experimental investigations of ion charge distributions, effective

The Astrophysical Journal, 702:838–850, 2009 September 10  C 2009.

doi:10.1088/0004-637X/702/2/838

The American Astronomical Society. All rights reserved. Printed in the U.S.A.

EXPERIMENTAL INVESTIGATIONS OF ION CHARGE DISTRIBUTIONS, EFFECTIVE ELECTRON DENSITIES, AND ELECTRON–ION CLOUD OVERLAP IN ELECTRON BEAM ION TRAP PLASMA USING EXTREME-ULTRAVIOLET SPECTROSCOPY 1 ´ G. Y. Liang1,2,5 , J. R. Crespo Lopez-Urrutia , T. M. Baumann1 , S. W. Epp1 , A. Gonchar1 , A. Lapierre3 , P. H. Mokler1 , 1 1 1 ¨ , K. Yao4 , G. Zhao2 , Y. Zou4 , and J. Ullrich1 M. C. Simon , H. Tawara , V. Mackel 1

Max-Planck-Institut f¨ur Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany; [email protected], [email protected] 2 National Astronomical Observatories, CAS, A20 Datun Road, Chaoyang District, Beijing 100012, China TRIUMF, Canadian National Laboratory for Particle and Nuclear Physics, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada 4 EBIT Lab, Modern Physics Institute, Fudan University, Shanghai 200433, People’s Republic of China 5 Department of Physics, University of Strathclyde, Glasgow G4 0NG, UK Received 2009 May 6; accepted 2009 July 7; published 2009 August 17

3

ABSTRACT Spectra in the extreme ultraviolet range from 107 to 353 Å emitted from Fe ions in various ionization stages have been observed at the Heidelberg electron beam ion trap (EBIT) with a flat-field grating spectrometer. A series of transition lines and their intensities have been analyzed and compared with collisional-radiative simulations. The present collisional-radiative model reproduces well the relative line intensities and facilitates line identification of ions produced in the EBIT. The polarization effect on the line intensities resulting from nonthermal unidirectional electron impact was explored and found to be significant (up to 24%) for a few transition lines. Based upon the observed line intensities, relative charge state distributions (CSD) of ions were determined, which peaked at Fe23+ tailing toward lower charge states. Another simulation on ion charge distributions including the ionization and electron capture processes generated CSDs which are in general agreement with the measurements. By observing intensity ratios of specific lines from levels collisionally populated directly from the ground state and those starting from the metastable levels of Fe xxi, Fe x and other ionic states, the effective electron densities were extracted and found to depend on the ionic charge. Furthermore, it was found that the overlap of the ion cloud with the electron beam estimated from the effective electron densities strongly depends on the charge state of the ion considered, i.e. under the same EBIT conditions, higher charge ions show less expansion in the radial direction. Key words: line: identification – methods: analytical – methods: laboratory Online-only material: color figures

Since the advent of electron beam ion traps (EBIT), such spectroscopic measurements based upon EBIT have greatly improved in accuracy (Lepson et al. 2002) and are providing new interpretation of astrophysical global fitting models. EBITs are of growing interest for laboratory astrophysics (Silver et al. 2000). They are increasingly used to test model calculations (Chen et al. 2004; Yamamoto et al. 2008), thereby improving the level of confidence that one has in the interpretation of astrophysical data using the same models (Liang et al. 2004). Consequently, it is important to improve our knowledge of the exact conditions (such as the electron density) inside EBITs, and for astrophysicists to know how an EBIT is similar, and different, from astrophysical sources (so they can judge how far to believe the EBIT validations of model calculations). Indeed, by varying the EBIT operational parameters (particularly electron energy over 100 eV to r¯e ) between the spatial distributions of the monoenergetic

Figure 6. Schematic representation of the overlap of electron beam and ion cloud in the trap. re and ri represent the radius of electron beam (dark blue circle) and of ion cloud (trajectories), respectively. If ions in some electronically excited states populated in electron collisions have long lifetimes, they may decay outside the overlap region after excitation. Notes: this is an artist’s representation, a real physical simulation is given in the work of Gillaspy et al. (1995).

