Electron - Ion Recombination Data for Plasma Applications

Electron - ion recombination data for plasma applications

Results from Electron Beam Ion Trap and Ion Storage Ring

Safdar Ali ⃝c Safdar Ali, Stockholm 2012

ISBN 978-91-7447-497-8

Printed in Sweden by US-AB, Stockholm 2012 Distributor: Department of Physics, Stockholm University To my parents

ABSTRACT

This thesis contains results of electron-ion recombination processes in atomic ions relevant for plasma applications. The measurements were performed at the Stockholm Refrigerated Electron Beam Ion Trap (R-EBIT) and at the CRYRING heavy-ion storage ring. Dielectronic recombination (DR) cross sections, resonant strengths, rate coefficients and energy peak positions in H-like and He-like S are obtained for the first time from the EBIT measurements. Furthermore, the experimentally obtained DR resonant strengths are used to check the behaviour of a scaling formula for low Z, H-and He-like iso-electronic sequences and to update the fitting parameters. KLL DR peak positions for initially He-to B-like Ar ions are obtained experimentally from the EBIT measurements. Both the results from highly charged sulfur and argon are compared with the calculations performed with a distorted wave approximation. Absolute recombination rate coefficients of B-like C, B-like Ne and Be- like F ions are obtained for the first time with high energy resolution from storage ring measurements. The experimental results are compared with the intermediate coupling AUTOSTRUCTURE calculations. Plasma rate coefficients of each of these ions are obtained by convoluting the energy dependent recombination spectra’s with a Maxwell-Boltzmann energy distribution in the temperature range of 103-106 K. The resulting plasma rate coefficients are presented and compared with the calculated data available in literature.

List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Photo-recombination studies at R-EBIT with a Labview control and data acquisition system S. Ali, S. Mahmood, I. Orban, S. Tashenov, Y. M. Li, Z. Wu, and R. Schuch Journal of Instrumentation, 6: C01016, 2011 II The new Stockholm Electron Beam Ion Trap (S-EBIT) R. Schuch, S. Tashenov, I. Orban, M. Hobein, S. Mahmood, O. Kamalou, N. Akram, A. Safdar, P. Skog, A. Solders, H. Zhang Journal of Instrumentation, 5: C12018, 2011 III Electron-ion recombination of H- and He-like sulfur S. Ali, S. Mahmood, I. Orban, S. Tashenov, Y. M. Li, Z. Wu, and R. Schuch Journal of Physics B: Atomic Molecular and Optical Physics, 44, 225203, 2011 IV Recombination and electron impact excitation rate coefficients for S XV and S XVI S. Mahmood, S. Ali, I. Orban, S. Tashenov, E. Lindroth, and R. Schuch manuscript accepted for publication in The Astrophysical Journal V Electron-ion recombination rate coefficients for C II forming CI S. Ali, I. Orban, S. Mahmood, Z. Altun, P. Glans, and R. Schuch manuscript accepted for publication in The Astrophysical Journal VI Experimental recombination rate coefficients of Be-like F recombining into B-like F S. Ali, I. Orban, S. Mahmood, S. D. Loch, and R. Schuch to be submitted to Astronomy & Astrophysics VII Recombination rate coefficients of Boron-like Ne S. Mahmood, I. Orban, S. Ali, Z. Altun, P. Glans, and R. Schuch to be submitted to The Astrophysical Journal

Reprints were made with permission from the publishers

9 The author’s contribution The work reported in this thesis is a result of collective efforts of all group members, lead by Prof. Reinhold Schuch. In the following I will try to sum- marize my individual contribution to the presented work: Paper I: I actively took part in assembling the beam line and took part in the the experiment. Following the experiment, I analysed the data and wrote the article in close collaboration with my supervisor and other co-authors. Paper II: I helped in assembling the S-EBIT. I also tested and installed the Metal Vapor Vacuum Arc Ion source (MEVVA) on the S-EBIT for injecting metal ions. Paper III: I analysed the data, wrote the first draft of the article, which was then modified in close collaboration with my supervisor and other co-authors. Paper IV: I contributed to the data analysis and in discussions on the results and manuscript. Paper V: I compared the experimental results with the calculated data and wrote the first manuscript, which was then modified after receiving comments from my supervisor and other co-authors. Paper VI: I was involved in the measurements, I compared the calculated data with the converted temperature dependent plasma rate coefficients. I also wrote a draft of the manuscript. Paper VII: I took part in writing the manuscript, discussion about the data analysis and in proof reading the manuscript for publication.

10 Contents

1 Introduction ...... 13 2 Electron-ion collisions ...... 17 2.1 Electron-ion recombination ...... 17 2.1.1 Radiative recombination ...... 17 2.1.2 Dielectronic recombination ...... 18 2.2 Electron-impact ionization and excitation ...... 20 2.2.1 Electron-impact ionization ...... 20 2.2.2 Electron-impact excitation ...... 22 3 Measurements at the Refrigerated Electron Beam Ion Trap ...... 25 3.1 Introduction and operation of EBIT ...... 25 3.2 R-EBIT control and data acquisition ...... 27 3.3 Gas injection system ...... 29 3.4 Experiments and data analysis ...... 29 3.4.1 Highly charged sulfur ...... 30 3.4.2 Highly charged argon ...... 32 3.5 Results and discussion ...... 33 3.5.1 Highly charged sulfur ...... 33 3.5.2 Highly charged argon ...... 36 4 Measurements at the CRYRING ion storage ring ...... 39 4.1 Data analysis ...... 40 4.2 Results and discussion ...... 42 4.2.1 Recombination of B-like C and Ne ...... 42 4.2.2 Recombination of Be-like F VI ...... 48 5 Summary and outlook ...... 51 6 Acknowledgement ...... 55 Bibliography ...... 57

1. Introduction

The fourth state of matter often called plasma and it is believed to be the most abundant and common form of matter in the universe [1]. It has been estimated that more than 99% of matter in the universe is in state of plasma that includes the sun, most of the stars, galaxies and a signiﬁcant fraction of the interstellar medium [2]. An important aspect of plasmas is the emission of radiation, which is the main signal to determine plasma properties such as ionization balance, temperature, density and elemental abundances. This emission take place as a result of electron-ion collision processes such as ionization, excitation, de-excitation, and electron-ion recombination [3]. Carbon, neon, silicon, sulfur and argon are among the most abundant elements in the universe and solar system, after hydrogen and helium [4, 5]. In recent years, the astrophysical observational data collected by space-based observatories, such as XMM-Newton has revealed the existence of highly charged ions (HCIs) of these elements in astrophysics in an enormous amount. For example, with the XMM-Newton X-ray observatory, it was found that ex- plosion in the Tycho supernova remnant produced characteristics X rays from HCIs of elements ranging from O to Fe [6]. Emission of UV and x-ray radiation from the active solar regions show the existence of HCIs with a con- siderable abundance of almost all elements ranging from H to Ni [7]. The spectral lines emitted from HCIs of Si and S are observed from early-type stars [7]. Highly charged C is very abundant in astrophysics, e.g. in the interstellar medium [8] and in a planetary nebula [9]. Vast amount of electron-ion collisions data is required in order to get precise information about the structure, elemental composition, energy balance, temperature distribution etc, of these astrophysical objects. It has been observed recently that HCIs are not only found in hot astrophysical plasmas but a large amount of the baryonic mass of the universe is in highly-ionized state, emitting and absorbing radiations in UV and X-ray regime [10, 11]. About 30-40% of the total baryonic matter missing from the nearby universe were found in the ﬁlaments connecting cluster of galaxies in the form of low-density warm-hot gas emitting X rays [12]. It shows the existence of HCIs in galaxies. Naturally occurring highly-ionized matter on the other hand is not common on the earth because of low-temperature conditions. The ions found on the earth (outside the laboratory environment) are from the light elements such as nitrogen and oxygen, which are created as a result of ionization by cosmic rays or solar wind [7].

