DPh-PFC-SCP EUR-CEA-FC-853
IONIZATION EQUILIBRIUM AND RADIATION COOLING OF A HIGH TEMPERATURE PLASMA
C. BRETON C, DE.MICHELIS M, MATTIOLI
December 1978
\I [)[ PHYSIUUf [)U PLASMA LA FUSION OONTKOL.FiF.. IONIZATION EQUILIBRIUM AND RADIATIVE
COOLING OF A HIGH TEMPERATURE PLASMA
C. BRETON, C. PE MICHELIS, H. MATTI0LI
ABSTRACT
The results of calculjtions of the ionization equilibriui u.d of the rate of radiative cooling of a high temperature plasmn are presen ted as a function of the electron temperature from a few eV up to some tens of keV. The most important elements detected in the Tokamak plasmas (0,N,C,Fe and Mo) are considered.
I I 1. INTRODUCTION
Recent measurements on high temperature Tokamak plasmas have shown that they are polluted by both light and heavy elements coming from the walls and from the limiter^ . For the electron temperature existing in
the plasma center (^ 1-2 keV)f light ions (e.g., oxygen) are completely ionized, whereas heavy ones (e.g., iron or molybdenum) are only partially ionized. However, since the electron temperature decreases towards the plasma border, all the ionization states (from neutral up to the maximum ionization degree reached in the center) exist in a Tokamak plasma. From the experimental results in long duration discharges it has been concluded that impurity ions diffuse to the walls in a high, but up-to-now unknown ionization state and that they recycle into the discharge as neutrals, which are successively ionized during their inward movement perpendicularly to the magnetic field lines. Energy is then lost to ionize these ions and to heat the produced electrons.
In this report the recycling processes will not be considered, and we will limit ourselves to the evaluation of the ionization equilibrium at steady state, which is attained only in the hot central plasma. These calcu lations are, however, useful for lower temperatures, since they allow to com pare the experimental radial ion distributions with the ones foreseen >y the attainment of the ionization equilibrium.
The ionization equilibrium of most of the elements up to nickel has been computed by a large number of astrophysicists in the last twenty years ; however, the necessity to include dielectronic recombination has been recogni zed only about ten years ago. The most recent and extended results are given in ; elements heavier than nickel have been considered in , but dielec tronic recombination has been neglected. The radiation cooling of these plasmas has also been evaluated
In this report we shall consider oxygen, nitrogen, carbon, iron, and molybdenum, which are the most important impurities detected in Tokamak plasmas.
In section 2,a the rate coefficients needed for the calculations are discussed and tables of the considered emission lines are given. A great amount of data is available for the light elements, and there is no large difference between the different authors. Enough data exist also for iron, as a consequence of the fact that solar corona iron emission is important (11 1') and that its emission has been calculated ; for molybdenum, on the contrary, the available data are very scarce. In section 2.b the formulae for the different losses are given explicitly. In section 3 the fractional abundances and the radiated powers are evaluated as a function of the elec
tron temperature Te.
2. THEORETICAL DATA
2.a. Rate_ccefficients_and_Hne_wavelengths
To evaluate the ionization state of impurities and the associated losses, ionization, recombination, and excitation rate coefficients are needed. For Tokamak plasmas, in ordei to calculate the excited state population, the sim ple coronal model is sufficient : excitation and ionization are due to electron collisions on the ground state, de-excitation is only radiative, whereas both radiative and dielectronic recombination are included.
For the ionization rate coefficient S„ of an ion of charge Z we use the following formula proposed by LOTZ
7 N a.r. S = 6.7 x ,o' I _i^i™ ù i=l TiU (I)
1 "^Tr—- Ï-7T-TT7 V-T-+Ci>)
3 S„ is in cm /sec, T is the electron temperature in eV, I„- is the ionization energy, in eV, of electrons in the i-th subshell. of the ion 7, C is the number of equivalent electrons in this subshell ; a-, b., c. -14 2 L are constants (for highly ionized ions LOTZ proposes a. = 4.5x10 cm eV^, b. = c^ = 0), E (X) is the exponential integral function. N is the number of subshells,contributing to the ionization (N = 1 for H and He-like ions, N = 2 for the isoelectronic sequences from Li to Ne ; from the Na-like sequence we took N = 3 as suggested by LOTZ). The subshell binding energies up to Zn have also been calculated by LOTZ .
