Measurement of ionization, charge exchange and ion confinement times in charge breeder ECR ion sources with short pulse 1+ injection of metal ions

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 3.0 https://creativecommons.org/licenses/by/3.0/ Measurement of ionization, charge exchange and ion confinement times in charge breeder ECR ion sources with short pulse 1+ injection of metal ions © Authors, 2022 Published version Luntinen, Miha; Angot, Julien; Tarvainen, Olli; Toivanen, Ville; Thuillier, Thomas; Koivisto, Hannu Luntinen, M., Angot, J., Tarvainen, O., Toivanen, V., Thuillier, T., & Koivisto, H. (2022). Measurement of ionization, charge exchange and ion confinement times in charge breeder ECR ion sources with short pulse 1+ injection of metal ions. In ICIS2021 : 19th International Conference on Ion Sources (Article 012009). IOP Publishing. Journal of Physics : Conference Series, 2244. https://doi.org/10.1088/1742-6596/2244/1/012009 2022 Journal of Physics: Conference Series PAPER • OPEN ACCESS Measurement of ionization, charge exchange and ion confinement times in charge breeder ECR ion sources with short pulse 1+ injection of metal ions To cite this article: M Luntinen et al 2022 J. Phys.: Conf. Ser. 2244 012009 View the article online for updates and enhancements. 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Published under licence by IOP Publishing Ltd 19th International Conference on Ion Sources – ICIS2021 Journal of Physics: Conference Series 2244 (2022) 012009 IOP Publishing doi:10.1088/1742-6596/2244/1/012009 1 Measurement of ionization, charge exchange and ion confinement times in charge breeder ECR ion sources with short pulse 1+ injection of metal ions M Luntinen1, J Angot2, O Tarvainen3, V Toivanen1, T Thuillier2and H Koivisto1 1University of Jyv¨askyl¨a, Department of Physics, Survontie 9D, 40500 Jyv¨askyl¨a, Finland 2Univ. Grenoble Alpes, CNRS, Grenoble INP, LPSC-IN2P3, 53 Avenue des Martyrs, 38000 Grenoble, France 3STFC ISIS Pulsed Spallation Neutron and Muon Facility, Rutherford Appleton Laboratory, Harwell, OX11 0QX, UK E-mail: mailto:[email protected] Abstract. The Consecutive Transients (CT) method is used for estimating the characteristic times of ionization, charge exchange and confinement within the plasma of a Charge Breeder Electron Cyclotron Resonance Ion Source (CB-ECRIS). The method reveals differences in the characteristic times between different source configurations, with K9+ charge breeding efficiencies of 8.9 % and 20.4 %, and allows qualitative explanation of the improved breeding efficiency. The increase in K9+ efficiency is accompanied by a decrease in ionization time for low charge states, a decrease of charge exchange time for high charge states, and an overall decrease of the ion confinement time, which increases non-linearly with the charge state. The charge exchange time exhibits a minimum near charge state K8+, indicating low neutral density near the plasma core. The CT-method yields a distribution of possible neand hEeicorresponding to the spatial distribution of different charge state ions. The results hint at a non-uniform plasma electron density and energy distribution as well as a nested-layer distribution for the ion populations — hot and dense plasma with high charge state ions near the plasma core. 1. Introduction The Consecutive Transients (CT) method has been used to obtain postdictions for the ionization, charge exchange and confinement times (τq inz,τq cx and τq) of charge state qion populations in a CB-ECRIS plasma [1]. The method is based on measuring the extracted current transients prompted by short pulse injection of metal ions into the plasma, making fits to the transients of (minimum) five consecutive charge states, and an optimisation procedure to obtain the plasma electron density neand average energy hEeiof the presumed Electron Energy Distribution (EED) as well as the times τq inz,τq cx and τq. The method is based on the balance equation [2, 3] describing the temporal evolution of the densities of each ion population. The method probes the plasma conditions (ne,hEei) of the support plasma, which determine τq inz,τq cx and τqof the injected ions. The results are spatially localised to the origin of the charge state qion population. Measuring five consecutive charge state transients poses experimental limitations on the support/injected species combinations, since one must avoid q/m overlap in the Charge State