with 66% of Ne, half the number of discharges had this degree of coincidence. For a few discharges with 49.9% and 66.1% of Ne, the time difference between the maximum compression and first dI/dt minimum was 40–70 ns (before tp1). These discharges were characterized by different late phases of evolution—see Fig. 9(f). More rapid and chaotic disintegration of the column was observed similar to sudden disruption, and expansion with “zipper effect” inferred.

In Fig. 10, determined values of four electric parameters of plasma/discharge are presented for each fraction of Ne (x)—Imax, Ip1, Ip and Umax (see Sec. III). As one can see, fluctuations of the electric parameters are large and do not appear to have relation to the Ne fraction. Total discharge currents at maximum compression were typically greater than 300 kA extending to 500 kA, even to 650 kA for some discharges. The measured values of maximum tube voltage show no increase with Ne fraction increase.

FIG. 10.

(a) Maximum discharge current (Imax), (b) discharge current at the time of the first dI/dt minimum (Ip1), (c) discharge current at the time of dI/dt minimum (Ip), and (d) maximum discharge voltage (Umax), measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., Imax) and average (e.g., ⟨Imax⟩) values of electric parameters are given with respect to the fraction of Ne (x) in the mixture. Errors presented only for average values—standard deviations.

FIG. 10.

(a) Maximum discharge current (Imax), (b) discharge current at the time of the first dI/dt minimum (Ip1), (c) discharge current at the time of dI/dt minimum (Ip), and (d) maximum discharge voltage (Umax), measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., Imax) and average (e.g., ⟨Imax⟩) values of electric parameters are given with respect to the fraction of Ne (x) in the mixture. Errors presented only for average values—standard deviations.

Close modal

In Fig. 11, determined values of six kinetic parameters of plasma/discharge are presented for each fraction of Ne (x)—tp1, tp, tUmax, vz, vz(Δt), and vr(Δrp) (see Sec. III). Values of tc parameter are not presented since vz ∼ 1/tc. The average values of tp1, tp, and tUmax are a bit higher for discharges with Ne fraction above 20%. The average values of vz also drop for Ne fraction above 20%. On the other hand, the average values of vz(Δt), which is also average axial velocity, are increased for Ne fraction above 20%. This could be due, for example, to the decrease in the effective gas mass sweeping or/and current flow through the plasma sheath in the run-down phase.

FIG. 11.

(a) Time to the first dI/dt minimum (tp1), (b) time to dI/dt minimum (tp), (c) time to the maximum discharge voltage (tUmax), (d) average axial velocity (vz), (e) average axial velocity between two points [vz(Δt)], and (f) radial velocity between two frames [vr(Δrp)], measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., tp1) and average (e.g., ⟨tp1⟩) values of kinetic parameters are given with respect to the fraction of Ne (x) in the mixture. For vr(Δrp), only values from single discharges are given. Errors presented only for average values—standard deviations.

FIG. 11.

(a) Time to the first dI/dt minimum (tp1), (b) time to dI/dt minimum (tp), (c) time to the maximum discharge voltage (tUmax), (d) average axial velocity (vz), (e) average axial velocity between two points [vz(Δt)], and (f) radial velocity between two frames [vr(Δrp)], measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., tp1) and average (e.g., ⟨tp1⟩) values of kinetic parameters are given with respect to the fraction of Ne (x) in the mixture. For vr(Δrp), only values from single discharges are given. Errors presented only for average values—standard deviations.

Close modal

The lower effective sweep of gas masses may be due to changes in the shape of the sheath and/or ion separation effect. For discharges above 30% of Ne fraction—no radial velocity greater than 14 cm/μs was measured. This lower speed can be attributed to less effective current flow through the CS, or to a change in the curvature of the sheath, or to greater effective sweeping of the gas mass in this phase. The lower maximum radial velocity of the CS leads to a lower plasma column temperature and a potentially more stable plasma pinch. The spread of determined values of tp1, tp, tUmax and vz from single discharges is significant for each fraction of Ne. The spread decreases as the Ne fraction increases. This confirms the stabilization (or increase in repeatability) of the entire discharge for higher Ne fractions.

