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Study of the Discrete-To-Continuum Transition in a Balmer

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Study of the Discrete-To-Continuum Transition in a Balmer View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by DSpace@MIT PFC/JA-97-26 Study of the discrete-to-continuum transition in a Balmer sp ectrum from Alcator C-Mo d divertor plasmas A. Yu. Pigarov y,J.L.Terry and B. Lipschultz Decemb er 1997 Plasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. This work is supp orted by the U.S. Department of Energy under the contract DE-AC02-78ET51013 and under the grant DE-FG02-910ER-54109. y also at College of William and Mary, Williamsburg, VA, USA. Perma- nent address: RRC Kurchatov Institute, Moscow, Russian Federation. 1 Abstract Under detached plasma conditions in Alcator C-Mo d tokamak, the mea- sured sp ectra show pronounced merging of Balmer series lines and a photo- recombination continuum edge which is not a sharp step. This phenomenon, known as a smooth discrete-to-continuum transition, is typical only for high 21 3 density>10 m low temp erature T 1 eV recombining plasmas. e A theoretical mo del capable of treating this kind of sp ectra has b een de- velop ed as an extension of the CRAMD co de. It is comprised of three parts: i a collisional-radiative mo del for p opulation densities of excited states, ii atomic structure and collision rates for an atom a ected by statistical plasma micro elds, and iii a mo del for calculating the line pro les and the extended photo-recombination continuum. The e ects of statistical plasma micro elds on the p opulation densities of excited states, on the pro les of Balmer series lines, and on the photo- recombination continuum edge will b e discussed. The changes in sp ectral characteristics with plasma parameters variation will b e given. The calcu- lated and measured sp ectra will b e compared. The relevance of volumetric plasma recombination to the sp ectra observed from the divertor is discussed. 2 I. Intro duction Recent exp erimental [1-3] and theoretical [4] investigations have demon- strated that volumetric plasma recombination plays a crucial role in divertor plasma detachment from the divertor target. With plasma detachment the signi cant reduction of charged particle ux and plasma heat ux on the target was measured. At the same time it was frequently observed that the plasma temp erature decreased to ab out 1 eV and the plasma density in- 21 3 creased up to 10 m near the target. Under these conditions volumetric recombination of the ma jority ions o ccurred in the divertor. The sink of plasma particles due to recombination inside the divertor volume mightbe comparable to the plasma current on the target. Imp ortant exp erimental evidence for the strong volumetric recombination of plasma in the detached divertor comes from the analysis of the plasma emission sp ectrum. The rst sp ectra relevant to the recombining divertor plasma were observed in the Alcator C-Mo d tokamak [1,2] and, later, in the other divertor tokamaks ASDEX-U [5] and JET [6]. The basic features of atypical sp ectrum from a recombining divertor plasma is exampli ed bya sp ectrum measured from the detached C-Mo d divertor plasma [1] shown in Fig. 1. Firstly, one can see the presence of a strong photo-recombination continuum. The continuum emmission corresp onds to a low, ab out 1 eV, temp erature of plasma. Secondly, the upp er lines of discrete sp ectrum show the signi cant Stark broadening. This fact means that the plasma densityis rather high. And, thirdly, there is sp eci c relation b etween the total inten- sities of sp ectral lines and the continuum intensity level. This relation is a 3 characteristic of a plasma where the upp er excited states of deuterium atom are p opulated via 3-b o dy recombination. The simple metho ds for plasma density and temp erature determination from the measured sp ectra were reviewed in Ref. [7] chapters 13-14. The electron temp erature T can b e estimated in a numberofways: i from the e ratio of the intensityofawell-resolved line to the continuum intensity, ii from the ratio of total emissivities of lines in a series, and iii from the ratio of continuum emissivities measured at some p oints for b oth sides of an ideal photo-recombination edge. The plasma density N can b e obtained from the e analysis of Stark broadening of lines. The simpli ed expression for the line width at half height 2=3 = C N ; 1 e where the tting constant C were tabulated in [8] for each Balmer line, is b elieved to b e valid and is frequently used in the plasma density estimate [9]. These metho ds were used in the analysis of C-Mo d sp ectra presented ab ove. Under simplifying assumption of a constant temp erature and density for the divertor plasma giving rise to this sp ectra, all the ab ove metho ds predict low 21 3 temp erature T =0:75 ! 