Distribution (CSD). The method takes into account the uncertainty of the ionization cross section data and resulting 19th International Conference on Ion Sources – ICIS2021 Journal of Physics: Conference Series 2244 (2022) 012009 IOP Publishing doi:10.1088/1742-6596/2244/1/012009 2 Table 1: The former (June 2020) and new (February 2021) charge breeder operating parameters. Configuration Parameter Former New Binj (T) 1.58 1.57 Bmin (T) 0.45 0.44 Bext (T) 0.83 0.84 µW power (W) 504 530 Support gas species He H2 Pinj (×10−8mbar) 9.0 13.6 K+intensity (nA) 710 500 Injection pulse width (ms) 5 5 rate coefficients by the means of a Monte Carlo approach. No assumptions need to be made regarding the confinement scheme i.e. the functional dependence of τq. Here we demonstrate that the CT-method can reveal the physical causes resulting in a change of the charge breeding efficiency. The comparison is made between the characteristic times obtained for potassium ions in the support plasma of a CB-ECRIS. The source configurations correspond to 39K9+ efficiencies of 8.9 % and 20.4 %, respectively. Identifying the mechanisms underpinning the factor of >2 improvement in the charge breeding efficiency of a stable isotope can guide the optimisation of Radioactive Ion Beam (RIB) production. 2. Experimental methods The 1+→N+ test bench [4] at LPSC Grenoble is dedicated to the development and characterization of the Phoenix CB-ECRIS. The 1+ beam line is used for generating, characterizing and injecting the 1+ ion beam into the CB-ECRIS and the N+ beam line for analysing the extracted multicharged beams. The CB-ECRIS and the test bench are continuously upgraded to increase the global and charge state specific breeding efficiencies, Σ and ηq, and to reduce the charge breeding time and impurities in the N+ CSD. Short pulse injection of 1+ ions is used for the measurement of the charge breeding times τCB; the time when 90 % of all ions of charge state qhave been extracted is designated as τCB[5]. In 2018-2019, the 1+→N+ test bench was upgraded to improve the vacuum and the alignment of the device [4]. The optimum efficiency of K10+ charge state measured in June 2020 was 10.6 % with τ10+ CB of 132 ms. The first data using the CT-method to obtain the plasma parameters were taken in this configuration [1] with He support plasma. The CB tuning and conditioning were then optimised to improve the CB efficiency to 20.4 % for K9+ with H2support gas (τ9+ CB of 131 ms). The CT-method was applied in this configuration in February 2021 to estimate which parameters could have caused the efficiency improvement. Table 1 compares the two CB configurations. The main differences are the support gas species, the Bmin value (+11.8%) and the microwave power (+5.2%). The charge breeding efficiencies ηq of the K charge states are shown in Table 2. A significant increase of K9+ efficiency was obtained (+11.5% absolute efficiency), accompanied by a small efficiency shift towards lower charge states. The extracted current transients of K3+–K12+ were measured to obtain the characteristic times for K5+–K10+ ion populations. The injected K+pulse was kept short (5 ms pulse width) and low in intensity (500 – 710 nA) to minimize the perturbance on the support plasma, while still resulting in high signal-to-noise ratio of the transient current. 19th International Conference on Ion Sources – ICIS2021 Journal of Physics: Conference Series 2244 (2022) 012009 IOP Publishing doi:10.1088/1742-6596/2244/1/012009 3 Table 2: The charge breeding efficiencies ηq, charge breeding times τq CB and the median values of the population confinement times τq. The global efficiency includes charge states K4+ – K12+. ηq(%) τq CB (ms) τq(ms) Ion Former New Former New Former New K3+ 1.2 1.3 9 10 K4+ 1.0 1.4 11 12 K5+ 1.1 1.9 13 15 3 3 K6+ 1.2 3.0 16 49 3 4 K7+ 1.5 5.8 20 90 4 4 K8+ 2.7 11.1 45 119 15 12 K9+ 8.9 20.4 98 131 16 8 K10+ 10.6 11.8 132 138 24 12 K11+ 8.5 4.7 149 K12+ 5.1 1.3 155 Σ (%) 41.8 62.7 3. Numerical methods 3.1. Principle of the method The method for analyzing the measured beam current transients of the q+ ions has been extensively described in Ref. [1] and is only briefly recapitulated here: The balance equations [2, 3] governing the evolution in time of the ion population densities are defined by dnq dt= +nehσviinz q−1→qnq−1−nehσviinz q→q+1 nq +n0hσvicx q+1→qnq+1 −n0hσvicx q→q−1nq−nq τq, (1) where the ionization and charge exchange rate coefficients (hσviinz/cx) together with the plasma electron and neutral densities (ne,n0) determine the characteristic times τq inz ≡hnehσviinz q→q+1i−1(2) τq cx ≡hn0hσvicx q→q−1i−1(3) and the loss term −nq/τqdefines the ion confinement time τq. Here nqrefer to the injected species, while neand n0are properties of the support plasma, which are assumed to be constant in time. Using the following identity [6, 7, 1] for the charge state qbeam current Iq=κFBLS nqqe τq,(4) where κis the beamline transmission efficiency, FBa factor dependent on the mirror ratio of the ion source, Lthe length of the plasma chamber and Sthe area of the extraction aperture, one can recast the balance equation in the form d dtIq=aqIq−1−bqIq+cqIq+1,(5) 19th International Conference on Ion Sources – ICIS2021 Journal of Physics: Conference Series 2244 (2022) 012009 IOP Publishing doi:10.1088/1742-6596/2244/1/012009 4 where Iq−1, and Iq+1 are the beam currents of charge states q−1 and q+ 1, respectively, and the coefficients aq,bqand cqare defined as aq=nehσviinz q−1→q q q−1 τq−1 τq(6) bq=nehσviinz q→q+1 +n0hσvicx q→q−1+ 1/τqand (7) cq=n0hσvicx q+1→q q q+ 1 τq+1 τq.(8) The coefficients aq,bqand cqcan be determined by fitting Eq. 5 to the experimentally measured current Iq. The fitting is done by taking Iq−1(t) and Iq+1(t) as input parameters of Eq. 5, and solving the differential equation for the middle charge state current (numerical solution for the charge state qcurrent denoted by Iq(t)). A least-squares method is then used to minimize the difference between Iqand Iqto obtain aq,bqand cq. Definitions 6, 7 and 8 then yield q q+ 1 aq+1 nehσviinz q→q+1 = bq+1 −nehσviinz q+1→q+2 −aq+1cq nehσviinz q→q+1 bq−nehσviinz q→q+1 −aqcq−1 nehσviinz q−1→q ,(9) which is an equation of two unknowns, neand hEei, since the rate coefficients hσviinz q0→q00 may be calculated as a function of the average energy hEeiof the EED. In lieu of experimental determination of the EED, we have thus far assumed the Maxwell-Boltzmann (MB) distribution. Equation 9 provides an infinitude of solutions for neand hEei, which may be constrained on physical grounds such that                τq>0, τq+1 >0, 1/n0hσvicx q→q−1>0, ne,low < ne< ne,co, hEeilow <hEei<hEeihigh , (10) where τq,τq+1 and hn0hσvicx q→q−1i−1≡τq cx can be calculated from the definitions of aq,bqand cq(c.f. Ref. [1] Eqs. (16) and (19)). The upper bound of neis the cut-off frequency [8] ne,co, while its lower bound ne,low is taken from the literature [9]. The lower limit of hEeiis set to be on the order of the plasma potential, i.e., ∼10 eV, while its upper limit can be constrained at 10 keV, since the fraction of electrons found with energies above a few keV is 20–50 % [7, 10]. We thus focus on the warm electron population, which is mainly responsible for the ionization. 3.2. Code enhancements While the numerical method has remained unchanged in principle since the introduction of the method [1], the code has been updated improving the precision and speed of the algorithm: (i) The rate coefficients are now calculated as a function of the average energy hEeiof the EED (not Te), which facilitates the comparison between different EEDs in the future. (ii) In Ref. [1] we adopted an “umbrella” uncertainty bound of 60 % for the rate coefficient as reported by Voronov [11]. The code now uses the experimental uncertainties of the cross section data [12]. (iii) The handling of the constraints has been improved: The penalty function is first minimized within the neand hEeibounds. After the minimum has been found, the characteristic times are calculated and minima leading to negative (unphysical) characteristic times are discarded. All the following results have been computed using the improved version (v1.2) of the code. 19th International Conference on Ion Sources – ICIS2021 Journal of Physics: Conference Series 2244 (2022) 012009 IOP Publishing doi:10.1088/1742-6596/2244/1/012009 5 101102103 ⟨ Ee ⟩⟨⟩eV) 1011 1012 ne ⟨⟩cm−3) 0.0 0.5 1.0 1.5 2.0 2.5 1e−15 K8+ 101102103 ⟨ Ee ⟩⟨⟩eV) 1011 1012 ne ⟨⟩cm−3) 0.0 0.5 1.0 1.5 1e−15 K9+ 101102103 ⟨ Ee ⟩⟨⟩eV) 1011 1012 ne ⟨⟩cm−3) 0.00 0.25 0.50 0.75 1.00 1.25 1e−15 K10+ 101102103 ⟨ Ee ⟩⟨⟩eV) 1011 1012 ne ⟨⟩cm−3) 0.0 0.5 1.0 1.5 1e−15 K8+ 101102103 ⟨ Ee ⟩⟨⟩eV) 1011 1012 ne ⟨⟩cm−3) 0.0 0.2 0.4 0.6 0.8 1.0 1e−15 K9+ 101102103 ⟨ Ee ⟩⟨⟩eV) 1011 1012 ne ⟨⟩cm−3) 024681e−16 K10+ Figure 1: The (ne,hEei) -solution sets of K8+–K10+ for the two charge breeder configurations Former (upper row) and New (lower row). 