The Effect of Plasma Profiles on the Critical Value of $$n\uptau_{E}$$ for Ignition

The effect of plasma profiles for ignition condition in a stationary D–T plasma is investigated using the energy conservation equations for ions and electrons, assuming that steady state fusion power is produced with no external power. The alpha power heating is sufficiently large to sustain the plasma and to balance the combined Bremsstarhlung and thermal conduction losses. The space dependent Lawson criteria is derived and critical condition is identified. As a result of this analysis we have shown that the optimum temperature might be \(\bar{T} \approx 26\,{\text{keV}}\) and that the peaked profiles with \(n\sim\left( {1 - \frac{{r^{2} }}{{a^{2} }}} \right)^{{v_{n} }}\), ν _n  = 1, and \(T\sim\left( {1 - \frac{{r^{2} }}{{a^{2} }}} \right)^{{v_{T} }} ,\,v_{T} = 2\) are good to minimizing \(\bar{n}\uptau_{E}\) for ignition. The results for these profiles show the critical value of \((\bar{n}\uptau_{E} )_{min} = 0.08 \times 10^{20 } \,{\text{m}}^{ - 3} \,{\text{s}}\) showing the reduction by 1/3 from the reference value limit ν _n  = ν _T  = 0. For a 26 keV plasma with an energy confinement time of 1 s, a pressure of about 6.24 atm is required for the plasma to be ignited; that is, it is sustained purely by the self-heating of the fusion alpha particles.     

Development of a Helicon Plasma Source for Neutral Beam Injection System of the Alborz Tokamak

Amirkabir Helicon plasma source (AHPS) has been designed and developed at the fusion laboratory of Amirkabir University of Technology for the neutral beam injection (NBI) system of the Alborz tokamak. The design parameters of the Helicon plasma source are determined to get the \( n_{e} \cong 10^{19} \,{\text{m}}^{ - 3} \) plasma density. However, the Nagoya type III antenna was used to excite the Argon plasma by the applied magneto-static field of 750 G and RF power up to 2 kW at the frequency of 13.56 MHz. Preliminary experiments are performed to confirm the Helicon mode operation of the AHPS. Mode changing from the ICP to the Helicon mode was proved by using the optical emission spectroscopy and polaroid photography technique of the plasma “blue core”. Spectroscopy measurements results show that the emission line intensity of the \( {\text{Ar}}\;{\text{II}} \) at 434.8 nm increases as the RF power increases in the range of values of 300–1000 W at the neutral background pressure of 0.7 mTorr. Also, we found that, in Helicon mode, the increase of the magneto-static field from 350 to 750 G not only increases the plasma density besides the efficiency of the RF power absorption increases.     

Fusion Cross Section of $${\mathrm{T(d,n)}}^{4}{\mathrm{He}}$$ and $${}^{3}{\mathrm{He(d,p)}}^{4}{\mathrm{He}}$$3He(d,p)4He Reactions by Four Parameters Formula

Fusion cross sections of light nuclei are calculated by a complex potential and taking into account of conservation of angular momentum and parity. The nuclear potential is assumed to be as simple as a spherical complex square well with a rigid core. Then the nuclear phase shift is extracted from continuity condition of inverse of the logarithmic derivative of the wave functions as a complex quantity. The quantum tunneling probability and cross section are obtained via real and complex components of nuclear phase shift. The obtained results for the two most important light nuclei reactions, \({\mathrm{T(d,n)}}^{4}{\mathrm{He}}\), \({}^{3}{\mathrm{He(d,p)}}^{4}{\mathrm{He}}\) are compared with other theoretical formulas and experimental data. Despite that the theory is simplified as much as possible and the complexities and details of nuclear interactions has been ignored, excellent agreements with experimental data are achieved.     