1:1 eV and high density N =2! 1 10 m . e e At the same time the range of plasma parameter variation expresses the uncertainty of simple metho ds mentioned ab ove. Nevertheless, the sp ectrum analysis p oints the plasma in the divertor b eing in a recombining state. Of particular interest in those high density C-Mo d discharge is that the measured divertor sp ectra show a pronounced merging of Balmer series lines and a photo-recombination PR continuum edge which is not a sharp 4 step. This phenomenon, also known as a smo oth discrete-to-continuum D- C sp ectrum transition see Refs. [10] page 201 and [11], has already b een observed and studied in many lab oratory plasmas with high density 23 3 N 10 m and low temp erature. By its nature, the smo oth D-C tran- e sition is indicativeofa weakly non-ideal plasma and the sp eci c e ects of this plasma should b e included in the sp ectrum analysis. The most imp ortant are the e ects of statistical plasma micro elds SPM which are necessarily present due to the break down of plasma quasi-neutrality in the elementary plasma volume with a size of ab out the Debye shielding radius. In this pap er we describ e a theoretical mo del capable of explaining the main features of measured sp ectrum from the strongly recombining plasma, the smo oth D-C transition in particular. This mo del is collisional-radiative CR and provides the calculation of p opulation densities of excited states and the detailed pro les of sp ectral lines and various continua. The mo del is considered as a to ol for a more precise estimation of plasma parameters by tting the whole measured sp ectrum. In the pap er we use n with any sub- or sup erscripts to denote the principle quantum numb er of atomic level and to denote the wavelength of a photon. The variables c, e,h,m,r refer to the usual physical constants. I = e B ohr a 2 4 e =2h is the ionization p otential of hydrogen atom isotop e a H; D; T ; e and = m m =m + m , m is the mass of an atom. e e a e a a 5 II. Disrete-to-Continuum sp ectrum transition The ideal photo-recombination continuum has a distinct edge corresp on- dent to the capture of zero-energy free electron by an ion into the n quantum pr level of an atom. The longest wavelength of the PR photon is 2 pr n =2ch [n ] =I : 2 pr pr a In the Balmer sp ectrum n = n 2 the photo-recombination edge o c- pr bpr bpr c pr curs at = n 364:6 nm for a deuterium plasma. The statistical bpr uctuations of ionization p otential of an atom [13,14] emb edded in a plasma cause the PR edge broadening. But this broadening is small compared to the shift of PR edge obtained in the high density plasmas [12] and, in the case of the C-Mo d divertor plasma, it is even less than the instrumental broadening. In earlier pap ers [15,7] the D-C transition was treated as a "spurious continuum" which is advanced ab ove the ideal edge, but which is still a sharp step.For instance, the Inglis-Teller mo del [15] combined all the lines, some of whose Stark widths exceeded the spacing b etween the lines, and considered their union as suchanadvanced "spurious continuum". In practice, since any sp ectroscopic instrument cannot distinguish among the continuum and broadened overlapping lines, such a mo del gives the crude estimate for the sl discrete series limit . The simpli ed analysis of Stark broadening [7] page 125 resulted in the following formulae for the series limit sl pr n =2ch=e ; 3 pr 2=15 pr 2 2 3 where e = I n n and n 0:5N r . a e pr B ohr 6 The b est explanation for the particular b ehavior of sp ectra near the PR edge observed in many lab oratory plasmas see the sp ectra presented in [12] and in literature cited therein is given by the theory which considers the merging of the discrete lines and the continuum as a smooth discrete-to- continuum sp ectrum transition. Tointro duce the smo oth D-C transition and b e close to the divertor plasma conditions, we place in Fig.
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