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CHARGE EXCHANGE IN LABORATORY AND ASTROPHYSICAL PLASMAS

D. Pequignot

To cite this version:

D. Pequignot. CHARGE EXCHANGE IN LABORATORY AND ASTROPHYSICAL PLASMAS.

Journal de Physique Colloques, 1988, 49 (C1), pp.C1-153-C1-163. �10.1051/jphyscol:1988131�. �jpa-

00227451�

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JOURNAL DE PHYSIQUE

C o l l o q u e C1, S u p p l d m e n t a u n 0 3 , Tome 49, M a r s 1988

CHARGE EXCHANGE IN LABORATORY AND ASTROPHYSICAL PLASMAS

D. PEQUIGNOT

O b s e r v a t o i r e d e P a r i s , S e c t i o n d e Meudon, F-92195 Meudon P r i n c i p a l C e d e x , France

RBsumB : De recentes experiences menBes sur des plasmas de tokamaks demontrent que les Bchanges de charges se manifestent dans une grande varietB de situations. On realise maintenant que des &changes de charges impliquant les Btats excites de Iihydrog&ne doivent etre pris en consideration : ces reactions representent un defi pour la physique atomique. la modBlisation detaillee du plasma et les diagnostics quantitatifs. Des Bchanges de charges entre ions peuvent dans certains cas modifier I'btat du gaz et produire une emission specifique.

Les Bchanges de charges ont une influence important sur I'Bquilibre d'ionisation de nombreux ions dans les plasmas coronaux ti&des aussi bien que dans les plasmas photolonises rencontres en Astrophysique. Des raies produites par Bchange de charges ont Ot4 decouvertes dans le spectre des nebuleuses planetaires et probablement dans celui de la chromosph&re solaire. L'introduction des Bchanges de charges modlfie d'anciens polnts de vue sur la structure de certains objets astrophysiques. Les nebuieuses semblent constituer des

"laboratoires" permettant de tester les sections efficaces d'Bchange de charges thdoriques trbs basse Bnergie. II est sugg6rB que la detection de certaines raies d'echange de charges dans l e spectre solaire fournirait de nouvelles indications sur la dynamique de l'interface entre l a chromosphere et la couronne. II est note que des &changes de charges entre particules lourdes pourraient avoir des effets significatifs dans le front d'ionisation de certaines n6buleuses.

Abstract : Recent experiments in tokamak plasmas demonstrate that charge exchanges manifest themselves in a wide variety of situations. It is now realized that charge exchanges

--

involving excited states of hydrogen should be considered : these reactions represent a chalienge for atomic physics. detailed plasma modeling, and quantitative plasma diagnostics.

Charge exchanges between ions can in some cases modify the state of the gas and produce specific emission.

Charge exchanges are important for the ionization balance of many ions in either warm coronal plasmas or photoionized plasmas of Astrophysics. Lines produced by ctiarge exchange have been discovered in the spectrum of nebulae and probably the solar chromosphere.

Introduction of charge exchanges modifies earlier views about the structure of some astrophysical objects. The nebulae appear as valuable "laboratories" to check theoretical charge exchange cross sections at very. low energy. It is suggested that the detection of charge exchange lines in the solar spectrum would provide new insights into the dynamics of the interface between the chromosphere and the corona. It Is pointed out that charge exchanges between heavy particles may have significant effects in the ionization front of some nebulae.

1. lntroduction

Charge exchange is often of practical consequence in plasmas when electrons are captured by charged particles from neutral particles. The importance of neutrals in plasmas can be ascribed to a special concourse of circumstances : ( 1 ) the Big Bang was too fast so that not much hydrogen was burned into helium and heavier element$, ( 2 ) the stars were lazy to terminate this burning so that hydrogen is still the most common element in nature. (3) mank~nd is willing to help nature in this titanic job so that we are building tokamaks filled with hydrogen. ( 4 ) at temperatures not exceeding about 10 keV. charge exchange is faster than any other inelastic collision so that a minute fraction of neutrals can induce sizeable effects, and (5) hydrogen is the only element with two ionization stages so that traces of neutral hydrogen are easily present even in hostile environments.

Unless otherwise stated. I therefore consider plasmas mainly composed of hydrogen isotopes (and helium). reminding however that the character of a plasma IS strongly influenced by the trace elements it contains.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1988131

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C1-154 JOURNAL

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PHYSIQUE

Several detailed reviews were recently devoted to the many aspects of charge exchange reactionsle2 and I restrict myself to a few very simple comments.

When the relative velocity in the reaction

is less than a typical electron orbital velocity (centre of mass klnetlc energy less than

-

25 keV/nucleon) , a quasi-molecular descriptlon is adequate. The reaction can then be seen as a transition taking place at the crossing between the input (quasi flat) and output (coulombian) channel energy curves. In the very low energy domain. the reaction mainly proceeds through radial coupling and on the condition that the energy jump 6E at the pseudo-crossing of the potential curves is of the right magnitude. This occurs when the separation at the pseudo-crossing, Rc

-

(q-p)p/aE. is In the range 5-12 a. u . . It follows that : (1) the reactlori must be exothermal by a few eV If q > 1 and almost resonant if q = 1.

(2) the Cross section Ute

-

n@, IS very large, and (3) the reaction only proceeds through a few definite states (n13 of Y+. For charge q

<

2 the selectivity may be so high as to suppress any favorable channel. At higher collision energies. new crossings become progressively favorable through rotational coupling. but the reaction remains quite selective. Thus, for the usual case p = 1, the reaction proceeds mainly through levels of Y+ of principal quantum number n

-

qO. 77 and the states (nl) are not statistically populated. Above

-

25 keV/nucleon.

ionization dominates.

The incident particles need not be in their ground state. In many plasmas the excited states of hydrogen can reach appreciable populations. The charge exchange reaction X+q + H(n) has a gargantuan cross section3

-

6n n4q (a. u. at centre of mass energies not exceeding

-

n-1 a. u. and is expected to preferentially populate levels n x qO. 77 of ~ + q - 1 .

Charge exchanges between charged particules. e. g. in the reverse of reaction ( 1 )

.

are sometimes important4.

The very low energy range ( K . E.

<<

100eV) is more specifically the realm of theorySe16. A wealth of experiments flourishes in the intermediate and high energy range17-l9 : there. because many processes are competing. theory is perhaps less exhaustive and is often reduced to "account" for experimental results. To date the total cross sections seem to be rather well understood and attention focuses on the difficult and essential problem of cross sections for individual channels.

2. dharae exchanne in laboratory plasmas 2. a. General comment

We have in mind the magneti_cally confined plasmas (tokamaks) which are ultimately designed for thermonuclear fusionzO.

Charge exchanges influence the state of a plasma by direct radiation losses following a reaction and by displacing ionization equilibria of trace elements. Charge exchanges tend to favour the survival of ionization stages lower than expected in ideal "coronal" conditions and therefore amplify radiation losses by electron collision excitation21. Overwhelmln even deleterious

-

effects may occur at the low-ionization boundary of many plasmasP2~

The selectivity of charge exchange is a rich source of plasma diagnostics in which the concentration of either residual neutrals or higly charged ions -including bare nuclei

-

can be spectroscopically measured by means of the radiative cascades following the reactione3, 24.

Active diagnostics make use of neutral beam injection.

The injection of fast neutral hydrogen beams is an elegant way to heat magnetically confined fusion plasmase5. However charge exchanges with thermal protons can hamper the penetratlon of the beams for. once a fast ion Is formed. it Is trapped in the strong magnetic field. Before being thermaiized the fast proton may even undergo a second resonant charge exchange wlth a residual H0 atom of the gas then removing energy from the plasma. increasing the sputtering on the walls. and rising the concentration of impurities. Overcoming these difficulties is essential for the new generation of large devices.

Several aspects of charge exchange in tokamaks are considered in other contributions to this conference and in many recent conferences devoted to multiply charged ionsz6. I just highlight a few recent experiments disclosing new interesting processes,.

2. b. wPassivee source of

eC.

The 0. 2-0. 5 nm X-ray spectroscopy of He--like emlsslon of high-Z trace elements provides ,,classical diagnostics of very hot plasmas.

Kallne e l al. 27 were able to measure the radial dependence of the n = 2 to n

-

1

~ r l ~ + emission with a high-resolution Bragg crystal spectrometer attached to the Alcator C tokamak. kept in a quiescent ohmically heated state.

In the bright core of the plasma it is known that the relative intensity of the resonance ( w )

.

intercombination (x and y) and forbidden (2) lines. as well as the satellite lines ( k and

(4)

q ) . are successfully explained by a combination of electron impact excitation and dielectronic recombination. Closer to the edge of the lasma. the temperature is lower and collisional excitation should vanish. In addition no ArP7+ should be present under corona equilibrium.

Nonetheless ~ remission is clearly observed, implying that highly charged ions can migrate ~ ~ + from the inner region before recombining. Then assuming the above mentioned excitation processes. all lines are expected to increase moderately relative to the resonance line as temperature decreases. On the contrary what was observed by Kailne et ai. is a strong increase. possibly followed by a level-off. of ( x + y + z) /w and an increase followed by a rapide decrease of ( k + q ) / w . Only radiative recombination and charge exchange seem a prlori capable to account for this low-temperature behaviour. At 2/3 the distance from the centre. the new excitation regime is established and the estimated temperature is

-

0. 35 keV.

The effective rates for collisional excitation. radiative recombination and charge exchange are respectively :

qexc = 5 10-l5 n (16+) n,. qrec = 3 10-l2 n (17+) ne.

qce =

loA7

n ( ? 7 + ) n ( ~ O )

The first process is weak if n ( 17+) / n ( 16+) is much larger than 10-3, which is beared out by direct detection of ~ reven quite far from the centre (confirming migration). And charge ~ ~ + exchange dominates if n ( t I O ) /ne is larger than 3 which is much larger than the corona equilibrium value but seems quite easily attainable when the diffusion of neutrals from the boundary. a process partly controlled by tIO +H+ charge exchangee8. is taken into account.

At this stage a very elaborate and possibly questionable description of the gas would be needed to decide if charge exchange is the dominant,,process recombining ~ rinto ~ r l ~ + . ~ ~ + Moreover the kind of measurement reported by Kallne et al. would get the status of a diagnostic - e. g. of HO concentration

-

.only insofar as a definite spectral signature could allow to distinguish radiative recombination from charge exchange. Such a signature may exist if the n = 2 substates are populated differently as a result of cascades following either charge exchange or radiative recombination. One can conjecture that ( 1 ) the difference would be quite subtle. ( 2 ) it would depend on density. and ( 3 ) the charge exchange process itself may not be sufficiently well known.

As pointed out by Kallne et al. a much more convincing case for charge exchange and eventually a much more sensitive diagnostic for could be obtained by observing directly the I s 2

-

1s nplp transitions with n 6 11 in order to detect the relative enhancement due to charge exchange. expected for n

-

9. Rice et al. 29 indeed found that the n = 9 and 10 lines were considerably enhanced relative to n = 7 and !1 close to the comparatively cold edge of the device. in the same physical conditions as Kallne et al. But a major surprise was the detection of a prominent enhancement of large-n transitions. which could be convincingly interpreted as a consequence of charge exchange between ~ rand the first excited states of ~ ~ +

HO. since peaks were apparent at wavelengths corresponding to n = 18. 27. and 36. From a rough modeling Rice et al. concluded that the neutral-density profiles derived from their data are in agreement with neutral-transport simulations. Use of such measurements as precise diagnostics would require a detailed description of charge exchanges. recombinations and cascades with explicit allowance for ( n . I) dependency and collisionai rearrangements. At this stage theoretical information may not yet be sufficiently complete. Reliable diagnostics for excited levels of hydrogen would obviously improve our understanding of physical processes in tokamaks.

2. c . "Active" source of tIO.

Examples of "active" diagnostics involving time-dependent injection of neutral beams and multichannel high resolution spectroscopy along different lines of sight are provided in the detailed analysis performed by Carolan et al. 30 using the ASOEX tokamak. The spatially resolved determination of physical parameters. including impurity concentrations. imply a careful modeling of beam attenuation and a complete identification of atomic processes.

The unambiguous identification of many charge exchange lines is obtained by supplementing the slow multichannel detectors with fast-response photomultipliers allowing to decide if the enhancement of a given line should be attributed to direct charge exchange from the neutral beam or to subsequent changes in ionization or ion transport.

The spectrometers used by Carolan et al. encompass the wavelength range 10-700 nm containing in particular many An = 1 or 2 transitions of important intermediate4 impurities such as oxygen. The visible lines are resolved and the profiles yield useful information on ion temperature and bulk plasma rotation. In the visible the charge exchange lines are also easily distinguished from background lines produced at the plasma edge because they are broader.

In view of the potential diagnostic capability of visible lines and of the obvious technical advantages of visible spectrosopy. Carolan et al. investigate possible candidates.

A particular difficulty is that the principal quantum number m

=

qO. 77 corresponding to maximum charge exchange cross section with t i 0 is smaller than the value n. corresponding to

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Cl-156 JOURNAL DE PHYSIQUE

the upper level of visible lines. Thus for 08+ + IiO. the m value is 5, while OVlll 606. 8-nm Is the n = 10-9 transition. The cross section for these large-n levels is believed to scale like (m/n13 but the experimental basis is limited and the ldistribution poorly known. which is unfortunate because I--mixing may not be complete at densities prevailing in tokamaks and the An = 1 transitions involve preferentially the I = n-1 sublevels.

In the spirit of Sect.2a. a second more fundamental difficulty comes from the excited-state population of HO. For example, the nv = 10 level of

o + ~

just considered corresponds to the maximum cross section of H0 ( n = 2) +

o + ~ -

H+

+

0+7*. In view of the n4 and cross section scalings already mentioned, the cross section of H0 ( n = 2) for populating 0+7 (n v = 10) by charge exchange is g7 times that of IiO ( n = 1)

.

so that equal contribution to excitation of OVlll 606.8 nm is obtained from both levels if one percent of hydrogen is in the n = 2 excited state. a value typical of tokamak conditions. Higher levels of hydrogen may contribute as well after cascades.

A quantitative interpretation of visible data may then become extreme1 involved. even if

J

all atomic data are assumed to be accurately known. In addition to the fast H of the beam. two kinds of thermal IiO must be considered : ( 1 ) the background IiO which diffuse from the boundary of the plasma (see Sect. 2b) and (2) the "halo" HO produced by charge exchange of a thermal proton with a beam ti0. Also each kind of IiO may or may not have time to build up a steady state population of their excited levels.

Clearly the amount of atomic data. modeling, technology. and clever work needed to extract from visible lines all the wonderfull informations they can tell us is gigantic.

2. d. !on-ion char e exchan e

Another aspect 0: charge :xchange is disclosed by Kato et a1.31 in an X-ray time-resolved analysis of TiXXl (He-like) produced in an ohmically heated JJPP-T-II-U tokamak plasma. Neon puffing after the initial discharge is a way to increase the effective charge of the plasma and therefore the ohmic heating.

Kato et al. are able to show that. sometimes after neon injection. the titanium is rapidly recombining. Simultaneously the line intensities can no more be fitted by atomic model calculations : the x. y and z lines become much too strong (see notation in Sect. 2b).

indicating a new population mechanism. They convincingly argue that the extra recombination and the anomalous emission of the intercombination and forbidden lines should be attributed to charge exchange with highly charged neon ions. Following the method of Bazylev and chibisov4, they are able to obtain rough rate coefficients and most probable capture levels n = 3-4 for :

In order to amplify x .t y + z. Kato et ai. must postulate that levels like 3 3 ~ and 4 3 ~ are selectively populated. This may provide a check of their description..

This ion-ion charge exchange is very selective. It best works when the charges are very different. which occurs more easily in non-equilibrium situations and when the ion loosing an electron is light. It can be concluded that this process should be given due attention in any plasma of high impurity concentration.

2. e. Concluding comments

These few recent examples demonstrate that. one decade after the full appraisal of the pratical importance of oharge exchange in tokamaks, this process is stili a source of surprises.

It is a challenge because of the complexity and amount of atomic data involved. It is a fascination because of the richness and elegance of plasma diagnostics it may provide.

Beyond the aim of controlled thermonuclear fusion. laboratory plasmas are interesting for physical studies. They are probably not the best place to get accurate cross sections but they offer a chance to tiisclose the unpredictable complexity of nature in concrete situations, if atomic data acquisition and spectroscopic technics reach required acuteness. The versatility and selectivity of charge exchange is an asset in this quest for ever flner diagnostics. The visual technics are promising but they will not develop without the help of X-ray and extreme UV technics which give the most direct access to the charge exchange process.

3. Charae exchange in astrophysical plasmas 3. a. Plasmas of astrophysics

Some typical plasmas of astrophysics are sketched in the log (density) versus log (temoerature) diaQran~ of Fiq. I . If one excepts the dense stellar photospheres, w!iere the state of the gas is usually close to thermodynamic equilibrium, directly observable astrophysical plasmas can be broadly divided In two categories :

1

-

The coronal plasmas in which ionization is primarily due to thermal collisions. the energy being supplied, for example. by mechanical or magnetical dissipation (chromosphere and

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corona of stars. hot interstellar and intergalactic med~a, supernova remnants. e t c . ) . 2

-

The non-coronal plasmas In which ionization is primarily due to photoionizat~on by relatively hard radiation ("Hll regions" surrounding hot massive young stars, "planetary nebulae"

surrounding hot low-mass old stars. some supernova remnants, parts of the warm interstellar medium. probably most of the line-emission regions of active galactic nuclei and quasars.

etc. 1 .

I I I I

ilog [density cm3)

'

,#e fision)

1

-

hydrogen

density

---.--

electrons

in I ):log caracteristic size in cm

Distinguishing between these two categories is not always meaningful. For example the cooling tail of a shock wave can be kept ionized by radiation lost by the hotter (coronal) zone.

Also a sufflclently strong and hard radiation field can produce a hot coronal plasma dominated by Compton gain and loss. Conversely a gas submitted to a sufficiently hard but weak radiation fleld is heated by thermalisation of fast Auger and photoelectrons and may share most characteristics of a "warm" coronal plasma : this may be the case of. e.g.

.

some

low-ionlzation llne emlssion reglons in active galactic nuclel.

3. b. Coronal plasmas

3. b. 1. Corona equilibrium

Because of the large scales involved in most very hot astrophysical plasmas. a concentration of neutrals significantly in excess of the corona equilibrium value is most often not expected. The relevance of charge exchange is therefore restricted to relatively cold gases and perhaps to some sufficiently narrow interfaces between hot and cold gases (see below).

Below 1. 5 1 0 4 ~ . ionization of H is low or moderate in an approximately coronal plasma.

Because of charge exchange ionization by collision with protons or charge exchange recombination by collision with neutral hydrogen. one or at most two species of a given element can survive.

In the range T4 ( = T ~ / I O ~ K ) = 2-13. the coronal equilibrium of hydrogen reads approximately :

NHO/NH+ = 4.6

lo-s

T ~ - exp (15. 78/T4) ~ . ~ (2)

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C1-158 JOURNAL

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PHYSIQUE

To order of magnitude. the rate coefficients for radiative recombination and charge exchange

(with HO) of an ion of charge q are given by

and a N

-1.4 -0.1

-

O.15q T~ exp(15.7e/T4) a rad Ne

Charge exchange with H O can in some cases dominate ion recombination up to T4

-

5 and

detectable effects may exist up to T4

-

10 even after taking into account dielectronic recombination.

The helium a b ~ ~ n d a n c e is usually 10% by number in astrophysical plasmas. In coronal conditions, neutral helium is more abundant than neutral hydrogen in the range Tq

--

1.8-10.. but very few heavy ions normally present at such temperatures can exchange charge with He0. Ionization by He+ and He++ collisions is common.

The example of silicon in the solar chromosphere have been worked out by Baliunas and Butler32. The reaction :

proceeds through the ground state of Si+ and is moderately exothermal. the reverse reaction ionizes Si+ much more than electron collisions up to T4

-

10. Similarly :

dominates electron impact ionization by a factor of 10 at T4 = 5. Then it is found that the dominant ionization Stage of silicon is

si2+

in the range T4 = 2-10. When charge exchanges are taken into account. the peak intensity of the diagnostic line Si 111 189.2 nm occurs at a temperature twice lower and is increased by one order of magnitude.

Before introducing charge exchanges. the uncomfortably strong Si Ill emission obliged to postulate some extra process heating the ~ i 2 + zone.

Qualitatively sirnilar results may be expected for numerous metals including iron but atomic data are lacking. New interesting effects may be expected if reactions employing different routes ( i n c l ~ ~ d i n g low lying excited states) are competing.

3. b. 2. Chromosphere/Gorona transition region

The "upper chromosphere" of the sunds. thermostated by H(Lya) radiation losses. is characterized by a temperature plateau at T4 = 2. The electron density is 5 1010

~ m - ~ . Most of helium and 5% of hydrogen are neutral. The chromosphere is separated from the corona by the "transition region" situated 2

l o 3

km above the photosphere. in a plane-parallele steady-state description the maximum temperature gradient is reached for T4 = 10 at typically 10 km from the upper chromosphere. This zone. where spicular structures are conspicuous, looks highly turbulent with a most probable velocity of 15 km s-l. The very concept of a steady transition region is questionable in either active or quiet zones of the sun.

This region is propitio~ls to non-equilibrium

situation^^^-^^.

The study of this plasma would be eased by new diagnostics for recombination. Lines produced by charge exchange might prove useful in that they are extremely sensitive to the "degree of mixing" of ions with neutrals. This possibility should be given some attention.

As an example, a rough scenario of the large-scale circulation which may apply in at least some active regionsS6 includes localized "explosive events" (probably related to MHD instabilities). which heat and project high density material in the lower corona. and long duration almost steady "downward flows" (confined by magnetic fields), which consist of relatively low-density cooling material.

The cooling and recombining material. as depicted. e. g.

.

by CIV 155 nm. often reaches downward velocities of 50 and 100 km s-.l above "plages" and "sunspots"

respectively36. Column 3 of Tabie 1 gives the cooling time-scale tcooi for several (T. Ne) corresponding to meart physical conditions expected in the upper chromosphere and the lower corona.

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Table 1 : Cooling and recombination times i n the solar transition region.

T N e t c o o ~ trec/tcool.

1 O ~ K 1&crn-3 ( s )

o + ~

0+5 0+4.

Charge exchange in upper chromosphere conditions.

Efficient coolin is initiated at T4 s 40. when a sizeable fraction ( - 20%) of oxygen is i n 05+

(U-like) and Oq+ forms. The corresponding mean tcooi is on the order of 200 s which Is the duration required to accelerate free falling material to the above velocities. This suggests that cooling may keep pressure sufficiently low to allow approximate free fall. If no important heating source is present. the time spent by the gas in a given temperature regime is on the order of tcool. Columns 4-6 of Table 1 give the ratio of the recombination time-scale trec (09') to tcool for the oxygen ions 0q+, q = 7. 5. and 4. The time-scales for the infalling material may be longer than in Table 1 if the densit of the gas is comparatively low but the ratios of col. 4-6 are much less sensitive to conditionsJ4. Below T4 = 40. tCool is signiflcantly shorter than treC for q = 7. 6. and 5. Then as the gas cools. the oxygen ions q

<

5 progressively cascade to lower charges (col. 6) while the ions q 6 are almost freezed out. in some cases as much as one third oxygen may still be in He-like form when the gas reaches T4 = 3 and even larger fractions of He-like C and N may survive.

The high-velocity material is eventually slowed down and compressed as it "splashes"

on the dense upper chromosphere. In chromospheric conditions. an ion like 05+ i s slowed down by coulomb frictionS7 after

loe2

second and it can penetrate one kilometer if its incident velocity is 100 km s-l. This is probably sufficient to reach the partlally lonlzed gas where charge exchange with HO and He0 is much faster than recombination (last line of Table 1 ) . The ions are suddenly neutralized by repeated captures of electrons onto specific exclted states and emit specific EUV and UV lines.

Char e exchange lines are available at least for intermediate charge ions studied theoretically8-11.38. Heil st a l l1 notlce for example that a line at 53. 8 nm. unidentified i n the UV spectrum of the sun compiled by Vernazza and ~ e e v e s ~ ~ , may be C Ill charge exchange line. A complete catalog of charge exchange lines for highly charqed ions of the most abundant elements would be useful. The UV spectrum of the sun is now observed very accurately40.

About half the lines are not identified in the range1 17-171 nm. The emission we have in mind may be transient and may require special technic&'.

3. c. 1. Ionization balance of H

That charge exchange must be important in nebulae can be understood from simple balance considerations.

Assume a gas mainly made of hydrogen at uniform density NH surrounding a star of radius R* radiating like a black body at temperature T*. The number of ionizing photons emitted by the star is :

where f a r l corrects the Stefan law for the non-ionizing photons., of energy less than 1 Rydberg. Let Rs be the radius of the ionized zone (the so-called "Stromgren radius" of the H+

region). within which the number densities verify

and aH the radiative recombination coefficient of hydrogen to excited states :

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C1-160 JOURNAL

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PHYSIQUE

At a distance r = pRs from the star a typical upper limit

r

($ to the photoionizat~on rate TH of hydrogen is

where u l is the photoionization cross section of hydrogen at thereshold and s

<

1 (typically s

-

0.5) corrects for the fact that the mean energy of the photons absorbed is greater than 1 Rydberg. Expression

r #

is an upper limit in that the absorption of radiation by layers closer to the star is neglected. Strictly speaking this limit might be moderately by-passed at some places because of radiation transfer effects. involving notably helium. If thermal ionization is negligible. the ionization balance of hydrogen reads :

using the upper limit

r #

and the above relations. expressing the result in units T*5 = T*. T4 := I O - ~ T . and recalling the solar radius Ro = 7 10l0 cm, it is found :

In a sphere filled with gas a mean value of p is <F, = 3 / 4 . However in real nebulae the gas may be somewhat clumpy and a central hole often develops around the star due for example to a stellar wind : in such cases c p ,

-

1 might be more appropriate.

Finally If the gas is only present far from the star. say beyond Rs as defined above. the H+ region becomes a thin shell with c p , greater than 1 . Notice in eq. (4) that the degree of ionization increases for increasing NH because. for a full sphere. the gas tends to be closer to the star. If, on the other hand. one considers a gas at fixed distance from the star, an increase of N H induces a decrease of NH+/NH, as expected. because p becomes larger.

Assuming equality in eq. ( 4 ) provides a rough estimate of N,q+/NHo in the bulk of the nebula. Evidently close to the edge of the H+ region, the flux of Ionizing stellar photons decreases exponentially wlth optical depth so that NH+/NH, Is much smaller than the upper limit ( 4 ) . As hydrogen recombines. the optical depth Increases rapidly wlth radius and the boundary. of the H+ region is extremely narrow.

3. c. 2. Other ions

For a sufficiently hot star, an He2+ zone develops In the inner parts of the nebula because most photons above 4 Rydbergs are absorbed by He+ and reprocessed as softer recombinatlon radiation photoinizing H'. The expression for f l S ( ~ e 2 + ) Is similar to ( 5 ) except that the numerical coefficient is 10 to 15% larger. and f* should be replaced by fqx, the fraction of stellar photons with energy in excess of 4 Ryd. No highly charged ion can exist beyond Rs(He2+). However for Tt5 2 1. 5. R , ( H ~ ~ + ) / f l s ( H f Is larger than 3 / 4 I f the black body approximation ispplies.

Considering now a heavy ion ~ 9 - 1 , whose ionization potential P is significantly larger than kTx, it can be shown that. to order of magnitude :

where UT is the threshold photolonlzatlon cross sectlon. In this expression It is assumed that f x

=:

1 (hot star). and that the radiative and dielectronlc recombinatlon rates of Xq- are approximately equal. Ion Xq will be present in the bulk of the (radiation bounded) nebula i f N ( x ~ ) / N ( x ~ - ~ )

-

1 when N ( H f ) /N(H') is given Its mean value (4) (wlth appropriate mean D l . Ions wlth P/kT* as large as 5 or 10 can reach sizeable lonizatlon fraction in nebulae.

3. c. 3. Thermal balance

A rough sketch of the thermal balance of the nebula is as follows. A typical energy of a photoelectron is kT* so that the thermal energy gained by the gas Is

Assume for simplicity that the radiative coollng of the gas at one particular place is mainly due to

one

coilislonally excited llne of energy € 1 2 and effective collision strength

n12.

belonging to an ion with ground state statistical weight gl and number denslty Ni. The thermal energy loss is :

(10)

Equating G and L. using previous relations. assuming f~

- r #

and expressing the line excitation energy €12 in eV. one obtains the gas temperature :

T4

-

0.5 e12 ( e v ) / loglOA

An equilibrium temperature can exist insofar as A is larger than unity. However in order to achieve a well-defined equilibrium temperature the radiation losses should increase significantly with temperature, which occurs, roughly speaking. when kT is significantly less than "12 or else A greater than 10.

According to the nature of the dominant cooling ilne, several temperature regimes can be disttnguished :

1 - The UV permitted iines (ns sequence. e. g CIV. €12

-

8. n12/g1

-

5) and

intercombination iines stabilize the gas at T4 = 1. 7 for a cosmic carbon abundance Ni/NH = 3 For extremely low heavy element abundance. Lya keeps the gas around

r4

= 2.

2

-

The optical forbidden lines (npq sequences. e. g . COIill. €12

-

3. n,2/g1 -0.3). have a thermostatic effect for T4 a 1. that Is as long as Ni/NH a 10 '3 T x ~ , a condition fulfilled for a typical cosmic abundance N+O+Ne

-

10-3 even for T*5

-

1. Cooling is effective only for densities not exceeding Ne

-

105 cm-3 because of coilisional quenching.

3

-

The fine structure iines (npq sequences. e, g. [Oilil. e l 2 -0.03. n12/g1 a 1) can keep the gas around lOOK if N ~ / N H 2 T*5 (large overabundance) and Ne less than l o 3 cm-3.

in conclusion the temperature of photoionized nebulae Is most often T

-

1 0 4 ~ , while.

for large T*. "ionization temperatures" of

l o 5

to T O ~ K are qulte easily reached.

3. c . 4. Charge exchange In nebulae

From this discussion and expression (4) it is concluded that in either "Hi1 regions"

(A=

-

10RO, T t 5 = 0 . 4 . s

-

0 . 6 . f= = 0 . 2 , n, = 700 ern-3) or "planetary nebulae"

LR* = 0. 1 Rg. Txg = 1. 5. s

-

0 . 4 . f~ = 1 . . nH = 104 cm-3) the neutrai hydrogen fraction in the bulk_ of the gas will be given by :

where the mean value of p = r/Rs cannot be significantly less than 1

once

enough gas surrounds the star to absorb radiation (the so-called "radiation bounded" case).

Then from ( 1 ) and ( 2 ) :

and the ionization balance of many ions can be influenced by charge exchange.

Using (6) with the condition

which expresses that charge exchange and recombination are equaly important at displacing the ionization balance of Xq. and with o-r/ul

-

q- (taken for conver~ience : this is roughly true for 2pq qnd 2sq ions of oxygen). ~t is found, :

This ratio is

-

1 and 0. 3 assumlng ( T x ~ = 1. 5. q = 3) and (Tx5 = 3, q : 4) respectively.