In Fig. 12, determined values of minimum plasma column radius (rpmin) are presented for each fraction of Ne (x). Figure 12 shows both single (rpmin) values and median values [m(rpmin)]—average values. The determined values of rpmin show that the minimum pinch radius decreases as Ne fraction increases. The drop in rpmin value on average is not big—about 0.02–0.03 cm for each increase in Ne fraction (uncertainty in the measurement is estimated to be ±0.01 cm). It is noted that the spread of single radius values for discharges with D2 and 14.2% of Ne is significantly higher in comparison with discharges with Ne fraction above 20%. This proves more stable/repeatable discharges for higher Ne fraction.

FIG. 12.

Single (rpmin) and median values [m(rpmin)] of minimum plasma column radius vs Ne fraction (x) in the (1-x)D2 + xNe mixture for discharges in a medium-sized plasma focus under constant total mass conditions. Errors presented only for the median values. Errors of rpmin are usually not bigger than ±0.01 cm (based on the pinch radius determination method).

FIG. 12.

Single (rpmin) and median values [m(rpmin)] of minimum plasma column radius vs Ne fraction (x) in the (1-x)D2 + xNe mixture for discharges in a medium-sized plasma focus under constant total mass conditions. Errors presented only for the median values. Errors of rpmin are usually not bigger than ±0.01 cm (based on the pinch radius determination method).

Close modal

In Fig. 13, six images (using VUV/SXR pinhole camera) from 6 discharges in different 6 mixtures with Ne percentage: (a) 0%, (b) 14.2%, (c) 26.8%, (d) 39.2%, (e) 49.9%, and (f) 66.1%, show pinch at or very near the time of maximum compression. The chosen images present minimum plasma column radius closest to the median value for a given gas mixture—m(rpmin). As one can see, the pinch has decreasing radius with increasing Ne %, while its column becomes more uniform and stable.

FIG. 13.

The images from 6 different discharges, with Ne fraction (x) equal to: (a) 0%, (b) 14.2%, (c) 26.8%, (d) 39.2%, (e) 49.9%, and (f) 66.1%, in a medium-sized plasma focus under constant total mass conditions [(1 − x)D2 + xNe].

FIG. 13.

The images from 6 different discharges, with Ne fraction (x) equal to: (a) 0%, (b) 14.2%, (c) 26.8%, (d) 39.2%, (e) 49.9%, and (f) 66.1%, in a medium-sized plasma focus under constant total mass conditions [(1 − x)D2 + xNe].

Close modal

In Fig. 14, total D-D fusion neutron emission yield (Yn) is presented for each fraction of Ne (x)—see Sec. III. Figure 14 shows both single (Yn) values and median values [m(Yn)]. Total yield decreases with increase in Ne fraction. This tendency is observed despite simultaneous decrease in the minimum radius of a plasma pinch. The spread of Yn values decreases with increase in Ne fraction—another indication of more stable/repeatable discharges as Ne fraction increases.

FIG. 14.

Single (Yn) and median values [m(Yn)] of total D–D fusion neutron emission yield vs Ne fraction (x) in the (1 − x)D2 + xNe mixture for discharges in a medium-sized plasma focus under constant total mass conditions. Errors presented only for the median values. Errors of Yn have the size of points—average values of errors based on the counter calibration factor.

FIG. 14.

Single (Yn) and median values [m(Yn)] of total D–D fusion neutron emission yield vs Ne fraction (x) in the (1 − x)D2 + xNe mixture for discharges in a medium-sized plasma focus under constant total mass conditions. Errors presented only for the median values. Errors of Yn have the size of points—average values of errors based on the counter calibration factor.