For Mo the ionization energies were taken in ref. (14) ; for the inner subshells we took the ionization potentials of the first electron of the inner subshell when it becomes the external one. According to KUNZE* * ' experimental results for Li- and Be-like light ions and for some low ionization potential Fe ions are on the average 60% of the values given by formula (1). However, it must be observed that the accuracy of the experimental measurements is estimated to be a factor of 1.5 at best.
The radiative recombination rate coefficient a 7 of an ion of charge Z can (17) can be calculated by modifying the well-known formula for the H-like ions
a- - 2.6 x I0""4 (a, + a,) (2) arZ *'" " '" wl
where
z2( Jy/2 i hçL- >'"» VWV (3a) e n e
2 2 f *** IH3/2[Z IH/(n + v) Te] l\ I ô (sr-) e E ( y—) (3b) V"! (n+v) e (n + v) T
2z2 ),/2 (Z ou is in cm 3//sec , I„ • 13.6 eV is the ionization potential of hydrogen, I-, the ionization potential of the ion after recombination : the functions viously defined. a? represents the recombination on the excited levels consi dered as hydrogenic, a, is the contribution from the valence shell (of prin cipal quantum number n) which is partially filled. It is supposed to have an effective quantum number n I„/I__. ; the statistical weight factor, which is 2/n for hydrogen-like ions;is now y/n^,where p is the number of empty places 2 in the valence shell (there are 2n places in an empty shell). In formula (3) the free-bound Gaunt factor has been taken equal to 1. The dielectronic recombination rate coefficient a,„ has been calculated by several authors ; the proposed values can differ considerably at the electron temperature of maximum abundance. The influence of n on et, has been considered f / \ {i fi\ eoo only in and in . Neglecting it, u,7 can be expressed in the following (19) aL way B(Z) I A(Z,j) e ùi e W T372 the sum being over the resonance levels j of the recorabining ion of charge Z in order to obtain the total recombination rate : E_ . is the energy of the resonance transition j , and B(Z) and A(Z,j) are, for a given atomic species, functions of the charge Z and of the excited levci j. For light ions it is suf ficlenficient to consider only one resonant transition ; according to formula (4) can be written in the following form 10 3 2 1 8 ,dZ - l^uT *,^) ' ,"^ " ' (5) e ou is in cm'/aec, T in eV, E_. (in eV) is the excitation energy of the first resonant transition of the ion of charge Z existing before the recombination. M is a coefficient depending on the type of resonance transition (for a tran- sition nJl +• n £ , nJt , M - -^r—T—r» for a transition n il , nJl •*- n I , .or oo 2£ + 1 OÙ o o ' nJL1" ', M -- 2 -m/(2£+l) with £« £ °+ I, N - 2(21 +I)),C i'i a coefficient o o Z which has been evaluated numerically for light ions of the isoelectronic sequences f~ Jm He to Ne and for Fe ions . For iron and molybdenum ions having An = 0 transitions, it is not sufficient to consider only one resonant transition. Indeed, for highly ionized ions, the importance of the un => 1 transitions (as com pared to the An=0ones) increases with the charge Z. Since not all the required coefficients C„ have been calculated for Fe and they ?.re not at all known for (19) Mo, we used for B(Z) and A(Z,j) the expressions proprsed by BURGESS 2 /2(Z 0 B(Z) - 6.5x,0-'° ' * W2 (6a) A(Z,j) = ^ 2J _ (6b) 1 + 0.105 x„. + 