Lee Model Code Research Articles

Numerical experiments on the total D–D fusion neutron yield versus deuterium pressure for different energy plasma focus devices using the Lee model code

Numerical experiments using the Lee model code were carried out to compute the total D–D fusion neutron yield versus initial deuterium pressure for nine different plasma focus devices [PF50, AACS, PF400J, PF2.2, UNU-ICTP, PFZ200, PF24, PF78, Poseidon]. The computed data were compared with the published experimental results. In addition, the maximum discharge current, the pinch current and the pinch ion number density, as a function of initial deuterium pressure, were discussed, as well as their effect on the neutron yield. The optimum pressures that correspond to the maximum neutron yield Y n were obtained for all considered devices, with reference to the specific plasma focus properties. The scaling laws for the D–D fusion neutron production, in terms of storage energies E 0 and pinch current I pinch, were derived. The scaling of Y n with I pinch and E 0 over the whole range of investigated energies up to 300 kJ has been obtained as follows: . These laws are important in the planning and design of a plasma focus as a potentially powerful pulse neutron source.

Understanding Plasma Dynamics of Argentina Nano Focus Machine Using the Lee Code

Argentina Nano Focus Machine is a small plasma focus machine used as an intense neutron source. To understand the working of its plasma dynamics, the Lee model code is used. The results obtained from the Lee code agree reasonably well with the experimental data in terms of the peak current, radial start time and the pinch duration. Additionally, this code also produces information such as the optimum neutron yield (6.2x104), maximum ion beam energy (1.2 J) and the dependence of these yields and various speeds on operating pressure. The resultant data is reliable and all the input that is required is just one experimental current waveform together with the actual machine and operating parameters.

Results of plasma radiative compression investigation in the PF-24 device operated with D2, Ar and (100%-x)D2+x%Ar mixtures obtained using the 5-phase Lee model code

The article presents new results for plasma radiative compression in high-current discharges in the z-pinch configuration. The results are based on the 113 discharges performed in the plasma-focus PF-24 device operated with D2, Ar and (100%-x)D2+xAr mixtures, with Ar pressure fractions x ≈ 3–60% (mole fractions). The constant initial total pressure is about 2.9 mbar and the constant initial pressure of Ar is 1.2 mbar. Each experimental discharge was simulated individually using the 5-phase Lee model code to carry out the fitting procedure of the total discharge current waveform. The results from these 113 computed discharges fitted to the corresponding 113 experimental discharges show that the increase of the effective atomic number of the gas mixture increases the probability of occurrence of plasma radiative compression phenomenon. Relatively weak radiative compression was found for part of the discharges in 15–60% range of Ar mole fractions and in Ar, while the stronger radiative compression occurred for part of discharges in Ar only. This is because there was too little total x-ray line radiation emission during the equilibrium pinch lifetime related to the very small amount of swept up mass and the low current flow through pinched plasma, represented by the decreasing values of model parameters as the Ar mole fraction increases. The results show that the main pinch parameters influencing the occurrence and strength of radiative compression are: total x-ray line emission yield, effective atomic number, initial pinch radius, initial pinch ion number density and initial pinch ion/electron temperature.

Application of Lee Model Curve on Fitting of Discharge Current Curve of Plasma Focus Device

A dense plasma focus is a table top machine producing a short-lived extremely popular plasma and cause fusion. Lee Model Code is a computer-based visual basic simulation package, which was successfully utilized in the plasma focus devices. The dynamics of plasma focus discharge is quite complicated, so to review and simplify the complication Lee Model couples electrical circuit with the plasma focus dynamics, radiation and therefore the thermodynamics. This enables us to simulate all of the gross focus properties. In this paper the numerical experiments are carried out to compute the current trace as a function of time for plasma focus (PF) device NX2. Results obtained by the numerical experiments are compared with the published laboratory measured data. This current fitting is completed to get the model parameters.