The Efficacy of Hydrodynamic Compression Using a Conical Cavity

A technique for controlled hydrodynamic compression of gases using a conical cavity driven by liquid metal was proposed by Lei (2016) as a convenient, low-cost, repetitive instrument to achieve a very high compression ratio of up to \(10^9\). If the compression is fully adiabatic, such compression will raise the gas temperature by a factor of \(10^6\) for monoatomic gases. In this paper, we develop a 0-D semi-analytic model to examine in detail the adiabatic assumption, taking into account in particular the physical processes of dissociation, ionization, radiation, and energy exchange between the compressed gas and the wall, and provide an assessment of the temperature of the gas or plasma that may be attainable using the technique. The numerical results show that these physical processes drastically lower the temperature attainable. Nevertheless, the results still indicate that final gas temperature of more than 10 eV, and volume-compression-ratio more than \(10^6\), are still attainable that might enable a number of interesting applications. The modeling results also revealing some interesting effects of partially ionized gases under high ratio of compression.     

The Role of the Collisions on the Weibel Instability Growth Rate in the Fast Ignition Scenario

In this paper, the effects of Coulomb elctron-ion collisions and plasma density gradient, \(\eta\), on the Weibel instability in inertial confinement fusion are investigated. The results are indicative that the corrected collision of Weibel instability growth rate of the relativistic region near the corona, \(\eta >0.3\), increases with increasing relativistic parameter, \(\upgamma\). Also, near the fuel core as \(\eta\) goes down, the corrected collisional growth rate decreases with increasing \(\upgamma\) for \(\mathrm{{\upgamma }}<6\) and and increases with increasing \(\upgamma\) for \(\upgamma >6\). Therefore, for \(\upgamma <6\), the effect of collision and fuel density gradient tend to stabilize the Weibel instability in fuel core, with the Weibel growth rate below the collisionless value. Also deposition condition of relativistic electron beam energy can be shifted to the fuel core for the suitable ignition.     

Measurements of the Thermal Neutron Macroscopic Absorption Cross Section for Neutron Absorbing Layers

Objective of this study is measuring the macroscopic cross section of a neutron absorbing layer for thermal neutrons. For this purpose a neutron source and BF ₃ detector have been applied. For measuring macroscopic cross section of thermal neutrons by the \( I = BI_{0} e^{{ - \sum\nolimits_{tot} t}} \) Formula, it is necessary to provide suitable geometric conditions in order to assume the production and build-up coefficient to be the unit value (=1). To fulfill required conditions for this assumption, surface of the detector is covered with a 2 mm thick layer of cadmium. Radiation window of the detector has a 3 cm diameter, situated directly in front of the source. By placing the cadmium cover over the detector, variation of \( Ln{\frac{{I_{0}^{{}} }}{I}} \) values verses thickness of absorbent layer, renders linear function behavior, making it possible to measure the macroscopic cross section. The next stage is applying the MCNP code by simulating F1 tally and cosine-cards for calculating Total Macroscopic Cross-Section. Validation of this study is achieved through comparison of simulation by the MCNP code and results rendered by experiment measurements.     

Scaling Laws of Nitrogen Soft X-ray Yields from 1 to 200 kJ Plasma Focus

Numerical experiments are carried out systematically to determine the nitrogen soft X-ray yield for optimized nitrogen plasma focus with storage energy E₀ from 1 to 200 kJ. Scaling laws on nitrogen soft X-ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found. It was found that the nitrogen X-ray yields scales on average with $ {\text{Y}}_{\text{sxr,N}} = 1.93 \times {\text{E}}_{0}^{1.21} {\text{J}} $ (E₀ in kJ) with the scaling showing gradual deterioration as E₀ rises over the range. A more robust scaling is $ {\text{Y}}_{\text{sxr}} = 8 \times 10^{ - 8} {\text{I}}_{\text{pinch}}^{3.38} $ . The optimum nitrogen soft X-ray yield emitted from plasma focus is found to be about 1 kJ for storage energy of 200 kJ. This indicates that nitrogen plasma focus is a good water-window soft X-ray source when properly designed.     