0.015 xZ. Zj Zj where f7 . is the absorption oscillator strength of the resonant transition j of the ion 2 and x„. = E„./(Z+1)I„. In the calculations for Fe and Mo, we took irto account two resonance tran sitions, except for H ,He and Ne-like ions, where "".he first transition is a An = 1 one. For the excitation rate coefficients of the light ions the most extended calculations can be found in the book by VAINSHTEIN, SOBELMAN, and YUK0Vk , They calculate the excitation cross sections and the exictation rate coefficients by means of the Coulomb-Born exchange II approximation. The results are expressed analytically as a function of two parameters (A and x f°r the excitation rate coefficients) obtained by the method of the least squares from the results of the numerical calculations. The proposed formula for the excitation rate coeffi cient Q is « - ,0"8 <ï->3/2 srVr <^> m o o Q is in cm /sec, AE - E - E is the excitation energy in eV (E and E being respectively the ionization energies of the lower and upper levels). & - AE/T , q is a coefficient which depends m the azimuthal quantum numbers i and I of the electron before and after the transition (for a transition without change NN N-l of spin AS •- 0 of the type S,H •*••* l^~*, I t £& , , q q «• N N) , and G(8) is a function given by the following expressions in the case of ions G(B) - A(jj+ '>. *^P for AS - 0 transitions (8a) P + X 3/2 G(B) = AA for AS = I transitions (8b) P * X In (21) curves or tables are given for A and x f°r tne most usual transitions starting from the principal quantum numbers n = 1 and n=2 for the isoelectronic sequences from H to Ne. Table I shows the oxygen transitions included in the calculations described in section 3 , together with the excitation energies AE, the wavelengths (22) X (taken fronT ), and the parameters B = Aq/(2£ +1) and x • For C and N the same transitions were considered. In the calculations all the terms belonging to a single electronic configuration are grouped together. (21) Since the curves of cannot be extended up to iron and molybdenum > we used for Q in this case the following formula based on the Bethe-Born approxima- (23) tion for optically allowed transitions 5 f & Q = J.6K10- **)f e" (9) AE^ where Q and T are in cm /sac and in eV, AE is the excitation energy i\t ev, 3 = AE/T , f the absorption oscillator strength and g(B) is the average effec tive Gaunt factor. For g($) we took the following interpolation formula proposed by MEWE(24) i(e) - A + (BB - Ce2 + D) e^CB) + C$ (10) where A,B,C,D are adjustable parameters. This formula can include also optically forbidded monopole or quadrupole transitions (e.g., for H-like v'.ons the Is •> ns or Is •+ nd transitions, respectively) and spin-exchange transitions (e.g., the singlet-triplet transitions in He-like ions). In these cases f in (9) assumes the J;-value of the allowed transition to the level with the same principal quantum -number. This means, for example, that for the transitions Is +• ns and Is •* nd 2 I 3 in the H sequence the f-value of la •* np is taken, for la S -*• Is 2s S in 2 I 1 the He sequence that of Is S -+ Is 2p P, Table 2 shows the iron transitions included in the calculations described in section 3 , together with the wavelengths X, the excitation energies AE, and the f-values. For the parameters A,B,C, and D we follow MEWE , who gives these values