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X-ray plasma diagnostics
L. Presnyakov, A. Urnov
To cite this version:
L. Presnyakov, A. Urnov. X-ray plasma diagnostics. Journal de Physique Colloques, 1979, 40 (C7), pp.C7-279-C7-288. �10.1051/jphyscol:19797443�. �jpa-00219447�
JOURNAL DE PHYSIQUE Colloque C7, suppliment au no 7, Tome 40, Juillet 1979, page C7-279
X-ray plasma diagnostics
L. P. Presnyakov and A. M. Urnov
P. N. Lebedev Physical Institute, USSR Academy of Sciences, Moscow, USSR
Abstract. - Results and methods are given for the investigation of hot laboratory and astrophysical plasmas parameters in a soft X-ray region 1 = 1-40 A. Line spectra of multiply charged ions are usually studied expe- r~mentally, and relative Intensities of spectral lines are measured. Achievements of modern physics of electron- ion collisions and theoretical spectroscopy make it possible to obtain for transient plasma the electronic tempe- rature, density, ionization stage, and to investigate time and spatial distributions of these parameters.
Introduction. - X-ray spectroscopy of high tem- perature plasmas, as a new direction in plasma physics, has been developed recently by efforts of many scientists in different laboratories. This field deals mainly with line spectra of multiply charged ions in the spectrum region 1-40
A,
and more hard adjacent continuous component is of interest. From physical point of view the X-ray plasma spectroscopy has the following background. In a case of ions with a high charge Z is> 1 any excitation decays mainly due to radiation. Other channels, both colli- sions and autoionization exist being well controlled corrections in comparison with radiative one. It leads to simple and understandable connections bet- ween spectral line intensities and mechanism of spectra formation. Modern physics of electronic and atomic collisions provides sufficient and accurate methods for calculations of cross sections and rate coefficients involving multiply charged ions. Theore- tical spectroscopy has also reliable methods for classification and calculations of spectral lines in the X-ray region. Simultaneously, experimental tech- nique has been developed with appropriate spectral, time and spatial resolution. It is worth noting that in the most of important cases low density astro- physical plasmas (electron density N, 5 1014 ~ m - ~ ) and laboratory plasmas (N, 5 1020-1023 cmP3) are optically thin for the X-ray radiation. It helps much for interpretation of experimental results, and theo- retical analysis.Therefore, the X-ray plasma spectroscopy contains three important parts : new sources and measurement methods of highly charged ion spectral data
+
physics of electronic and atomic collisions+
theoretical spec- troscopy of ions. For plasma physics the X-ray spectroscopy provides new and effective methods of contactless plasma diagnostics. It is essential that X-ray spectroscopy methods are equally valid for investigation both of astrophysical (active regions and Solar flares) and laboratory plasmas. At the present time this field has many hundreds of originalpapers and just few review publications. Among the latter papers [l-61 contain some systematization and extended list of references to earlier works.
1. Plasma parameters obtained from X-ray spectra.
- Multiply charged heavy ions are small impurities (much less than 1
%)
in astrophysical plasmas and in stationary laboratory sources (Tokamak, Stella- rator, etc.). Inertial plasmas produced by laser or electronic beams, plasmas of exploding wires and low-inductance sparks may be chemically homoge- neous or consist of few heavy elements. X-ray spec- troscopy provides universal diagnostic methods valid for all the cases mentioned. It is important to under- line that plasma parameters can be obtained with the help of relative intensities of spectral lines, and one can avoid absolute flux calibration. Still absolute measurements provide the additional information (emission measure, etc.). Plasma parameters and types of spectral line used for the determination of them are listed in table I.Table I.