electron beam and those of the ion cloud in the trap region. Indeed, the effective electron density (neff e ) governs basically the actual rates of all excitation and ionization processes in the EBIT. g The geometrically averaged electron density (ne ) can be estimated from the electron beam size:   nge = Ie / eπ re2 ve , (5) where e, Ie , re , and v e are the electronic charge, the electron beam current, radius, and velocity, respectively. We estimate the g geometrical electron density ne of 1.6 × 1013 cm−3 under the present conditions (Ee = 5.64 keV, Ie = 320 mA, re = 30 μm). However, we have no information on the spatial distributions of ions in the present experiment and only those forbidden lines can give a true representation of the ion spatial distributions, since the long elapsing time between excitation and radiative decay essentially decouples the light emission spatial pattern from the geometry of the narrow excitation region defined by the electron beam. Then, we have to infer the effective electron density neff e by a suitable spectroscopic diagnostic method, and then derive information on the ion–electron beam overlap factor for each charge state. 5.1.1. Fe xxi Ion Lines

The diagnostic potential of EUV lines from Fe ions for determining neff e had been pointed out previously. The intensity ratios of several partner lines of the carbon-like Fe xxi ion are known to be sensitive to the electron density but rather insensitive to the electron temperature (Ness et al. 2004). This feature follows from the fact that the upper level is populated mainly through collisional excitation from a density-sensitive lower metastable level. As shown in Figure 7, the 2s2p3 3 D2

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Figure 7. Scheme of the processes responsible for the electron density-sensitive lines of the n = 2 → n = 2 transitions in Fe xxi. Only the lowest levels belonging to 2s2 2p2 and 2s2p3 configurations are depicted. Wavelengths (in Å) and radiative branching ratios different from 100% are indicated (dashed lines). Relative magnitudes of collisional excitation strengths at Ee = 5.64 keV are given in percentage as well as represented by the thickness of the corresponding solid lines. (A color version of this figure is available in the online journal.)

level of this ion has a high excitation rate from and decay rate to the metastable 2s 2 2p2 3 P1 level, which is forbidden to decay to the ground state. By increasing the electron density, a significant fraction of the 3 P1 population can be re-excited to the 3 D2 state, which relaxes to the 3 P1 state and, therefore, the line intensity at 142.148 Å increases. On the other hand, through depopulation of the ground state 3 P0 due to the shelving of electrons into the metastable level (if production of the 3 P0 level of Fe xxi from lower charge states is too slow), the excitation to the 3 D1 state and therefore the first resonance line (3 D1 –3 P0 ) intensity at 128.755 Å decreases at high electron densities, as illustrated in Figure 8(a). It is important to note that the 2s2p3 3 D1 state can also decay to the metastable 3 P1 state with a low branching ratio. As this transition line (at 142.278 Å) cannot be resolved from

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the 142.148 Å line due to the limited spectrometer resolution, we have to take this blending effect into account. Since the 2s2p3 3 D1 level is directly populated from the ground state, the intensity of 142.278 Å line has a dependence on ne which is similar to that of the 128.755 Å resonance line, and its relative contribution to the total line intensity becomes dominant below the electron density of ne = 1.0 × 1012 cm−3 . On the other hand, at higher electron densities, the 142.148 Å line becomes more intense. As shown in Figure 8(a), the line intensities, I(142.148 Å), I(142.278 Å), and I(128.755 Å), are calculated for a plasma excited by monoenergetic electrons (Ee = 5.64 keV) and also for thermal electrons (Te = 1.0 × 107 K) as a function of the electron density. These results indicate that the intensity of 142.148 Å line is greatly affected by the electron energy distributions (see the dashed red line in Figure 8(a)). The monoenergetic electron beam populates predominantly the high-lying levels (3 D1 ), whereas thermal energy electrons preferentially feed states with lower excitation energies. These effects result in a difference of the line intensity ratio in the two cases as shown in Figure 8(b). With increasing electron density, the deviations get weaker. By applying the collisional-radiative model described above, we calculated the intensities of the lines of interest for different electron densities for both monoenergetic and thermal electrons. Figure 8(b) demonstrates the intensity ratios of I (142.148 Å)+I (142.278 Å) as a function of the electron density for I (128.755 Å) both cases. The line intensity ratios for monoenergetic electron beam are depicted with three separate lines (blue: 4.5 keV, red: 5.0 keV, and black: 5.64 keV). The hatched bands (gray) indicate the ratio obtained for thermal electrons with the temperatures ranging from 5.0 × 106 to 5.0 × 107 K, showing that the line ratio is not too sensitive to the electron temperature. A noticeable difference of this ratio can be seen between monoenergetic and thermal electrons below the electron density of 3.0× 1012 cm−3 . This different behavior between two modes of excitation is due to the fact that the population of the 2s 2 2p2 3 P1 level, a major excitation channel to the upper 3 D2 level which emits the 142.148 Å line, is greatly influenced by the electron

(b)

Figure 8. (a) Relative line intensities (without polarization effect) of three interest Fe xxi lines as a function of the electron density for mono-energetic electrons at Å)+I (142.278 Å) 5.64 keV (solid lines) and thermal electrons (at Te = 1.0 × 107 K, dashed lines) (b) Line intensity ratio, I (142.148 of Fe xxi as a function of the electron I (128.755 Å) density for monoenergetic electron beams (at 4.5, 5.0, and 5.64 keV) and for thermal electrons at Te = 1.0 × 107 K. Symbols with error bars are the measured line ratios. The hatch areas show predictions for thermal electrons in the temperature range of 5.0 × 106 –5.0 × 107 K. The expanded inset clearly shows the line intensity ratios with polarization effect. (A color version of this figure is available in the online journal.)

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Figure 9. (a) Scheme of the processes responsible for the electron density-sensitive lines of the n = 3 → n = 3 transitions in Fe x. Only the levels of 3s 2 3p 5 and 3s 2 3p 4 3d configurations involved in the transitions of interest are depicted. Wavelengths (in Å) and radiative branching ratios different from 100% are indicated (dashed lines). Relative magnitudes of collisional excitation strengths at Ee = 5.64 keV are given in percentage as well as represented by the thickness of the Å)+I (175.475 Å) corresponding solid lines. (b) Line intensity ratio, I (175.265 , of Fe x as a function of the electron density for monoenergetic electron beam (at 4.5, 5.0, and I (174.526 Å) 5.64 keV). Symbols with error bars are the measured line ratios. (A color version of this figure is available in the online journal.)

energy distributions, as shown in Figure 8(a), resulting from features of electron collision processes that the excitation efficiencies of low energy electrons are higher than those of high energy electrons. By comparing the calculated line intensity ratio I (142.148 Å)+I (142.278 Å) with the present experimental result I (128.755 Å) (0.15 ± 0.01 at 5.64 keV/320 mA, the error in line intensities results from a quadrature sum of the errors from fitting the line shapes and spectrometer response uncertainty shown in Figure 2), the effective electron density was determined to be +0.4 12 −3 neff e = 2.60−0.39 ×10 cm . At slightly different electron beam conditions (taken on different occasions), namely 5.0 keV/ 400 mA and 4.5 keV/197 mA, we have obtained 2.30 ± 0.42 × 11 −3 1012 cm−3 and 7.8+4.0 −3.9 × 10 cm , respectively. The relatively large uncertainties are mainly due to the fact that the observed ratios are already close to the lower density limit (∼ 1011 cm−3 ). When the polarization effect is taken into account, the effec12 tive electron densities are estimated to 1.40+0.35 cm−3 −0.32 × 10 +0.37 12 −3 (5.64 keV/320 mA), 1.12−0.34 ×10 cm (5.00 keV/400 mA), and an upper limit 1.9 × 1011 cm−3 (4.50 keV/197 mA), respectively, indicating that exact information on the polarization is important. 5.1.2. Fe x Ion Lines

We have tried to check our EUV spectroscopy technique for estimating the electron densities using a different ion charge, namely Fe x ions, produced simultaneously under the same EBIT conditions. The upper level (3s 2 3p4 3d 2 D5/2 ) of resonance transition line at 174.526 Å are populated dominantly by direct excitations from the ground state (3s 2 3p5 2 P3/2 ), as shown in Figure 9(a). The population of the excited level 2 D3/2 is dominantly populated by excitation from the metastable level (2 P1/2 , 51%). So the line intensity of the transition (3s 2 3p4 3d 2 D3/2 → 3s 2 3p5 2 P1/2 , with a wavelength of 175.265 Å) is sensitive to the electron density. The upper level (2 P1/2 ) of the transition line at 175.475 Å is also dominantly populated by excitation from the metastable level (25%). Its intensity (relative to that of the resonance line at 174.526 Å) is