Thus. although highly charged ions

and

substancial fractions of neutrai hydrogen are easily produced i n nebuiae ionized by hot stars. it is increasingly difficult to make them to coexist to the extent that the ionization equilibrium of the formers is strongly affected. This is due in part to the rapid increase of recombination coefficients with charge. Nonetheless for very high Tx, the mixing of highly charged ions and HO is amply sufficient to produce reasonably intense charge exchange lines because the rate coefficients are large.

Closer to the boundary of the nebula, the neutral fraction of H0 is much enhanced and charge exchange can entirely control the recombination of some ions. For q a 2, not ail ions can effectively exchange charge with 1-1' and this selectivity induces surprising effects. For

(11)

C1-162 JOURNAL

DE

PHYSIQUE

example CNellll Is observed to correlate well with COlll but not with COlll: in outer parts of many nebulae because 02+ but not ~ e 2 + exchanges charges with H'. Also CS I l l 3 and CS 113 emissions can coexist even In the lonlzatlon front of nebulae because the charge exchange of

s2+

with HO is slow.

Not all nebulae need be photoionlzed by black body radiation. Nonetheless most previous statements can be quite straightforwardly extended to, e. g. , power- law primary spectra by attributing a typical radiation temperature to the effectively ionizing radiation. The presence of an excess of hard photons does not really help to mix highly charged lons with H?

3. C . 5. Planetary nebulae

Despite their apparent complexity. the planetary nebulae are among the best astrophysical objects to make ,rather definite statements about atomlc physics because the basic p;ocesses are not questionable and the physical conditions are a ~rio;i clean. Planetary nebulae often raised apparently dlfflcult problems just because it was not sufficiently realized to which extent they atomic physlcs laboratories. Charge exchange offers an illustration.

Twenty years ago. the first rnodel nebulae were rather successful at explaining emission llnes on assuming a prlori the simplest astrophyslcal inputs. In retrospect this merely proved that the basic energy requlrernents were fulfilled and that the few most important atomlc data used were correct to order of magnitude. But this success was sufflclently Impressive to lead to the belief that the remaining discrepancies

-

notably for low-Ionization llnes such as C0111

-

should be attributed to the supposedly oversimplified astrophysical assumptions. Countless speculations and exotic proposals flourished In order to displace the discrepant ionization equilibria without questioning the atomlc physics. In the late 70's a prevailing opinion was that the small scale structure of the nebulae was universally complex. We now know that this was due to the neglect of charge exchangedL3, 44.

At the present time there is no proof that the spectra of planetaries imply, for example, iarge density fluctuations of the Ionized gas on a small scale. Except for a few somewhat controversial astrophyslcal outputs, detailed self-consistent modeling of planetarles are therefore basically useful to check atomlc physlcs. A recent rnodel of the planetary nebula NGC 7027 suggests that the lonlzatlon balance is not yet fully understood and that some charge exchange rate coefficients may need revision (Gruenwald and POquignot. i n preparation).

Concerning lonlzatlon equilibria of low Ionization species. it should be recalled that not all of them exchange charges with H or He. Their lonlzatlon may then be slgnlflcantly influenced by other heavy lons since the heavy element abundances are on the order of

lod3

by

number while the charge exchange rates are 103 times the radiative recombination rates. This may require some attention.

Some charge exchange llnes of 0111 and Nelil have now been detected. There Is a general consensus that. to the accuracy of current observations. the line Intensities confirm theoretical rates. Interesting developments are expected45-52,38.

References

--

1

-

Janev. R.K., Wlnter. H. : 1985, Phys. Reports 117. 265.

2

-

McCarroll, R. : 1986. in Workshop on Model Nebulae, PBqulgnot. D.

.

ed.. Publication de I'Observatolre de Paris, p.

3 .

3 - Olson. R. E. : 1980. J. Phys. B

13.

483.

4

-

Bazylev, V.A.. Chiblsov. M. I. : 1979. Sov. J. Plasma Phys. 5, 327.

5

-

McCarroll, R.. Vallron, P. : 1975. Astron. Astrophys.

44,

465.

6

-

Dalgarno, A . , Butler. S. E. : 1978. Comments At. Mol. Phys. 7. 129.

7

-

Butler, S . E . , Heil, T.G., Dalgarno. A. : ,1980. Astrophys. J.

-=.

442.

8

-

Butler, S. E.

.

Dalgarno, A. : 1980. Astrophys. J.

241.

838.

9

-

Dalgarno, A . , Hell. T. G . . Butler, S. E. : 1981, Astrophys. J.

245,

793.

10

-

Blenstock, S . . Dalgarno. A . , Heil. T . G. : 1984. Phys. Rev. A

29.

2239.

11

-

Hell, T . G . . Butler. S . E . , Dalgarno. A. : 1981. Phys. Rev. A

23.

1100.

12

-

Felkert, C. A.

.

Bllnt. A. J . . Surrat. G. T.

.

Watson. W. D. : 1984. Astrophys. J. 289.

371.

13

-

Gargaud, M . . McCarroll, R. : 1985. J. Phys. B

s.

463.

14

-

Opradolce, L.

.

McCarroll, R. , Valiron. P. : 1985, Astron. Astrophys.

148.

229.

15

-

Phaneuf, R.A. : 1983. Phys. Rev. A

3.

1310.

16

-

Church, D . A . , Hoizschelter. H. M. : 1982. Phys. Rev. Lett. ffP_. 643.

17

-

d r i ~ , D . , Brazuk. A . . Dljkkamp, D . , de Heer. F. J . . Wlnter. H. : 1985. J. Phys. 8 18. 3629.

18

-

m k l e , F. G . , Youslf. F. B . . McCullough. R. W.. Geddes. J . . Gilbody. H. 8. : 1985.

J. Phys. B

18.

479.

(12)

19

-

Politis. M. F.

.

Jouln. H . . Bonnefoy, M., Bonnet. J. J . . Chassevent. M.. Fteury. A

.

Bliman. S . . Harei. S. : 1987. J. Phys. B

20.

2267.

20

-

Proceedlngs

loth

Inter. Conf. on 'Plasma Physlcs and controlled nuclear fuslon research" (London. 1984)

.

21

-

Hulse, R . A . . Post. D . E . , Mlkkelsen, D.R. : 1980. J. Phys. B

13.

3895.

22

-

Ashby. D.E.T.F., Hughes, M. H. : 1981. Nucl. Fusion

gt.

911.

23

-

Fonck, R. J . , et at. : 1982, Phys. Rev. Lett.

9 .

737.

24

-

Schumacher. U. : 1987. Physica Scripta

16.

143.

25

-

Glrard, J. P., Marty. D . A . , Morlette, P. : 1975. Proceedings 5th Int. Conf. on 'Plasma Physlcs and controlled nuclear fuslon research". (Tokyo. 1974). p. 681.

26

-

Proceedings Conf. Phys. of "Multiply charged ions". Anderson. H. H . . Picraux. S.T..

eds. In Nucl.ear Instrument and Methods in Physics Research. Vol B

23

(1987).

27

-

Kailne,E.. Kallne, J., Dalgarno. A.. Marmar. E.S.. Rice. J. E . . Pradhan. A. K. : 1984, Phys. Rev. Lett.

52,

2245.

28

-

Gllllgan. J. G.

.

Gralnick. S. L. , Price, W. G.

.

Jr.

.

Kammash. T. : 1978. Nucl. Fusion 10.63.

29

-

Rice. J. E . . Marmar. E . S . . Terry. J. L . . Kallne. E. Kallne, J : 1986, Phys. Rev.

Lett.

56.

50.

30

-

Carolan. P. G.

.

et al. : 1987. Phys. Rev. A

35.

3454.

31

-

Kato. T.. Morlta. S . . Masai. K. : 1987. Phys. Rev. A

36.

795.

32

-

Baliunas. S. L.

.

Butler. S. E. : 1980, Astrophys. 'J. Letters

235.

L45.

33

-

Marlska. J. T. : 1986. Annual Rev. Astron. Astrophys. 24. 23.

34

-

Raymond. J. C.. Dupree, A. K. : 1978. Astrophys. J.

@.

379.

35

-

Dere, K. P . , Bartoe, J. -D. F. , Brueckner, G. E.

.

Dykton. M. D.

.

VanHouster. M. E. : 1981. Astrophys. J.

249,

333.

36

-

Brueckner, G. E. : 1980, In Solar Active Regions, Orrall. F. Q.

.

ed.

.

Colorado

Associated University Press. p. 113.

37

-

Spitzer, L.

.

Jr. 1978.

38

-

Shields. G.A.. Dalgarno, A.. Sternberg. A. : 1983. Phys. Rev. A

3.

2137.

39

-

Vernaua. J. E . . Reeves. E. M. : 1978. Astrophys. J , suppl.

37.

485.

40

-

Sandlln. G. D . , Bartoe. J.-D. F . . Brueckner. G. E . . Tousey. 13.. Van Houster. M. E. : 1986. Astrophys. J. Suppl. 61. 801.

41

-

Doschek. G.A. : 1987, In ~<goretlcal Problems In High Resolution Solar Physics 11.

Athay. G.

.

Spicer, D . S.

.

eds.. NASA Conf. Pubi. 2483, p . 37.

42

-

Osterbrock. D. E. : 1974, Astrophysics of gaseous nebulae (San Francisco : Freeman).

43

-

POquignot, 0 . . Aldrovandl, S. M.V., Stasinska. G. : 1978. Astron. Astrophys.

E.

313.

44

-

POquignot. D. : 1983. IAU Symposium N 103. Planetary Nebulae. Flower. D. R.

.

ed.

.

p. 173.

45

-

Dalgarno. A . . Sternberg. A. : 1982. Astrophys. J. Letters

257.

L87.

46

-

Dalgarno. A . . Sternberg, A. : 1982, Mon. Not. R. Astr. Soc.

200,

77P.

47

-

Clegg. R. E. S.

.

Harrlngton. J. P.

.

Barlow. M. J.

.

Walsh. J. R. : 1987. Astrophys. J.

314. 551.

48

- c G g .

R. E. S.. Harrlngton, J. P.

.

Storey. P. J. : 1986. Mon. Not. R. Astr. Soc.

m.

61P.

49

-

Clegg. R. E. S.. Walsh. J. R. : 1985. Mon. Not. R. Astron. Soc. c 5 , 323.

50

-

Likkel. L.. Aller, L. H. : 1986. Astrophys. J.

301.

825.

51

-

Osterbrock. D. E . . Daharl, 0 . . Ekberg. J. 0. : 1983. Astrophys. J. Letters 273. L31 52

-

Sternberg. .A.

.

Dalgarno. A. : 1987. Comments Astrophys.

.

In press.

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