13 Figure 1.1: X-ray spectrum from the Tycho type Ia supernova remnant, observed with the XMM-Newton. (Credit: XMM-Newton SOC and ESA/A. Decourchelle et al. [6])

The atomic ions such as C, Ne, Si, S and Ar are also very important for fusion plasma applications. For example, these are present in fusion plasmas as an impurity [13, 14, 15]. The radiation produced by these impurities leads to plasma cooling [16] and are the principal medium to determine plasma properties such as density and temperature. Ne and Ar pellets are injected into tokamak fusion reactors to reduce plasma disruptions [17, 18]. In plasma, ions constantly make collisions with each other or with electrons. As a result various types of reactions can be induced, such as ionization, excitation and recombination. Therefore, to understand the complete behaviour of plasma, each physical process need to be studied separately. Especially, recombination processes such as radiative recombination (RR) and dielectronic recombination (DR) are among the basic atomic processes and contribute sub- stantially to the line emission and ionization balance in plasmas [3]. DR, in particular is a dominant recombination channel and therefore has been the sub- ject of intense study since many decades. The importance of this mechanism in plasma was not appreciated until Burgess correctly estimated its signiﬁ- cance in 1964 [19]. Since that study, DR is considered to be one of the key mechanisms for both atomic and plasma physics [20]. Due to experimental difﬁculties DR studies were mainly carried out theoretically before 1980s. This process was not studied experimentally before the resonant transfer and excitation (RTE) measurements performed by Tanis et al. [21] in 1982. In RTE a projectile ion captures an electron from a target atom with the simultaneous excitation of a bound electron in the projectile, producing a doubly excited state of projectile similar to the DR process. In

14 such accelerator based experiments high current beam of ions was delivered to the experimental chamber for interaction. The chamber contains a target such as atomic or molecular gases placed in the beam path. The direct measurements for DR cross sections and rates were carried out in 1983 for the first time by using merged beam [22, 23] and crossed beam techniques [24]. These techniques were limited to study DR in low-charge states of ions with poor energy resolution and relatively large errors. More recently, powerful new techniques such as Electron Beam Ion Sources and Traps (EBIS/Ts) [25, 26, 27, 28, 29] and Heavy-Ion Storage Rings [30, 31, 32, 33] brought a revolution in the electron-ion recombination studies. These devices are successfully utilized to investigate reactions between electrons and ions such as RR, DR, laser induced recombination, and dissociative recombination with high resolution [34, 35]. In these experimental facilities the ions can be trapped or stored under excellent vacuum and well controlled conditions for electron-ion collisions studies [31]. The Electron beam ion trap (EBIT), in particular is a compact and relatively inexpensive device with a total length of ∼1 m. In such a device a tunable highly compressed electron beam is used to create and study HCIs. It provides a unique environment to study atomic physics processes, in particular electron impact phenomena, such as RR and DR. The advent of this advanced instrument enables the study of DR processes in unprecedented details, by observing the emitted X rays or by extracting the trapped HCIs. It has the advantage of allowing electron-ion collisions studies in the range of high-collision energies. Besides the low-cost and small size of this instrument it has the ability to generate large sets of high quality atomic data in a rather short amount of time [36]. Once it is tuned for experiment, e.g. for DR measurements, it produced data covering a wide range of energy by sweeping the electron beam energy in the desired energy range. So far EBIT has been utilized extensively to study DR processes in HCIs for several elements. The first experimental study for DR cross sections with an EBIT was reported by Marrs et al. [37], for highly charged Ne-like barium ions. Few years later the same group performed measurements for highly charged nickel, molybdenum and barium ions [27, 38], where they demon- strated new experimental techniques for measuring DR for ∆n ≥1. This work draws an immediate attention of the researchers worldwide working in the filed of atomic physics, resulting in the development of many more EBITs around the globe. A series of articles related to EBIT work was published in the 86th volume of the Canadian Journal of Physics [39]. In contrast to the compact size and low-cost of EBITs, ion storage rings are rather big and expensive laboratory instruments. In such machines the ions are confined in a vacuum system with the help of magnetic fields, where they are kept rotating with ∼106 revolutions per seconds. On storage rings one can also use electron cooling techniques to improve the ion beam quality by reducing its geometrical size and angular divergence, which is essential for

15 high resolution recombination measurements. High energy resolution of storage rings enables to measure very low-energy DR resonance positions with extreme precision [40]. Accurate low-energy DR resonance positions and intensities are very important in order to derive reliable plasma recombination rate coefficients (see for example section 4.2.1), required for plasma applications. A list of storage ring recombination experiments for the ions relevant for astrophysical plasma can be found in [41]. In this thesis electron-ion recombination results from the measurements performed at the Stockholm Refrigerated Electron Beam Ion Trap (R-EBIT) and at the CRYRING Heavy-Ion Storage Ring are presented. Recombination data for H- and He-like S ions have been obtained from the R-EBIT. Also recombination into KLL of initially He-to B-like Ar ions have been investigated and DR resonances energy positions were measured. The obtained total DR resonance strengths results of H- and He-like S are used to check the behaviour of a scaling formula [42] for low Z, H- and He-like iso-electronic sequences and to obtain the new fitting parameters. Both of these results from highly charged sulfur and argon are compared with calculations performed by Y. M. Li and Z. Wu from Institute of Applied Physics and Computational Mathematics, China. Absolute recombination rate coefficients for B-like C, B-like Ne and Be-like F have been derived for the first time with high energy resolution from storage ring measurements at CRYRING. The results are presented and compared with calculated data available in the literature and the AUTOSTRUCTURE calculations performed by Z. Altun from Marmara University, Turkey and S. D. Loch, from Auburn University, USA. The thesis is structured as follows: In the following chapter a short description of the relevant electron-ion collision processes is given. Chapter 3 is dedicated to the R-EBIT experiments, where I describe experimental method, data analysis, results from the measurements and their comparison with the calculations. In chapter 4, I describe the storage ring experiments, data analysis and results. The spectra of B-like C, B-like Ne and Be-like F are discussed and compared with the calculations. The plasma rate coefficients of these ions are presented and compared with the calculated data available in the literature. Chapter 5 summarizes the results and gives an outlook for future experiments and an upgrade of the R-EBIT to a super-EBIT.

16 2. Electron-ion collisions

The charge changing electron-ion collisions are critically important in plasmas whether of astrophysical nature or man made, as they play their vital role in determining the plasma properties and ionization balances. One needs atomic collisions data, such as recombination cross sections, rate coefﬁcients, and resonance energy positions for modelling and diagnosing the state of high- temperature plasmas, as discussed by Mark & Dunn [43] and Summers et al. [44]. There are several electron-ion collision mechanisms, which are important for plasmas such as ionization, excitation and recombination. All of these can take place either directly in one step by single interaction or by indirect collisions in two or more steps. In the following, all of these processes relevant to the experimental data presented in this thesis are reviewed.

2.1 Electron-ion recombination Electron-ion recombination is a highly exothermic mechanism in which a free electron is captured by an ion after collision. At low and moderate electron densities there are two most important recombination channels through which an ion can recombine with a free electron, namely radiative recombination and dielectronic recombination. The radiative recombination is a non resonant process and categorized as a direct mode mechanism, while dielectronic recombination proceeds in an indirect resonant mode involving two steps. In both of these channels the excess energy and momentum of the recombining electron are carried away by a photon.

2.1.1 Radiative recombination Radiative recombination (RR) is a non-resonant, one step recombination process in which a free electron recombines with an ion, emitting excess energy in the form of a photon:

RR : Xq+ + e− −→ X(q−1)+ + hν, (2.1) where the photon energy hν is given by

hν = Ee + Eb(nl). (2.2)

17 Where Ee is the kinetic energy of the free electron and Eb(nl) is the binding energy of the state in which the free electron is captured. This process can take place at any collision energy, and a finite probability exists for recombination to all available levels of the ion. The process is schematically illustrated in figure 2.1(a). The first expression to obtain the RR cross sections for bare ions interacting with free electron, was derived theoretically by Kramers in 1923 [45], in the semi-classical approximation

2 4 σ Kramers × −22 Ry Z 2 RR (n,Ee) = 2.105 10 2 2 cm . (2.3) nEe(n Ee + RyZ )

Where Ry is the Rydberg constant, n is the principal quantum number of the recombined ion. The Kramers formula gives accurate cross sections for electron capture into high n states. For recombination into low-n states the above formula need to be corrected by the Gaunt factor gn. The Kramers formula can also be used to calculate RR cross section for non-bare ions by introducing an appropriate charge, called effective charge Ze f f . To estimate the effective charge a simple expression was given by Hahn & Rule [46] and Kim & Pratt [47], 1 Z Z = (Z + Z ) for Z ≥ Z ≥ C , (2.4) e f f 2 C I C I 2 and √ Z Z = Z Z for C ≥ Z ≥ 1, (2.5) e f f C I 2 I where ZC is the nuclear core charge and ZI is the ionic charge before electron capture.

2.1.2 Dielectronic recombination Dielectronic recombination (DR) is a resonant recombination channel in which a free electron is attached to an ion with the simultaneous excitation of a core electron forming an intermediate doubly excited state. These doubly-excited states can decay either by autoionization or by radiative decay. The autoionization channel returns the ionic system to the original charge state, whereas radiative decay leads to the completion of DR process. As a result the ion charge decreases by one. Assuming an initial charge state of the ion Xq+, the DR process can be described as: DR : Xq+ + e− −→ [X(q−1)+]∗∗ −→ [X(q−1)+]∗ + hν. (2.6) By energy conservation DR can take place only if the total energy of the free electron and the binding energy of the Rydberg electron equal to the energy required for the excitation of a core electron in the initial system:

Ee = ∆Ecore − ERyd(nl), (2.7)

18 Figure 2.1: Schematic diagram of (a) radiative recombination and (b) dielectronic recombination in He-like ions.

where Ee is the kinetic energy of the free electron, ∆Ecore is the excitation energy of the core electron in the initial system, and ERyd(nl) is the binding energy of the outer Rydberg electron with respect to the excited target. A schematic illustration of the DR process is displayed in ﬁgure 2.1(b) for a He-like ion (contains two electrons). A free electron is captured into an empty L shell of the ion and a K shell electron is simultaneously excited into the L shell forming an intermediate doubly excited state. The created doubly excited state decays radiatively by emitting photon to accomplish the DR process. The DR resonances produced in such a case are denoted by KLL. Approximate binding energy ERyd(nl) of the Rydberg electron can be calculated by a simple hydrogenic formula:

Q2 E (nl) = 13.6 [eV], (2.8) Ryd n2 where Q is the ionic charge of the ion prior to recombination and n is the principal quantum number of the recombined Rydberg electron. The excitation energy of the core electron and the binding energy of the captured electron are quantized. Consequently, the doubly excited states can be formed only for discrete energy values of the free electron [48]. This shows the resonance nature of the DR process. Depending on the collision energy many different states might be populated, forming a Rydberg series of resonances which have the same excited core. The excitation of the initially bound electron can be inter-shell (∆n ≥ 1) or intra-shell (∆n = 0), corresponding to the excitation of the bound electron to a higher or within the same main quantum number, respectively. For intra- shell excitation less energy is required, so this is true mostly in the case when electron is captured into high Rydberg states. The two excitation channels are sparse when n is small and becomes dense as n gets larger.

19 In the isolated resonance approximation, which ignores the interference between close lying resonances, the DR cross section associated with an intermediate doubly excited state can be expressed as: Γ σ DR S /2 (E) = 2 2 , (2.9) π ((Ee − Eres) + Γ /4) where Eres the resonance energy at which DR take place and Γ the natural width of the doubly excited state. The energy integrated cross section or DR resonance strength S is given by ∫ h¯ 3π2 g 1 A (d → i)Σ A (d → f ) S = σ DR(E)dE = d a f rad , (2.10) 2me gi Eres ΣkAa(d → k) + Σ f Arad(d → f ) where gi and gd are the multiplicity of the initial target state and that of intermediate doubly excited states, respectively. Aa(d → i) is the rate of autoionization from doubly excited state d to i, Σ f Arad(d → f ) denotes the sum of radiative transition rates from state d to f below the ﬁrst ionization limit and ΣkAa(d → k) is the sum of all possible autoionizing decay channels of doubly excited state d.

2.2 Electron-impact ionization and excitation Ionization and excitation are among the most important atomic processes. Both of these mechanisms have been studied extensively in the past due to their importance in different research ﬁelds [49, 50, 51]. If an electron impacts a target atom with sufﬁcient kinetic energy, it can excite the atom to some high excited states or ionize it. The minimum requirement for these processes to occur is that the projectile electron must have a kinetic energy exceeding the excitation or ionization energy of the target atom. In the following, I will give a short overview of these processes.