Plasma parameter Relative intensities
- -
Electronic tempera-
i d =
<
= j l ( T ) , all ionsture T YR
Ionization stage ; ef- ipn =
= j2(Tz), all ions fective ionization IR
temperature
Tz fRIH]/lRIHe] = j;(T,), H-like and He- like ions
Electronic density I
a = G - I = 2 = fS(Ne), He-like ions
Ne IT
x = Is(I)/l,(Il) = j,(N,), all ions 1(2p112 -t Is'
= jS(Ne), H-like ions
'
= 1(2~3/2 * 1?'1:2)Energy distribution lK=/lR of electrons ;
Presence of electro- IK,/IR H- and He-like ions
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19797443
C7-280 L. P. PRESNYAKOV A N D A. M. URNOV
Here I, are the intensities of the resonance lines, and I, are intensities of the intercombination lines in He-like ions. For the satellite line intensities I t and 1:"" mean satellites produced by the dielectronic recombination and the direct electron impact inner shell excitation respectively. The lines, K, and Kp, are usual characteristic lines produced by ions with K-shell vacancies. Determination of Ti with the help of the Doppler shift is well known in classical spectroscopy (spectroscopy of low-temperature plas- mas). Some methods of density diagnostics, for example, intercombination-to-resonance line ratio for He-like ions, a, take also their origin in classical spectroscopy. All other have been developed during the last decade simultaneously with the development of the X-ray spectroscopy.
2. Satellites of spectral lines. - General spectral structure of a multiply charged ion resembles a spectrum of a neutral atom of the same isoelectronic series. Ions with a charge Z % 1 contain bright satellite lines which arise due to radiative decay of doubly-excited autoionization states of ions. Consider usual (one-electron) radiative transition, y, -+ yo, in an ion with a charge Z, where y, denotes the set of quantum number of excited states. Radiative decay of autoionizing state y, nl (nl are the additional electron quantum numbers) in an ion with charge Z - 1, y , nl + yo nl, gives a satellite line to the transition y, -t yo. For large Z the wavelength difference bet- ween the parent line and its satellite is very small
Radiative transitions from doubly-excited states in He-like ions, 2pnl -t lsnl, give satellites to the reso- nance line of H-like ion, 2p -+ 1s. The resonance line of He-like ion, Is 2p('P) + 1 s2('S), has satellites from Li-like ions (transitions 1 s 2pnl -t 1 s2 nl), Be- like ions, B-like ions and so on. One may consider the K,-lines as satellites to the resonance lines of He-like ions radiated from ions with filled L-shells.
With n = 2 for the additional electron the satellites are well separated from the parent line and have red shift; n = 3 satellites are much closer and may be located on both red and blue sides of the parent line.
Satellites with n 2 4 are usually located within the Doppler width of the parent line. The first observa- tions and interpretation of weak satellite lines have been published by Edlkn and Tyren in 1939 [7] for the case of .ions with small charge (see also [8]).
Modern development of X-ray spectroscopy and diagnostics has begun about 10 years ago when hot plasma sources (both laboratory and astrophysical) became a subject of investigation [9-171. For highly charged ions with Z > 10 satellite lines have inten-
sities comparable with the resonance line intensity.
Diagnostics requires good spectral resolution A/AL w lo4 for 2 = 1 - 1 0 A .
At present we have theoretical calculations [2, 18-22, 241 and experimental measurements [3, 23, 241, which are in reasonable agreement 42, 23-24] with them.
3. Mechanisms of spectra excitation. - Ionic X-ray spectral lines are formed mainly due to electron-ion collisions. In hot plasmas collisions between ions are less important because of the Coulomb repulsion.
They give some contribution to collisional transitions within limited groups of neighbouring ionic levels.
At present time the influence of charge transfer process is studied insufficiently, although under certain circumstances they may be important for excitation of lines belonging to higher members of the resonance series [25]. Binary electron-ion colli- sions lead to the following processes : i) impact excitation and ionization, ii) dielectronic recombi- nation, iii) radiative recombination. Three-body col- lisions give smaller contribution to X-ray spectra excitation even in the case of superdense laser- produced plasmas.
i) Direct impact excitation of an outer ionic shell produce usual (one-electron) excited states :
e
+
B,(Yo> + e+
BXy,) -, e+
Bz(yo)+
h a . (1) Here hw is the energy of a quantum after radiative decay. Impact ionization of the K-shell in Li-like ions leads to excited He-like ions. Impact inner shell excitation gives autoionization states of ions B:?, with two (or more) excited electrons :e
+
Bz-,(yo nl) + e+
B;?,(y, nl).