also sensitive to the electron density. In the present measurement, this transition line cannot be resolved from the line at 175.265 Å. By taking this blending effect into account, we calÅ)+I (175.475 Å) of Fe x as culate the line intensity ratio I (175.265 I (174.526 Å) a function of the electron density for monoenergetic electron beam (see Figure 9(b)). Based upon this curve and from the present observed ratios, we have determined the effective electron densities to be +1.0 +0.7 11 10 11 −3 1.3+0.5 under −0.3 × 10 , 4.6−0.8 × 10 , and 1.5−0.4 × 10 cm 4.5 keV/197 mA, 5.0 keV/400 mA, and 5.64 keV/320 mA electron beams, respectively. Polarization effect on this line ratio is found to be negligible. Note that the errors are much smaller than those in Fe xxi because the observed ratios in Fe x ions are in the most density-sensitive region, compared with those in Fe xxi (see Figure 8). 5.1.3. Other Ion Lines

Other EUV line intensity ratios have been used to determine the electron density in solar corona, EBIT plasma, etc. (Keenan et al. 2005b—Fe xi; Del Zanna & Mason 2005— Fe xii; Yamamoto et al. 2008; Watanabe et al. 2009—Fe xiii). Here, we selected ne -sensitive lines without blending from emission lines of other ionic states to further estimate the electron density in the EBIT plasma under the electron beam energy and current of Ee = 5.64 keV and Ie = 320 mA, respectively. For example, the line intensity ratios (see Figure 10) I (179.763 Å) with nearby wavelengths of Fe xi: I (181.801 , Fe xii: Å)+I (182.176 Å) I (191.049 Å) Å) Å) , Fe xiii: II (213.768 , Fe xiv: II (219.130 , I (195.119 Å)+I (195.179 Å) (200.021 Å) (211.317 Å) Å) Fe xxii: II (156.020 . The corresponding transitions are listed in (13.5812 Å)

Table 2. The resultant effective electron densities are listed in Table 3. Note that the polarization correction is critical in some cases. We note that there is significant difference in the electron densities estimated from different ions under the completely same EBIT running conditions. It seems that there is a trend that higher effective electron densities are obtained from higher ionic charge under the same operation conditions. However, the result from Fe xiii slightly deviates from the trend.

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Figure 10. Line intensity ratios of Fe xi, Fe xii, Fe xiii, Fe xiv, and Fe xxii as a function of the electron density for monoenergetic electron beam at 4.5, 5.0, and 5.64 keV. Symbols with error bars are the measured line intensity ratios at 5.64 keV/320 mA. Green dash-dotted lines and marks represent ratios corrected for polarization. (A color version of this figure is available in the online journal.)

Watanabe et al. (2009) performed the electron density diagnostic for the solar active region with Fe xiii line ratios and Hinode8 EUV imaging spectrometer (EIS) spectra, in which many line ratios were presented (see Figure 3 in their work). However, most emission lines of Fe xiii are blended by lines of other ionic charge states in our present measurement. In this work, we try to use ratios of lines without contamination. So the two contamination-free density-sensitive lines are used here (see Figures 3 and 11), which differs from other cases, e.g., Fe x and Fe xxi, one resonance line and one density-sensitive line (the population of the upper level is dominated by excitations of the metastable level). Due to the different competitions for level population, the line intensity ratio between them also 8

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shows a good sensitivity to the electron density. As explored by Watanabe et al. (2009), different models show a slight discrepancy using different atomic parameters. Generally, the atomic parameters for forbidden transitions (decays from metastable levels) show a larger uncertainty than those for resonance transitions. Hence, the ratio between two density-sensitive lines shows a slightly larger deviation than other ratios between the density-sensitive line and the resonance line. 5.2. Ion Cloud Sizes and Electron–Ion Beam Overlap At first glance, it is quite surprising that the effective electron densities neff e observed from the transition lines are so small (less than 2 orders of magnitude), compared with simple geog metrical electron densities ne (see Equation (5)) and also much

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Table 2 Transition Lines Used in Estimation of the Effective Electron Density neff e λ( Å) 174.526 175.265 175.475 179.763 181.801 182.176 191.049 195.119 195.179 213.768 200.021 264.789 274.203 128.755 142.148 142.278 135.812 156.020

