The Rydberg Series of Heliumlike Cl, Ar and S and Their High n Satellites in Tokamak Plasmas

The Rydberg series up to n=14 of heliumlike chlorine, argon and sulphur have been observed in Alcator C-Mod plasmas. High n satellites to these lines of the form 1s2s { 1s2snp and 1s2p { 1s2pnp with 3 n 12 have also been seen for chlorine and argon. Accurate wavelengths of these satellites have been obtained, comparison has been made with the theoretical predictions from the atomic structure codes RELAC and MZ, and the agreement is good. Measured line intensities have also been compared with collisional radiative modeling that includes the contributions from dielectronic recombination and inner shell excitation rates to each line's emission, again with good agreement.


I. Introduction
The high n Rydberg series of medium Z heliumlike ions have been observed from Z-pinches 1,2 , laser produced plasmas 3 , exploding wires 2 , the solar corona 4 , tokamaks 5-7 and ion traps 8 .Always associated with x-ray emission from these two electron systems are satellite lines from lithiumlike ions.Comparison of observed x-ray spectra with calculated transitions can provide tests of atomic kinetics models and structure calculations for helium-and lithiumlike ions.From wavelength measurements, a systematic study of the n and Z dependence of atomic potentials may be undertaken.From the satellite line intensities, the dynamics of level population by dielectronic recombination and inner shell excitation may b e addressed.
Satellites to the Ar 16+ Rydberg series for n=2 9,5 , n=3 2,7 and n=4,5 5,6 have been examined extensively.Theoretical calculations of n3 satellites for argon and other elements are plentiful 6,10-13 .For n6 satellites, some wavelengths have been reported 2,5,6 , and wavelengths and oscillator strengths have been calculated up to n=7 1,2 , but various wavelength calculations di er from the measured values by 3 m A. Observations for Cl 15+ n=2 transitions have been made in Alcator A 14 , Alcator C 15 , JET 16 and COMPASS-D 16 plasmas, and n=3 transitions have been seen in laser produced plasmas 3 .
The organization of this paper is as follows.The code description and experimental setup are given in Section II.Observations and code comparisons for the Rydberg series of heliumlike C l 15+ between n=3 and 14, and the high n satellites of Cl 14+ with 3 n 10 are presented in Section III.Similar results for argon are shown in Section IV.The observed Rydberg series of S 14+ and calculations, including S 13+ satellites, are given in Section V.

II. Code Descriptions and Experiment
Ab initio atomic structure calculations for the lithium-, helium-and hydro-genlike isosequences of S, Cl and Ar Z=16, 17 and 18 with 2 n 14 have been generated using the HULLAC package.HULLAC includes ANGLAR, which uses the graphical angular recoupling program NJGRAF 17 to generate ne structure levels in a jj-coupling scheme for a set of user-speci ed electron con gurations.HULLAC then generates atomic wavefunctions using the fully relativistic, parametric potential code RELAC 18,19 , which calculates the full multi-con guration, intermediate coupled level energies and radiative transition rates.RELAC also computes semi-relativistic autoionization transition rates 20 to the ground and excited levels of an adjacent ion.The CROSS 21 suite of codes in the HULLAC package uses the factorization theorem of Bar-Shalom, Klapisch and Oreg to compute the distorted wave approximation electron-impact excitation rates between all levels of each c harge state mentioned above.This includes levels formed by exciting valence shell electrons as well as deeply bound inner shell electrons.
Energy levels and transition probabilities have also been calculated by using the Z-expansion method MZ code.The energy matrix is constructed in an LSJ coupling scheme and relativistic corrections are included within the framework of the Breit-Pauli operator using a perturbation approach.The MZ method uses hydrogenic wavefunctions.However, the calculation energies and other characteristics by this method are greatly improved by using many-body perturbation theory to include the Coulomb i n teraction between electrons as well as relativistic corrections.The Z-expansion method has been described in detail in Refs.22,23 .
The ionic transition rates, including the autoionization rates from the Li-to He-like and He-like to H-like ions, as well as direct impact ionization including ionization from valence and inner shell orbitals and radiative recombination rate coe cients are used to construct the collisional-radiative rate matrix, R i!j , where n j is the population in level j, and R i!j is the total rate for transitions between level i and j.The inverse of each ionization process, namely dielectronic recombination and three body recombination has been found according to the principle of detailed balance.The bare nuclei for S, Cl and Ar are also included in the rate matrix; the relative populations of the four charge states are found in the steady state by setting the time derivative of the population in each level equal to zero and inverting the matrix.
The lithiumlike satellite transitions to the heliumlike resonance lines considered here can be excited by t wo mechanisms, inner shell electron impact excitation of the lithiumlike ion, 1s 2 2l + e !1s2lnl 0 + e 2 or dielectronic recombination from the heliumlike ion, 1s 2 + e !1s2lnl !1s 2 2l + 3 where 1s2lnl is a singly or doubly excited autoionizing lithiumlike level, 1s 2 2l is a stable lithiumlike level and is the observed photon.The emissivity of a line from level j of ion Z excited by electron impact excitation is given by where n e and n Z are the electron and ion densities, C Ex T e is the impact excitation rate coe cient and R j;f is the radiative branching ratio for the observed transition from level j to level f.The inner shell excitation channel makes a signi cant contribution to a lithiumlike satellite line's intensity only when the initial level is the lithiumlike ground level.For the lines in the tables of Sections III and IV that end on excited levels of the lithiumlike ion, the dominant excitation mechanism is via dielectronic recombination.
The emissivity " DR of a lithiumlike satellite excited by dielectronic recombination can be expressed as " DR = n e n He F 1 T e F 2 j; f 5; where all the temperature dependence is contained in exp,E i;j =T e 6; where a 0 is the Bohr radius, R is the Rydberg unit of energy and E i;j is the energy of the captured electron.The satellite intensity factor due to dielectronic recombination from level i of ion Z+1+ through level j of ion Z+ to level f is given by F 2 j; f = g j g i A A j;i R j;f 7; where the gs are the statistical weights of the intermediate autoionizing and initial recombining levels, A A j;i is the rate of autoionization from level j to level i, and is the branching ratio for radiative stabilization for the observed transition.The sum over i in Eq.8 runs over all levels in the next higher ion reachable from level j by autoionization, and the sum over f runs over all bound levels reachable from j by radiative decay.Radiative decays from level j to other autoionizing levels have been neglected; stabilization following transitions between continuum levels has a small e ect on the computed branching ratio.All atomic data required for Eq.5 have been generated ab initio with RELAC 19,20 .
A lithiumlike dielectronic satellite line j!f and the corresponding heliumlike resonance line w n can be used as a temperature diagnostic of the local plasma conditions by dividing Eq.4 by Eq.5, where the branching ratio for the heliumlike resonance line is assumed to be one, and recombination population of the upper levels of w n has been ignored.For n=2, this ratio has been routinely used for electron temperature determination 15,24 .The advantage of using these line ratios is that the result is independent o f t h e heliumlike c harge state density.
The x-ray observations described in the following sections were obtained from the Alcator C-Mod 25 tokamak, a compact minor radius a22 cm, elongation 1:8, high eld device with all molybdenum plasma facing components.All of the results here are for Ohmic deuterium plasmas, with the central plasma parameters in the range of 0.910 20 m 3 n e0 1.810 20 m 3 and 900 eV T e0 2600 eV.
The x-ray spectra presented were recorded by a v e c hord, independently spatially scannable, high resolution spectrometer array 26 .Each spectrometer has a resolving power, , of 4000, a 2 cm spatial resolution and a luminosity function of 7 x 1 0 ,9 cm 2 sr.Measured line widths are usually dominated by Doppler broadening.Recently, one of the ve spectrometers has been t with an ADP crystal, which has a 2d spacing of 10.640 A, to allow access to longer wavelengths.In the present paper, high resolution x-ray observations in the wavelength range 2.98 A 4.52 A are shown.Wavelength calibration 27 has been achieved after determining the instrumental dispersions in reference to H-and He-like argon, chlorine and sulphur lines and previously measured molybdenum 28 lines.Lines from hydrogenlike 29,30 ions are taken to have precise wavelengths, either measured or calculated.The accuracy of measured wavelengths described here is 0.3 m A, determined mainly from the quality of the line ts, and is less than the di erences in various calculated Li-like w avelengths.The argon was pu ed into the plasma through a piezo-electric valve and the chlorine was introduced by freon C 2 Cl 3 F 3 injection utilizing a fast scanning probe 31 .Chlorine is also present a s a n i n trinsic impurity from solvents used to clean vacuum components.Presumably sulphur is a trace impurity in the molybdenum.

III. Chlorine Experimental Observations and Code Comparsions
To provide adequate chlorine levels in the plasma, freon tri-chloro-tri-uoroethane has been injected using the fast scanning probe.Shown in Fig. 1 are the time histories of the electron and chlorine densities, the electron temperature and the brightnesses of spectroscopic lines from uorine F 6+ , 883.1 A and chlorine Cl 15+ , 4.44 4.50 A for a discharge that had freon injections at 0.5 and 0.8 seconds.The impurity con nement for these halogens is very similar to that for other nonrecycling impurities injected by laser blow-o into L-mode plasmas 32 .At the beginning of the discharge there is substantial intrinsic chlorine and uorine from solvents and exposed te on present u n til the plasma becomes diverted around .25 s, when impurity penetration drastically decreases 33 .The chlorine density has been determined from the brightnesses of the n=2 to 1 transitions 14-16 of Cl 15+ in a similar fashion to the argon density measurements 34 .The electron density w as measured by a t wo color interferometer and the electron temperature was determined from electron cyclotron emission measurements.An x-ray spectrum in the vicinity of the n=3 resonance line of Cl 15+ , 1 s 2 1 S 0 1s3p 1 P 1 w 3 , is shown in Fig. 2. The upper level is 0.75 , 1s 1=2 3p 3=2 1 + 0.25 , 1s 1=2 3p 1=2 1 in jj-coupling notation.This admixture of the two J=1 levels for 1snp has almost the exact same proportion 75:25 for all n values that have been checked n 14.Also visible in this spectrum is the intercombination line y 3 , 1s 2 1 S 0 1s3p 3 P 1 , at 3794.7 m A, and four groups of unresolved satellites denoted A 3 , B 3 , A 0 3 and C 3 .A 3 and A 0 3 have upper levels of the form 1s2p3p which are populated by dielectronic recombination of Cl 15+ , while B 3 and C 3 have upper levels of the form 1s2s3p which can either be populated by dielectronic recombination or inner shell excitation of Cl 14+ .The brightest chlorine lines contributing to the spectrum of Fig. 2 are listed in Table I, which includes the transition designations jj-coupling, calculated wavelengths from MZ and RELAC, satellite capture energies as in Eq.6, oscillator strengths satellite intensity factors Eq.7 and inner shell excitation rates as in Eq.4,evaluated at 1500 eV.Shown for comparison in the lower frame of Fig. 2 is a synthetic spectrum, generated with the calculated wavelengths from RELAC, Doppler and instrumental line widths and intensities from the collisional radiative model described above.The line intensities are determined from the emissivities of Eqs.4 and 5, using mea-sured electron temperature and density pro les, with charge state density pro les calculated from the impurity transport code MIST 35 including the appropriate impurity transport coe cients 32 .The line brightness is then determined by integrating the emissivity pro le along the observation line of sight for each transition.The observed spectrum was obtained from a plasma which had a central electron temperature of 1200 eV and a central electron density of 1.810 20 m 3 .The agreement b e t ween the calculated and the observed spectra is good.There is strong con guration interaction in the RELAC calculations between the 1s2p3p upper levels of the A 3 and A 0 3 transitions and the 1s2s3s and 1s2s3d levels.Here the con guration interaction pushes up" or raises the 1s2p3p level energies.When the con guration interaction is turned o , the calculated wavelengths for the transitions making up A 3 and A 0 3 increase by about 3.5 m A these shifted wavelengths are what is plotted in Fig. 2.This interaction is seen to diminish rapidly with increasing n.Molybdenum lines 28 at 3785.7, 3831.0 and 3834.6 m A contaminate this spectrum.
While the relative i n tensities calculated for the satellites are in good agreement, the predicted intensity for the intercombination line y 3 is too low.The observed ratio of y 3 w 3 is 0.05 while the calculated value is 0.030.This has also been observed in argon 7,6,8 and iron 36 .There is a predicted feature at 3810.5 m A that is due to lithiumlike transitions of the form 1s 2 3l 1s3l3l 0 .These satellites to the w 3 and y 3 lines are fed almost exclusively by dielectronic recombination from the ground level of Cl 15+ , although some of the low-lying excited levels of that ion are also reachable by autoionization.Transitions of the type 1s 2 3l 1s3lnl 0 for n 3 appear on the long wavelength side of the w 3 line.Blending of these high-n satellites with the y 3 line may contribute to the underestimate of the y 3 intensity in the collisional-radiative model 7,8,36 , however since the 1s 2 3l 1s3l3l 0 feature is so weak, it is unlikely that this is the cause of the remaining discrepancy.There is a phenomenon that is known in the study of con guration interaction where the strength of a class of transitions is transfered to a higher energy class of transitions when the upper levels of the two classes are interacting 37 .This was seen with the 2p 5 1=2 6d and 2p 5 3=2 7d levels in Ne-like Zr, Nb, Mo and Pd ions; when the 2p 5 1=2 6d and 2p 5 3=2 7d levels crossed, the direction of the strength transfer was reversed 38 .It could be that mixing between the two 1snp 1;3 P 1 levels transfers strength from the lower energy 3 P 1 level to the higher energy 1 P 1 level, thus suppressing the y 3 line.There is no way to turn o this mixing in the RELAC calculations.