2.2.1 Electron-impact ionization The ionization of an atom or ion by electron impact may be completed via one of the two ionization channels, i.e. through direct or indirect channel. In the direct process, the incident electron ejects one of the bound electrons from the outer or inner shell of the target by making direct impact, resulting in an increase of the ionic charge by unity from q to q + 1. In order for this process to occur, the kinetic energy of the projectile electron must be greater than the ionization potential of the bound electron to be ionized q+ − → (q+1)+ − − X + e1 (Ee) X + e1 (E1) + e2 (E2). (2.11) By energy conservation the sum of energy of the two scattered electrons is equal to the kinetic energy of the projectile electron minus the ionization

20 potential of the bound electron

Ee − Ip = E1 + E2. (2.12)

The above given result is observed as a single ionization of the parent ion Xq+ and is termed as direct ionization. For ionic system with many electrons, multiple ionization can take place, in which more than one electron can be removed from an atom or ion:

Xq+ + e− → X(q+n)+ + (n + 1)e−. (2.13)

Thus the charge of the ion increases by n, i.e. from q+ to q + n. One of the indirect ionization mechanisms termed as excitation autoionization is given by: Xq+ + e− → [Xq+]∗ + e− → X(q+1)+ + 2e−. (2.14)

-21

1,0x10 ) 2

-22

5,0x10

Cross section (cm

-23

1,0x10

0 2 4 6 8 10

Electron Energy/I [keV]

P 18+ 17+ Figure 2.2: EII cross section vs electron energy/IP for producing Ar from Ar , calculated with the Lotz formula given in 2.15.

The ionization process rapidly becomes more difﬁcult as the ion charge state increases. This is due to the fact that the deeply bound electrons require more energy to remove them from the ionic shell (ionization cross section decreases), and neutralizing collisions with background gas atoms also decreases the step-wise progress towards the desired charge state (charge exchange cross sections increase) [51]. The EII plays a crucial role for charge breeding in different ion sources such as in ECR, EBIS, and EBIT. A semi-empirical Lotz formula [52] is often used to calculate the ionization cross sections of positive ions:

σ Lotz × −14 N ln(u + 1) 2 Ee − EII = 4.5 10 2 cm ,u = 1, (2.15) Ip (u + 1) Ip

21 where Ee is the energy of the free electron and Ip is ionization potential of the bound electron in eV. N is the number of electrons in a given shell. The EII cross section strongly depends on the incident electron energy, the ionization potential of the electron to be removed and the ion’s particular electronic conﬁguration. Figure 2.2 shows the EII cross sections calculated by using the Lotz formula for the formation of Ar18+ from Ar17+. It can be seen that the cross section increases sharply for electron energies above the ionization potential of Ar17+ (4.426 keV) and reaches a maximum value at ∼11 keV, which is about 2.5 times higher than the the ionization potential of Ar17+. This relation generally holds for all HCIs. Therefore to maximize the yield of a particular charge state, the electron beam energy of the EBIT is set to be a factor of two higher than the ionization energy of the ion to be ionized.

2.2.2 Electron-impact excitation The electron-impact excitation (EIE) takes place either by direct Coulomb interaction or through a resonant manner. In such processes the excited electron is stabilized through the emission of a photon with a speciﬁc energy, a number of photons in a cascade or by Auger decay. The direct excitation process (see ﬁgure 2.3(a)) can be described as:

Xq+ + e− → [Xq+]∗ + e− → Xq+ + e− + hν. (2.16)

The probability of this process is described by the effective excitation cross section. The empirical formula proposed by Van Regemorter [53] provides a good estimate of the excitation cross section. The direct electron-impact excitation (dEIE) cross section depends on the incident electron energy Ee and the atomic structure of the target ions. The cross section for this process is maximum as kinetic energy of the free electron becomes equal to the excitation energy of the atomic system.

σVR × −13 fi jg¯ 2 2 EIE = 2.36 10 [cm eV ], (2.17) EeEi j where Ei j is the excitation energy, Ee is the kinetic energy of the free electron, fi j is the oscillator strength for the transition from the excited state j to the ground state i, and g¯ is the effective Gount factor. At energies close to the excitation threshold the value of g is ∼ 0.2 and at Ee>2Ei j, g¯ = 0.28ln(Ee/Ei j) [48]. In resonant electron-impact excitation (rEIE) a free electron is attached to an ion while exciting a bound electron producing an intermediate doubly excited state (see ﬁgure 2.3(b)). For this process to occur at least one electron

22 Figure 2.3: Schematic diagram of (a) direct electron-impact excitation (dEIE) and (b) resonant electron-impact excitation (rEIE) mechanisms. is needed in the atomic ion. This means it involves two electrons and it is therefore termed as dielectronic capture (DC). The intermediate doubly excited state thus formed decays preferentially by Auger electron emission for highly excited ions. The rEIE process is given by the scheme:

Xq+ + e− → [X(q−1)+]∗∗ → [Xq+]∗ + e−. (2.18)

The results from rEIE can not always be distinguished from dEIE channel. As a consequence the two processes show interferences between their amplitudes [54].

3. Measurements at the Refrigerated Electron Beam Ion Trap

The Electron Beam Ion Trap (EBIT) is one of the unique laboratory instruments to investigate electron-ion collisions. The production and conﬁnement of ions in an EBIT enables spectroscopic studies in unprecedented details. The apparatus uses an adjustable electron beam energy for production of HCIs via ionization, which then probes/scans in a step wise fashion to cover the desired energy range. For example, photo-recombination can be investigated by observing X rays which are emitted in RR or during the relaxation of the doubly excited states formed in the DR process. An appropriate data acquisition system allows to record the electron beam energy, x-ray energy, and time of the detected photon in event mode. In the following, we will describe the EBIT device, data acquisition and gas injection systems, experimental methods, and the results from the EBIT measurements.

3.1 Introduction and operation of EBIT An EBIT is a versatile laboratory instrument capable of producing, trapping and studying HCIs. The ions are almost at rest, within the small volume of a highly compressed electron beam. The EBIT is not the only instrument that can create ions in highly charged states, but certainly it is the most compact and efﬁcient machine, offering great control over the experimental conditions in which HCIs are produced and studied. The most important feature of EBIT, is the ability to obtain high resolution atomic data from trapped HCIs in a wide range of electron impact energies and available charge states [55]. Another remarkable feature of this machine is its size, which is typically not much larger than a table-top device, and yet can strip virtually all of the electrons from any naturally occurring atom on the periodic table [56]. This instrument can also be used as an ion source to deliver HCIs for other experiments and applications, which shows the dual nature of this device. The success of this machine is proven by a large number of widely cited articles that have been reported since its inception. A short description of such a device is given as following. The EBIT device has three main subsections: i) an electron gun for producing electrons ii) a trap region for creating, trapping and studying highly charged ions and iii) an electron collector for collecting electrons

25 (see Fig. 3.1). The electron gun region consists of a cathode, an anode, a focusing electrode, and a transition electrode. The cathode is usually made of tungsten impregnated with barium oxide to lower the work function. The electron gun assembly is surrounded by a magnetic bucking coil to reduce the strong magnetic field effect produced by the superconducting magnet and maintains a near zero magnetic field at the cathode, to ensure maximum beam compression. The emitted electrons are extracted from the cathode by applying a biased voltage in the order of kV to the anode, depending on the beam current required. The electrons are then accelerated towards the trap region, which is surrounded by a pair of superconducting Helmholtz coils and composed of a drift tube assembly containing three drift tubes. The entire drift tube assembly of the R-EBIT is on an adjustable high voltage platform, with a maximum potential of +30 kV. The magnetic field produced by the superconducting magnet compresses the electron beam to 70 µm diameter as it advances through the drift-tube assembly. Beam steering, to compensate for small mechanical mis- alignments can be achieved with two pairs of magnetic coils situated outside the vacuum chamber. The current on each magnetic coil can be controlled separately to produce a field of several Gauss perpendicular to the electron beam. The three drift tubes are individually biased such that the outer two drift tubes are on high positive potentials compared to the middle drift tube, thus forming an electrostatic trap which confines the ions in the axial direction. Radial trapping of the ions is provided by the combination of strong magnetic field and the attractive space charge of the high-density electron beam advancing through the trap region. In old type EBITs, the superconducting magnet and drift tubes assembly were cooled with liquid nitrogen and liquid helium, but nowadays a number of liquid nitrogen and liquid helium free EBITs and Electron Beam ion Source (EBIS) are in operation of which Stockholm R-EBIT was the first one [57]. In R-EBIT the superconducting magnet and the trap drift tube assembly are cooled by using a 4 K cold-head connected to a helium compressor. The vacuum in the trap region of the R-EBIT is kept <10−10 mbar during the experiments. The schematics of the R-EBIT are shown in figure 3.1, while its operating parameters are given in table 3.1. After leaving the trap region, the electron beam is decelerated and dumped on the walls of the collector, a conical cylinder which is biased with around a kV positive potential with respect to the cathode. As the beam advances towards the collector it diverges by the declining magnetic field of the superconducting magnet and the reversed magnetic field of the collector magnet. At the entrance of the collector a suppressor electrode is used to prevent secondary electrons from being accelerated back into the trap and electron gun region. On the exit of the collector a negatively biased electrode called extractor is located. This electrode helps to guide the ions from EBIT during ion

26 Figure 3.1: Schematics of the Stockholm R-EBIT for recombination measurements. extraction. It is also useful to stop the escape of the secondary electrons from the back of the collector.

Table 3.1: R-EBIT parameters. Parameters Value Magnetic ﬁeld 3 T Max. electron beam energy 30 keV Max. electron beam current 150 mA Electron beam radius 35 µ m Max. central current density 4 kA/cm2 Trap length 2 cm Electron density 10 11cm−3 Ion density 10 9cm−3

3.2 R-EBIT control and data acquisition A schematic diagram of the data taking scheme used for electron-ion recombination measurements at the R-EBIT, presented in this thesis is shown in ﬁg- ure 3.2. We have developed two multi-parameter LabView programs to control R-EBIT operational parameters and the data acquisition system. The ﬁrst program controls the potentials of the electron gun anode and focus, transition,

27 suppressor and extractor electrodes, electron collector, and also the currents through the bucking and collector magnets. Another important feature of this program is that it constantly monitors the emitted and collected electron current, the power deposited on the electron gun anode, power dissipation in the high voltage system, and the pressure and temperature in R-EBIT. In case of a deviation of more than 10% of the set and actual value, or an anode power exceeding 1 W, the program decreases the anode voltage and thus decreases/stops the electron current. Several other automatic safety features are also implemented in the program which allows for a continuous two weeks measurement without close operator monitoring and reduced risk of human errors. The R-EBIT settings can be saved and hence stable operation can be started or restored quickly.

Figure 3.2: Schematic view of the data acquisition system for electron ion- recombination measurements at the Stockholm R-EBIT.

The other program is used to control voltage of the drift tube assembly using a National Instruments card NI PCI-6703. The same program is also used to ac- quire event mode x-ray data during the experiments. Following ampliﬁcation and shaping, the x-ray pulse heights are registered by a NI PXI-6133 National Instruments card. The card samples the pulses received from the shaping am- pliﬁer with 1 MHz sampling rate and the acquisition program determines the maxima of the pulses. Such a scheme should also allow for a pile-up rejection, although this feature has not been implemented yet.

28 X rays are acquired only during the probing/scanning time. X-ray detection were performed using a Si(Li) (paper III) and a high purity Ge detector (paper I) with energy resolutions of 200 eV and 132 eV at 5.9 keV, respectively. For each detected X ray a three parameter x-ray event (x-ray energy, electron beam energy, and time) were recorded and stored to the data ﬁle. The same program is also used for Time of Flight (TOF) measurements (paper IV). It receive pulses from a fast Tektronix TDS620 oscilloscope connected to the TOF detector. For each probing energy several such pulses were averaged to reduce the noise and were stored to a separate ﬁle.

3.3 Gas injection system The R-EBIT facility is equipped with a two mode gas injection system, i.e. one with continuous molecular gas-flow and the other with a pulsed gas jet using a piezoelectric valve. This gas injection system has been used to create HCIs of a number of elements ranging from fully-stripped O, Ne, Si, S, Ar to Li- like Kr33+. The gas injection system also allows the mixing of different gases, useful for evaporative cooling of the HCIs by lighter ions. In the electron-ion recombination measurements discussed in this thesis, a pulsed gas injection mode was used for injecting gas atoms into R-EBIT. A detailed description of the used gas injection system can be found in [58]. The use of pulsed gas injection have several advantages over continues gas injection. Figure 3.3 shows a magnet scan of Ar ions extracted from R-EBIT, with an ionization time of 500 ms, at a constant electron beam current of 35 mA, and an electron beam energy of 8 keV. The gas is injected in continuous mode (dotted line) as well as in pulsed mode (solid line). It can be seen from figure 3.3 that the pulsed gas injection deliberately enhances the production of ion abundances at higher charge states compared to the continuous gas injection. This is due to the fact that a short duration of the gas pulse decreases electron capture by HCIs from the neutral gas. In case of continuous gas injection, the HCIs can easily capture electrons from the continuous flow of neutrals, which decrease the step-wise progress towards the high charge states. Pulse mode also allows for minimizing the amount of gas injection into the trap which reduces the load on EBIT cryogenic pumping. This is also very useful when corrosive and expensive gases such as SH2 are used for experiments.

3.4 Experiments and data analysis In this section, I will report the experimental methods and data analysis for sulfur and argon measurements performed at the R-EBIT.

29 Figure 3.3: Comparison of the charge state spectra of Ar ions with continuous and pulsed gas injection.

3.4.1 Highly charged sulfur Electron-ion recombination measurements for sulfur ions was performed with two different approaches, i.e. by detecting the photons emitted from the trapped ions and by monitoring the ions extracted from the EBIT using time of flight (TOF) method. A detailed method of TOF measurements and data analysis is given in the attached paper IV. Here I will review the experiment in which photon are detected from the trapped ions. Figure 3.4 shows a timing cycle for recombination studies of highly charged sulfur in X rays measurement. At time t = 0, SH2 gas was injected into the trap region using a ballistic gas injection system in pulse mode as discussed in section 3.3, through one of the ports of the R-EBIT. Following the injection, the electron beam energy was set to an ionization energy of 8 keV, for 900 ms to produce a suitable charge state distribution of sulfur ions. After charge breeding the electron beam was ramped up and down linearly in between 1.6 keV and 3 keV. The ramping time in each direction was 50 ms. After completing one cycle for 300 ms, the ions were dumped and the trap was refilled with fresh gas atoms to start a new measurement cycle. The electron beam current was kept constant at about 10 mA, which is a count rate optimized value for a good count rate while keeping the beam space charge low. For low ions velocity spread, the trap depth was fixed at 10 V throughout the measurements. The latter two factors ensured a good energy resolution of the DR spectrum and a reasonable count rate. The X rays emitted from the trapped highly charged sulfur ions during the ramping time was observed with a Si(Li) x-ray detector, placed perpendicular to the electron beam direction at one of the observational ports of the EBIT.

30 Figure 3.4: Timing diagram for the electron-ion recombination measurement of highly charged sulfur with the R-EBIT.

For each detected X ray a three parameters event (x-ray energy, electron beam energy, and time) was recorded and stored to the data file. A fast LabView based data acquisition system, described in section 3.2 was used for this pur- pose. The time scheme employed is considered to be most appropriate for this type of recombination measurements because of its several advantages. For example, this method allows for fast ramping and thus guarantees that the electron beam does not spend enough time on any resonance to strongly effect the charge state balance equilibrium during the measurements. Second, it allows simultaneously observing of X rays in all electron-ion interactions processes, which can take place in the ramping energy range. To calibrate the electron energy, first photon energy calibration is required. The calibration of the photon energy was performed with x-ray fluorescence lines from Si, Cl and Ti irradiated with a 55Fe radioactive source. The Kα and Kβ characteristic x-ray lines of Mn produced by the 55Fe source were also used in the calibration. Figure 3.5 shows the calibration spectrum. The line profiles were fitted with Gaussian functions to determine their centroids. The resulting data points were fitted with a linear function to obtain the channel- energy conversion factor. After having calibration for the photon energy axis, it is rather straightfor- ward to calibrate the electron beam energy axis, which was performed using the centroids of the peaks associated with RR into the K shell of H-like sulfur ions by using the following relation:

Ehν = Ee + Eb(nl), (3.1) where Ee,Ehν , and Eb(nl) are the electron energy of the free electron, x-ray energy, and binding energy of the electron after recombination, respectively.

31 Figure 3.5: Calibration lines and ﬁt used for the SiLi-detector channel-energy conversion. The lines are produced by irradiating Si, Cl, and Ti with 55Fe radioactive source.

The detected X-ray count rates were corrected for absorption taking place between the trap region and the x-ray detector window, by using absorption coefﬁcient from the NIST database [59]. Then the DR resonance strengths were obtained by normalizing the observed count rates to the theoretical RR cross sections: IKLn SKLn = σ RR∆EW(90◦) f , (3.2) IRR ions where IRR is the count rate from the K-RR photons of H-like ions over an energy spread ∆E,IKLn is the DR count rates in each peak, σ RR is the theoretical RR cross section of H-like sulfur ions, and fions is the ratio of H-like to He-like ions. In eq.(3.2), W(90◦) = (3-PKLn)/(3-PRR) is the angular correction factor to the photons due to polarization of DR and RR. PKLn is the average polarization of the KLn (2 ≤ n ≤ 5) manifold and PRR is the polarization of X rays from K-shell of H-like RR.

3.4.2 Highly charged argon For the argon measurement the experimental cycles consist of charge breeding, probing, and extraction intervals. We probe the energy in very small steps, instead of ramping as in sulfur case. This is because in this experiment, we had planned to study recombination with TOF method, together with the x- ray detection technique (see the attached paper IV for more detail about this method). Unfortunately, our TOF detector was not very well aligned and we did not get reliable data from the TOF measurements. The results of the acquired X rays data were published in the JINST journal (paper I).

32 The timing scheme employed in this experiment consists of 600 ms charge breeding with an electron beam energy was set to 8 keV, to obtain the desired charge state distribution of argon ions. Then the electron beam energy was probed for 300 ms (see Fig. 2 in paper I). During the probing time the electrons had an adjustable energy ranging from 2 keV up to 3.2 keV. In each cycle the probing electron beam energy was increased by 4 eV. After probing the ions were extracted from the trap and a new gas pulse was injected before beginning the new time cycle. This sequence was repeated continuously in order to scan the energy range of predicted DR resonances. The electron beam current was kept constant at 6 mA throughout the measurement. A HPGe detector with an energy resolution of 135 eV at 5.9 keV was used to collect the X rays emitted from the trapped highly charged argon ions. The detector was placed perpendicular to the electron beam direction and moved inside the R-EBIT tank in order to increase its solid angle. The data acquisition program used in this measurement is same as that in the sulfur experiment. The detected x-ray count rates have been corrected for detection solid angle and for the absorption taking place in the Be window of the x-ray detector by using the absorption coefﬁcients from the NIST data base web page [59]. In order to compare the experimental results with calculations, the calculated data was adjusted using the following formula: Σ σ DR ◦ Rq(E) = neve qNq q (E)Wq(90 ), (3.3) where Rq(E) is the DR count rates as function of the electron energy, ne is the electron density, ve is the velocity of electrons, Nq is the number of the σ DR trapped ions with a charge state q interacting with the electrons, q (E) is the calculated DR cross section convolved with electron beam energy of 24 eV ◦ FWHM, and Wq(90 ) is the angular correction factor for X rays produced by DR. In the ﬁtting procedure the ion numbers Nq were taken as free parameters.

3.5 Results and discussion 3.5.1 Highly charged sulfur A two dimensional scatter plot of the x-ray data acquired from highly charged sulfur ions is shown in ﬁgure 3.6(a). Different recombination channels, such as DR and RR are prominent in the spectrum. In addition, X rays produced from other physical processes such as electron-impact excitation can also be seen at high electron beam energy. The DR resonances are labelled according to inverse Auger notation of the intermediate doubly excited states through which DR process take place. For example, He-like KLL means that a free electron is captured into the L shell of the ion, with the simultaneous excitation of a K shell electron to the L shell to produce a doubly excited state. X rays emitted from L to K transitions are denoted as L-K. The RR process gives rise to a continuum x-ray emission, which appears as slanted line, since

33 the photon energy increases linearly with the electron beam energy. The RR ridges corresponding in transitions to the K and L shell are labelled with K- RR and L-RR, respectively. The resonances that appear along the L-RR ridge are due to the transition of the outer electron attached to the ion.

Figure 3.6: a) Photon vs. electron energy spectra acquired from highly charged S ions. Different DR resonances are designated using Auger notion of the doubly excited states. Figure b), represents the L-K ridge and L-RR ridge obtained by projecting the counts (from Fig. a) onto the electron beam energy axis.

The 2D photon-electron energy spectrum allows to project selected regions either onto the photon energy axis or on the electron beam energy axis. Fig- ure 3.6b is obtained by projecting the L-K and L-RR ridges onto the electron beam energy axis. The X rays emitted through different recombination channels are clearly seen in the spectra. The vertical bars in this figure, shows the approximate energy positions of different DR peaks for ∆n = 1 and ∆n = 2 transitions of H-like and He-like ions obtained by using equation 2.7. In figure 3.7a and 3.7b the experimental results are compared with theoretical calculations convolved with 24 eV FWHM of the electron beam. Both results show a good agreement in resonances energy positions and intensities. The measured and calculated DR resonance strengths are summarized in paper III. The experimental peak appearing at an energy of 2.282 keV is due to contributions of KLM and KLN resonances of H-like and He-like ions, respectively. If we sum up the theoretical results of these two peaks and compare with the experimental results, they are consistent as shown in figure 3.7a and 3.7b (red solid lines). Besides H- and He-like ions, Li-like ions may also contribute to the photon emission spectrum. However, we did not observe a

34 signiﬁcant amount of X rays from this charge state in the spectrum. This shows a very small abundance of Li-like sulfur ions in the trap, compared to H-and He-like charge states.

