Journal of Physics & Astronomy

Transcription

1 Jounal of Physcs & Astonomy Reseach Vol 4 Iss Tempeatue and Velocty Estmaton of the Imploson n We Aay Z-Pnch Abdoleza Esmael * Plasma Physcs and Nuclea Fuson Reseach School, Nuclea Scence and Technology Reseach Insttute, Tehan, Ian * Coespondng autho: Abdoleza Esmael, Plasma Physcs and Nuclea Fuson Reseach School, Nuclea Scence and Technology Reseach Insttute (NSTRI), P.O. Box , Tehan, Ian, Tel: ; Fax: ; E-mal: aesmael@aeo.og. Abstact Z-pnch nuclea fuson system s the mechansm of ceatng nuclea fuson by magnetc confnement method. In ths pape, tempeatue and velocty of mploson s estmated. By ntoducng a pope model, the paametes of Z-pnch ae estmated and calculated and then the ntoduced model s confmed by usng expemental data of Sanda lab. At the end, by compang these two models and the expemental esults, the valdty of the model s nvestgated. In pactce, all estmates based on assumptons ae often coect only wthn the ode of paametes magntude. Keywods: Confnement magnetc; We aay; Dynamc Z-pnch; Imploson velocty Intoducton A Z-pnch s a column of plasma n whch cuent s dven n the axal (z) decton poducng an azmuthal magnetc feld that confnes the plasma. In expements usng Z-pnch, when the we aays mploded and tuned nto gas, mmedately pnch occued. Pnch plasma esponse to the appled cuent at fst seems smple, but n spte of the smplcty, complexty s. Pnch undestandng s dffcult to undestand qualtatvely let alone quanttatvely [1]. Bght spots may appea n dynamc Z-pnches n the low mploson velocty. Soft x ays ae emtted manly fom these spots. The amount and specta of ths adaton s vey senstve to the dynamcs of the mploson. Many physcal models ae descbed Z-Pnch that each of them may be appopate to descbe a specfc Z-pnch. Choce of a pope model s sometmes vey dffcult. In ths pape, by usng smple physcal concepts and matchng wth the selected model, we ted to ntoduce an appopate model fo Z-pnch. Ou am n ths pape s to vefy the model that was pesented pevously n 198 by Hussey et al. In the followng, calculatons of the tempeatue and mploson velocty of Z-pnch ae pesented. Fst model: A smple theoetcal model Consde a we-aay lne whch made of wes. Electc cuent that passes though the we, a magnetc feld s ceated aound t that can be calculated. An electomagnetc foce ( J B) s appled to each we. In ths way, we can compute the extenal magnetc feld aound the lne, wth assumpton: the feld was ceated by wes wth nfnte length that s not the ealty. So, ths calculaton only gves some ode of magntude. Some evdence of a helcal m=1 unstable knk mode at late tmes n the dschage, but t does not appea at stagnaton. The tme of stagnaton, manly long wavelength m= modes can be. Calculatons and estmaton at the confnng tme s dffcult because of the pessue and feld gadent [1,]. But, these gadents ae not at stagnaton and equatons become ease. So, all calculatons wee pefomed fo stagnaton moment. Fgue 1 shows the confguaton of Z-Pnch at the stagnaton. So fo Magnetc feld can be wtten [3]: Ctaton: Abdoleza Esmael (16) Tempeatue and Velocty Estmaton of the Imploson n We Aay Z-Pnch, Jounal of Physcs & Astonomy, Tade Scence Inc 1

2 June-16 B (1) Whee B s magnetc feld, s pnch adus and I s cuent passng though. Fgue 1: Z-pnch confguaton. If n s the numbe of wes, electc cuent that passes though each we s equal to I / n. usng the Loentz foce ae: I B () n n If M, s the mass pe unt length of the we, we have: ab - (3) M Whee a s adal acceleaton due to the Loentz foce, eplaced wes by plasma cylndcal that an electc cuent passes B though t. Plasma pessue s suffcent to balance magnetc pessue at stagnaton. Ion pessue s equal to: P n kt (4) Whee k s Boltzmann constant, T s the on tempeatue and n s the numbe of ons pe unt volume. The pessue foce actng on each plasma cylndcal pe unt length s: The equaton of moton s as follows: M a nkt (5) n n n Whee a s adal acceleaton and n N /, yelds: NkT a (6) M M Whee N s the numbe of ons pe mete. Snce the tempeatue vaes ove tme, we cannot get t at all tmes. But the acceleaton s zeo at stagnaton. So, the tempeatue can be estmated at stagnaton: T (7) 4 Nk If V s the adal velocty of ons at stagnaton condton, we have: 1 3 mv kt (8) K s Boltzmann constant, Yelds: 3kT V (9) m Note: 3% of the mass lost dung the mploson that should be consdeed n the calculatons [4]. Second model: Thn shell model, an appopate model fo pedctng the knetc enegy, speed and tme of exploson Dynamcal popetes of the pnch mploson can be computed easonably n the thn shell model. In ths model, the mplodng plasma s assumed n the fom of a vey thn laye wth cylndcal symmety and the adal poston of the plasma shell s defned as a functon of tme, lnea densty of mass and acceleaton whch s detemned by the Loentz foce. The equaton of moton the shell of adus R(t) s [1]:

3 June-16 d R I () t dt Rc (1) Whee s the mass pe unt length of the shell. Wth the ntegaton of the above equaton fo and wth ntal condtons R() R, R() we obtan: dr R R ln (11) dt A R() t 1/ A c R / I s the Alfvѐn tanst tme. max I I max The next equaton s ccut equaton. Z-pnch equvalent ccut s as follows (Fgue ): d 1 ( R RP) ( L LP) I Idt dt C (1) Fgue : Z-pnch equvalent ccut. Whee R, L ae espectvely the esstvty and nductance of the ccut. R and P L ae espectvely the esstvty and P nductance of the plasma and C s capactance. z LP ln( ) (13) P Whee s the ntal adus of plasma and z s the length of Z-pnch Evaluton of the two models and compason wth the expemental data Except Sanda, some othe countes such as Gemany, Span [5], and Fance and moe ecently n Egypt [6-8] on devces wth dffeent enegy, 1 kj and 5 kj, actvtes have taken place. But the laboatoy Z Pnch appaatuses ae much smalle than the Z machne n Sanda. Substtutng nto above elaton the paametes of Z Pnch expements wth the 3TW Satun acceleato, one of dves at 4 Sanda Natonal Laboatoes (1989) Imax 1MA, 5 1 g / cm we obtan (Table 1): Fst model Second model Velocty (km/s) Tempeatue (kev) Table 1: Paametes of Z Pnch expements (1989). Substtutng nto above elaton the paametes of Z machne, one of the most poweful dves at Sanda Natonal 5 Laboatoes (6) Imax 18MA kg / m we obtan (Table ):, 3

4 June-16 Fst model Second model Velocty (km/s) Tempeatue (kev) Table : Paametes of Z machne expements (6). The velocty ae n both models vey close togethe, Shows, These fomulas ae sutable fo devces wth we aays. The fomulas and estmates, s only an estmate and t s possble, n pactce, the measued paametes ae less than the estmated values o vce vesa. Ths calculaton apples only fo Z Pnch devces wth we aays [9,1]. Fgues 3 and 4 show the esults of the two models usng paametes Sanda Laboatoes n 1989 and 6. The esults ae n easonable ageement wth the expemental data. Fgue 3: The changes of mploson velocty wth espect to cuent; dak ponts: fst model, lght ponts: second model. Fgue 4: The changes of mploson tempeatue wth espect to cuent; dak ponts: fst model, lght ponts: second model. 4

5 June-16 Concluson Fo the desgn of systems and devces, physcs of them must be ecognzed. Obvously, wthout suffcent knowledge of the physcs of the system o Tal and eo method to acheve an optmum desgn, just waste tme and money. Dsegadng the physcal ssues n the desgn of systems, especally n the fuson systems, t may endange the safety of people and expensve equpment. Attenton to ths equaton and usng them to pedct and estmate the paametes of the devce play a fundamental ole n the optmzaton, wll ncease the effcency and safety systems. In ths pape, by usng smple physcal concepts and matchng wth the selected model, we ted to ntoduce an appopate model fo Z-pnch. In Z-pnch devces, t s dffcult to calculate and obtan the equatons. In pactce, all estmates based on assumptons ae often coect only wthn the ode of paametes magntude. Theefoe, they ae convenent and, theefoe, conventonally used. Snce, thn shell model s a pope model, n the futue, can numecally solve equaton (11) and (1) and obtan the pnch adus at evey tme of confnement. Of couse, we must thank M. Jean-Pee Pett (Fench scentst, seno eseache at Natonal Cente fo Scentfc Reseach as an astophyscst n Maselle Obsevatoy, now eted) that we used some of hs analyss n ths pape. Refeences 1. Lbeman MA, Goot JS, Too A, Spelman RB (1998) Physcs of hgh densty Z pnch plasmas. Spnge, New Yok.. Wesson J, Tokamaks (4) Claendon Pess, Oxfod, Unted Kngdom. 3. Jean PP (6) The Z machne: Ove two bllon degees. Maselle. 4. Hanes MG, LePell PD, Covedale CA, Jones B, Deeney C, et al. (6) Ion vscous heatng n a magnetohydodynamcally unstable Z pnch at ove x 1(9) Kelvn. Phys Rev Lett 96: Cotázaa OD, Pza AR, Petoa GR, Hoffmannb DHH, Tahb NA (8) Pelmnay Results of a 1 kj Z Pnch. AIP Conf. Poc: 996: Abdel KME, Abd Al-Halmb MA, Eltayeba HA, Shagaa AM (14) Analyss of the toodal and polodal magnetc feld behavos n the concal Z pnch plasma thuste. 47: Abdel KME, Al-Halm MA, Shaga AM, Eltayeb HA, Algamal HA, et al. (14) Pelmnay esults of cone Z-Pnch devce wth 5 kj. J Fuson Enegy 33: Abdel KME, Al-Halm MA, Shaga AM, Eltayeb HA (15) Effect of the gas pessue and the chagng voltage on the plasma cuent densty dstbuton n concal Z pnch plasma thuste. J Fuson Enegy 34: Aleksandov VV, Gabovsk EV, Mtofanov KN, Olenk GM, Smnov VP, et al. (4) Relaton between the electc paametes of a Z-pnch dschage and plasma poducton n the load dung the mploson of a cylndcal we aay. Plasma Physcs Repots 3: Vkhev VV, Koolev VD (7) Neuton geneaton fom Z-pnches. Plasma Physcs Repots 33: