Total neutron emission from deuteron fusion and plasma pinch compression in a medium-sized plasma focus operating with D₂ and D₂ + Ne gas mixtures—Experimental results

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).

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—I_max, current at the dI/dt minimum (current value in the center of dI/dt jump)—I_p, current at the first dI/dt minimum (if many minima)—I_p1, time to the beginning of radial compression (approximated time to the beginning of current drop)—t_c, time to global dI/dt minimum (time to the center of dI/dt jump)—t_p, time to the first dI/dt minimum (if many minima)—t_p1, average axial velocity—v_z = (l_a − l_ins/2)/t_c (l_a is the total length of the anode inside the experimental chamber and l_ins is the length of insulator ring inside the experimental chamber), maximum discharge voltage—U_max, and time to maximum discharge voltage—t_Umax. In the rest of this article, t_p1 parameter was always taken as the t = 0 ns point, for each analyzed discharge—t_p1 determined for each investigated discharge in this work independently.

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)—v_z(Δt) = l_a12/(t₂ – t₁). The l_a12 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.

The total D-D fusion neutron emission yield (Y_n) 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 (r_pmin)—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—v_r(Δr_p) = (r_p1 – r_p2)/t_r12, where t_r12 is the time between independent frames of the camera, r_p1 is the pinch radius at time t₃ and r_p2 is the pinch radius at time t₃ + t_r12. 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 r_p1 and r_p2 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 r_pmin, wherein only the frames presenting the maximum compression moment (or very close) were used in the analysis. Additionally, for the more precise determination of r_pmin 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 r_pmin value was determined for each plotted profile independently. The average value of r_pmin was calculated using all plotted profiles for a given discharge: r_pmin = (r_{pmin_1} + r_{pmin_2} + ⋯ + r_{pmin_n})/n (n is the total number of plotted profiles).

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.

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.

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 t_p1. 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 t_p1). 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)—I_max, I_p1, I_p and U_max (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.

In Fig. 11, determined values of six kinetic parameters of plasma/discharge are presented for each fraction of Ne (x)—t_p1, t_p, t_Umax, v_z, v_z(Δt), and v_r(Δr_p) (see Sec. III). Values of t_c parameter are not presented since v_z ∼ 1/t_c. The average values of t_p1, t_p, and t_Umax are a bit higher for discharges with Ne fraction above 20%. The average values of v_z also drop for Ne fraction above 20%. On the other hand, the average values of v_z(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.

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 t_p1, t_p, t_Umax and v_z 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 (r_pmin) are presented for each fraction of Ne (x). Figure 12 shows both single (r_pmin) values and median values [m(r_pmin)]—average values. The determined values of r_pmin show that the minimum pinch radius decreases as Ne fraction increases. The drop in r_pmin 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.

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(r_pmin). As one can see, the pinch has decreasing radius with increasing Ne %, while its column becomes more uniform and stable.

In Fig. 14, total D-D fusion neutron emission yield (Y_n) is presented for each fraction of Ne (x)—see Sec. III. Figure 14 shows both single (Y_n) values and median values [m(Y_n)]. 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 Y_n values decreases with increase in Ne fraction—another indication of more stable/repeatable discharges as Ne fraction increases.

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 Y_n should be proportional to 4(±1) power of current flowing through plasma pinch. In Fig. 15, plots of Y_n 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 Y_n vs I_p1 is presented. The expected increase in Y_n with increase in I_p1 is not seen. The expected dependency is also not obtained when I_p1 is raised to the power of 4(±1) and plotted against Y_n. On the other hand, plot of Y_n vs t_p1 [Fig. 15(b)] shows clearly a dependency between the two parameters—smaller values of t_p1 result in bigger values of Y_n. The same behavior is obtained by plotting Y_n vs I_max or I_p and Y_n vs t_c or t_p—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 Y_n vs v_z (v_z ∼1/t_c)—see Fig. 15(c). The found dependence of Y_n 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 Y_n value and similar I_p1 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 Y_n and I_p1 over the 5 discharges, the following scaling law is obtained: ⟨Y_n⟩ ∼ ⟨I_p1⟩^3.7. 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 Y_n vs U_max plot show that higher maximum voltages measured in the collector area of the device lead to higher values of Y_n. Also, similar dependence of Y_n on t_Umax 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.

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: Y_n ∼ n_piD ∼1/r_p². In this relation, r_p is the pinch radius and n_piD 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 Y_n vs r_pmin 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)] Y_n 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 Y_n is present for 0.25 cm r_pmin. This means that for part of discharges during which obtained minimum pinch radii are not smaller than 0.25 cm, Y_n values increase with decrease in r_pmin values. On other hand, when discharges result in r_pmin values smaller than 0.25 cm, Y_n 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 r_pmin values rather results in decrease in Y_n 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 r_pmin and the large spread of data, the existence of the described dependencies (Y_n vs r_pmin) cannot be confirmed definitively.

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 I_max, 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 I_max, I_p1, U_max, v_z, t_p1 and t_Umax values vs initial Ne fraction in the mixture are presented for 91 discharges for which I_max = 540(±40) kA. Similarly, in Fig. 18, plots of r_pmin and Y_n 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 I_max = 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 I_max values (from 372 to 60 kA) resulted in a significantly smaller reduction on average in the spread of the absolute U_max (21%), v_z (35%), t_p1 (30%), t_Umax (27%), r_pmin (51%), and Y_n (26%) values and the maximum spread of I_p1 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: I_max = 660(±21) kA, I_p1 = 554(±27) kA, U_max = 32(±1) kV, v_z = 7.5(±0.1) cm/μs, t_p1 = 2.04(±0.01) μs, t_Umax = 2.06(±0.02) μs, r_pmin = 0.35(±0.02) cm and Y_n = 3.4(±0.1) n/discharge. For discharge #20101501: I_max = 657(±19) kA, I_p1 = 528(±34) kA, U_max = 38(±1) kV, v_z = 7.6(±0.1) cm/μs, t_p1 = 2.04(±0.01) μs, t_Umax = 2.06(±0.02) μs, r_pmin = 0.25(±0.01) cm and Y_n = 7.2(±0.2) n/discharge. Despite almost the same values of I_max and I_p1 and also v_z, t_p1 and t_Umax significantly different values of U_max, r_pmin, and Y_n are obtained. For discharge in 73.2% D₂ + 26.8% Ne gas mixture r_pmin value is significantly smaller and Y_n 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.

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 Y_n 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—Y_n ∼ I^x 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.