Comparison of measured and computed neutron yield from PF1000 plasma focus device operated with deuterium gas

The measured current wave shapes of PF1000 plasma focus discharged at 16 kV in deuterium in the pressure range 1.05–1.2 Torr are fitted to the computed current wave shapes using the Lee model code. Very good fit is achieved which suggests that the code is configured very well for the PF1000 for these shots. This is borne out by the computed neutron yield arising from each shot agreeing well with the measured yield. The computed average yield of 8 shots at 1.2 Torr is 1.78 × 109 neutrons per shot (n/sh) compared to the measured average yield of (1.75 ± 0.2) × 109 (n/sh). The computed average yield of 16 shots at 1.05 Torr is 2.33 × 109 (n/sh) compared also to the measured average of (2.29 ± 0.2) × 109 (n/sh). The conclusion is that the neutron production of the PF1000 is well estimated by the Lee Code simply by fitting the computed current wave shape to the measured current wave shape.

High yield (⩾108/pulse) DD neutron generator based on a compact, transportable and low energy plasma focus device

A pulsed DD neutron generator based on the plasma focus (PF) device has been developed. The PF device was assembled using a single energy storage capacitor (10 µF) and a triggerable spark gap switch in a compact geometry. The anode of the PF device was made of SS304 material with its tip modified using a high purity tungsten insert. Excluding the power supply, the size of the overall system was 0.6 × 0.6 × 1.0 m and the weight was less than 100 kg. A maximum DD neutron yield of (3.1 ± 0.2) × 108 neutrons/pulse and average DD neutron yield of (2.24 ± 0.16) × 108 neutrons/pulse (pulse duration = 35 ± 4 ns) into 4π sr were observed at a capacitor bank energy of 3.1 kJ (25 kV) and at 4.5 mbar D2 gas filling pressure. The experimentally observed average neutron yield was found to be around 30% more than the estimated yield obtained using scaling laws for neutrons (Y n ≈ 1.7 × 10−10 I 0 3.3; I 0 is the peak discharge current in A). For a peak discharge current of 258 kA at 3.1 kJ, the neutron yield was estimated to be 1.23 × 108 neutrons/pulse. The higher neutron production was attributed to the efficient design of the PF device as well as to the low erosion of the anode tip because of the tungsten insert. Using the time-of-flight method, maximum neutron energy was calculated to be 3.91 ± 0.16 MeV in the radial direction at 4.5 mbar filling pressure. Numerical parametrization using the five-phase Lee model code was performed and found to be similar to PF devices developed across the world.

Numerical experiments on D-T gas filled PF1000 device with pressure variation

Numerical studies have been conducted using the Lee model code to compute the neutron yield of the PF1000 plasma focus device as a function of operating gas pressure (). The result is compared with the available experimental data. The operating gas Deuterium (D) is substituted with Deuterium-Tritium (D-T) (1:1) gas mixture in the numerical studies and then the is investigated with the function of Associated plasma dynamic properties such as axial velocity radial shock front speed piston speed and maximum pinch temperature are studied and correlations of the parameters with the pressure variation are established. Relevant plasma focus properties such as peak discharge current pinch current ion density and energy input into the pinch EINP are discussed as functions of pressure thus provide correlation of with other relevant plasma focus properties over the operating gas pressure range. The neutron yield performance of the D-T gas mixture is compared to that of the D gas and the optimum gas pressure for the highest neutron yield is identified.

Using the Modified Lee Model Code to Calculate the Optimum Length of NiZn Ferrite to Enhance the DPF Argon SXR Emission

A modified version of the Lee Model Code with better calculation of the magnetic field inside the Dense Plasma Focus (DPF) tube has been used to investigate the NiZn ferrite effect on the Amirkabir Plasma Focus (APF) machine behavior. It has been explained how various lengths of the ferrite can affect the discharge current trace.The minimum ferrite length which had sensible effects on APF working in 10 kV filled with 0.1-Torr argon has been determined. Regarding the optimum conditions for energy-transfer and argon Soft X-Ray (SXR) emission, the optimum length of the NiZn ferrite has been calculated for various charging voltages and pressures and a scaling-law curve has been presented. Measurements have proved increase in the SXR emission by employing ferrites.