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 f_c, f_cr and f_mr were obtained 0.43, 0.55 and 0.05 respectively for the neon gas in all values of pressure and voltage. f_m varies as a function of pressure and voltage. f_m 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, f_c and f_cr are found 0.3 and 0.4 respectively. In this case, \({\text{f}}_{\text{m}}\) varies between 0.028 and 0.1 and f_mr varies between 0.05 and 0.20. It is noted that in the case of deuterium gas, f_m and f_mr decrease with the pressure increasing approximately and in the case of neon gas f_m increases with pressure increasing. So we calculate neutron yield and soft X-ray yield using the Lee model code for the different operational conditions.     

Soft X-ray Emission Optimization Studies with Krypton and Xenon Gases in Plasma Focus Using Lee Model

The X-ray emission properties of krypton and xenon plasmas are numerically investigated using corona plasma equilibrium model. Numerical experiments have been investigated on various low energy plasma focus devices with Kr and Xe filling gases using Lee model. The Lee model was applied to characterize and to find the optimum combination of soft X-ray yields (Y_sxr) for krypton (~4 Å) and xenon (~3 Å) plasma focus. These combinations give Y_sxr = 0.018 J for krypton, and Y_sxr = 0.5 J for xenon. Scaling laws on Kr and Xe soft X-ray yields, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found over the range from 2.8 to 900 kJ. Soft X-ray yields scaling laws in terms of storage energies were found to be as $ {\text{Y}}_{{{\text{sxr}},{\text{Kr}}}} = 0.0003 \times {\text{E}}_{0}^{1.43} $ Y sxr , Kr = 0.0003 × E 0 1.43 and $ {\text{Y}}_{{{\text{sxr}},{\text{Xe}}}} = 0.0064 \times {\text{E}}_{0}^{1.41} $ Y sxr , Xe = 0.0064 × E 0 1.41 for Kr and Xe, respectively, (E₀ in kJ and Y_sxr in J) with the scaling showing gradual deterioration as E₀ rises over the range. The maximum soft X-ray yields are found to be about 0.5 and 27 J from krypton and xenon, respectively, for storage energy of 900 kJ. The optimum efficiencies for soft X-ray yields (0.0002 % for Kr) and (0.0047 % for Xe) are with capacitor bank energies of 67.5 and 225 kJ, respectively.     

Numerical Experiments on Oxygen Plasma Focus: Scaling Laws of Soft X-Ray Yields

Numerical experiments have been investigated on UNU/ICTP PFF low energy plasma focus device with oxygen filling gas. In these numerical experiments, the temperature window of 119–260 eV has been used as a suitable temperature range for generating oxygen soft X-rays. The Lee model was applied to characterize the UNU/ICTP PFF plasma focus. The optimum soft X-ray yield (Y_sxr) was found to be 0.75 J, with the corresponding efficiency of about 0.03 % at pressure of 2.36 Torr and the end axial speed was v_a = 5 cm/μs. The practical optimum combination of p₀, z₀ and ‘a’ for oxygen Y_sxr was found to be 0.69 Torr, 4.8 cm and 2.366 cm respectively, with the outer radius b = 3.2 cm. This combination gives Y_sxr ~ 5 J, with the corresponding efficiency of about 0.16 %. Thus we expect to increase the oxygen Y_sxr of UNU/ICTP PFF, without changing the capacitor bank, merely by changing the electrode configuration and operating pressure. Scaling laws on oxygen soft X-ray yield, in terms of storage energies E₀, peak discharge current I_peak and focus pinch current I_pinch were found over the range from 1 kJ to 1 MJ. It was found that the oxygen soft X-ray yields scale well with $ {\text{Y}}_{\text{sxr}} = 2 \times 10^{ - 7} {\text{I}}_{\text{pinch}}^{3.45} $ and $ {\text{Y}}_{\text{sxr}} = 6 \times 10^{ - 7} {\text{I}}_{\text{peak}}^{ 2. 9 2} $ for the low inductance (L₀ = 30 nH) (where yields are in J and currents in kA). While the soft X-ray yield scaling laws in terms of storage energies were found to be as $ {\text{Y}}_{\text{sxr,O}} = 5.354 \times {\text{E}}_{0}^{1.12} $ (E₀ in kJ and Y_sxr in J) with the scaling showing gradual deterioration as E₀ rises over the range. The oxygen soft X-ray yield emitted from plasma focus is found to be about 8.7 kJ for storage energy of 1 MJ. The optimum efficiency for soft X-ray yield (1.1 %) is with capacitor bank energy of 120 kJ. This indicates that oxygen plasma focus is a good soft X-ray source when properly designed.     