Close modal

The fusion neutron emission yield should be dependent on the following parameters (Gribkov , 2007; Velikovich , 2007; and Lee and Saw, 2008a): number density of deuterium ions in pinched plasma, number density of accelerated deuterium ions (in the case of beam-target fusion), size of pinched plasma (radius and length of plasma column), ion accelerating voltages and duration of neutron production. In the case of thermonuclear fusion, the temperature of the well-compressed plasma, rather than the voltage that accelerates the ions, is an important parameter. Additionally, current flowing through plasma pinch should also be an important parameter since it influences plasma compression (Bernard , 1998; Lee and Saw, 2008a). Voltage induced by compressing plasma pinch should also be important since it is connected to plasma compression as well as it may be connected to voltage which accelerates the ions—higher voltages induced by the compressing plasma can result in higher energies of accelerated ions (Lee and Saw, 2008a). In general, various scaling laws for fusion neutron yield in plasma focus devices have been investigated (Bernard , 1998; Gribkov , 2007; Lee and Saw, 2008b; and Auluck , 2021). Many studies, for example, have found that Yn should be proportional to 4(±1) power of current flowing through plasma pinch. In Fig. 15, plots of Yn vs various electro-kinetic plasma/discharge parameters (from Sec. IV C) are presented. Only the data for discharges in D2 are shown, since the data collected during discharges in D2 + Ne gas mixtures present similar type of relations found. In Fig. 15(a), plot of Yn vs Ip1 is presented. The expected increase in Yn with increase in Ip1 is not seen. The expected dependency is also not obtained when Ip1 is raised to the power of 4(±1) and plotted against Yn. On the other hand, plot of Yn vs tp1 [Fig. 15(b)] shows clearly a dependency between the two parameters—smaller values of tp1 result in bigger values of Yn. The same behavior is obtained by plotting Yn vs Imax or Ip and Yn vs tc or tp—the dependence of total neutron emission from D-D fusion on total discharge current was not found, but a dependence on total discharge dynamics was observed. This is also evidenced by the results of plotting Yn vs vz (vz ∼1/tc)—see Fig. 15(c). The found dependence of Yn on the discharge dynamics applies in most cases only to the parameters describing the total dynamics. The increased velocities in the later run-down phase do not necessarily lead to higher neutron yields. These observations may be due to the fact that the entire discharge current does not flow through the plasma sheath and that maximum compression is not always coincident with the first dI/dt minimum. This is possible due to the high variability of discharge currents during different discharges, re-strikes along the anode during a discharge (behind the plasma sheath and over the insulator) and also due to some statistical effects (changes) of high-voltage discharges in the area close to insulator (during the initial current sheath built-up phase). On the other hand, when one takes 5 discharges having the highest Yn value and similar Ip1 value (±35 kA), assumes 70% of the effective current flow through the compressing plasma during each discharge (Malir , 2022), and then averages the values of Yn and Ip1 over the 5 discharges, the following scaling law is obtained: ⟨Yn⟩ ∼ ⟨Ip13.7. It should also be mentioned that despite the nonexistence of a dependence on the total discharge current for all investigated discharges, a dependence on the discharge voltage was observed (both measured in the collector area of the PF-24 device)—see Fig. 15(e). The observed changes in Yn vs Umax plot show that higher maximum voltages measured in the collector area of the device lead to higher values of Yn. Also, similar dependence of Yn on tUmax was found—dependence on total discharge dynamics. The data indicate that earlier phases of a discharge affect the later phases. In general, more rapid discharges lead to higher maximum discharge voltages perhaps through higher number densities and more rapid development of instabilities.

FIG. 15.

