Time Dependent Performance of ITER90H-P Fusion Reactor with Considering D-T and D-He Fuel

In thermonuclear fusion research using magnetic confinement, the tokamak is the leading candidate for achieving conditions required for a reactor. An international experiment, ITER is proposed as the next essential and critical step on the path to demonstrating the scientific and technological feasibility of fusion energy. ITER is to produce and study plasmas dominated by self-heating. This would give unique opportunities to explore, in reactor relevant conditions, the physics of α-particle heating, plasma turbulence and turbulent transport, stability limits to the plasma pressure and exhaust of power and particles. Our studies show that in the dynamical state physical quantities are dependent on temperature and time .Each has its own specific variations and also at the temperature 70 (Kev) these quantities produce the maximum fusion gain for both of fuels D – T and D-He such that their values are equal to 81.311 for D-T fuel-and the 0.0429 for D-He at one second after occurring fusion t=1s ,respectively.


Introduction
Motivation for development of fusion for power generation is ample. The world is in dire need of a safe, clean, sustainable source of power. In the future as we see it today, population growth continues its march upward, and energy demand, especially in developing countries, rises with only limited adoption of improvements in conservation and renewable. Tokamak fusion reactor that uses deuterium (D) and tritium (T) as its fuel is one of several types of magnetic confinement devices and a leading candidate for producing fusion energy. Fusion energy is produced by the following reactions: D + T → 4 He + n + 17.6 MeV D + 3 He → 4 He + p + 18.4 MeV The International Thermonuclear Experimental Reactor (ITER) project is in progress (see figure1), and the primary purposes of this project are demonstrations of controlled ignition, long-pulse burning with steady-state, comprehensive technologies for blanket, superconductive coil and plasma facing wall. The DT burn control is one of the key issues for the ITER tasks. Several types of algorithm for the plasma control were developed, and the performances and applicability of them have been considered [1]. Over the years, the physical and technological feasibility of different methods for controlling the burn condition have been studied [2, 3, and 4] considered: modulation of auxiliary power, modulation of fueling rate and con-trolled injection of impurities. The paper is organized as follows. In Section 2, nonlinear point Kinetic equations governing on the ITER 90 HP fusion reactor for the D-T and D-3 He fuel is described. The reactivity parameter for D-T and D-3 He in two ways (A:Buckey and B:Bocsh Hale) are presented in Section 3.The detailed of numerical calculations for these equations and our obtained results are stated in Section 4.Finally, the conclusions and some suggestions about future work are presented in Section 4.

Nonlinear Point Kinetic Equations Governing on the ITER 90 HP Fusion Reactor ITER 90 HP for the D-T and D-3 He Fuels
In this work, we have used fusion reactor in which approximately particle energy balance equations for two D-T and D-3 He fuels are given by: In these equations, n I ‫و‬ n n , n D3He, n DT , n α are the alpha particle, deuterium -tritium, deuterium -helium 3, and the neutral fuel (defined as the number of fuel atoms divided by the core volume) and impurity densities, respectively.   is the confinement time for the alpha particles, S is the refueling rate , τ DT , τ D3He are the confinement time for ionized fuel particles of D , T and 3 He , D , respectively. τ d is the controller lag time ,E is the plasma energy, τ E is the energy confinement time, τ I is the confinement time for the impurities, S I is the impurity injection rate, Q ∝ = 3.52MeV is the energy of the alpha particles. P α , P aux , P rad , P ℎ , P and , P are the alpha power, auxiliary power , Ohmic power, radiation loss, the net plasma heating power and fusion power ,respectively that are given for D -T and D-3 He fuels in the following: [  η is the Spitzer resistivity in which for D -T and are given by: [8,9]  Also, the gain (Q) of this type of reactor for the D -T and D-3He reactions D -T are given in the following: ) According to the above equations and the data in Table (2-2 As shown in Figure 2, the reactivity of D -T fusion reaction is greater than D-3 He . Because < > DT at 70 Kev temperature has a maximum value thus 70 kev is temperature resonance.the value of D -T reactivity at this temperature approximately 10 times is greater than D-3 He . By viewing the obtained numerical values and Figure2 we find that the difference between the two ways of calculating reactivity is minimal and since that the method of Bucky is newer than Bosch-Hale in our calculations we use this.   such that in both reactions alpha particles are produced and therefor value of its densities are growing then due to the existence of escape probability and leakage from the system the amounts of them are decreased and after certain time since the system goes to the relative equilibrium the values of densities are fixed. Initially the particle density D, T, and 3 He is declining because due to the fusion of D with T and D with 3 He particles of D, T, and 3 He are consumed and their amounts are decreasing and after a certain time the system goes toward a relative balance and the values of densities can be a fixed .Over time, the density of fuel neutral particles in both reactions is declining because in fusion of D with T and D with 3 He fuel-neutral are consumed and values of them are going down, and after a certain time the system goes toward an relative equilibrium also density values can be a fixed amount. Since at temperature 70kev which is resonance temperature of D-T fusion reaction the maximum number of fusions are occurred. Therefore, we have largest consumption of D and T and highest production occurred.

Numerical calculations
In this section, we calculate total energy, auxiliary power, power and fusion gain for ITER90H-p fusion reactor for two fuels D-T and D-3He in terms of time at temperature 70(Kev).Also, from equations (13 -a), and (13 -b) total energy density variations versus time at temperature 70 (Kev) for both fuel D -T and D-3He are as follows. (See fig.5).    With Comparing the two diagrams of fusion gain for D -T and D-3 He, we can conclude that fusion gain of D-T is more greater than D-3 He .Such that at resonance temperature of D-T (70(Kev)) the maximum accessible fusion gain for D-T is about 80 however for is nearly equal to 0.043. Therefore we recommended that for having high fusion gain in fusion reactor ITER90H-p D -T fuel is used instead of D-3 He.

Conclusions
With studying and analyzing of ITER90H-P fusion reactors and solving the non-linear point kinetic equations governing on the two-fuel D-T and D-3 He at dynamical state, we find that the main quantities in determining the fusion gain are the densities of alpha particles, deuterium, tritium, helium, neutral fuel, electron , fusion energy and the total energy , and density of total particles, the effective charge of all ions, radiative power loss, auxiliary and fusion power ,respectively In order to be commercially competitive, a fusion reactor needs to run long periods of time in a stable burning plasma mode at working points which are characterized by a high Q , where Q is the ratio of fusion power to auxiliary power. Active burn control is often required to maintain these near-ignited or ignited conditions (Q = ∞). Although operating points with these characteristics that are inherently stable exist for most confinement scalings, they are found in a region of high temperature and low density. Our studies show that in the dynamical state above quantities are dependent on the temperature and time .Each has its own specific variations and also at the temperature 70 (Kev) these quantities produce the maximum fusion gain for both of fuels D-T and D- 3 He, such that their values are equal to 81.311 for D-T fuel-and the 0.0429 for D-3 He at one second after occurring fusion t=1s, respectively. Fusion using D-3 He fuel requires significant physics development particularly of plasma confinement in high performance alternate fusion concepts.
Countering that cost, engineering development cost should be much less for D-3 He than D-T, because D-3 He greatly ameliorates the daunting obstacles caused by abundant neutrons and the necessity of tritium breeding. D-3 He fusion fueled fusion reactor would also possess substantial safety and environmental advantages over D-T.