Transition 3s 2 3p 4 3d 2 D5/2 3s 2 3p 4 3d 2 D3/2 3s 2 3p 4 3d 2 P3/2 3s 2 3p 3 3d 1 F3 3s 2 3p 3 3d 3 P0 3s 2 3p 3 3d 3 D2 3s 2 3p 2 3d 2 D5/2 3s 2 3p 2 3d 4 P5/2 3s 2 3p 2 3d 2 D3/2 3s 2 3p3d 3 P2 3s 2 3p3d 3 D2 3s3p 2 2 P3/2 3s3p 2 2 S1/2 2s2p 3 3 D1 2s2p 3 3 D2 2s2p 3 3 D1 2s2p 2 2 D3/2 2s2p 2 2 D5/2

Ion

→ 3s 2 3p 5 2 P3/2 → 3s 2 3p 5 2 P1/2 → 3s 2 3p 5 2 P1/2 → 3s 2 3p 4 1 D2 → 3s 2 3p 4 3 P1 → 3s 2 3p 4 3 P1 → 3s 2 3p 3 2 P3/2 → 3s 2 3p 3 4 S3/2 → 3s 2 3p 3 2 D3/2 → 3s 2 3p 2 3 P3 → 3s 2 3p 2 3 P1 → 3s 2 3p 2 P3/2 → 3s 2 3p 2 P1/2 → 2s 2 2p 2 3 P0 → 2s 2 2p 2 3 P1 → 2s 2 2p 2 3 P1 → 2s 2 2p 2 P1/2 → 2s 2 2p 2 P3/2

Fe x Fe x Fe x Fe xi Fe xi Fe xi Fe xii Fe xii Fe xii Fe xiii Fe xiii Fe xiv Fe xiv Fe xxi Fe xxi Fe xxi Fe xxii Fe xxii

Table 3 Effective Electron Densities (cm−3 ) for Iron Ions With Different Charges in the EBIT Plasma Ion Fe x Fe xi Fe xii Fe xiii Fe xiv Fe xxi Fe xxii

Figure 11. Scheme of the processes responsible for the electron density-sensitive lines of the n = 3→ n = 3 transitions in Fe xiii. Only the levels of 3s 2 3p 2 , 3s3p 3 , and 3s 2 3p3d configurations involved in the transitions of interest are depicted. Wavelengths (in Å) and radiative branching ratios different from 100% are indicated (dashed lines). Relative magnitudes (>1%) of collisional excitation strengths at Ee = 5.64 keV are given in percentage as well as represented by the thickness of the corresponding solid lines. (A color version of this figure is available in the online journal.)

Effective Electron Density neff e +0.7 1.5−0.4 × 1011 11 3.0+0.8 −0.7 × 10 11 4.03+0.48 × 10 −0.47 10 6.1+0.7 × 10 −0.3 11 3.03+0.43 × 10 −0.35 +0.40 2.60−0.39 × 1012 13 1.10+0.23 −0.23 × 10

neff e (Correction for Polarization) 11 1.5+0.7 −0.4 × 10 11 3.4+1.1 × 10 −0.9 11 3.98+0.47 × 10 −0.43 11 1.7+0.3 × 10 −0.9 11 3.03+0.43 × 10 −0.35 +0.35 1.4−0.32 × 1012 13 1.12+0.22 −0.23 × 10

Note. Effective electron densities (cm−3 ) for iron ions with different charges in the EBIT plasma under Ee = 5.64 keV/Ie = 320 mA, estimated from line intensity ratios without and with polarization corrections (see Figures 8–10) of Fe x–Fe xxii.

different between differently charged ions observed under the same EBIT conditions. In order to understand such features, it is interesting to compare the observed “effective” electron deng sities neff e with the “geometrical” electron densities ne calculated from Equation (5). These results are summarized in Table 4 demong strating that the neff e /ne ratios vary by almost 2 orders of magnitude. Low charged ions show low ratios and higher charged ions show higher ratios. Similar observations of the effective electron densities under quite different electron beam conditions (1–3 keV and 1–10 mA) in an EBIT at Livermore were performed based upon soft X-ray spectroscopy of helium-like N vi ions (Chen et al. 2004). Silver et al. (2000) and Matranga et al. (2003) also performed similar diagnostic of the electron densities for the NIST EBIT plasmas using K-shell X-ray spectroscopy. The lifetimes of the levels observed are much shorter than the present metastable levels of Fe ions. A linear behavior between the electron densities and 1/2 [Ie /Ee ] was indeed suggested under a fixed electron beam radius by Chen et al. (2004) (see Figure 6 in their work) based upon their limited experimental data. Considering that most of EBITs all over the world have similar (designed) electron beam radii, we combined the data available so far into our present analysis as shown in Figure 12. The relative normalized electron

