Discharge initiation and plasma column formation in aspect ratio A=2 tokamak.

Transcription

1 Discharge initiation an lasma column formation in asect ratio A toama... Khayrutinov E.A. Azizov, A.D. Baralov, G.G.Glaush, I.L.Taibaeva, Ph.W.West 3 Troits, Moscow eg., ussia NNC, K 3 General Atomics, USA

2 Introuction To escribe a current ram-u rocess at toamas it is imortant to now lace where lasma is initiate, conitions for breaown an ynamics of lasma current rise. This is necessary to create conitions for better lasma confinement, for minimization of breaown voltage an to ecrease a volt-secon consumtion. At the same time a stuy of hysics of breaown an lasma initiation is not comlete yet. After avalanche an creation of quasi-neutral lasma it is necessary to um through the ionization-raiation barrier. This is connecte with henomena that the initially lasma volume is less than the vacuum vessel one an the lasma ensity also is much more less than neutral ensity. So at the beginning a burnthrough of neutrals shoul tae lace.

3 Plasma initiation consists of several arts:. Creation of maximum oloial flux value at the lasma region by increasing of current in the inuctor to the maximum available value.. Programme change of currents in the inuctor an P coils to rouce a require External Voltage at the lasma region (ue to ey currents at the vacuum vessel an assive structure there is elay at aearance of esire voltage at the lasma region). 3. ormation of iel Null an Programme Voltage in the lasma region at time of breaown with taing into account of ey currents. 4. Avalanche Phase of initial lasma current formation (most art of lasma current flows along the oene magnetic surfaces) an ensity rise. 5. Quasi-neutral lasma hase, lasma current increase, formation of close magnetic surfaces. 6. ormation of initial lasma for ram-u hase (all neutrals are burne-through an magnetic surfaces insie lasma are close).

4 Toay s status of lasma initiation moel Phases -3 are well stuie theoretically an exerimentally an are almost stanar for the all existing toamas an ITE. Phases 4-6 are usually relace by the only one hase, in which: There is no lasma D equilibrium to be solve. Plasma is consiere to be a circular; Aroximate equations for circular lasma are use to calculate magnetic fiel to be necessary to ee lasma at rescribe osition; D equations are solve for the lasma an neutrals ensity, electron an ion temerature an emirical equations are alie for Imurity; Circuit equations are solve for P coils, ey an lasma currents. Plas ma is reresente as a single filament

5 In eveloe D moel of lasma initiation the each 4-6 hases are consiere searately: Avalanche hase: - lasma region an initial values of lasma current an ensity are calculate in D region for each gri oint with use of Avalanche Moel; - D lasma equilibrium is calculate taing into account ey currents; -the most art of lasma current flows along the oen fiel lines;

6 Quasi-neutral hase: -Plasma is consiere to at quasi-static D equilibrium; -Time eenent equations for P coils an ey currents are self-consistently solve together with lasma free bounary equilibrium roblem (lasma current flows along the oen an close fiel lines); -Plasma current ensity an total lasma current are calculate by use of -D iffusion of magnetic fiel an Gra-Shafranov equations. -As a result lasma current ensity an total lasma current are calculate; - Set of -D non-stationary equations are solve for neutral ensities, electron an ion temeratures an for imurity secies; - as a result, initial lasma is obtaine for ram-u hase (all neutrals are burnethrough an the magnetic surfaces insie lasma becomes close).

7 Plasma start-u at toamas can be ivie into three hases: Avalanche hase, a breaown hase an lasma current ram-u hase. During the avalanche hase, electrons multily until the ionization rate becomes.. During breaown hase, electric resistance ue to Coulomb collisi ons becomes imortant an almost all hyrogen atoms are ionize, emitting bright light. Entering the ram-u hase, oule heating increases T e, an Ω bec omes low to obtain I ram-u.