Opacity Structure of Glass Ablator in ICF Target Design

Opacity is dependent on the radiation temperature, material temperature and density of the material. The collisional ionization and the excitation rate can have direct effect on the temperature and the electron density of plasma. The plasma density can be determined by measurements of Stark-broadened K-shell spectral lines. Because Silicon may be used as dopant in the ablator of ignition target, the knowledge of their opacities is very important. The purpose of this work is to obtain a more detailed structure of opacity in regards with broadening effects in the form of Voigt profile. For this aim the opacity frequency dependency and the mean opacity of mixed plasmas are calculated under local thermodynamic equilibrium conditions. The final results show that the Stark-broadened line shape is dependent on the density. Also it is shown that the resonance peak and spectrum broadening of opacity spectrum of mixed plasma such as the \(\hbox {SiO}_2\)-plasma is larger than a single atom plasma such as Silicon, Si. Eventually these results can be used in the design of fuel pellets in Inertial Confinement Fusion.     

Flow Characteristics and Charge Exchange Effects in a Two-Dimensional Model of Electrothermal Plasma Discharges

Electrothermal (ET) plasma discharges are capillary discharges that ablate liner materials and form partially ionized plasma. ET plasma discharges are generated by driving current pulses through a capillary source with peak currents on the order of tens of kA and pulse lengths on the order of \(100\,\upmu \hbox {s}\). These plasma discharges can be used to propel pellets into magnetic confinement fusion devices for deep fueling of the fusion reaction, ELM mitigation, and thermal quench of the fusion plasma. ET plasma discharges have been studied using 0D, 1D, and semi-2D fluid models. In this work, a fully 2D model of ET plasma discharges is presented. The newly developed model and code resolve inter-species interaction forces due to elastic collisions. These forces affect the plasma flow field in the source and impede the development of plasma pressure at the exit of the source. In this work, these affects are observed for discharge current pulses peaking at 10 and 20 kA. The sensitivity of the model to the inclusion of charge exchange effects is observed. The inclusion of charge exchange has little effect on the integrated, global results of the simulation. The difference in total ablated mass for the simulations caused by the inclusion of charge exchange reactions is <1 %. Differences in local plasma parameters are observed during discharge initialization, but after initialization, these differences diminish. The physical reasoning for this is discussed and recommendations are made for future modeling efforts.     

Effect of Various Parameters on Edge Plasma Stability in IR-T1 Tokamak

Edge plasma turbulence was investigated over a wide range of plasma and field parameters in the IR-T1 tokamak for the first time. Fluctuation levels and spectra were measured using two arrays of Langmuir probe in the region r/a = 0.75–1.2. Under almost all conditions the edge plasma was turbulently unstable, with a broadband fluctuation spectrum in the drift wave range of frequencies f = 10–1000 kHz. A stable state was observed only in the very cold, low-current discharge formed at unusually high neutral filling pressure. Otherwise, the relative fluctuation level as monitored by the ion saturation current was very high, in the range $ {{\tilde{\rm J}^{ + } } \mathord{\left/ {\vphantom {{\tilde{\rm J}^{ + } } {\bar{\rm J}^{ + } }}} \right. \kern-0pt} {\bar{\rm J}^{ + } }} \cong 0.2{-}0.8 $ , while the fluctuation power spectra were roughly invariant in shape. The relative fluctuation level was always highest near the wall and decreased monotonically toward the plasma centre.     