Figure 3.7: a) L-K ridge b) L-RR ridge. The grey shaded area shows the experimental results for H-and He-like ions. The calculated results are shown with black dotted and solid lines for H-like and He-like ions, respectively, convolved with 24 eV FWHM resolution. The red solid peaks are the sum of theoretical KLM and KLN peaks of H-like and He-like ions, respectively.

Previously a scaling formula was proposed by Watanabe et al. [42], to check the behaviour of DR resonance strengths in He-like ions as a function of atomic number KLn 1 S = 2 −2 , (3.4) m1Z + m2Z where Z is the atomic number and m1 and m2 are fitting parameters. In deriving the above formula following scaling were used, Ar ∝ Z4,Aa remains 2 constant with Z and Ee ∝ Z . By using our DR resonance strengths results of sulfur and silicon in this formula, together with the previous experimental and theoretical results we obtain the fitting parameters for H-and He-like iso-electronic sequences. The obtained fitting parameters for He-like ions are given in table 3 of the attached paper III, while these values are plotted in figure 3 of the same paper.

Experiments H-like KLL

Theory eV]

40 2 cm -20

30 [10

10 Resonance Strength

0 20 40 60 80 100

Atom ic Num ber [Z] Figure 3.8: DR resonant strengths vs atomic number for H-like iso-electronic sequence. The data points with vertical dotted lines are our results of S15+ and Si13+ ions. The other experimental and calculated data points are H-like ions of O7+ from [60], Ti21+ from [61], C5+,O7+, Si13+,S15+ from [62], from Ge31+, Se33+,Kr34+ from [63] and U91+ from [64]

For KLL DR resonant strength of H-like ions, we obtain the fitting parameters 15 20 −2 −1 m1 and m2 with values 1.95×10 and 6.90×10 in units of cm eV , respectively. Our experimental results for DR resonant strengths of H-like sulfur and silicon is shown in figure 3.8 as a function of Z, together with the previous experimental and calculated data points. The results obtained from our measurements are in very good agreement with the trend predicted from the previous experimental and calculated data points of H-and He-like ions for different elements. For higher atomic number the scaling formula starts to predict smaller values of the resonant strengths than those measured experimentally. This deviation might be due to the sim- plification of a scaling formula and omission of relativistic as well as quantum electrodynamical (QED) effects. The generalized Breit-interactions e.g. gets very important with highly charged ions and significantly increases the DR resonant strengths [64, 65, 66].

3.5.2 Highly charged argon A two dimensional histogram of the recorded x-ray data as a function of electron energy is shown in ﬁgure 3.9. The horizontal and vertical axis represents the projectile electron energy and the X rays energy, respectively. DR resonances are labelled according to the Auger notation as already discussed in the sulfur case. Here our interest is to determine the KLL DR resonance peak positions of different charge states in highly charged argon. The other peak positions such as KLM, KLN and KLO has already been extensively inves-

36 L-K L-RR

3,2

3,0

KLN

2,8

KLM

2,6

2,4 Electron Energy [keV] Energy Electron

KLL

2,2

2,0

2,5 3,0 3,5 4,0 4,5 5,0

Photon Energy [keV] Figure 3.9: Two dimensional scatter plot of the x-ray data acquired for highly charged argon.

Figure 3.10: Top: Comparison of the experimental results with calculations for the KLL dielectronic recombination features. The solid line represents calculated DR cross sections for Ar convolved with 24 eV FWHM of the electron beam and adjusted with the ion numbers (see eq. 3.3). The dotted line shows experimental results. Bottom: Two dimensional map of the KLL DR region of initially He-to B-like argon.

37 Table 3.2: Experimental and theoretical KLL DR peak positions with initially He- to B-like argon. The experimental uncertainties are given in parentheses. Charge state Theoretical (keV) Experimental (keV) Li-like 2.219 2.218 (0.0033) Be-like 2.259 2.260 (0.0026) B-like 2.301 2.310 (0.0031) C-like 2.355 2.357 (0.0044) tigated by various groups working on EBIT/S. We can also derive DR cross sections and resonant strengths but unfortunately we could not get number of ions from this measurement, required for normalization. The upper panel of figure 3.10 shows the KLL data cut from figure 3.9, projected onto the electron beam energy axis. The calculated results fitted by using equation 3.3, are also shown for comparison with the experimental results. Within each group of resonances (for each charge state), only few resonances have a large enough resonance strength to contribute significantly to the distribution as shown in the figure 3.10. For strong resonances the doubly excited states formed during recombination of electrons into initially He-to B-like ions are also shown in the figure 3.10. The experimental and calculated peak centroids of the initially He-to B- like argon are summarized in table 3.2 The experimental values are obtained by fitting Gaussian function to each peak. The agreement between theory and experiment is excellent for the Li-, Be- and C-like ions. An energy shift of 9 eV arises in case of the B-like 2 2 2 1 2 2 2 KLL peak. The calculated intensities for 2s 2p ( D5/2) , 2s 2p ( D3/2), 2 2 2 2 2 2 2 2 2 2s 2p ( S1/2), 2s 2p ( P3/2) and 2s 2p ( P1/2) resonances do not explain the centroid of the observed peak. Underestimated contributions of 2 2 2 2 2 2 1s2s 2p ( S1/2) and 1s2s 2p ( P3/2) resonances might be the reason for this discrepancy.

11s state is ignored in writing the electron conﬁguration

38 4. Measurements at the CRYRING ion storage ring

The storage ring measurements reported in this thesis were performed at the CRYRING Heavy-Ion Storage Ring that was located at Manne Siegbahn Lab- oratory at Stockholm University, Sweden. A detailed description and principal parameters of this machine can be found in [67]. The ions for which we have performed measurements were produced in a plasmatron ions source, MINIS, and an electron cyclotron resonance (ECR) ion source. These ions were pre- accelerated by a radiofrequency quadrupole accelerator (RFQ) to energies up to 300 keV/amu. After injection and placement of the ions on a stable orbit, the fast acceleration mode of the ring brings the ions quickly to high energy for storage. Final acceleration of the ions is provided by a radio frequency (RF) drift tube. The maximum energy of the stored ions is given by the following formula: Q2 E = 96 × [MeV/amu], (4.1) max A2 where Q and A are the charge number and mass of the ion in atomic mass units, respectively. The maximum ion energy is necessary, since otherwise electron capture from residual gas at the injection energy would cause high beam losses. For recombination measurements, the most important part of the CRYRING is the electron cooler. A schematic of the CRYRING electron cooler is shown in ﬁgure 4.1. The electron cooler play a double role in our experiments, i.e. it improves the ion beam quality by electron cooling and acts as an electron target for the stored ions. The electron beam in the electron cooler is produced by thermal emission from a hot cathode at T=1000 K. This corresponds to an initially isotropic temperature of ∼100 meV. The reduction in the transversal temperature of the electrons is achieved through adiabatic expansion of the magnetic ﬁeld guiding the electron beam. As a result the transversal temperature can therefore be reduced by a factor of 1/100 of its original value, i.e. T⊥=∼1 meV. Along the longitudinal direction the acceleration to an energy 2 Ee=(me/2)v compresses the electron momentum spread to reduce the temperature with a typical value of T∥=∼0.1 meV. In the electron cooler the circulating ion beam is completely immersed in the constant density electron beam of typically few tens of mA over an effective length of 80 cm [68]. The ion cooling takes place by repeated Coulomb interactions between the constantly refreshed low-temperature electrons and