4. Results and analysis 3 4 5 6 7 8 9 10 11 12 Charge state 0 5 10 15 20 25 30 τq cx (ms) τq cx (Former) τq cx (New) −20 −10 0 10 20 Δ( η ) (Δ) Δ( η ) (a) 3 4 5 6 7 8 9 10 11 12 Charge state 0.0 2.5 5.0 7.5 10.0 τq inz (ms) τq inz (Former) τq inz (New) −20 −10 0 10 20 Δ( η ) (Δ) Δ( η ) (b) 3 4 5 6 7 8 9 10 11 12 Charge state 0 10 20 30 40 τq (ms) τq (Former) τq (New) −20 −10 0 10 20 Δ( η ) (Δ) Δ( η ) (c) Figure 2: Comparisons of τq cx,τq inz and τqand the absolute difference ∆(η) of CB efficiencies. Figure 1 shows heatmaps of the (ne,hEei) i.e. viable solutions of Eq. 9 in both CB 19th International Conference on Ion Sources – ICIS2021 Journal of Physics: Conference Series 2244 (2022) 012009 IOP Publishing doi:10.1088/1742-6596/2244/1/012009 6 Table 3: The most probable values of neand hEeiin the two CB configurations. ne(×1011 cm−3)hEei(eV) Ion Former New Former New K5+ 1.0 1.0 96 129 K6+ 1.3 1.4 124 115 K7+ 1.2 1.0 156 168 K8+ 1.4 2.1 150 214 K9+ 1.0 2.6 288 357 K10+ 1.4 2.5 353 518 configurations for K8+–K10+. These examples represent the set of (ne,hEei)-pairs satisfying Eq. 9 in the vicinity of their respective ion population nq. It must be recalled, that the Iqbeams are extracted from the whole plasma, and the neand hEeivalues represent averages for a given ion population. The variation of the neand hEeias a function of qthus reflects the average spatial variation of each nq. Hence, the characteristic times calculated at these (ne,hEei) also yield a distribution of results. Further constraining (if possible) of the neand hEeispans, and the uncertainty of the ionization cross sections, would decrease the uncertainty of the results. Histograms of the solution sets are projected onto the neand hEeiaxes (note the logarithmic scale). Comparison of the histograms and the most probable values of neand hEei— tabulated in Table 3 — reveals that in the new configurations the local neand hEeiare higher in particular for the HCIs. This is commensurate with the decrease of their τq inz. Increase of neis also to be expected from the increased neutral gas input compared to the former configuration, as the increased n0allows for a higher ne, particularly in the core of the plasma where the highly charged ions (HCIs) are believed to be confined in the potential dip [3], which itself is generated by the higher concentration of hot, well-confined electrons. Figure 2 shows τq inz,τq cx and τqas a function of qfor the two data sets. The characteristic times are overlaid with the absolute charge breeding efficiency change between the CB configurations. The uncertainty bounds enclose a one sigma (34.1 %) fraction of all results around the median value, represented by the data point. The distribution of values is typically sharply peaked around the lower values, with the most probable value lying below the median. The size of the uncertainty bounds is affected by both, the uncertainty of the experimentally measured ionization cross sections (e.g. at worst for K8+ the uncertainty is δσinz q→q+1/σinz q→q+1 = 200 %) and the limits imposable upon the solution space (ne,hEei). Especially the K9+ efficiency is improved between the two configurations. Each of the characteristic times, in particular τq cx and τqhave decreased for the HCIs, although in most cases the uncertainty bounds overlap. Molecular hydrogen has a larger diameter and smaller ionization potential than helium, which may explain the decrease in τq cx, the charge exchange cross section being inversely proportional to the square of the ionization potential [13], i.e. σcx q→q−1∝I−2. Hence, switching to a H2 support plasma increases σcx q→q−1. There is a minimum in τq cx around K7+ and K8+ for both of the data sets. This minimum is attributable to the increase of σcx q→q−1with qand the nested-layer structure of the ECRIS plasma. The latter is consistent with simulations and experiments [14, 15, 16, 17, 18] suggesting that the HCIs originate in the plasma core near the plasma chamber axis, while lower charge states originate from the peripheral plasma forming an overlapping layered structure. The increase of τq cx towards the HCIs implies a decrease of neutral density toward the plasma core, since the σcx q→q−1increasing with qwould otherwise imply a further decrease in τq cx. The decreased τq cx of the HCIs is in line with the increased 19th International Conference on Ion Sources – ICIS2021 Journal of Physics: Conference Series 