Experimental Study of Effects of the Internal Inductance on the Energy Confinement Time in IR-T1 Tokamak

In this paper we present an experimental study of effects of the internal inductance on the energy confinement time, in IR-T1 tokamak. For this purpose, four magnetic pickup coils were designed, constructed, and installed on the outer surface of the IR-T1, and Then Shafranov parameter (asymmetry factor) is obtained from them. On the other hand, also diamagnetic loop were constructed and installed on IR-T1, and poloidal Beta is determined from it. Therefore, the internal inductance obtained. Also, energy confinement time is obtained using diamagnetic loop. Experimental Results show that maximum energy confinement time (which correspond to minimum collisions, minimum microinstabilities, and minimum transport) in IR-T1, relate to the low values of internal inductance (\( 0.61 \, < \, li \, < \, 0.72 \)). This is agreement with theoretical approach.     

Effect of Internal Breeding of Tritium and Helium-3 on the Ignition of an ICF Fuel Pellet

Self-heating condition and following ignition in an Inertial Confinement Fusion (ICF) fuel pellet is evaluated by calculating the power equations, dynamically. In fact, the self-heating condition is a criterion that determines the minimum parameters of a fuel (such as temperature, density and areal density) that can be ignited. Deuterium is the main component of ICF fuels as large amounts of it are naturally available. In addition, the use of deuterium as a fuel in ICF causes the production of tritium and helium-3. However, pure deuterium has a high ignition temperature (\(\hbox {T}\ge 40\,\hbox {keV}\)) which makes it inefficient. In this paper, the power equations are solved, dynamically, and it has been indicated that internal tritium and helium-3 production at early evolution of compressed deuterium fuel causes ignition at lower predicted temperatures.     

Thermodynamics and Kinetics of Deuterium Absorption in Scandium System

Thermodynamic and kinetic characteristics of the Sc-D system are investigated as a complement to the earlier studies of the Sc-H system. A Sieverts apparatus is employed to conduct the measurements. The Sc-D system is characterized by two phase regions: the metal-rich and the deuteride phases. The equilibrium plateau relationships in the two-phase regions are determined from the Van’t Hoff plots and found to be: $ \ln P({\text{Pa)}} = {{\left( {-{\text{ 16374}}{\text{.48}} \pm{\text{188}}{\text{.88}}} \right)} \mathord{\left/ {\vphantom{{\left( {{\text{ - 16374}}{\text{.48}} \pm{\text{188}}{\text{.88}}} \right)} T}} \right.\kern-0em} T} + ({\text{23}}{\text{.56}} \pm{\text{0}}{\text{.18)}}$ _. The enthalpy and entropy of reaction are calculated to be (?136.14 ± 1.57) kJ mol^?1 D₂ and (?100.06 ± 1.50) J mol^?1 K^?1 D₂, respectively. From the relationship of ln[(P₀?P_f)/(P?P_f)] and time t, the reaction of the Sc-D system is confirmed to be a first-order reaction in the temperature range of 923–1,073 K. The temperature has a negative effect on the reaction rate (k_a), which decreases from 0.0717 to 0.0130 s^?1 with the temperature increasing from 923 to 1,073 K. In addition, a minus activation energy of (?93.87 ± 6.22) kJ.mol^?1 is acquired. However, once increasing temperature up to 1,123 K, the relationship of ln[(P₀?P_f)/(P?P_f)] and time t firstly satisfies an exponential equation of y = ?0.5471exp(?x/9.1879) + 0.00272. After 50 s, it begins fitting a linear equation again, indicating the various reaction mechanisms.