8 Moel escrition Determination of lasma initiation region (avalanche hase). Townsen s criteria for avalanche breaown: αl ln +, γ α first Townsen s ionization, γ.. coefficient of seconary emission, an integral is taen along magnetic fiel line. Magnetic lines, for which conition () is correct, will etermine bounary of region for avalanche an lasma initiation. ()

9 As an examle on the ig., the regions of lasma initiation are resente for KTM toama, which were calculate for ifferent values of hyrogen ressure an at fixe value of loo voltage. It is seen that with increasing ressure the avalanche region is increase too. Bounary of avalanche regions in the КТМ toama for ifferent values of ressure:,,, мp. - Z, см , cм

10 3 3 ( n t t ( n e e -D equations for quasineutral lasma T ).6 P i e T ).6 P Δ OH P P cx Δ P ne ne nnesi t τ n nev VV nne S iv t τ 3 n ion e τ T E i 3 n e τ T E.6 e.6 V - volume of lasma region, V v - vacuum chamber volume, T e и T i - electrons an ions temeratures, P OH - ohmic heating ower, P Δ - equilibration ower between electrons an ions, P ion - neutral gas ionization losses, P cx - charge exchange losses, τ Е, τ Р - confinement times

11 EQUATIONS O MAGNETIC IELD DIUSION The roection of the general Ohm s along the magnetic fiel is given by: ΕΒ σ Β Β a t t t t Β Β + ΕΒ +Ε Β ) σ ( Β Ε t t 4 Φ Ε Ε Β Ε + + Β t t Β 4

12 / 4 4 Β + Φ σ a Φ σ 4 l G > > + < >< < ext l B A + ) ( ) ( t Z + t 4 + Let s enote by inex each magnetic surface then using relation that total is a sum of - lasma flux an - external flux l ext ext l + Gra-Shafranov equation:

13 Plasma current, electrons temerature, minor raius an feebac current behavior uring breaown simulation

14 Algorithm of solution As first ste in the iteration scheme the D free bounary equilibrium equation on rectangular gri is solve at given external P an assive structure currents self-consistently with circuit equations for these currents. Plasma can flow at oen an close fiel lines. As secon ste, after fining equilibrium configuration, averaging is carrie out to fin all metric coefficients an coefficients for matrix equation. Value for electron temerature use to calculate lasma conuctivity is taen from results of solution of D set of transort equations. As a result lasma current ensity an total lasma current I are calculate. As thir ste set of D equations is solve. Value of I is use to calculate Ohm s heating of electrons. Average value of minor lasma raius a is calculate as S /, where S is area occuie by lasma. Plasma ressure rofile in this case is equal to zero. As a result of solution new value of electron temerature is obtaine, which is use in the ste.

15 Stes, an 3 are iterate until require accuracy is achieve. Then next time ste follows. Test simulation for eveloe moel has been carrie out for KTM toama, which inclues all three stages of lasma breaown. Examles of magnetic configuration for KTM toama at the beg inning of initiation an at the en of breaown are resente b elow at igs.

16 Poloial configuration of КТМ toama at the beginning of lasma initiation, lasma current is I 3A. Poloial configuration of КТМ toama at the en of lasma breaown, lasma current is I 5A.

17 Conclusion.. Plasma initiation moel with D lasma equilibrium solver has been eveloe.. All necessary equations have been erive. 3. Preliminary stage with use of D equilibrium an D transort is rogramme an teste. 4. Next stage will consist of in eveloing NEW coe which will be integration of TANSMAK [] coe an this D breaown moel [].. V.A. Beliaov, V.I. Vasiliev, K.I. Lobanov, L.P. Maarova, Л.П. A.B. Mineev, VII Int. Conf. of Thermonuclear eactor Engineering Problems, 8-3 Oct. г. St.- Petersburg, E.A. Azizov, A.D. Baralov, G.G. Glaush,.. Khayrutinov. Int. Conf. an School on Plasma Phys. an Controlle usion, Alushta, Uraine, Set. 6,.