The corresponding spectrum near w 4 1s 2 1 S 0 1s4p 1 P 1 i s s h o wn in Fig. 3, and two groups of satellites are apparent, A 4 and B 4 , with a trace of C 4 also A 5 , in addition to molybdenum lines 28 at 3621.1 and 3671.0 m A. The line at 3649.6 m A is of unknown origin.A 4 is composed of lines which h a ve upper levels of the form 1s2p4p which are populated by dielectronic recombination, while B 4 and C 4 have upper levels of the form 1s2s4p which can either be populated by dielectronic recombination or inner shell excitation.The transitions contributing to these satellite groups are summarized in Table II.This spectrum was obtained from a c hord viewing 8 cm below the midplane r a=0.3 in a discharge that had n e0 = 1.610 20 m 3 and T e0 = 1260 eV.Also shown in Fig. 3 is a synthetic spectrum, as described above, with satellite wavelengths from MZ, and the agreement with the observed spectrum is very good.Moving to higher n, the spectrum near w 5 1s 2 1 S 0 1s5p 1 P 1 is shown in Fig. 4, which also includes w 4 and the Cl 16+ Ly doublet the individual lines of which are unresolved.The satellite groups A 5 and C 5 are seen, but B 5 is hidden beneath w 4 .As the w n series crowds closer together in wavelength, so do the corresponding satellite groups, and A 6 , B 6 , A 7 and B 7 are also present in this spectrum.Tables III and IV include the relevant information for these lines.The synthetic spectrum using the satellite wavelengths from MZ is shown at the bottom for comparison, again with good agreement.T e0 and n e0 for the discharge for which this spectrum was obtained were 1260 eV and 1.610 20 m 3 , respectively.Another mystery line, at 3570.4 m A, is present.
Finally, the Rydberg series with up to w 14 resolved is shown in Fig. 5, for two di erent times during a 5.4 T, deuterium discharge.In the bottom frame is the spectrum from the early portion, when the discharge was limited, with n e0 = 1.410 20 m 3 and T e0 = 1650 eV; there are molybdenum lines at 3439.2, 3442.8,3445.0,3447.8 and 3450.3 m A, respectively 28 , which dominate over w 8 .The spectrum in the top frame is from later in the discharge, with n e0 = 1.610 20 m 3 and T e0 = 1260 eV, which also had argon injection, and satellites from w 3 in argon 7, and next section cover the chlorine w 9 , w 10 and w 14 .The dotted vertical lines show the calculated RELAC wavelengths.Between the two spectra, all the lines from w 7 to w 14 are resolved.Two sets of calculated wavelengths, from RELAC and MZ, for the Rydberg series of Cl 15+ are presented in Table V.The agreement between the two calculations is very good, with the largest di erences of one part in 10 4 , within the experimental uncertainty.
The measured wavelengths of the high n satellite groups unresolved in Cl 14+ are also summarized in Table V, along with the wavelength di erences between the observed satellite groups of a give n n n umber and the corresponding resonance line calculated from RELAC.The theoretical wavelengths RELAC for the resonance lines for the Cl 15+ Rydberg series have been used for the wavelength calibration.The measured wavelength di erences between the resonance lines, w n , and the satellite groups A n , B n and C n , as a function of n are shown in Fig. 6.The curves are the theoretical values, from the calculated wavelengths of Tables I V; the solid lines represent the wavelengths from MZ while the dash-dot-dot-dot lines use the wavelengths from RELAC.These values are taken from the centroids of the calculated satellite groups, as shown in the synthetic spectra.Overall the agreement b e t ween theory and experiment i s v ery good, although there is a systematic shift of about 3 m A for the A n lines calculated from RELAC.This o set is possibly due to the con guration interaction in RELAC described above b e t ween the 1s2pnp and the 1s2sns and 1s2snd levels which raises the energy of the upper levels in the A n transitions.The con guration interaction between 1s2s4p and 1s2p4s levels and between 1s2s5p and 1s2p5s levels causes the bumps in the C n and B n curves at n=4 and n=5, respectively.

IV. Argon Observations and Code Comparison
The corresponding high n transitions and satellites have also been observed in argon.Because argon is a recycling gas, it remains in the plasma for a much longer duration than the chlorine, which allows for weaker lines to be studied.Shown in Fig. 7 is a spectrum from argon including w 4 , w 5 and w 6 from Ar 16+ , L y from Ar 17+ and the satellite groups A 5 -A 12 , B 5 -B 8 and C 5 -C 7 .Plasma parameters for the discharge from which this spectrum was obtained were n e0 = 1.310 20 m 3 and T e0 = 1550 eV.A synthetic spectrum using the calculated satellite wavelengths from MZ is shown in the bottom frame, and the agreement is quite good.The transition designations, calculated wavelengths, satellite capture energies, oscillator strengths satellite intensity factors and inner shell excitation rates evaluated at 2000 eV for Ar 15+ satellites between n=4 and n=12 may be found in Tables VI-X.The measured wavelength di erences between the resonance lines, w n , and the satellite groups A n , B n and C n , as a function of n for argon are shown in Fig. 8. Also shown are the theoretical values curves, from the calculated wavelengths of Tables VI-X; the solid lines are from the MZ wavelengths and the dash-dotdot-dot lines represent the wavelengths from RELAC.The agreement b e t ween the observed wavelengths and those calculated from MZ is excellent.This Figure may be compared to Fig. 3 in Ref. 6 .The theoretical B n and C n RELAC curves are seen to undergo an appearent discontinuity a t n = 8 .The RELAC calculations for the energy of the 1s2snp levels that give rise to the B n and C n features show strong con guration interaction between the 1s2snp and the 1s2pns and 1s2pnd levels for 3 n 7 that pushes down" the energy of the 1s2snp levels.The calculations predict that this interaction is almost non-existent for n 8, and thus, the upper levels of the B n and C n features jump up" in energy.Again, the calculated wavelengths from RELAC for the A n series are systematically shorter than the observations by a b o u t 2 m A. Here, the con guration interaction between the 1s2pnp and the 1s2snd and 1s2sns for 3 n 7 pushes up" the energy of the 1s2pnp levels.The measured wavelengths and di erences from the RELAC resonance lines of the observed satellite groups are presented in Table XI, along with two sets of calculated resonance line wavelengths.As in the chlorine case, the two calculations for the Rydberg series wavelengths for argon are in excellent agreement.
As demonstrated above, the calculated wavelengths for the heliumlike Rydberg series lines from MZ and RELAC are in excellent agreement.The agreement between the observed wavelengths and those calculated for the lithiumlike satellite groups B n and C n by the two methods is also quite good.For the satellite groups A n , the observed wavelengths and the MZ calculations are also very good, while those from RELAC are systematically 2-3 m A too short.This may be due to residual Coulomb i n teractions among di erent terms of a single con guration in the upper levels of the A n transitions.A comparison may also be made for the satellite intensity factors calculated via the two approaches.Shown in Fig. 9 are the satellite intensity factors calculated from RELAC and MZ for the satellites of Ar 15+ .There is excellent agreement for the transitions which contribute to A n and B n , over two orders of magnitude.In general, most of the points are within 20 of each other for the two calculations.The largest deviations are found for the transitions contributing to C n , and in particular for C 3 .H o wever, for the plasma conditions considered here, where the population of the upper levels of C 3 is dominated by inner shell excitation of lithiumlike argon, it is di cult to distinguish between the F 2 's computed by the two methods.Spectra of w 4 and satellites for plasmas with di erent central electron temperatures are shown in Fig. 10.As the temperature decreases, the intensities of the satellite groups relative t o w 4 increase; in the bottom frame with an electron temperature of less than 1000 eV, the satellite group A 4 is nearly as bright as the resonance line.Similar observations were made from Alcator C 5 , from radial pro le measurements; in fact near the plasma periphery, the satellite group A 5 was actually brighter than w 5 .Also shown in the Figure are the corresponding synthetic spectra, generated as described above using the MZ wavelengths, which h a ve been normalized to w 4 .The relative i n tensities of the satellites A 4 , B 4 and C 4 and A 5 are well reproduced for these three di erent electron temperature plasmas, supporting the dielectronic recombination and inner shell excitation rates presented in the Tables.A strong molybdenum 28 line at 3230.1 m A is visible in these spectra.
There is evidence for the argon intercombination line y 4 on the long wavelength side of w 4 .Shown in Fig. 11 is the spectrum in the immediate vicinity o f w 4 ; the observed spectrum is depicted by the asterisks.The solid green curve centered 3199.6 m A is the calculated resonance line, normalized at the peak, with the appropriate width from the instrumental resolution and Doppler broadening.The green curve centered at 3201.6 m A is the intercombination line y 4 , with the calculated wavelength but with the observed intensity.Shown in purple are two heliumlike satellites to Ar 17+ Ly , 1s2s 1 S 0 2p3s 1 P 1 and 1s2p 1 P 1 2p3p 1 D 2 , with calculated wavelengths of 3197.7 and 3206.6 m A, respectively.The former decay is enabled by con guration interaction between the 2p3s 1 P 1 level and the 2s3p 3 P 1 and 2s3p 1 P 1 levels the calculation of the interaction is actually carried out in intermediate coupling on jj-coupled basis functions.In the collisional-radiative model, at T e = 2 k eV these lines are excited more than 99 by dielectronic recombination from the ground level of the hydrogenlike ion.The solid black curve is the composite calculated spectrum, which agrees well with the data points.Without inclusion of the theoretical y 4 line, there would be excess emission around 3202 m A. The actual best t experimental wavelength for y 4 is 3201.3m A, which agrees well with the calculation.The calculated ratio of y 4 w 4 for these discharge conditions 2050 eV and 1.110 20 m 3 is 0.029, whereas the observed ratio is around 0.05 in Fig. 11.This may be related to the ratio y 3 w 3 observed to be a factor of two higher than predicted 7 .Spectra near the Ar 16+ Rydberg series limit 5 are shown in Fig. 12.The top spectrum was taken along the central chord of a plasma with n e0 = 0.910 20 m 3 and T e0 = 2600 eV.The resonance lines from w 6 to w 14 are clearly resolved, and there is a region of enhanced brightness from w 15 up to the series limit at 3008.8 m A, presumably due to unresolved lines.Along this chord, most of the line emission is from the plasma center where electron impact excitation is the dominant mechanism for populating the upper levels.The continuum at wavelengths shorter than the limit is greater than the continuum level between the resonance lines, and is due to radiative recombination 5 .Ar 17+ Ly near 2987.4m A is also prominent.The corresponding spectrum from an identical plasma, but taken along a chord viewing through r a = 0.67, where the electron temperature was 1100 eV and the electron density w as 0.810 20 m 3 , i s s h o wn in the middle frame of Fig. 12.The lines are greatly reduced in intensity and the widths are very narrow due to the lower ion temperature.The intensities of w 9 and w 10 are enhanced relative to the trend of decreasing intensity with increasing n number, which is due to population by c harge exchange recombination with intrinsic neutral deuterium in the ground state, near the plasma edge 39,5 .Emission from the very high n levels n 25 is also visible just on the long wavelength side of series limit.Along this chord, however, the lines w 11 through w 14 are not visible.The viewing chord of the middle spectrum was 18.5 cm above the mid-plane in a discharge with a lower X-point.The spectrum shown in the bottom frame is from a somewhat similar plasma, from a chord viewing through r a = 0.62, but 19.7 cm below the mid-plane, for a lower X-point discharge.In this case w 10 is enhanced relative to the other w n lines due to population by c harge exchange with intrinsic neutral deuterium in the ground state and the feature on the long wavelength side of the limit is now dominant.This feature is from n numbers between 30 and 40, and is due to charge exchange between hydrogenlike argon and intrinsic neutral deuterium in the n=3 and n=4 excited states 39,5 .The reason that this feature is so prominent in the bottom of the plasma near the X-point is because the neutral density is concentrated there 24,33 .Why there is no feature from n20 at 3018 m A, which w ould be from charge exchange n=2 excited deuterium, is unknown.In this spectrum, w 12 through w 14 are again absent.Why w 11 is visible here but not in the spectrum from above the midplane is not clear, but may be related to the fact that w 10 is strong here, and w 9 was dominant in the middle spectrum.The bottom spectrum was obtained from a di erent plasma on a di erent d a y from a di erent spectrometer.

