Microsoft Word - 256-264 256 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Plasma Power Density Produced by D-T Fusion Reaction Raad H. Majeed Dept. of Physics/College of Education For Pure Science (Ibn al-Haitham) / University of Baghdad Muayad M. Abed Directorate of Education in Najaf /Ministry of Education Received in:12May 2014,Accepted in:1Scptember2014 Abstract Calculation of the power density of the nuclear fusion reactions plays an important role in the construction of any power plants. It is clear that the power released by fusion reaction strongly depended on the fusion cross section and fusion reactivity. Our calculation concentrates on the most useful and famous fuels (Deuterium-tritium) since it represents the principle fuels in any large scale system like the so called tokomak. Key words: D-T reaction, fusion cross section, plasma power density, reactivity. 257 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Introduction Fusion energy is considered as a clean source of energy with a basic fuel that is abundant, cheap, and available to all of humanity. It is now being realized in the Cosmos in stellar systems and on Earth in the form of thermonuclear or hydrogen weapons. However, a controlled fusion reaction releasing energy on Earth in a controlled manner remains unfulfilled until some time in the future. Hydrogen isotopes such as deuterium and tritium can be used to produce fusion energy. Fusion fuels are cheap and uniformly distributed on Earth. Seawater contains deuterium D in practically inexhaustible quantities Tritium, a radioactive isotope of hydrogen with a short half-life of 12.33 years, hardly occurs in nature. It can, however, be produced in a power plant from lithium, which is likewise abundantly available. Since a fusion power plant will have ecologically favorable properties, fusion could make an enduring contribution to the future energy supply. The following applications are foreseen for fusion energy:[1] 1. Electrical power production. 2. Fresh water desalination. 3. Hydrogen production. 4. Deactivation of fission reactors waste. 5. Production of fissile fuel for fission reactors. 6. Space rocket propulsion. Advantages of Fusion Energy 1-Abundant fuel supply. The major fuel, deuterium D, may be readily extracted from ordinary water, which is available to all nations. The surface waters of the earth contain more than 1012 metric tons of deuterium, an essentially inexhaustible supply. The tritium required would be produced from lithium, which is available from land deposits or from sea water which contains thousands of years' supply. The world-wide availability of these materials would thus eliminate international tensions caused by the imbalance in the fossil fuel supplies. 2- Non critical design. Since no fossil fuels are used, there will be no release of chemical combustion products because they will not be produced. 3- No air pollution. Since no fossil fuels are used, there will be no release of chemical combustion products because they will not be produced. 4- No high level nuclear waste .Similarly, there will be no fission products nor transuranic formed to present a handling and disposal problem. Radioactivity will be produced by neutrons activating the reactor structure, but careful materials selection is expected to minimize the handling and ultimate disposal of the activated materials. 5- No generation of weapons material .Another significant advantage is that the materials and by-products of fusion are not suitable for use in the production of nuclear weapons The DT reaction produces neutrons that can activate the structure of the reactor, creating some radioactivity. A fast neutron from the fusion reaction can in principle produce two tritons in these two reactions, sine it is re-emitted from the fast reaction, and is available, if not absorbed by other nuclei, to induce the second reaction at low energy. [ 2, 3] 258 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Theory Fusion Reaction Cross Section For the D-T fusion reaction, which is by far the most important one for present fusion research, the following expression is used to calculate the fusion cross section [4]. √⁄ (1) here the coefficients , , , , are called the Duane coefficients and are given in the table[1] for D-T fusion reaction. Plasma reactivity calculations require reaction cross sections for energies well below those at which direct measurement are practicable [5]. And the equation bellow is used to calculate the reactivity for D-T reaction. 〈σv〉 3.68 10 T ⁄ e . ⁄ (2) where T is plasma temperature in keV. The power density released in the form of charged particles, for the D-T Reaction is: 5.6 10 〈 〉 (3) here , represent the deutron and tritium density in respectively, 〈 〉 represents the reactivity as discribed in eq(2) Calculations and Results It is necessary to note that there exists many experimental or empirical formulas for measuring the fusion cross section for D-T reaction; and we found that each formula gives a different data or results corresponding to other. As shown in Fig. 1, the fusion reaction cross sections are dependent on the temperature of the plasma or its energy in units of keV.And the calculated results about the total D-T fusion reaction are presented in Table (2) and described in Fig. (2). The D-T fusion reactivity as a function of the deuteron temperature is calculated according to Eq.