Figure 12. Comparison of “relative” normalized effective electron density (cm−1 ) among various EBIT experiments. The data of Livermore (blue triangles) are taken from the work of Chen et al. (2004); NIST data within the rectangle with dash boundary are from Silver et al. (2000) (circles: N vi, O vii, and Ne ix) and Matranga et al. (2003) (diamonds: Ne ix); The data of Heidelberg at low energies and currents (0.07–0.5 keV/2.1–8.0 mA, dark-green filled square) are from our re-analyzing to the spectra of Liang et al. (2009) with polarization effect taken into account. The open symbols refer to the present results. Notes: the electron densities from literatures are normalized by the corresponding values 1/2 of [Ie /Ee ]. (A color version of this figure is available in the online journal.) 1/2

density neff e /[Ie /Ee ] clearly deviates from such expectation. 1/2 Particularly such deviations at high [Ie /Ee ] values with high electron current (like in the present work) region are significant, 1/2 compared with those at low [Ie /Ee ] values (like in Livermore experiment by Chen et al. 2004). This trend can be understood: at high electron currents, the ions tend to be more heated and thus their radii get large, resulting in a lower effective electron density. As the effective electron density depends on the overlap between ion cloud and electron beam, the deviation observed indicates a significant change of the ion–electron beam overlap 1/2 f which depends on [Ie /Ee ], and also the axial trap voltage applied on the end cap drift tubes on both sides of the central

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Table 4 g Estimated Electron Density Ratios (neff e /ne ) and Ion Radius Ratios (ri /re ) g

Electron Density Ratio (neff e /ne )

Ion 4.5 keV/197 mA Fe x Fe xi Fe xii Fe xiii Fe xiv Fe xxi Fe xxii

5.0 keV/400 mA

−2 1.2+0.5 −0.3 × 10 −2 1.8+0.4 × 10 −0.3

−2 1.6+0.4 −0.3 × 10 < 1.7 × 10−2 −1 6.8+2.6 −2.2 × 10

−2 5.3+1.8 −1.6 × 10

ri /re 5.64 keV/320 mA −3 9.4+4.4 −2.5 × 10 −2 2.1+0.7 × 10 −0.6 −2 2.5+0.3 × 10 −0.3 −2 1.1+0.2 × 10 −0.6 −2 1.9+0.3 × 10 −0.2 −2 8.8+2.2 × 10 −2.0 +1.4 7.0−1.4 × 10−1

8.5–12.0 5.9–8.0 6.0–6.7 8.9–14 6.8–7.8 3.0–3.8 1.1–1.4

g

Note. Estimated electron density ratios (neff e /ne ) and ion radius ratios (ri /re ) from highly charged iron ions taken under slightly different EBIT conditions.

drift tube as explored by Porto et al. (2000). The significant deviations for lower charged iron ions in the present results mean a smaller overlap than previously found at high electron energy/high current results. By taking the polarization effect into account, we re-analyze our previous measurements with low energies and currents (Ee = 70–500 eV and Ie = 2.1–8.0 mA) at the Heidelberg FLASH-EBIT (Liang et al. 2009). Significant deviation appears again as illustrated by dark-green square symbols in Figure 12, indicating a smaller overlap for the lower charged ions. The large scattering in the present results is due to the overlap f (or ri2 /re2 ) dependence on the ionic charge as will be explained in the following. The ratios, ri /re , of the ion cloud radius over the electron beam g radius obtained from the observed neff e /ne ratios are illustrated in the last column of Table 4. The range of ion radius ratio against the real electron radius thus estimated show that the ion clouds significantly expand far outside (∼10 times) the geometrical electron beam radius re for lower charged ions in the Heidelberg FLASH-EBIT, particularly for Fe x and Fe xiii (see Table 4 and Figure 13) in the present measurement. This large expansion of the ion could be understood due to the axial trap of 360 V applied on the end cap trap tubes. Porto et al. (2000) experimentally demonstrated that the width of ion cloud (Ar13+ ) would increase by a factor of ∼5 from an open trap to a deep trap with the static trapping voltage of 300 V (see Figure 6 in their work). However, for higher charged ions (Fe xxi and Fe xxii), the ion cloud was found to be less expanded. Thus, it is concluded that the expansion of ion clouds has a dependence on the ionic charge. Though the present data are limited, there is a clear trend that ions with higher charge (Fe20+ and Fe21+ ) have less expanded. Assuming the diameter of electron beam to be ∼ 60μm in the work of Silver et al. (2000), Matranga et al. (2003), and Liang et al. (2009), we further derive the ion expansion in their measurements. Though these measurements were performed with different trap conditions at different EBITs, a quantitative relation between the expansion of ion clouds and the effective charge of ions can be concluded. Figure 13 demonstrates that the expansion (ri /re ) of iron ion cloud has a relation with the effective charge of ions 1/(qi /Z)α with 1 < α  2. It is noted that the Levine’s model (Levine et al. 1988) of the inverse exponential expansion of ion cloud size seems to be slightly off from the general trend including all the possible ion charge data available. At comparable values of the effective charge of ions, the expansion of Ne8+ ion cloud in works of Matranga et al. (2003) and Silver et al. (2000) shows a similar expansion as Fe21+ ion cloud extracted in the present measurement though they are generated at different EBITs with different conditions. Measurements by Silver et al. (2000) at