V. Sulphur Observations and Code Comparison
Finally, the Rydberg series of heliumlike S 14+ from w 5 to w 13 is shown in Fig. 13, which w as obtained from a plasma with n e0 = 2.010 20 m 3 and T e0 = 1100 eV.Unlike the cases of argon and chlorine, for sulphur the hydrogenlike L y doublet is on the short wavelength side of w 5 .Also apparent is a molybdenum line at 3834.8 m A 28 , in addition to A 3 in Cl 14+ .The wavelengths and oscillator strengths for the heliumlike lines calculated by RELAC and MZ are presented in Table XII, again with the wavelengths in excellent agreement.The simulated spectrum is also shown in Fig. 13.The strongest components of the satellite groups A n are the transitions of the form 1s 2 2p J= 3  2 1s2p 3=2 np 3=2 5=2 1s 2 2p 2 P3 2 1s2p 3 Pnp 2 D5 2 in LS coupling notation.The wavelengths and satellite intensity factors for these transitions calculated from MZ and RELAC with 3 n 10 for S 13+ are presented in Table XIII.Similar to the cases for chlorine and argon, the RELAC wavelengths are 3.5 m A longer, while the F 2 values are in excellent agreement.
The sulphur levels in Alcator C-Mod are too low for these satellites to be measured.