(2) ii) Dielectronic recombination is the inverse pro- cess of autoionization :e
+
B,(Yo> @ BZTl(y, nl).
(3) The intensity of the satellite line depends on the branching ratio for the decay of by radiation (rate, A) and autoionization (rate,r )
As a rule, A G
r
for Z < 15 and A 2r
for Z > 15.iii) Radiative recombination leads to population of usual states (ground and excited) of ions and gives some contribution to continuous spectrum
X-RAY PLASMA DIAGNOSTICS C7-381
The major part of information on excitation and decay rate coefficients is provided by theoretical calculations. The experimental data, with very few exceptions, are not available now, whereas the theoretical methods are developed with sufficient accuracy. In a case of highly charged ion, Z % 1, we have the natural small parameter, Z - ' , which gives a tool for estimation of calculation accuracy.
Consider a physical picture of an electron-ion collision :
/
B*(Y 1)+
e' ( 6 4 e+
BZ(Y0) -+ B,*_*,(Y nl) + BZ(Y ,)+
e' (6b)\ B , - ,
+
ho. (64The process (6a) means potential (direct and exchange) excitation; (6b) denotes resonance excitation : elec- tron capture into doubly excited states with the principal quantum number n % 1 and autoionization decay; (6c) represents radiative decay of the reso- nances (radiative capture). For Z % 1 the compli- cated collision problem can be solved in an explicit analytic form [2, 261. The results show that the resonance excitation is important when the excitation threshold has a value few times less than the one electron ionization threshold. In this case the effect of the electron exchange has small influence to the potential part of a cross section (for example, excita- tion of Li- and Be-like ions from the ground state).
If the excitation threshold is comparable with the ionization one the exchange effect is important [27], and resonance excitation is small. Influence of both effects is shown in figure 1. In the case of electric dipole transitions with small energy difference AE, between the initial and final levels these effects do not contribute to excitation rates if AE
<
kT, where T is the electron temperature. For this specific case simplified calculations can be done in a pure analytic form (see, for example, [6] and [28]). Extended cal- culations for the wavelengthsA,
and for the rate coefficients (radiation A, autoionizationr ,
and exci- tation C =<
ua )) are given in papers [2, 6, 18-22, 24, 281.4. Physical principles of transient plasma X-ray diagnostics. - We start our analysis with the Maxwell distribution for plasma electrons and the effective electron temperature T. If electrons have some noti- ceable deviation from Maxwell distribution (for example, electronic beams) it can be also noticed and investigated using spectroscopic methods. In transient plasmas the ionization stage (distribution of ions over different ionic charges) is determined by the electron temperature, electron density N,, and the initiallboundary conditions. The ionization stage can be obtained from the ratio (Nz-,IN,), where N, is the ion concentration with the charge 2. Fol- lowing to Gabriel [18] we use the ionization para- meter T, :
Fig. 1. - Excitation cross sections for electron-ion collisions.
a) Transitions IsZ -t Is 2p in 0 V11 ion [27] : 1) for 2 'P level with exchange ; 2) the same without exchange; 3) for 2 3P level with exchange; 4) the sum of cross sections 1 and 3. b) Transi- tion ls2 2p -t ls2 3s in 0 VI ion [26] : dashed curve is the potential excitation, solid curve.is the total (potential
+
resonance) cross section.defined as the steady-state temperature for the given (experimentally observed) ratio (Nz- ,IN,). Then, T, = Tcorresponds to the steady state, T, < Tmeans supercooled plasma, and T, > T overheated. If the electron temperature remains constant, T, goes to T, which means recombination of overheated plasmas and ionization of supercooled plasmas.
Strictly speaking, all the line intensities depend on T, N,, and T,. The problem lies in the selection of the spectral lines which are the most sensitive to one of the chosen plasma parameters. The great part of
C7-282 L. P. PRESNYAKOV A N D A. M. URNOV
diagnostics based on relative intensity measurements requires the knowledge of the excitation and relaxa- tion rate coefficients.
4 . 1 ELECTRON TEMPERATURE T. - The resonance line intensity of the ion with the charge Z is equal to
where N, and N, are the ion and electron densities, CR is the effective excitation rate for the resonance line, AR is the radiative decay probability, QR is the collision relaxation rate. Since in all the cases A R B Q R ,
If a doubly excited state of the ion B,-, is populated by the dielectronic recombination (3) exclusively the related satellite line intensity is equal to
where a, is the Bohr radius, go and g, are the statis- tical weights of the ground state of B,, yo, and of the autoionization level in B,-,, y, nl, respectively, and E, = E(y nl) - E(yo).
The relative satellite intensity has well-defined temperature dependence
I," A - T
i,d =
-
= constantIR ~ + c A '
In practice the effective excitation rate, CR(T), has also some dependence of the electron density N,, due to cascading processes, which is usually taken into consideration. For more details see, for example, [2, 6, 18-19, 281.
4 . 2 IONIZATION STAGE T,. - Inner shell excita- tion (3) leads to the satellite intensity
where C, is the inner shell electron excitation rate.
Since the ratio (C,/C,) practically does not depend on the electron temperature, the relative intensity
Nz- 1
= constant
-
= f2(Tz) (1 3) Nzcan be used for the measurements of the ionization parameter T, [2, 18-1 91.
For the same purpose can be used the resonance line intensity ratio for the He-like ions and H-like ions
It is worth noting that some satellites can be mainly excited by dielectronic recombination, and the others by inner shell excitation. For the most of them the both processes lead to comparable contributions.
Relevant selection rules are given in [2, 19, 21, 241.
For this reason determination of T and Tz has to be done simultaneously.
4 . 3 ELECTRON DENSITY N,. - In the limiting cases of both the coronal model and Boltzmann equili- brium relative line intensities do not depend on the electron temperature. For electron density measure- ments one has to choose the spectral lines sensitive to the density, to solve relevant balance equations, and to compare experimental results with the calcula- tions. This program has its origin in the classical spectroscopy. New element, consists in using the satellite lines. He-like ions. The resonance and inter- combination lines.
For He-like ions the probability of the radiative decay of the 1s ~ P ( ~ P , ) level is several orders of magnitude less than the decay probability of the Is 2p('P,) level, whereas their excitation cross-sec- tions have the same order of magnitude (Fig. la).
As was pointed out by Edlbn [29] the intensity ratio of the resonance line to the intercombination line
is a function of a plasma electron density, which is quite useful in its determination [30]. Recent calcula- tions (see Fig. 2) [5, 6, 27, 28, 311 show that in the region of N, 4 101° ~ m - ~ , cr is independent of the N, (coronal model). In the region
collision relaxation of all the 2 3L, levels leads to their radiative decay via the 2 3Pl level, and a goes down.
For loi6 < N , < 1019 cnC3 the ratio a is determined by the ratio of the total excitation rates of the singlet to triplet groups of the n = 2 levels, and a is close to 1.
In the region N, > 1019 cm-3 radiative decay of triplets is suppressed by collisions, and a increases proportionally to N,, which is convenient for density diagnostics of superdense plasmas (Fig. 2). Calcula- tions and comparison with the experimental results [32]
are given assuming T, z T. Results for supercooled and over-heated plasmas [31] (with T, # T) give some corrections for the ratio a within 25
%.
X-RAY PLASMA DIAGNOSTICS
Fig. 2. - a ) The dependence cc(N,) for Mg X I [5, 331. b) The b) dependence cc(N,) in dense plasmas. Solid curves : calculations [28].
Crosses : experimental data [32]. Fig. 3. - a ) The dependence x ( N J for Mg XI [5]. b) The depen- dence P(N,) for M g XI1 [28].
H-like ions. The resonance line and related satel- lites.
The resonance line has two groups of density sensitive satellites
(I) 2s 2p 3P0,,,2 -+ 1s 2s 3S1,
(11) 2p2 3P2 -+ 1s 2p 3P1,2, 2p2 3P1 --, 1s 2p 3P0,1, which are useful for diagnostic purposes [28, 331.
In the coronal limit the 2s 2p configuration is popu- lated by the dielectronic recombination, whereas the population of the 2p2 configuration is small. With density increasing the collisions lead to the Boltzmann distribution within the triplet system, and the ratio of the line intensities of groups (I) and (II),
increases as it is shown in figure 3a. It is worth noting that the distribution between the triplet and singlet level systems remains still close to the coronal distri- bution in the region of electron densities
Ne = 1020-1023 ~ r n - ~ for Z = 10-15.
Similar situation takes place for the ratio of inten- sities of the fine structure components of the Lyman doublet of H-like ions [28],
Results of calculation are shown in figure 3b. Addi-
tional aspects of the density dependence are given in the Appendix.
The methods discussed here provide possibilities for sumultaneous measurements of the parameters T, T, and Ne using the lines with small wavelength differences. All the lines belong to the ions with the charge Z and Z f 1, i.e. to the ions which can be excited under similar conditions. It helps much for the better understanding of spatial (and time) plasma properties.
5. Interpretation of experimental data. - The methods presented here are widely used for the X-ray diagnostics of hot laboratory and astro- physical plasmas. Some results are given in this section. The continuous curve is the observed spec- trum while the straight vertical lines represent wave- length and intensities of the computed lines. The He-like spectra are shown by broken lines. For the satellites, the dielectronic recombination contribution is shown by solid lines while the inner-shell excitation contribution is shown by dotted lines. The lines are denoted according to Gabriel [18] (see also Appendix).
5.1 SOLAR FLARE SPECTRA. - The H-like and He- like ion spectra and associated satellites are only emitted during X-ray solar flares. Although they have been observed by several workers, by far the best spectra are those obtained by Lebedev Physical Institute experiment from the Intercosmos IV orbiting platform 115-17, 34-36]. Figure 4 shows the spectra of the initial, maximum and final phases for the
C7-284 L. P. PRESNYAKOV A N D A. M . URNOV
Fig. 6. - Kg-lines in iron ion spectra [36].
X-ray flares with good spectral resolution. By way
Fig. 4. - Highly charged iron ion spectra obtained by the Inter- of an example, the theoretical calculations f i r twb
cosmos IV experiment 134-351. of these spectra in comparison with observations are given in figure 5. The results show that the electron temperature was the same for both scans, and the ionization balance was one of recombination during the first scan (T, > T ) but reached steady state during the second (T, = T ) .
Another example is given in figure 6. Presence of the K, and Kg lines shows effective K-shell ionization of the iron ions with Z = 7-17 at the initial (cool) stage of the flare. The interpretation includes appea- rance of electron beams 1361 and detailed calculations are in good agreement with the results of simultaneous observations of radiation polarization and the abso- lute X-ray flux measurements.
1 8 6 A t B ) I a 7 X-RAY ENERGY ( k e V )
185
Fig. 5. - Fe XXV spectra and associated satellites recorded at Fig. 7. - Fe XXV-Fe XXIV ion spectra of the PLT Tokamak [37]
two times [17] and compared with calculations [19]. in comparison with the Intercosmos IV [17].
X-RAY PLASMA DIAGNOSTICS
Fig. 8. - Fe XXV-Fe XXIV ion spectrum of a low-inductance vacuum spark [23] in comparison with calculations 1191.
5.2 LABORATORY PLASMAS. - Non-time-resolved spectrograms of laboratory plasmas are given in figures 7, 8 and 9. An analysis of plasma conditions in tokamaks, vacuum sparks and laser plasmas shows that the values of N,z are close to l o t 2 ~ ms - ~ (or even less). This suggests a non-steady-state conditions in the cases of highest ionization stages observed for heavy elements (T, < T for Z > 15).
Time-resolved spectra of some H- and He-like ion resonance lines [38] and associated satellites have been recently obtained at Lebedev Physical Institute (Fig. 10-1 2). With the Nd-laser pulse duration about 5 ns, the time resolution of the spectra obtained
Fig. 9. - Ca XIX-Ca XVIII ion spectrum of a laser produced plasma [3] in comparison with calculations 121.
Fig. 10. - Time dependence of the A1 XI11 and A1 XI1 resonance lines observed in a laser plasma [38]. The upper curve represents a laser pulse.
was about 1.5 ns. The time dependences of N , and T have been obtained from the relative intensities of dielectronic satellites (H-like and He-like ions) and of intercombination line (He-like ions) to the reso- nance line [38].
Fig. 1 I . - Experimental values of electron temperature T and density N , as a function of time 1381.
C7-286 L. P. PRESNYAKOV A N D A . M . URNOV
Further investigations of time-resolved spectra are extremely useful for better understanding of plasma dynamics.
Conclusions. - The results and methods discussed here show that the line spectra of highly charged ions provide a great deal of information on the properties of hot plasmas. The X-ray spectroscopy is of special importance for all cases where the appli- cation of contact methods for diagnostics is practically impossible (solar flares, laboratory plasmas with large electron densities and short lifetime).
Acknowledgments. -The authors would like to thank V. A. Boiko, M. A. Mazing, L. A. Vainshtein, A. V. Vinogradov, E. A. Yukov and I. A. Zhitnik of Lebedev Physical Institute for the useful discussions.
Appendix.
-
All diagnostics methods based on the satellite lines suggest the coronal model conditions, which are valid for rather high electron densities up to N, 11 1020-22 cmP3 for 2 = 15-25. At higher densities N, > N, the collisional mixing between excited levels due to electron impact becomes impor- tant. The satellite relative intensity occurs sensitive to the electron density and therefore provide fairly good method of density diagnostics for superdenseplasma until the Boltzmann equilibrium between excited levels will happen. The latter case is realized at the densities N, %- N,, where characteristic density N2 is of order 1024-26 ~ m for the same - ~ Z = 15-25. The populations of all doubly-excited levels are proportional to their statistical weight when N, %- N2, and intensities of satellite lines are propor- tional to the probability of radiative decay.
It happens so that all upper levels which give arise to satellite lines may be divided into two groups with different total spin, S. These states are, for example, singlet and triplet states of He-like system (satellites to the H-like resonance line) and doublet and quadruplet states for Li-like one. Taking into account only the most effective dipole transitions it is possible to derive equations for the states with definite total spin S which belongs to one configuration only (for example for levels : q, r, s, t of the 1s 2s 2p configuration for Li-like ions). These equations may be written in the form :