Figure 13. Expansion of ion cloud radius (ri ) relative to the electron beam size (re ) as a function of the effective charge of ion (qi /Z, Z is the nuclear charge of ion). The NIST data from Silver et al. (2000) (for N, O, and Ne ions) and Matranga et al. (2003) (for Ne ions), as well as Livermore data from Chen et al. (2004) (for N ions) were added by assuming re = 30 μm. The data point at qi /Z = 1.0 is not a “real” data, which is based upon the assumption that the bare nucleus should completely overlap with the electron beam. The three curves represent analytic relation between ri /re and the effective charge of ion (qi /Z), where c1, c2, c3, and c4 are constant values making the curves to fit the present measured data points. (A color version of this figure is available in the online journal.)

slightly different conditions for N5+ and O6+ (2.0 keV/35.9 mA), as well as Ne8+ (2.2 keV/39.5 mA) also show such dependence on the effective ion charge. The data from Chen et al. (2004) demonstrate the dependence of the expansion of ion could (N5+ ) on the operation conditions of EBIT as revealed in Figure 12. There are only very few direct observations on such large expanded ion clouds. NIST group has reported their results for ion cloud sizes in their EBIT by measuring lines from metastable state ions (Porto et al. 2000). Under their EBIT conditions, these ions have been found to spread out up to 400 μm radius, compared with their estimated electron radius (35 μm). Their results for Ar13+ ions provide some clues and support in understanding the present results. This is generally in agreement with a recent observation based upon visible photon spectroscopy at MPI. Another observation shows that the Ar13+ ion cloud radius is observed to reach 250 μm (Draganic 2007) under lower energy electrons. These measurements support our present estimations based upon the EUV spectroscopy. In the following, we present an analytical representation for the dependence of the overlap f on the charge of ions for an

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EBIT plasma. We assume a radial Boltzmann distribution for the ion cloud of charge state qi nqi (r) = nqi (0)exp(−eqi φ(r)/kTqi )

(6)

and a Gaussian shape for the electron beam density radial distribution  2  r ne (r) = ne (0)exp − 2 ln2 , (7) re where re refers to the electron beam radius estimated by Herrmann’s theorem (Herrmann 1958), Tqi is the temperature of thermalized ions with charge of qi . The potential function φ(r) = φe (r) + φi (r) accounts for the space charge potential of the compressed electron beam and radial screening by ions, respectively. φe (r) is expressed as follows by Gillaspy (2001):     2 r 2 Ie re + ln −1 (8) φe (r  re ) = 4π 0 ve re rdt

φe (r  re ) =

  Ie r , ln 2π 0 ve rdt

(9)

where rdt represents the radius of the central drift tube of the EBIT, 0 is permittivity and v e is the electron velocity. The ion charge density ni and the potential are connected by Poisson’s equation, which can be solved numerically: −

 0 d dφ(r) r = − ene (r) + eqi nqi (r). r dr dr

(10)