VI. Conclusions
The high n Rydberg series of heliumlike Cl, Ar and S have been observed from Alcator C-Mod plasmas.The associated lithiumlike satellites up to n=12 for Cl and Ar have also been seen.Comparison of observed satellite wavelengths has been made with calculations from two di erent atomic structure codes, RELAC and MZ, and there is good agreement in general, although the A n s from RELAC, with lower levels of the form 1s 2 2p, di er by 2-3 m A. Calculated wavelengths for the heliumlike resonance lines, w n , from the two di erent methods are in excellent agreement.The calculated intensities of the satellite groups relative to the resonance lines are also in good agreement with the observed line brightnesses, verifying the dielectronic recombination and inner shell excitation rates.The large majority o f the satellite intensity factors, F 2 , computed by the two approaches, is within 20.The intercombination line y 4 has been observed for argon.

Table Captions
Table I.
The Cl 15+ n=3 resonance and intercombination lines, with Cl 14+ satellites.The transition designations the largest basis function in the intermediatecoupling calculation, calculated wavelengths, satellite capture energies, oscillator strengths satellite intensity factors and inner shell excitation rates at 1500 eV are given for the strongest lines.In the 3 rd and 4 th columns are the calculated wavelengths, in m A, from the MZ and RELAC codes, respectively.The satellite capture energies from RELAC in the 5 th column are in eV.For the resonance and intercombination lines, the entries in the 6 th column are the oscillator strengths from RELAC, while for the satellites, the entries in the 6 th column are the satellite intensity factors, F 2 , from Eq.7 RELAC, in units of s ,1 .The units for the inner shell excitation rates from RELAC in the 7 th column are cm 3 s.Powers of 10 are in brackets, .
Table II.
The calculated Cl 15+ n=4 resonance and intercombination lines, with Cl 14+ satellites.The legend is similar to that in Table I.

Table III.
The Cl 15+ n=5 resonance and intercombination lines, with satellites.

Table V.
Two calculations of the Cl 15+ Rydberg series wavelengths, from MZ in the 2 nd column and from RELAC in the 3 rd column.Measured satellite group wavelengths, and measured wavelength di erences between the resonance lines and the satellite groups are in columns 4-9.All wavelengths are in m A.

Table VI.
The Ar 16+ n=4 resonance and intercombination lines, with satellites.The transition designations, wavelengths, satellite capture energies, oscillator strengths satellite intensity factors and inner shell excitation rates at 2000 eV are given for the strongest lines.The legend is similar to that in Table I.

Table VII.
The Ar 16+ n=5 resonance and intercombination lines, with satellites.

Table VIII.
The Ar 16+ n=6 resonance and intercombination lines, with satellites.

Table IX.
The Ar 16+ n=7 resonance and intercombination lines, with satellites.
Table XI.Two calculations of the Ar 16+ Rydberg series wavelengths, measured satellite group wavelengths, and measured wavelength di erences between the resonance lines and the satellite groups.All wavelengths are in m A.

Table XII.
Two calculations of the S 14+ Rydberg series wavelengths in m A, along with radiative transition probabilities s ,1 and oscillator strengths.