Total D–D fusion neutron emission yield (Yn) vs (a) total discharge current at the first dI/dt minimum (Ip1), (b) time to the first dI/dt minimum (tp1), (c) average axial velocity (vz), (d) average axial velocity between two points [vz(Δt)], (e) maximum discharge voltage (Umax), and (f) time to the maximum discharge voltage (tUmax), for discharges in a medium-sized plasma focus operating with D2. Errors of Yn have the size of points (based on the error of counter calibration factor). The values of each parameter divided into 11 ranges and average Yn values (⟨Yn⟩) calculated and plotted, for each range. Power functions (y = a * x^b) fitted to the average values.

FIG. 15.

Total D–D fusion neutron emission yield (Yn) vs (a) total discharge current at the first dI/dt minimum (Ip1), (b) time to the first dI/dt minimum (tp1), (c) average axial velocity (vz), (d) average axial velocity between two points [vz(Δt)], (e) maximum discharge voltage (Umax), and (f) time to the maximum discharge voltage (tUmax), for discharges in a medium-sized plasma focus operating with D2. Errors of Yn have the size of points (based on the error of counter calibration factor). The values of each parameter divided into 11 ranges and average Yn values (⟨Yn⟩) calculated and plotted, for each range. Power functions (y = a * x^b) fitted to the average values.

Close modal

Dependence of neutron yield on radius of plasma column can be predicted for quasi-equilibrium pinch conditions, based on Bennett balance (Liberman , 1999; Haines, 2011). This indicates the following dependency: YnnpiD ∼1/rp2. In this relation, rp is the pinch radius and npiD is the pinch deuterium ion number density. In general, as the quasi-equilibrium pinch radius decreases, the total ion number density increases (assuming that mass losses are not significant enough). In addition, for different masses of ionized gases confined in the quasi-equilibrium pinch and different currents flowing through this pinch, the minimum radius of this pinch is different (consistent with the spread of data in Fig. 12). On the other hand, a decrease in radius of the quasi-equilibrium pinch, caused by a significant decrease in the amount of mass in the pinch, will not lead to an increase in the total ion number density and this, in turn, will not lead to an increase in total neutron emission from D–D fusion (assuming constant values of the other pinch parameters affecting the efficiency of total D–D nuclear fusion). In Fig. 16, plots of Yn vs rpmin are presented for each fraction of Ne (x). For discharges in D2 [Fig. 16(a)] and 85.8%D2 + 14.2%Ne [Fig. 16(b)] Yn values rather tend to decrease with increase in minimum pinch radius—this confirms the general trend based on quasi-equilibrium pinch conditions and importance of the maximum compression phase to the late phases during which ion beams are emitted and accelerated. At the same time, big fluctuations of values are present, which may be related to different effective amount of mass sweep, current flow, quasi-equilibrium pinch lifetime and different development of internal structures and instabilities in the late phases of pinch evolution. For discharges in 73.2%D2 + 26.8%Ne [Fig. 16(c)] the relation appears to be different—a maximum of Yn is present for 0.25 cm rpmin. This means that for part of discharges during which obtained minimum pinch radii are not smaller than 0.25 cm, Yn values increase with decrease in rpmin values. On other hand, when discharges result in rpmin values smaller than 0.25 cm, Yn values decrease. This suggest problems with mass sweeping and compression into pinch for part of discharges. For discharges in 60.8%D2 + 39.2%Ne [Fig. 16(d)], 50.1%D2 + 49.9%Ne [Fig. 16(e)], and 33.9%D2 + 66.1%Ne [Fig. 16(f)] only reversed trends appear to be present (dominating)—decrease in rpmin values rather results in decrease in Yn values. Again, this suggest problems with mass sweeping and compression for discharges with Ne fraction above 26.8%—for discharges with higher Ne fraction than 26.8% narrower pinches are formed on average, but this probably does not lead to significant increase in pinch ion number density (narrower plasma target is formed with a lower or similar deuterium ion number density). Finally, it should be emphasized that due to the small number of measured values of rpmin and the large spread of data, the existence of the described dependencies (Yn vs rpmin) cannot be confirmed definitively.

FIG. 16.