for several transitions in the H, He, Li and Ne sequences by fitting the function g(B) to the available theoretical and experimental data. For other ion sequences, with an accuracy to within a factor of three, h-2 proposes A=0.15 (An * 0) or A « 0.6 (An " 0), B = C = 0, D - 0.28 for allowed transitions, A = 0.15, B = C - D « 0 for forbidden monopole or quadrupole transitions, and A=B=D=0, C = 0.1 for spin-exchange transitions. Table 3 shows the molybdenum transition included in the calculations, to gether with the wavelengths X , the excitation energies AE and the f-values. The isoelectronic sequences and the transitions considered are the same as for iron; HI ) the wavelengths A were taken from the most recent calculations , otherwise they were obtained by extrapolation. The absorption oscillation strengths f were taken, if available, in (29 ) or in (32), otherwise we used the systematic trends of (29) f m the isoelectronic sequences as a function of ';he nuclear charge ZN, starting from the values for iron. Therefore, for An = 0 transitions, we used : f ^ f,/Z ; whereas, for An ^ 0 transition i a, f + f1/Z„. In this second case, IN O 1 N ' we have assumed that f,/Z„ < f and have tak-an for Mo the same values as for Fe (this is justified by the fact that in all cases considered inv the variations of f between Fe and Mo are smaller than 50%). 2.b. Radiation_losses. In the radiation losses we include line,bremsstrahlung and recombination radiations. If n2 is the density of the ion of charge Z, the power density ?p(W/cm ) - 7 emitted as line radiation by the ion Z is 19 Pj, « l.6xio" nenz J Q^ (II) where the summation over j is over all the transitions of the ion Z included in the tables. It is assumed, as already said, that lines are emitted by radia tive deexcitation of the upper levels of the transitions excited from the ground state. For bremsstrahlung (free-free) radiation due to collisions of electrons with ions of charge Z we take the usual formula with the Gaunt factor equal 3 to one. The power density P. (W/cm ) 1B 32 Z T 2 (12) Pb > I.53XIO- Vz ff£ y Z -f is the effective charge for bremsstrahlung emission ; it is comprised between the electric charge Z and the nuclear charge Z , For heavy ions incom- . (33) pletely stripped, Z f, can be quite different from Z, as discussed in * , and this has been taken into account. In the radiative recombination processes (free-bound radiation), if the capture takes place on an excited level, the ion decays to the ground level by radiative cascade ; then the total ionization energy I_ , is emitted. The ave rage energy of the captured electron <£-> is lower than the average electron kinetic energy, since the radiative capture cross section decreases towards high electron energies. 9 Pr = ..6 x HT' nenzarZ(Iz., + In the dielectronic recombination processes the emitted energy is I., . + E_ i (the incident electron excites the resonance transition E„. of L~\ Là ij the ion Z, it is then captured in a high principal quantum number level with excitation energy = I ., and the doubly excited ion is stabilized by radiative 3 emission taking it into the ground state). Then the power density V,(W/cm ) lost by dielectronic recombination is ~E /T 19 A z e zj e + E } pd - i.exio" vz^fr I < >J> 3. NUMERICAL RESULTS 3.a. Ionizacion_eguilibrium The fractional abundances f„ • n„/ j n_ - n-/n. are calculated in the Z Z k Z o imp. standard way by starting from the balance equation (15) They depend on the electron temperature T only, since cc,_ has been taken independent of n . The results obtained are shown in figure \ for 0, N,and C, in figure 2 for 24+ Fe and in figure 3 for Mo. For this element Mo (an Ar-like ion) has been ta ken as the initial ion, since not enough data were available for the less io nized ions. For Fe and Mo the dielectronic recombination rate coefficients were calculated including for each ion the first two transitions of tables 2 and 3, except for the H, He and Na-like ions, where, as already said, only the first transition was considered. The comparison with the results previously reported is shown in figure 4 for two 0 ions and two Fe ions. Curves 1 refer to the calculations presented in this report, curves 2,3 and 6 have been taken respectively in the papers by (2) JORDAN (neglecting the reduction of a,? due to the exclusion of levels above the collision limit), by SUMMERS^ (for n ^ 1012cm~3) and by MERTS and al.*10*. Curves 4 and 5 have been obtained by taking the ionization rate coefficients S7 . (13) . in ; in curves 4 the recombination rate coefficients oe are those tabulated 7 13 -3 by SUMMERS and extrapolated to high charges Z for n ^5.x10 cm , in curves 5 the a7 coefficients are those utilized in , where equation (5> was used for 22+ <* . The agreement is satisfactory, except for Fe . In this case curve 5 is displaced towards lower electron temperatures (as already pointed out, this is due to the fact that only one resonant transition was considered in ). Curve 4 , on the contrary, is displaced towards higher electron temperatures (this means that the extrapolation to high charges Z of the tables of gives va lues of ou too high).No comparison with other calculations is possible for Mo? since no results have been reported up to now. - 9 - 3.b. ggdiatign_losses. The radiation losses are calculated as a function of T using formulae 3 e (II) to (14). In figure 5 the ratios P/n n. in W cm are plotted for oxygen *" e imp as a function of the electron temperature (P • P. + Pj, + P + P, is the total radiation loss per cm ). The high values of P. for T < 50 eV are associated with the excitation of lines of the oxygen ions up to OVI. The minimum at ^ 80 eV is due to the fact that then most of the ions are in the 0 state (He- like ions), which cannot be excited at that temperature, P. has the same shape as Pp since dielectronic recombination starts from the electron collision excita tion of the recombining ion. When T is larger than ^ 300 eV oxygen is prac- -3/2 tically completely stripped and line radiation decreases rapidly (^ T ) ; -1/2 e P also decreases but more slowly (M ' ) and at T ^ 3 I_„ ^2.5 keV r ' e e OVIITTIr is lower than P, , which becomes then the dominating loss. In figure 6 the same curves are given for carbon and nitrogen. They are very similar to those for oxygen, all the peaks being however slightly displaced towards lower temperatures. The P curves of figures 5 and 6 agree very well with the corresponding ones given in . In figure 7 the same curves are given for iron. These curves have the same shape as those for oxygen, but they are displaced towards higher temperatures. P is a decreasing function of T above 100 eV, and it is between one and two orders of