Characteristics of Fast ion beam in Neon and Argon filled plasma focus correlated with Lee Model Code

In this paper, results of time-of-flight measurements of fast ion beam generated and accelerated in the final pinch phase of a 2 kJ dense plasma focus device at 12 kV in Neon and Argon are presented. The measurements were made using a 50 Ω F Cup and these results were correlated with Lee Model Code computations. The results include fast ion beam properties such as ion speed, energy, flux and fluence at 2–4 Torr Neon and 0.5–1.5 Torr Argon. Ion signals with FWHM minimum values of 42 ns and 47 ns respectively for 2.5 Torr Neon and 0.9 Torr Argon were measured. The maximum most common ion energy of 450 ± 30 keV at 2.5 Torr Neon and 1230 ± 90 keV at 0.9 Torr Argon were measured. Ion time-of-flight measurements including ion speed and energy, ion flux, ion fluence by Faraday Cup show very consistent correlation with Lee Model Code results for Neon and Argon. This paper validates the computation of plasma focus ion beam properties by the Lee Code.

Optimization of neon soft X-ray yield in a low-energy dense plasma focus device

The modified version of Lee model code is used in numerical experiments for characterizing and optimizing neon soft X-ray yield ([Formula: see text]) of the United Nations University/International Center for Theoretical Physics Plasma Focus Facility (UNU/ICTP PFF) device operated at 14 kV and 30 [Formula: see text]. In our present work, the neon yield [Formula: see text] is improved with an optimized UNU/ICTP PFF device by computing the optimum combination of static inductance ([Formula: see text]), anode length ([Formula: see text]), anode radius ([Formula: see text]) and cathode radius ([Formula: see text]), keeping fixed their ratio ([Formula: see text]) at 3.368, through a lot of numerical experiments at six operating pressures ([Formula: see text]). At lower [Formula: see text] (e.g. 2.0, 2.5 and 3.3 Torr), the optimum [Formula: see text] value, together with the corresponding optimum combination of [Formula: see text], [Formula: see text] and [Formula: see text], is found to be 15 nH, whereas at higher [Formula: see text] (e.g. 4.0, 5.0 and 6.0 Torr), it is obtained as 10 nH. Though the computed maximum neon yield [Formula: see text] (57.2 J with the corresponding efficiency of 1.94%) is found at [Formula: see text], assuming an achievable range of incorporating low-inductance technology, the best optimum combination of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] is found to be at [Formula: see text], resulting in the computed optimum neon yield [Formula: see text] of 54.60 J with a corresponding efficiency of 1.9%. This computed neon yield [Formula: see text] is about 11 times higher than the measured value [Formula: see text] at optimum [Formula: see text] of UNU/ICTP PFF. It is also observed that our computed neon yield [Formula: see text] is improved by around six times from the previously computed value, which was 9.5 J at the optimum [Formula: see text] Torr for optimum anode configuration of this machine. In addition, neon yield [Formula: see text] is obtained with our optimized combination of [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text] at 11.5 kV and compared with the measured neon yield [Formula: see text] of the NX2 machine.

Correlation of Characteristic Ne SXR Signal Pulse With Computed Plasma Focus Dynamics in the Ne (97.5%)–Kr (2.5%) Admixtures of the INTI PF Machine at 12 kV

This paper shows the correlation of the characteristic Ne soft X-ray (SXR) signal pulse with computed dynamics of the plasma focus using doped neon in Ne (97.5%)/Kr (2.5%) admixtures. The Lee model code is coupled with a specifically designed correlation excel template. The results show that typically, the characteristic Ne SXR pulse signal starts after the start of the reflected shock (RS) and before the beginning of the pinch. Specifically, in the illustrated shot, the RS phase starts at $3.375~\mu \text{s}$ while the pinch phase starts at $3.384~\mu \text{s}$ . The characteristic Ne SXR signal pulse starts at $3.377~\mu \text{s}$ , which is 2 ns after the start of the RS and 7 ns before the pinch starts. There is a consistent trend of Ne SXR correlation with the computed dynamics in the Ne doped with Kr admixtures up to a doping level of 2.5%.

The Effect of the Shape of the Anode Head on the Nitrogen Soft X-Ray Emission from a Dense Plasma Focus Device: a Numerical Investigation Using the Modified Lee Model Code Accompanied by Experiments

An alternative way for calculating the magnetic field in the Lee Model Code has been used. The effects of the various anode-tip shapes on the DPF behavior have been studied. The current and impedance calculations have been employed for these investigations. For the conical anode tip, the best pinch current and soft x-ray radiation have been seen in simulations which was in good agreement with the empirical results. The investigations were carried out for the voltages of 11, 12, and 13 kV and the pressure range of 1–6 Torrs. The asymmetry in the discharging current has been investigated through three arbitrarily defined cathode current distribution patterns. The simulations showed that asymmetry in the axial discharge current increased the plasma Impedance and consequently reduced the soft x-ray emission.

