The Study of Lawson Criterion in Fusion Systems for the

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1 Interntonl Archve of Appled Scences nd Technology Int. Arch. App. Sc. Technol; Vol 6 [] Mrch : -6 Socety of ducton, Ind [ISO9: 8 ertfed Orgnzton] OD: IAASA IAAST OLI ISS - 6 PRIT ISS ORIGIAL ARTIL The Study of Lwson rteron n Fuson Systems for e Rectons He D, P nd B p, Kh. Benm *, S. Msoud, S.H.Gnjpour, Deprtment of Physcs, Islmc Azd Unversty, Dehdshtnch, Dehdsht, In Deprtment of Physcs,PymoorUnversty,Tehn, In * enmkh@gml.com ABSTRAT We hve otned e pmeter of e son recton te (Sgmv)for e mportnt son rectons He(D, p)α nd B(p,α)α.Usng e result, we hve otned energy lnce equton whch s e formul of Lwson crteron. Keywords:Pmeter of e Fuson Recton Rte (Sgmv), Lwson rteron, Fuson Rectons, Bermesslung dtons Receved 8// Revsed // Accepted // tton of s rtcle Kh. Benm, S. Msoud, S.H.Gnjpour. The Study of Lwson rteron n Fuson Systems for e Rectons He D, P nd B p,. Int. Arch. App. Sc. Technol; Vol 6 [] Mrch : -6. DOI../st ITRODUTIO In son systems, some energy s lost y dton or oer processes. In s rtcle we consder energy losses rough Bermesslung dtons for He(D, p)α nd B(p,α)αrectons. In fct, externl energy s njected to e son system to compenste e lost energy. onsequently, we otn put energy from e son recton. From pctcl pont of vew, e energy otned must e more n e nput energy or e source of externl energy n [,]. Ths lnce equton of energy s e Lwson crteron. SUMMARY OF TH THORY Genelly, f two cores nd do son recton ccordng to e followng relton, ey produce e nd d. d e Q () Q Is e energy relesed from e sonrecton. The power of son recton s expressed y e followng relton []. P V Q () nd re denstes of core nd respectvely. The quntty recton te. The quntty shown s follows [-]. V s e son V s e pmeter of son recton te t s clled Sgmv nd () V fv fv v v v v d vd v V V IAAST Vol 6 [] Mrch P g e Socety of ducton, Ind

2 s reltve cross-secton of e recton, nd s mesured n Brn. Trough fttng S P model [,] y expermentl dt, cross-secton cn e pproxmtely otned. Here, e structure fctor S() depends wekly on energy or s even ssumed to e constnt. The mn energy dependence comes from e potentl rrer PenetltyP(). It s defned y e to of e prtcle flux tversng e respectve f re e Mxwell speed potentl rrer to e ncdent flux.the nctons v dstruton nctons[-]. y usng f v, f v nd kt f nd v n eq. we hve [,] : 8 V kt e d () Snce e cross-secton ncton nd e ntegl of eq. re computed pproxmtely, so ere s often hgh te of error for V whch s clculted y eq.. In s pper, e followng model for prolems [6]. V s proposed n order to decrese e ove mentoned YX KT KT e 6 V X Y e () Where X KT KT KT 6 KT KT KT 8 8 (6) Y () KT ow we clculte sgmv for e followng mportnt rectons []. D He p 8. p B MeV (8) MeV (9) In e rectons ove, α represent Hend D represent H. ps proton. In e model suggested for V, constnt coeffcents to 8 re clculted y fttng e eq. w vlle dt [] for ech of e ove rectons. The results hs shown n tle ()nd we hve otned e ncton of Sgmv n respect to KT.The gph of Sgmv w respect to KT s dwn n fgures nd for ech of e ove rectons. lcultng Lwson crteron for ech of e dscussed rectons: At frst, for e rtry recton of eq. e reltons re wrtten. Then susttutng desred cores w nd ccordng to wht ws sd n ntroducton, f e put nd nput energy re nd n respectvely, e relton n must e correct durng determned tme. My e e tme needed for complete cycle n pulse or perodc son system t e system s expected to hve stedy stte [,]. IAAST Vol 6 [] Mrch P g e Socety of ducton, Ind