N,(A,
+
N, C,) = Q,+
a,+
N,. b,,, (A. 1)7'
where
A, =
c
A , ,+ r,
a'
Q,
= N,+ 1 N, C,d,,+
N, Nec::,"
(A. 2)Table 11. - Relative satellite line intensities (in
%
to the total sum over all satellite lines) in respect to electron density N,. H-like ions.Key N, 6 Nl Nl
<
Ne<
N2 N, & N2N Transition Mg : Fe : Mg : Fe : M g : Fe
- - - - - - - - -
1 2 ~ ~ ( ~ P , ) - l s ~ P ( ~ P , ) A 3.2 12.7 5.9 3.4 19.3 12.0 2 2 ~ ~ ( ~ P , ) - l s ~ P ( ~ P , ) B 1.1 4.0 2.0 2.1 6..4 7.5
3 2p2(3Pl)- i s ~ P ( ~ P , ) C - - 2.0 1.7 6.4 6.0
4 2 p 2 ( 3 ~ l ) - i s ~ P ( ~ P , ) D - - 1.2 0.9 0.4 3.4
5 ~ P ~ ( ~ P , ) - 1 s ~ P ( ~ P , ) E - - 1.6 1.35 5.2 4.7
6 2p2(3Pl)- 1 s ~ P ( ~ P , ) F 0.06 0.18 1.6 1.2 5.2 4.4
7 2p2(3P2)-l~ 2p(lP1) G - 4.5 - 1.2 - 4.2
8 2p2(3Pl)- 1 s 2p('P1) H - - - 0.09 - 0.3
9 2 ~ ~ ( ~ P , ) - l s 2p(lP1) I - - - 0.02 - 0.08
10 2p2(1D2)- 1 s 2p('P1) J 49.1 33.3 53.4 40.7 25.8 17.9
11 2p2(1D2)-ls ~ P ( ~ P , ) K 0.2 10.7 7.2 13.4 1.3 6.0
12 2p2('D2)- 1s L - 0.05 - 0.06 - 0.03
13 2p2(1So)-ls 2p('P1) M 4.0 1.7 0.9 9.4 0.6 4.2
14 2p2('s0)-is ~ P ( ~ P ~ ) N - - - - -
15 2s2('S0)-1s 2p(lP1) 0 2.2 2.2 2.2 1.1 1.0 0.4
16 2s2('S0)-1s ~ P ( ~ P ~ ) P - 1.8 - 0.9 - 0.4
17 2s ~ P ( ~ P , ) - 1s ~ P ( ~ S , )
Q
13.8 3.26 4.0 3.4 12.9 12.0 18 2s 2 ~ ( ~ p , ) - l s ~ P ( ~ S , ) R 8.3 2.9 2.4 1.95 6.4 6.8 19 2s 2 ~ ( ~ P , ) - l s 2 ~ ( ~ S l ) S 2.8 0.65 10.1 0.7 2.6 2.320 2s 2p(lP1)-1s 2p('S0) T 15.3 17.3 5.5 15.7 6.4 7.0
2 1 2s 2 ~ ( ~ P , ) - l s 2p('SO) U - 0.07 - 0.08 - 0.3
22 2s 2p('p1)-2s V - 0.7 - 0.6 - 0.3
X-RAY PLASMA DIAGNOSTICS C7-287
b,,. = N,2
x
Cfla'B ( A s
+
N , XP) 'Here C,, is the rate of optically allowed collisional mixing between two levels a,
p,
belonging to different configurations (for instance, 1s 2s 2p and 2s 2p2 in the case considered above) ; C , , is the rate of pumping of the level a due to radiative capture (dielectronic recombination) and/or direct electron impact. At low densities<
N, = min(C,
A,Here the sum is carried out over all coupled states y (both configurations in the case afore mentioned).
In the intermediate case the relative satellite inten- sities depend on Ne until the quasi-coronal, quasi- Boltzmann equilibrium will be achieved when all levels within one group (doublet or quadruplet for Li-like ions) are in Boltzmann equilibrium in accor- dance with (A .7), and levels from different group are in coronal conditions. When density becomes so high as
where C;nSt is the rate of intercombination transition, the Boltzmann conditions for all the states are valid.
Since the C$' is of about two order of magnitude less and we get the coronal equilibrium ; the population compare to CaB without changing of spin (AS = O), in this case is equal to : the N2 value is at least two order of magnitude higher
than N,.
(*. 6, The ratio
In the opposite case, N, % N,, when all the terms b = - I s
C
1 s ' (A .8)in (A. 1) proportional to N, are important, the Boltz- S mann equilibrium between all levels of choosed
group occurs and populations become proportional where Is is the intensity of a given satellite, can be to the statistical weight of the level : used as a good indicator of the electron density region.