Total D–D fusion neutron emission yield vs minimum plasma column radius for discharges in: (a) D2, (b) 85.8%D2 + 14.2%Ne, (c) 73.2%D2 + 26.8%Ne, (d) 60.8%D2 + 39.2%Ne, (e) 50.1%D2 + 49.9%Ne, and (f) 33.9%D2 + 66.1%Ne, in a medium-sized plasma focus. Errors of rpmin are usually not bigger than ±0.01 cm (based on the pinch radius determination method). Errors of Yn are based on the error of counter calibration factor.

FIG. 16.

Total D–D fusion neutron emission yield vs minimum plasma column radius for discharges in: (a) D2, (b) 85.8%D2 + 14.2%Ne, (c) 73.2%D2 + 26.8%Ne, (d) 60.8%D2 + 39.2%Ne, (e) 50.1%D2 + 49.9%Ne, and (f) 33.9%D2 + 66.1%Ne, in a medium-sized plasma focus. Errors of rpmin are usually not bigger than ±0.01 cm (based on the pinch radius determination method). Errors of Yn are based on the error of counter calibration factor.

Close modal

The analysis presented in this work is based on 269 discharges which are characterized in general with significantly different total discharge currents (see Fig. 10)—the spreads of the values of the presented total discharge current parameters tend toward Gaussian distributions. The main reason is probably poor synchronization of switches resulting in non-simultaneous energy release from all condensers. This results in current waveforms of different shapes in different discharges. On the other hand, the spread of current parameters obtained from discharges in different gas mixtures is similar to well as the spread of average values of these parameters (see Fig. 10). In order to determine the degree of influence of current parameter spread on the observed changes in discharge and plasma behavior, parameters from 91 discharges (from 269), having similar Imax, were separately analyzed. Within these 91 discharges is: 31 in D2, 17 in 85.8%D2 + 14.2%Ne, 10 in 73.2%D2 + 26.8%Ne, 14 in 60.8%D2 + 39.2%Ne, 14 in 50.1%D2 + 49.9%Ne and 5 in 33.9%D2 + 66.1%Ne.

In Fig. 17, plots of Imax, Ip1, Umax, vz, tp1 and tUmax values vs initial Ne fraction in the mixture are presented for 91 discharges for which Imax = 540(±40) kA. Similarly, in Fig. 18, plots of rpmin and Yn values are presented. All trends presented in Sec. IV C of this article are in general sustained when plotting data only for similar values of total discharge currents. Moreover, discharges with Imax = 540(±40) kA are still characterized with a relatively big spread of other plasma/discharge parameters. The 84% reduction on average in the absolute spread of Imax values (from 372 to 60 kA) resulted in a significantly smaller reduction on average in the spread of the absolute Umax (21%), vz (35%), tp1 (30%), tUmax (27%), rpmin (51%), and Yn (26%) values and the maximum spread of Ip1 values decreased by 78% on average. The data indicate high probability of significantly different development of discharges, despite the relatively small spread of operating parameters. In addition, an example of 2 discharges—in D2 (#20111103) and 73.2%D2 + 26.8%Ne (#20101501)—is presented and discussed below. For discharge #20111103: Imax = 660(±21) kA, Ip1 = 554(±27) kA, Umax = 32(±1) kV, vz = 7.5(±0.1) cm/μs, tp1 = 2.04(±0.01) μs, tUmax = 2.06(±0.02) μs, rpmin = 0.35(±0.02) cm and Yn = 3.4(±0.1) n/discharge. For discharge #20101501: Imax = 657(±19) kA, Ip1 = 528(±34) kA, Umax = 38(±1) kV, vz = 7.6(±0.1) cm/μs, tp1 = 2.04(±0.01) μs, tUmax = 2.06(±0.02) μs, rpmin = 0.25(±0.01) cm and Yn = 7.2(±0.2) n/discharge. Despite almost the same values of Imax and Ip1 and also vz, tp1 and tUmax significantly different values of Umax, rpmin, and Yn are obtained. For discharge in 73.2% D2 + 26.8% Ne gas mixture rpmin value is significantly smaller and Yn value is significantly bigger. This type of behavior indicates further an increase in plasma compression level combined with an increase in deuterium ion number density and potentially also higher energies of accelerated ions.