2244 (2022) 012009 IOP Publishing doi:10.1088/1742-6596/2244/1/012009 7 charge breeding efficiency of the lower charge states in the new configuration. There is a small decrease of τq inz of the low charge states, while a prominent decrease, attributed to the increase of neimplied by the solution sets (Fig. 1.), is seen for the HCIs in the new configuration. The effect of the faster ionization is to feed the high charge state populations. The electron shell closure at K9+ causes a discrete jump between τ8+ inz and τ9+ inz . The median of the confinement time τqsolutions has decreased in particular for K9+ and K10+. Especially the former data set shows a non-linear q-dependence for τq. A linear model for τq would yield negative confinement times for low charge states, while a power law fit is found to best represent the results [1]. In Ref. [7] a linearly increasing trend and much shorter values (∼5 ms) of τqwere found. Short τqhas been used as an argument in favor of a predominantly collisional or ambipolar ion confinement[19]. However, recent optical measurements of the Doppler broadening of ion emission lines [20] have found ∼10 eV ion temperatures, unattainable with such short τq. There is mounting evidence from emittance [15] and current density measurements [17, 18], simulations [14, 3], and afterglow experiments [21, 22], that the HCIs are confined within a potential dip ∆φof the plasma potential distribution. The HCIs remain confined until they obtain enough energy to overcome the electrostatic barrier, i.e. in excess of eq∆φ. The electrostatic confinement scheme is in accordance with the power law trend observed here. It is important to note that it is the combination of τq inz,τq cx, and τq(∀q∈ {0,1,2, . . . , qmax}) that determines the steady-state CSD of the plasma. The change in the K9+ efficiency can thus be explained through the characteristic times: (i) The decrease in τq cx for the HCIs indicates faster rate of charge exchange and a consequent shift of the CSD towards lower charge states. In effect, the K9+ population is fed from the HCIs via charge exchange; (ii) The decrease in τq allows the K9+ ions — once produced — to escape more rapidly, which increases the extracted beam intensity; (iii) The shorter ionization time of the low charge states supplies to the K9+ population (but is counteracted by the simultaneous decrease of τq cx). In short, the increase of the K9+ CB efficiency is explicable by the pile-up into q= 9 and its shorter confinement time. 5. Conclusion It has been shown, that the CT-method can be used to discern differences between the characteristic times in different CB configurations. It therefore enables the analysis of fundamental processes in the ion source plasma. Here, the source tune has been changed by varying multiple operating parameters, and the characteristic times are affected by multiple physical effects. In future experiments, the evolution of the characteristic times will be studied by varying one parameter at a time. It must be noted that an infinitude of (ne,hEei) pairs satisfies Eq. 9. It would be a great benefit to the method, if it were possible to set stricter constraints on neand hEei, and if the ionization cross section were known more precisely. The presumed EED also being a source of possible error, its experimental measurement in plasma is desired. In short term we plan to study the sensitivity of the results on the assumed EED. The CT-method provides a breakdown of τq CB to its components: The characteristic times τq inz,τq cx determine the rate at which ions of different charge states are generated, while τqgives the rate at which ions of a given population exit the plasma. It is important to note that τq CB is affected by the characteristic times of all charge states populations as a given particle may spend time as an ion at various different charge states before being extracted from the source. The τq CB is thus a measure of the cumulative confinement time [23] of an ion, including its charge state history, while τqmeasures the confinement time of ion population at charge state q, and is directly affected by changes in the ion confinement conditions. Based on the discussion of the causes underlying the change in K9+ efficiency, it can be said that in order to maximize the charge breeding efficiency of a given charge state one must maximize the pile-up into that charge state population the charge states both above and below,