(2) and their calculated results are completely presented in Table(3) and described in Fig.(3) Discussion and Conclusion It is clearly shown that the most important parameter in deducing the accuracy for our results is the fusion plasma power density since it included reactivity in addition to the physical parameters that describe any fusion collision phenomena i.e., incident energy for the projectile , target energy , density and ignition temperature. By comparing the cross section behavior for the D-T fusion reaction presented in Fig. (2) with the corresponding experimental published ,we observed a right agreement between our results and experimental published and this behavior leads to a fact that there exists a real precession for the choices of cross section formula which in turn reflect on the results about both the two other parameters 〈 〉 respectively. The above conclusions are very clearly shown in the physical behaves for the D-T plasma power density and reactivity in which a very approximated behavior with the other corresponding published results shown in figure (5). Finally, we suggest to support our efforts by using the above physical description in the future work by consideration to arrive a more suitable empirical cross section formulas especially the works that deal with the general thermonuclear fusion reaction. 259 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 References 1.Emrich, W. J. Jr., March (2001), Field-Reversed Magnetic Mirrors for Confinement of Plasmas, NASA Tech Briefs. 2-. Glasstone, S. (1980), Fusion Energy, U. S. Department of Energy, Technical Information Center. 3- Seifritz, W. (1983), Nukleare Sprengkörper-Bedrohung oder Energieversorgung fur d Menschheit?, Thiemig –Tascenbücher, Band 97, Karl Thiemig AG, München. 4- Xing Z. Li, Qing M. Wei and Bin Liu,(2008), A new simple formula for fusion cross- section of light nuclei Nucl. Fusion 48(12500) :5. 5-Jarvis,O.N.(2011),WWW.Kayelaby.npl.co.uk, Table of physics and chemical constants,chapter 4, section 4.7.4. 6‐ Decrton M. , Massaut V. , Inge Uytdenhouwen, Johan Braet, Frank Druyts and Laes E. ,(2007), Controlled nuclear fusion:The energy of the stars on earth", Open Report SCK.CEN- BLG-1049. 7‐   Commons-wikiedia.org/wiki/file DT-fusion-reaction-power-density-jpg 24 May( 2007) Table No.(1): coefficient used to represent the energy dependence of the total cross section ref.[4]He fusion reaction 4H (d,n)3 Coefficient  He fusion reaction4H(d,n)3   45.95   50200   1.368 10   1.076   409 Table No.(2): Energy dependence cross-section for D-T nuclear fusion reaction Deutron energy ( Cross section (ba Deutron energy ( Cross section (ba 5  6.024 10 140  4.390  10  1.324 10 160  3.775  20  5.337 10 180 3.181  30  0.2666  200  2.673  40  0.693  220  2.258  60  2.102  240  1.922  80  3.714  260  1.652  100  4.714 280 1.434  120  4.830  300  1.255  260 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Table No. (3): Temperature dependence fusion reactivity and plasma power density for D-T fusion reaction Temperature(keV)  Reactivity(cm3/sec) Plasma Power density(Watt/cm3) 5  1.085 10   6.077 10   10  7.579 10   4.244 10   20  3.222 10   1.804 10   30  6.224 10   3.485 10   40  9.239 10   5.174 10   50  1.209 10   6.772 10   60  1.473 10   8.252 10   70  1.716 10   9.61 10   80  1.937 10   1.085 10   90  2.141 10   1.198 10   100  2.327 10   1.303 10   200  3.556 10   1.991 10   300  4.176 10   2.338 10   400  4.527 10   2.535 10   500  4.736 10   2.652 10   600  4.864 10   2.723 10   700  4.940 10   2.766 10   800  4.984 10   2.791 10   900  5.005 10   2.802 10   1000  5.01 10   2.805 10   261 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 . Figure No. (1): Measured cross sections for different fusion reactions as a function of the averaged centre of mass energy. Reaction cross sections are measured in barn (1 barn= 10-28 m2) [6]. Figure No. (2): Variation of the D-T cross section with the incident deuteron temperature                262 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Figure No.(3) Variation of the D-T Reactivity with the incident deuteron temperature Figure No. (4): Variation of the D-T plasma power density with the incident deuteron temperature 263 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 Figure No.(5):Variation of the D-T plasma power density with the incident deuteron temperature.[7] 264 | Physics 2014) عام 3العدد ( 27مجلة إبن الھيثم للعلوم الصرفة و التطبيقية المجلد Ibn Al-Haitham Jour. for Pure & Appl. Sci. Vol. 27 (3) 2014 مترتيو -كثافة قدرة البالزما الناتجة بوساطة التفاعل االندماجي ديتريوم رعد حميد مجيد قسم الفيزياء / كلية التربية للعلوم الصرفة (ابن الھيثم )/ جامعة بغداد مؤيد محمد عبد مديرية تربية النجف/ وزارة التربية 2014ايلول1قبل البحث : 2014ايار12استلم البحث : الخالصة حساب كثافة القدرة للتفاعالت النووية االندماجية تؤدي دورا مھما في بناء اي محطة لتوليد القدرة .ويتضح ان القدرة المتحررة بوساطة التفاعل االندماجي تعتمد بشدة على المقطع العرضي االندماجي و التفاعلية االندماجية ,حساباتنا الحالية تريتيوم) النه يمثل وقودا اساسيا في اي نظام وعلى نطاق واسع -كثر فائدة والشھير (ديتريومتتركزعلى انواع الوقود اال والمعروف بالتوكوماك. تريتيوم , المقطع العرضي االندماجي , كثافة قدرة البالزما , التفاعلية. - : ديتريوم مفتاحيةالالكلمات