Comparison of measured pinch parameters versus pressure for SABALAN1 plasma focus facility against computed values using Lee model code

In this paper, we have studied the effect of working gas pressure on plasma pinch properties in a Mather type plasma focus (2 kJ, 20 kV, 10 μF), named SABALAN1. Argon at the various operating pressures ranging from 0.1-1.2 Torr has been used as working gas. The total current waveform has been measured for different pressures. Also, a numerical simulation was done using Lee model code to perform numerical experiments in SABALAN1. The numerical simulation was used to compute argon soft x-ray yield as a function of pressure, to anticipate the maximum soft x-ray efficiency at optimum operating gas pressure. The Lee model was configured for SABALAN1, by fitting a simulated discharge current waveform against a measured discharge current waveform was obtained by numerically integrating the output of a dI/dt calibrated Rogowski coil. The experimental and simulation curves for plasma pinch properties have been plotted. Some of the dynamic parameters of the plasma and the characteristics of the plasma pinch have been displayed at different argon pressures in two tables. In addition, the chart of the normalized parameters of the plasma pinch has been plotted in terms of pressure. The results of experimentally measured and numerical simulation show that better pinches with attention to their plasma pinch characteristics, generally were dependent on pressure and the best pinch is obtained at 0.6-0.7 Torr for argon at 14 kV in SABALAN1. Furthermore, in high pressures (higher than 0.7 Torr in our experiments), the discharge current can behave as short circuit discharge and resembles that of a simple L-C-R discharge which is a damped sinusoidal. Comparison of the experimental and numerical curves shows sensible agreement in some plasma pinch properties such as the time to pinch and depth of focus. The results from charts and tables have been discussed.

Modelling and Electrical Characteristics of the Thailand Plasma Focus-II (TPF-II)

The Thailand Plasma Focus II (TPF-II) is a 3.3 kJ dense plasma focus that was developed at Walailak University, Thailand. The aim of the device is to study the production of ion beams in the keV energy range and their applications for the color modification of gemstones. A high-energy ion beam is produced by heating and acceleration in the pinch phase of the plasma focus. The heating process is determined by the maximum electrical current, which can be optimized by variation of the system’s inductance. Lee model code was implemented to optimize the configuration of the electrodes. The current waveforms for the different initial conditions were used to obtain the system’s inductance, which was verified by a short circuit test. It was found that the inductance and resistance were about 153 nH and 12 mΩ, respectively.

Damage Study of Irradiated Tungsten using fast focus mode of a 2.2 kJ plasma focus

In this work, damage results of four 12 mm × 12 mm × 5 mm PLANSEE double forged tungsten target samples exposed in INTI PF device at different distances from anode operating in the fast focus mode at 12 kV, 2.5 Torr deuterium are presented. SEM and EDX images and analysis show the extent of damage on the exposed tungsten surface. Micro-cracks up to 300 nm and 500 nm to 5 μm holes together with signs of melting are found on the tungsten exposed surfaces depending on their distances from the anode top. Current waveforms fitting using Lee Model Code show yields of 3 × 106 neutrons and 8.5 × 1014 ions per shot with average ion energy of 56 keV per ion at pinch exit, generating heat flux of 1.8 × 1014 Wm−2 and damage factor (also called heat flux factor) of 1.6 × 1010 Wm−2s0.5 on a target at pinch exit.

Fast Faraday cup for fast ion beam TOF measurements in deuterium filled plasma focus device and correlation with Lee model

In this work, the design and construction of a 50 Ω fast Faraday cup and its results in correlation with the Lee Model Code for fast ion beam and ion time of flight measurements for a Deuterium filled plasma focus device are presented. Fast ion beam properties such as ion flux, fluence, speed, and energy at 2–8 Torr Deuterium are studied. The minimum 34 ns full width at half maximum ion signal at 12 kV, 3 Torr Deuterium in INTI PF was captured by a Faraday cup. The maximum ion energy of 67 ± 5 keV at 4 Torr Deuterium was detected by the Faraday cup. Ion time of flight measurements by the Faraday cup show consistent correlation with Lee Code results for Deuterium especially at near to optimum pressures.