FIG. 17.

(a) Maximum discharge current (Imax), (b) discharge current at the time of the first dI/dt minimum (Ip1), (c) maximum discharge voltage (Umax), (d) average axial velocity (vz), (e) time to the first dI/dt minimum (tp1), and (f) time to the maximum discharge voltage (tUmax), measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., Imax) and average (e.g., ⟨Imax⟩) values of parameters are given with respect to the fraction of Ne (x) in the mixture. Errors presented only for average values—standard deviations. Parameters obtained only from discharges with Imax = 540(±40) kA.

FIG. 17.

(a) Maximum discharge current (Imax), (b) discharge current at the time of the first dI/dt minimum (Ip1), (c) maximum discharge voltage (Umax), (d) average axial velocity (vz), (e) time to the first dI/dt minimum (tp1), and (f) time to the maximum discharge voltage (tUmax), measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., Imax) and average (e.g., ⟨Imax⟩) values of parameters are given with respect to the fraction of Ne (x) in the mixture. Errors presented only for average values—standard deviations. Parameters obtained only from discharges with Imax = 540(±40) kA.

Close modal
FIG. 18.

(a) Minimum plasma column radius (rpmin) and (b) total D–D fusion neutron emission yield, measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., rpmin) and average (e.g., ⟨rpmin⟩) values of parameters are given with respect to the fraction of Ne (x) in the mixture. Errors presented only for average values—±0.01 cm for rpmin and average values from single discharges for Yn. Parameters obtained only from discharges with Imax = 540(±40) kA.

FIG. 18.

(a) Minimum plasma column radius (rpmin) and (b) total D–D fusion neutron emission yield, measured during discharges in a medium-sized plasma focus operating with D2 and (100% − x)D2 + xNe gas mixtures. Single (e.g., rpmin) and average (e.g., ⟨rpmin⟩) values of parameters are given with respect to the fraction of Ne (x) in the mixture. Errors presented only for average values—±0.01 cm for rpmin and average values from single discharges for Yn. Parameters obtained only from discharges with Imax = 540(±40) kA.

Close modal

Based on the experimental data obtained and analyses performed, the following relevant information is summarized:

  • The minimum radius of plasma column was measured for each Ne fraction. It was confirmed that the radius of plasma column decreases with increasing Ne fraction. The data suggest that for discharges with Ne fraction up to 20%–30%, the dominant mechanism can be radiative compression and increased plasma compressibility. For discharges with Ne fraction above 20%–30%, the dominant effect is probably the decrease in mass sweeping and mass compression into plasma column.

  • The scheme (sequence) of plasma/discharge evolution was determined and described qualitatively. It is shown that the classical description of plasma-focus discharges up to maximum compression can be adequate. It is believed that radiative compression and/or the adiabatic compression can occur during discharges in a medium-sized plasma focus operating with a suitable mixture of deuterium and neon.

  • It was found that D–D fusion neutron yield decreased with increase of Ne fraction. The exception was a small, hardly useful, increase; for discharges in the lightly doped case of 14.2% Ne. Thus, the data conclude that there is generally no useful increase in fusion yield in D-Ne mixtures. The Ne-doped D pinches have smaller radius, potentially increasing the compressed number density and the energy of the fast ions in the generated beams. These factors are favorable to increased fusion neutron yield, but these favorable factors appear to be outweighed by the decrease in the initial amount of the fusion fuel and by possible unfavorable features of the plasma dynamics. However, the 6% increase in fusion yield at 14.2% doping level could possibly be further increased by a more systematic study of low- level doping perhaps in the range of 5%–20% Ne with constant initial deuterium pressure and mass in the mixtures.