Table XIII.
Two calculations of the strongest components of the A n series in S 13+ , 1 s 2 2p J= 3  2 1s2p 3=2 np 3=2 5=2 .W avelengths are given in columns 2 and 3, satellite intensity factors are presented in columns 4 and 5, capture energies from RELAC are shown in column 6 and in the last column are inner shell excitation rates at 1500 eV from RELAC.

Figure Captions
Fig. 1 The time histories of several parameters of interest for a discharge with freon injections at 0.5 and 0.8 seconds.In the top frame are the electron solid green and chlorine dash-dot-dot-dot red, 10 4 densities, in the middle frame is the central electron temperature and in the lower frame are the lithiumlike 883 A uorine green and heliumlike 4.44 4.50 A chlorine red line brightnesses, with an arbitrary scale.Fig. 2 The observed x-ray spectrum of the heliumlike C l 15+ resonance line w 3 with the intercombination line y 3 and satellites is shown on a linear scale in the top frame.In the bottom frame is a log plot, including a simulated spectrum with w 3 and y 3 shown in green, and the satellite groups shown in red.Fig. 3 The x-ray spectrum of the Cl 15+ resonance line w 4 with satellites.The calculated He-like Li-like spectrum is shown in green red.Fig. 4 The x-ray spectrum of the Cl 15+ resonance lines w 5 and w 4 , with satellites, and hydrogenlike C l 16+ Ly .The simulated H-like, He-like and Li-like spectra are shown in purple, green and red, respectively.Fig. 5 The high n series of Cl 15+ with n between 7 and 14.The top spectrum includes some argon lines which obscure the transitions with n = 9, 10 and 14, while the bottom spectrum contains several molybdenum lines which dominate the n = 8 transition.The vertical dotted lines indicate the calculated wavelengths.Fig. 6 The di erence between the satellite group wavelengths and the resonance line wavelengths in Cl 15+ as a function of n, for the three satellite groups.The measured values for A n , B n and C n are depicted as red asterisks, green triangles and purple dots, respectively.The satellite group A 0 3 is shown as the orange .The theoretical wavelength di erences are shown by the appropriately colored curves, with the calculated value for A 0 3 from RELAC given by the orange dot.The solid lines are from MZ, while the dash-dot-dot-dot lines are from RELAC.The largest error bars are shown.Fig. 7 The linear scale x-ray spectrum of heliumlike A r 16+ w 4 , w 5 and w 6 , with satellites, and hydrogenlike A r 17+ Ly , i s s h o wn in the top frame.In the bottom frame is the log scale observed spectrum black and the computed spectrum for Ar 16+ green, Ar 17+ purple and Ar 15+ red.Fig. 8 The di erence between the satellite wavelengths and the resonance line wavelengths in Ar 16+ as a function of n, for the three satellite groups, along with the theoretical wavelengths.The legend is the same as in Fig. 6.Fig. 9 The Ar 15+ satellite intensity factors computed from RELAC abscissa and MZ ordinate.The red asterisks, green triangles, orange s and purple dots are for the various transitions contributing to the satellite groups A n , B n , A 0 n and C n , respectively.Fig. 10 The observed x-ray spectra of Ar 16+ w 4 with satellites, for three di erent central electron temperatures, are shown in black.The calculated spectra for w 4 , A 4 and A 5 are shown in red, C 4 in purple and B 4 in green.Fig. 11 The observed spectrum in the immediate vicinity o f w 4 in Ar 16+ is shown by the asterisks.The solid green curves are the calculated lines for w 4 and y 4 , the red curve is for the satellite group A 5 and the purple curves are for two satellites to Ly in Ar 17+ .The solid black curve is the composite calculated spectrum.Fig. 12 Spectra near the Ar 16+ series limit.In the top frame is the spectrum from a central chord view, in the middle frame is a spectrum from an identical plasma with a view 18.5 cm above the midplane r a=.67 and in the bottom frame is a spectrum from a similar plasma with a view 19.7 cm below the midplane r a=.62.
The ionization limit is shown as the vertical line.The lower spectrum was cut o below 2990 m A. Fig. 13 The Rydberg series of heliumlike S 14+ for n5.In green purple is the simulated spectrum for S 14+ S 15+ .

Table I .
Cl 15+ n=3 Lines with Satellites

Table VI .
Ar 16+ n=4 Lines with Satellites

Table VII .
Ar 16+ n=5 Lines with Satellites

Table XII .
Calculated S 14+ w n Rydberg Series n M Z m A Rel m A A ij s ,1 g f