magnitude higher than the value for a light impurity (like oxygen) at the same electron temperature. In the region between I keV and 10 keV, where MERTS et al, have also calculated the radiation losses for iron, the agree ment between the two calculations is very good. Finally in figure 8 the case of molybdenum is represented. Also in this case P is a decreasing function of T ; in the 1-2 keV region the values for t e Mo are about 3 to 4 times higher than those for Fe. The curves of figures 7 and 8 agree to much better than 50£ with the cal- (9) culations of , where radiation losses were, evaluated for Fe and Mo between 10 and 40 keV, but neglecting dielectronic recombination (which is negligible for Fe above 10 keV and for Mo only above 20 keV). 4. CONCLUSION All the results presented in this report are based on theoretical formulae. The comparison of these formulae with a few experimental results has been revie wed in and inv . Only Light ions (C, N, 0, F and Ne) have been studied (a few results have been presented recently in concerning low ionization Fe icns) ; there is agreement between theory and experiment, if we consider that both the calculations and the measurements are not accurate to better than a factor of two. The only problem with light ions concerns the influence of the electron density on the dielectronic recombination, since levels higher than the collision limit do not contribute to it ; but figure 4 shows that this is not very dramatic (curves 2 have been obtained neglecting the reduction of 12 -3 arfZ and curves 3 considering it for n ^10 cm ). The validity of all these theoretical formulae for the ionization and recombination rate coefficients when applied to heavy ions is not evident. How ever, we now have aome confidence in their validity, since the results of the ionization equilibrium calculations for Mo are supported by TFR Tokamak expe riments( '. TABLE I Isoel Transitions 6E Ion scq. Configurations Terms (eV) A) B X 0 VIII H Is - 2s 2S -2S 650 19 5 0.84 Is - 2p 2S -2? t50 19 20 0.26 Is - 3s 2S-2S 7T5 16 4 O.06 Is - 3p 2S - 2P 775 16 16 0.30 Is - 3d 2S - 2D 775 16 1.25 0.3Ï Is - 4s 2S - 2S 315 15.2 '( 0.87 o p Is - 4p "S - dF 315 15.2 14.8 0.31 P P Is - 4d S - dD 815 15.2 l.ti 0.36 2 0 VII He Is - Is 2G !S - !S 568 21.8 11 0.83 2 IS - Is 2p 1S - h 574 21.C 'to 0.21 1B" - In Jo h - h 660 18.8 9.2 0.8; l IB2 - Is 3p s - h 665 18.6 3 '?. 5 0.25 is2 - Is 3d ]S - ]D 66* 18.6 2.4 o.3'i ; Is2 - Is as s - -*s 56). 22 ' 2.4 0.33 l as2 - is 2p s-h 568 21.8 15 0.625 p 3 IS - IS ?B h - S 660 18.8 2.5 0,40 3 is2 - is 3r *s - r 665 18.6 16.5 0.70 is" - is "Jd *S - 3E 667 18.5 3.9 0.95 C VI Li 2s - 2p 2S - 2" 12 103* 5 0.75 2s - 3s 2S - \" 79.1 156 4.75 0.86 2 2 2s - 3p 82.5 150 2.8 0.05 s - r ?• 2 2s - 3d 'S - SD 83.5 148 9.6 0.63 0 V We 2s' - 2s 2p XS - *F 19.7 63c 13 C.65 2s2 - 2s 3s XS - *S 69 . 180 9.2 0.84 P 2s - 2s Jp *S - !p /2 172 4.5 0.015 p l r 2s' - 2s 3d !S - 'D 7 -4 165 IS 0.6 2s~ - 2s 2p ^•s - -^p ;.o 1218 0.6 0.1 x 3 as1' - 2s 3s s - s 68 1B2 0.75 0.4 3 2s" - 2s 3p -s - 5P 72.5 170 1.5 0.37 2s2 - 2s Jd 166 7 0.56 !S -\ 7».3 0 IV B 2s" 2p - 2s 2p2 2P - 2P,2S,2D 19 650 13 0.6 G III C 2s" 2p - 2s 2D-5 5P - JP,-S,^D 18.5 -fiso 13 0.5 o i; N 2s2 2p3 - 2s 2p* "a - *P 15 833 12 0.4 - 13 - TABU 1 , „ U»ol. Tr*n»ition» ÛE * Io" S.,. configurât ion. T.