C
Y l Q Y Tables I1 and 111 show the b-values for three limiting cases considered above. Calculations have been N,=g;---.C
g, (A'7) done for the temperature at which the resonance lines have their maximum intensity.Table 111. - Relative satellite line intensities (in
%
to the total sum over all satellite lines) in respect to electron density N,. He-like ions.Ke Y N e e N , N , G N, G N" N, 9 N"
N Transition M g : Fe : Mg : Fe : M g : Fe
- - - - - - - - -
1 I s 2~2(2P3/2)-1 s2 2 ~ ( 2 P y z ) a 8.1 10.7 24.8 23.9 24 23.6
2 Is 2p2(2P312)-l s2 2p(=P) b 1.1 0.15 3.5 0.3 3.5 0.3
3 I s 2 p 2 ( 2 ~ 1 s2 ~ P ( ~ P ) c 0.94 0.03 4.5 3.1 4.4 3.1
4 1 s 2p2(2Pli2)-l s2 ~ P ( ~ P ) d 1.9 0.1 9.6 10.5 9.4 10.3
5 1 s 2 ~ ~ ( ~ P , / ~ ) - l s ~ ~ P ( ~ P ) e 0.3 1.8 - 1.2 0.9 2.0
6 1 s s2 ~ P ( ~ P ) f - 0.25 - 0.2 - 0.4
7 1 s 2p2(4P,/2)- l s2 2p(2P) g - - - - - -
8 Is ~ P ~ ( ~ P , / ~ ) - 1 s2 ~ P ( ~ P ) h - - - 0.001 - 0.002
9 1s 2p2(4P112)-1~2 ~ P ( ~ P ) i 0.4 - - 0.2 - 0.4
10 I s 2 p 2 ( 2 ~ 5 1 2 ) - l s2 ~ P ( ~ P ) j 32.7 37.2 14.8 12.4 14.4 12.3 1 1 Is 2 ~ ~ ( ~ D , / , ) - l s2 ~ P ( ~ P ) k 20.7 27.0 9.0 12.6 9.0 12.4
12 1 s 2p2(2D312)-l s2 2p('P) 1 1.5 1.6 0.6 1.5 0.6 1.5
13 Is 2p2(2S 1/2)-1~2 ~ P ( ~ P ) m 5.6 2.6 3.2 4.7 3.0 4.6
14 1 s 2p2(2S 112)-1 s2 ~ P ( ~ P ) n 2.2 0.1 1.3 0.2 1.2 0.2
15 1 s ~ s ~ ( ~ S 1 s2 ~ P ( ~ P ) o 0.7 1.7 - 0.2 0.3 0.2
16 1 s ~ s ~ ( ~ S 1 s2 ~ P ( ~ P ) P 0.3 2.1 - 0.2 0.2 0.2
17 1 s 2s 2~(~P,,,)-l s2 ~ S ( ~ S ,/,) 9 10.6 0.1 18 18.7 17.8 18.5 18 1 s 2s ~ P ( ~ P , / , ) - l s2 ~ s ( ~ S ,/,) r 7.1 5.0 8.7 6.2 8.5 6.1 19 Is 2s 2 ~ ( ~ P , ~ , ) - l s2 ~ s ( ~ S ,/,) s 3.5 0.2 1.6 0.03 1.5 0.03 20 Is 2s ~ P ( ~ P , / ~ ) - 1 s2 ~ s ( ~ S ,/,) t 2.6 7.9 0.1 3.4 1.1 3.4 2 1 I s 2s ~ P ( ~ P , / , ) - 1 s2 ~ s ( ~ S I/,) U - 0.1 - 0.4 - 0.6 22 i s 2~ ~ P ( ~ P ,12)-1 s2 ~ S ( ~ S ,/,) v 0.07 - 0.06 - 0.1
C7-288 L. P. PRESNYAKOV AND A. M. URNOV
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