3 The clssc eorem of gs knetcs cn e used s ss for e study of son envronment. onsequently, for e cse of genel tomc densty w tomc numer Z,we hve complete onzton product ons per unt volume, nd e= Z electron per unt volume, so t = + e = + Z, ecuse e cores re lght, t cn e pproxmtely sttedt. In son system, energy cn e consdered n ree dfferent wys. Frst, energy relesed from son recton t we shown y. Second ll e energes lost v dton ( ), nd fnlly het energy of prtcles expressed s. In son envronments % effcency s not possle. So just fcton of energy s vlle.hence we hve[,]: () In whch s re fcton coeffcents for ech coordnte of energy. nergy njected to e system ( n) s s follows: e n n () If we ssume, for smplcty, t fcton coeffcents re equl ( n stte.tht cn produce constnt power n determned tme, we hve [,]: ) nd system works P,, e kt () The lost energy y dton s ecuse of Bermesslung dtons, we hve [,]: r P r A r kt () In whch A r s Bermesslung dtons power constnt nd equls e Lwson crteron s wrtten s [,,8]: kt kt A r m 8. J, Then s kt n () n Q v A r A r For e dscussed rectons w ssumpton n Lwson crteron s clculted. The results hs shown n tle (). The gph of w respect to KThs dwn n fgures nd. Tle ():Vlues of to 8 nd forrectons He(D,p)α nd B(p,α)α. Recton He d, p Bp, KeV.. m s KeV IAAST Vol 6 [] Mrch P g e Socety of ducton, Ind

4 KeV.8. KeV.9. KeV KeV.96 KeV.98 m 8 s. rror % % s ( m ) x - 6 < V> ( m /S ) D + He- = + P +8. MeV our meod vlle dt KT( kev ) Fg.Sgmv gph n terms of KT for recton He(D,p)α. IAAST Vol 6 [] Mrch P g e Socety of ducton, Ind

5 Fg. Sgmv gph n terms of KT for recton B(p,α)α. x 9 8 D + He- = + p +8. MeV ( s / m ) K T ( k e V ) FgLwson's crteron ounds for recton He(D,p)α. IAAST Vol 6 [] Mrch P g e Socety of ducton, Ind

6 x B- + p = MeV ( s / m ) KT( kev ) Fg. Lwson's crteron ounds for recton B(p,α)α. OLUSIO The suggested model for Sgmv hs cceptle nswers n low energy. The vlues clculted for Sgmv re equl to ose of dfferent references. Fgurese nd llustte very well t reches ts lowest vlue n specfc tempeture. The lest vlue of s Lwson crteron t we hve otned.ths result s very usel ecuse t defnes e necessry condton etween prtcles densty nd energy confnng tme nd e tempeture of e system. But e dsdvntge of s system s t ll e pmeters re not consdered. For exmple, djustng some pmeters to constnt vlues durng tme my not e possle. However, s equton hs mny pctcl pplctons. RFRS. M.R. skndr, Prncple of ucler Fuson, ShzUnverstyPress, In (99).. Keshro.IU,ucler Fuson, mrdgunversty press (989).. W. B. Thompson, Thermonucler recton te, The proceedngs of e physcl socety secton B Vol.,o.B (9 ).. V.T. Voronchev,V.I.Kukuln, ross secton of L t, d L.8 nd 6 Lt, p L.98 nucler rectons n e -Mev energy nge, J. Phys. G: ucl. Prt. Phys, 6, L ().. V. T.Voronchev, V. I. Kukulne, Rte pmeters of 6 L(d, p α)t nd 6 L(d, n α) He nucler rectons t ermonucler tempetures, J.Phys. G:ucl.prt.phys.6,L ( ). 6. S. Atzen, J. Meyer, The Physcs of Inertl Fuson, OxfordUnversty Press ().. R nd Mcnlly, nd et l, Fuson Rectvty Gph nd Tles for hrge nd Prtcle 8. Rectons, Ok, Rdge t. L, ORL/TM69,Ok Rdge,T (99). 9. K.S. Kne, Introductory ucler Physcs (988). IAAST Vol 6 [] Mrch 6 P g e Socety of ducton, Ind