™. Mo»CV Ar 3p6 - 3pS 3d 's - lF l$l 77 7.34 ttoJCXVI Cl 3»* 3pJ-ï» 3p* S - 2S 88 1*1 0.105 3pS-3p* VI S»-2D,2P,25 I8D «9 I.7S 5 3p -3» 3P - 3p3 3d ll» " 'o.'r *s - *p 3pJ - 3pZ 3d K - ', 3p3 - 3p2 «d j ,S " J 660 18.5 0.9* 1 t - *V 3lï3pï-3i3pJ 3P-3r,3S,5D B6 14? 0.375 3p: - Jp 3d ( .'' " ." lîi 79 O.JJ 3p! - 3p 4d | ,r " ." ABÎ 17.8 O.JA 3iîîp-l»3p1 1r-1t,îs,2D no isi o.** )p - 3d r- 'D il* IOU o,il ]p - *d Jr-'u 771 1b 0,77 0.37 0.3Î 5 ! 2 lp 3^ - 2P 3i S - *P Ï^OO ïp6 - 2pS 3 2p - 2p* 3d 's - 3D 2603 îp6 - 2p5 *d 's - 'p J3S0 S S 2p - 2p 4d 'S . '0 iJi0 2i îp - 7» 2p Jp S - 'p 280O 6 3 2" ïp - 2a ïp 3p 's - p Z800 1 2 2 î. V - î. 2P" P . S 3JS 7» 2pS - 2»22p*îd 2F - V2P 2600 S 2 2 TV 2p - 2. 2p*3, P - îr,îD î3iD 1 3 7» îp" - 2* îp p - ^p ;7J ΫV - î.J2p33d 3P - Vl> 2750 KoXXXVI 3 4 4 2« Jp - î» 2p* S - P 2S0 2 2p3 - 2»22p2ld 6S - *P 290Q 1 2 TtoXXXVIl c 2. 1? - I, Ip3 2 2 2 3 3 T.» 2P - 2« 2p 3d P - h, ? 1 2 MoXm-Ul B 2» ÎP - J, 2p *V . 2p 2£ 2, 2 2 2. 2p - 2, M 2, . V 2 2 î 3 2 I. Î. 7P-I->.V P- p, n 3300 1300 3300 17300 M mo 3250 3250 1730Q 17400 17400 17400 17400 20600 18000 IBOOO 21400 - 14 - REFERENCES (la) - BIU3TZ H., DIMOCK D.L., GREENBESGER A., HINNOV E., MESERVEY E.B., STODIEK W., VON GOBLER S., in Plasma Physics and Ccr.trolled Nuclear Fusion Research (Pre:. 5 Int. Conr. Tokyo, 1974) ± (IAEA, Vienna), 55 (1975). (lb) - BOL K,, CECCHI J.L., DAUGHNEY C.C., DE MARCO F., ELLIS R.A. Jr., EUBANK H.P., HSUAN H., MAZZUCATO E., SMITH R.R., in Plasma Physics and Controlled Nuclear Fusion Research ("roc. 5 Int. Conf. Tokyo, 1974) J_ (IAEA.Vienna), 83 (1975). 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Fractional abundances f7 • n_/ ![ n7 of molybdenum ions as a function Z 24+ of the electron temperature T (eV) , Mo is assumed to be the initial Fig- 4. Comparison of different calculations of f_ as a function of T for 0 , 0 , Fe , and Fe . Curves I refer to the calculations des cribed in this report ; curves 2 were taken from (2) with n ^ 0 ; 12-3 e curves 3 were taken from (4) with n ^ 10 cm ; curves 4 were obtai ned by taking S, from (13) and a from the extrapolation to high char- 7 13-3 ges Z of the tables of (4) with n ^ 5.10 cm : curves 5 and 6 were e taken, respectively, from (Id) and from (10). Fig. 5. Radiution losses from oxygen at corona equilibrium as a function of the electron temperature T (eV). All powers F are inW/cm ; n is ths elec- -3 e -3 e tron density (cm ) and n. the impurity density (cm ) ; P„;line radiation, P, : bremsstrahlung radiation. P and P, : losses associated D r a with, respectively, radiative and dielectronic recombination events ; Pt ~ P£ + Pb + P + pd:toCal radiated power. Fig. 6. Same as figure 5 for carbon and nitrogen. Fig. 7. Same as figure 5 for iron. Fig. 8. Samt as figure 5 for molybdenum. 1000 10* Te (eV) Fig. 2 Fig. 3 6.5 7 Log10 (Te)Ko 7.5 8 Log (T ) ° Fig. 4 10 e K P/nenimp (Wcm3) 10-25 i 1—r~r 1—n-] 1 1—r~r OXYGEN CORONA EQUiLIBRIUM 10-26 10-27|_ 10-28 10-29 T (eV) Fig. 5 e 3 3 P/ne njmp(Wcm ) P/ne njmD(Wcm ) 10n-2 5 nn 1 r-r-rj 1 TTTT 1—I 10" rTT-|—i 1—rq 1—r—rrf—i—; CARBON NITROGEN CORONA EQUILIBRIUM. CORONA EQUILiBRIUM. 10' û 3 J 10 T leV) 10 Te(eV) e Fig. 6 3 P/n•ee n• 'imimDp (Wcm ) -24 10 IT] I TTT~| I J IRON CORONA EQUILIBRIUM icr25h 10-2 6 10-2 7 10,-2 8 J 1 M I J i I I I i 10' 10J 10* Te(eV) Fig. 7 3 P/ne nMo(Wcm ) r24 10 C I~^T ~i r MOLYBDENUM CORONA EQUILIBRIUM i \ T28| | L 10' J L 10 10' Te (eV)