  • The effect of stabilization of discharges with initial Ne fractions above 20% (decrease in the spread of kinetic parameters of discharges, minimum plasma column radii and Yn values) was confirmed. It is also possible that there is an increase in the homogeneity of plasma columns at maximum compression for discharges with up 50% Ne.

  • The sensitivity (existence of a clearly defined dependency) of the total neutron emission yield from D–D fusion to various discharge/plasma parameters was investigated. Sensitivity was confirmed for parameters describing full dynamics of a discharge and maximum tube voltage. Also, the existence of this type of dependency for the minimum radius of a plasma column in the maximum compression moment is possible. In contrast, there was little sensitivity to the total discharge current—YnIx type dependencies were not found for all investigated discharges. The likely reason is that the pinch current is a fraction of the total discharge current, and the fraction changes from discharge to discharge. Moreover, the situation is further complicated by our observation that usually there are more than one dI/dt minimum and that sometimes the maximum compression occurred more than 10 ns before the first dI/dt minimum.

  • All the data obtained show in general a relatively big spread of plasma/discharge parameters. This is suspected to be due to: not simultaneous release of electrical energy from all condensers, not uniform current flow in the collector area of the device, statistical changes in the initial breakdown phase over the surface of insulator and initial plasma sheath formation, possible restrikes during discharges, and fluctuations in the amount of impurities (especially impurities from the anode material) in the plasma during different discharges.

  • Based on acquired data, it is impossible to say which mechanism of nuclear fusion occurrence is dominant. Still, the 4-frame imaging performed in VUV and SXR shows that different mechanisms of ion acceleration (based on e.g., magnetic field line reconnection, turbulence growth, disruptions and plasma diode) are possible in the phases after the maximum compression moment and confirms that all of the mentioned mechanisms may be present during a single discharge.

M. Akel would like to express his thanks to the Director General of the Atomic Energy Commission of Syria for his encouragement and permanent support. M. Akel would also like to thank the members of the PF-24 laboratory (Institute of Nuclear Physics Polish Academy of Sciences), PF-1000 laboratory (Institute of Plasma Physics and Laser Microfusion) and International Centre for Dense Magnetized Plasmas in Poland for all support.

The authors would also like to thank Krzysztof Tomaszewski from the Institute of Plasma Physics and Laser Microfusion in Warsaw, Poland, for construction and preparing the 4-frame pinhole camera for the experiments.

The research was funded by the National Science Center Poland under Grant No. 2018/29/N/ST2/02804 and by the Ministry of Education, Youth and Sports of the Czech Republic under the Grant No. CZ.02.2.69/0.0/0.0/18_053/0016980.

The authors have no conflicts to disclose.

Lukasz Marciniak: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Methodology (lead); Project administration (equal); Resources (equal); Software (equal); Supervision (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (lead). Agnieszka Kulinska: Conceptualization (supporting); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (supporting); Project administration (equal); Resources (equal); Supervision (equal); Validation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Marek Scholz: Conceptualization (lead); Funding acquisition (equal); Methodology (equal); Project administration (supporting); Resources (lead); Supervision (supporting); Validation (supporting); Writing – original draft (supporting); Writing – review & editing (supporting). Mohammad Akel: Conceptualization (supporting); Methodology (supporting); Project administration (equal); Resources (lead); Software (lead); Supervision (equal); Validation (supporting); Writing – review & editing (equal). Sing Lee: Conceptualization (lead); Methodology (equal); Resources (equal); Software (equal); Supervision (supporting); Validation (supporting); Writing – review & editing (equal). Sor Heoh Saw: Conceptualization (supporting); Methodology (supporting); Resources (equal); Software (equal); Validation (supporting); Writing – review & editing (supporting).

The raw experimental data that support the findings of this study are available upon reasonable request from the authors. Please contact the corresponding author of this article via e-mail.

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