Numerical Experiments on IR-MPF-100 Plasma Focus Operated in Neon and Deuterium Gases

In this paper, using the current fitting method, the Lee model parameters are computed for the IR-MPF-100 plasma focus (maximum energy ∼115 kJ) operated in the neon and deuterium gases and the results are presented in the different operational conditions. The values of fc, fcr and fmr were obtained 0.43, 0.55 and 0.05 respectively for the neon gas in all values of pressure and voltage. fm varies as a function of pressure and voltage. fm varies from 0.03 to 0.04 for 23.3 kJ of energy and it is almost constant equal to 0.024 for 10.2 kJ of energy. In the case of deuterium gas, fc and fcr are found 0.3 and 0.4 respectively. In this case, \({\text{f}}_{\text{m}}\) varies between 0.028 and 0.1 and fmr varies between 0.05 and 0.20. It is noted that in the case of deuterium gas, fm and fmr decrease with the pressure increasing approximately and in the case of neon gas fm increases with pressure increasing. So we calculate neutron yield and soft X-ray yield using the Lee model code for the different operational conditions.

The circuit parameters measurement of the SABALAN-I plasma focus facility and comparison with Lee Model

The circuit parameters are investigated in a Mather-type plasma focus device. The experiments are performed in the SABALAN-I plasma focus facility (2kJ, 20kV, 10µF). A 12-turn Rogowski coil is built and used to measure the time derivative of discharge current (dI/dt). The high pressure test has been performed in this work, as alternative technique to short circuit test to determine the machine circuit parameters and calibration factor of the Rogowski coil. The operating parameters are calculated by two methods and the results show that the relative error of determined parameters by method I, are very low in comparison to method II. Thus the method I produces more accurate results than method II. The high pressure test is operated with this assumption that no plasma motion and the circuit parameters may be estimated using R-L-C theory given that C0 is known. However, for a plasma focus, even at highest permissible pressure it is found that there is significant motion, so that estimated circuit parameters not accurate. So the Lee Model code is used in short circuit mode to generate the computed current trace for fitting to the current waveform was integrated from current derivative signal taken with Rogowski coil. Hence, the dynamics of plasma is accounted for into the estimation and the static bank parameters are determined accurately.

Comparison of Plasma Dynamics in Plasma Focus Devices PF1000 and PF400

<p>In this work we have simulated two different sizes of plasma focus devices: PF400, a small sub-kJ plasma focus device in operation at the Atomic Energy Commission in Chile and PF1000, a 1 MJ device at the International Centre for Dense Magnetised Plasmas (ICDMP) in Warsaw, Poland. Our aim is to compare the plasma dynamics observed in two different sizes of the devices. We compare the experimentally obtained data with the data predicted from our numerical experiments using the Lee model code. It has been observed that the peak current of the total current waveform, pinch current calculated from total current, and neutron yield agree reasonably well with published experimental data, however, slight differences are found in other parameters.</p><p>Journal of Nepal Physical Society Vol.3(1) 2015: 55-59</p>

Plasma Kinetics in Deuterium-Filled Plasma Focus with Step Anode Configuration

A numerical analysis of a plasma focus device with step anode as the central electrode is carried out with Lee Model Code for a stepped central electrode configuration. The snowplow model is employed to describe the dynamics of current sheath between the electrodes using momentum conservation of the swept gases. The discharge current and the tube voltage are determined by circuit equation. Different plasma parameters including plasma temperature and speed of current sheath are simulated for the step anode configuration. The step anode model is compared with the standard electrode configuration to observe the dynamical behaviour of the plasma during the axial and radial phase. The results indicate that the current dip and the spike voltage are slightly higher and an increase in the speed of current sheath at both axial and radial phases are observed. The step anode has shown peak current of 0.4% less than the cylindrical anode. However, the current sheath speed is enhanced at both axial and radial phases up to 20.1% for step anode configuration. The step anode configuration is also contributed to rise the plasma pinch temperature. The new configured anode in Lee's model can carry a new tube parameter for optimizing the plasma focus device for SXR yield and neutron yield based on numerical experiment.