From Equations (6)–(10), we can see that the overlap factor  r¯ 2 fqi = r¯qei has a strong dependence on the ionic charge. 6. SUMMARY AND OUTLOOK EUV spectra (107–353 Å) of highly charged Fe ions were observed under unidirectional electron beam with slightly different energies (4.5–5.64 keV) and currents (197–400 mA) by a flatfield grating spectrometer mounted at the Heidelberg FLASHEBIT. The results obtained can be summarized as follows: 1. Collisional-radiative simulations under monoenergetic and thermal electrons were carried out, and the results obtained in the monoenergetic excitation case satisfactorily reproduced the observed EUV emission spectrum of highly charged Fe ions in the EBIT, helping line identification and disentanglement of satellite lines. 2. Comparison of the simulated spectra with and without polarization from unidirectional electron impact reveals that the polarization effect can either reduce or enhance some line intensities up to 24%. 3. Through analysis of the measured line intensities (corrected for the spectrometer efficiencies) among different ion charges under 5.64 keV/320 mA electron impact, it has been found that the resulting CSD peak at Fe23+ among the observed ions, though with the present EUV spectrometer we could not observe any lines from Fe24+ , and tail toward lower charge states. A simulation also reproduces nicely this behavior, indicating that a shift to lower charge states with increasing injected gas pressure is due to electron capture into HCI from neutral atom.

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4. Based upon the electron-density-sensitive EUV line intensity ratios of ions from Fe x to Fe xxii, the estimated effective electron densities of the EBIT plasmas under only slightly different electron beam conditions were found to be critically dependent on the ionic charge which we analyzed: the cloud of lower charged ions (e.g., Fe x) expand up to nearly 10 times beyond the electron beam radius, whereas those of higher charged ions expand less, and e.g. the Fe xxii ion cloud is close to the geometrical electron size (of 2re ). For the first time, we have observed a significant difference of the ion–electron overlap strongly depending on the ion charge even under the same EBIT running conditions. 5. Combining the present results with those obtained in previous experiments for a wide range of the ions (N vi ∼ Ne ix) under very much different (a few hundred electron volt and a few milliampere electron beam) conditions, we have found a relatively simple scaling rule for estimating the ion cloud/electron beam size ratios as a function of the effective ion charge (q/Z). In conclusion, the present EUV spectroscopic measurements have provided detailed insights into the ionization and excitation conditions of HCI confined in the EBIT, suggesting that the EBIT is a powerful, convenient laboratory plasma source which can provide crucial information on interpretation of the observations and diagnostics applicable to various plasma processes. The existing discrepancies between the present observations and simulations still demand more detailed studies on EBIT-produced plasmas. However, these are small despite of the fairly simple models used in the present simulations, compared to those typically used in the description of high temperature, low-density astrophysical plasmas. Furthermore, more detailed investigations of the ion–electron beam overlapping should be performed under various EBIT running conditions in order to get more exact insight in electron–ion interactions including the cross sections such as ionization and excitation obtained from the EBIT and the ionization time or charge balance of ions or more general simulations in the EBIT. G.Y.L. acknowledges the help from the whole HD-EBITteam. Funding is provided by MPI-K, and partially from support of National Science Foundation of China under grant Nos. 10603007 and 10821061 and National Basic Research Program of China (973 program) under grant No. 2007CB815103. REFERENCES Brosius, J. W., Davila, J. M., Thomas, R. J., & Monsignori-Fossi, B. C. 1996, ApJS, 106, 143 Brosius, J. W., Thomas, R. J., Davila, J. M., & Landi, E. 2000, ApJ, 543, 1016 Chen, H., Beiersdorfer, P., Heeter, L. A., Liedahl, D. A., Naranjo-Rivera, K. L., Tr¨abert, E., Gu, M. F., & Lepson, J. K. 2004, ApJ, 611, 598 Del Zanna, G., & Mason, H. E. 2005, A&A, 433, 731 Dere, K. P. 1978, ApJ, 221, 1061 Draganic, I. 2007, PhD thesis Edelstein, J., Hettrick, M. C., Mrowka, S., Jelinsky, P., & Martin, C. 1984, Appl. Phys., 23, 3267 Epp, S. W., et al. 2007, Phys. Rev. Lett., 98, 183001 Fournier, K. B., Finkenthal, M., Pacella, D., May, M. J., Leigheb, M., Soukhanovskii, V., & Goldstein, W. H. 2001, ApJ, 550, L117 Gillaspy, J. 2001, Trapping Highly Charged Ions: Fundamentals and Applications (New York: Nova Science Publishers) Gillaspy, J., et al. 1995, Phys. Scr., T59, 392 Gu, M. F. 2008, Can. J. Phys., 86, 675 Gu, M. F., Savin, D. W., & Beiersdorfer, P. 1999, J. Phys. B: At. Mol. Opt. Phys., 32, 5371

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