39 Figure 4.1: The experimental setup showing the electron cooler section of the CRYRING and the position for placing surface barrier detector (SBD) to detect recombined species.

hot ions as they pass through the cooler about a million times per second during their circulation in the ring. Thus at thermal equilibrium the ion beam energy spread reduced by a large factor from MeV energy to few eV [31]. Also because of cooling the diameter of the ion beam is reduced to approximately 1 mm from its initial 2 cm diameter. In our measurements the ion beam was electron cooled typically for 2 s. After electron cooling the electron beam energy was scanned in a zig-zag pattern to cover the desired energy range for recombination studies (see Fig. 4.2b). The electron-ion collision energy was scanned, ﬁrst with electron faster and then with electrons slower than the circulating ion beam. After the electron energy scan, the acquisition window was closed and the ion beam was dumped. The above sequence was repeated by starting a new cycle with the ion beam injection. In the interaction region of the electron cooler recombination can take place between electrons and ions. After recombination the charge changed ions/atoms are separated from the primary beam as they pass through a dipole bending magnet following the electron cooler segment. These separated ions/atoms were detected using a solid state surface barrier detector with approximately 100% efﬁciency. For each detected ion/atom, the program records pulse height, electron acceleration potential, and cycle time.

4.1 Data analysis Figure 4.2, shows the collected counts as a function of time containing four spectra from B-like Ne measurements. The ﬁrst two spectra are with an electron velocity greater than the ion velocity (ve > vi) and the last two with an electron velocity less than the ion velocity (ve < vi). The associated cathode voltage is shown in ﬁgure 4.2b, while an electron-ion collision energy in the

40 Figure 4.2: (a) Collected counts for recombination of Ne5+ recombining into Ne4+. (b) The energy scan used in this measurements. The dotted lines indicate the cooling voltage. (c) Collision energy in the center-of-mass frame as a function of acquisition time. center-of-mass frame is shown in the figure 4.2c. A sharp peak in the central region of figure 4.2a, shows that recombination rate is maximum when electron and ion velocities matches (indicating that the cooling condition is fulfilled). The data analysis involves an electron-energy correction to compensate for space-charge effects inside the interaction region of the electron cooler and an ion-energy correction to compensate for longitudinal drag force effects that occurs as the cathode potential is ramped. A detailed procedure of the data analysis is described in [69, 70, 71]. Ideally, the cathode voltage should be used to determine the electrons energy, but this is not a correct representation due to space charge induced by the electron beam. Thus, the space charge correction must be done to obtain the precise electron energy. The true electron energy is thus obtained by

Ee = e(Ucath +Usp), (4.2) where e is the electron charge, Ucath is the calibrated cathode potential, and Usp is the space-charge potential of the electron beam. The ion energy must also be corrected for the drag force that an ion expe- riences from the electron beam during the energy scan. This force tends to decrease the velocity difference between electron and ion beam. The corre-

41 sponding change in ion velocity vi as a function of time is obtained by

dvi η li = Fz(t), (4.3) dt Mi LR where Mi is the mass of the ion, Fz(t) is the longitudinal component of the drag force, li/LR is the ratio of the interaction length to the ring length and represents the fraction of time over which the force is applied as the ions cir- culate in the ring. η is a free parameter that compensates for possible magnetic effects in the drag force, the errors from uncertainties in the interaction length and beam temperature. The electron and ion corrected energies are then used to calculate the electron-ion collision energy in the center-of-mass system [72]: [ 2 2 2 ECM = (Ei + Ee + Mic + mec ) (4.4) ( ) ] 1 √ √ 2 2 − 2 2 2 2 − 2 2 Ei + 2Mic Ei + Ee + 2mec Ee (Mic + mec ), where ECM is the center-of-mass energy, Ei is the drag force corrected ion energy, Ee is the space charge corrected electron energy, Mi is the mass of the ion, and me is the mass of the electron. The experimental DR rate coefﬁcients, α(E), are derived from the background subtracted count rate recorded in each channel:

R(E)γ2 α(E) = , (4.5) N n ( li ) i e LR √ where γ = 1/ 1 − β 2 is the Lorentz factor, with β = v/c, R(E) is background subtracted count rate of the recombined ions, ne is the electron density, Ni is the average number of ions stored in the ring. li and LR are same as deﬁned earlier.

4.2 Results and discussion 4.2.1 Recombination of B-like C and Ne In the past recombination studies of C and Ne were reported for ions up to Be-like charge states (see references in the attached paper V and VII). No recombination experiment for B-like carbon and neon has been performed previously that can provide high resolution data. Only one measurement for DR cross sections of B-like carbon, over a very narrow energy range of 9.04- 9.32 eV has been reported by Mitchell et al. [22]. The resolution of their experiment was very poor and they did not observe any discernible resonance structure. In order to provide high resolution experimental DR data, we have

1200

2 2 900

2s2p ( P)nl )

-1

600

s 2 2

3 2s2p ( S)nl

300 cm -12 10 (

2 2

2s2p ( D)nl

20 RateCoefficients

0 3 6 9 12 15

Center of Mass Energy (eV) Figure 4.3: Recombination rate coefficients spectrum of B-like C up to the 2s2p2 2 ( PJ)nl series limit. The grey area shows experimentally determined rate coefficients, while the solid and dotted lines show the results of AUTOSTRUCTURE calculations for ncutoff and field-ionization-free rate coefficients, respectively. Vertical bars indicate approximate DR resonance positions calculated with equation 2.7. The principal quantum number of the recombined electron is written above first few bars. The last bar in each series marks the series limit.

500

400 ) -1 s 6 7 89 2 4 3

2s2p ( P ) nl

2 2 J

2s2p ( P )nl

J cm

4 5 6 7 8

-12 80

4 5 6 7 8

2 2

2s2p ( D )nl

20 Rate Coefficients (10 Coefficients Rate

0 5 10 15 20 25 30

Center of Mass Energy (eV)

Figure 4.4: As in Fig. 4.3 but for B-like Ne.

43 performed recombination measurements for B-like carbon and neon ions, using the CRYRING heavy-ion storage ring. The merged-beam recombination rate coefficients spectrum of singly charged carbon recombining into neutral carbon is shown in figure 4.3, while the recombination spectrum of Ne5+ recombining into Ne4+ is shown in figure 4.4. The approximate DR peak positions were obtained by using equation 2.7, where the energy of the Rydberg electron was calculated using equation 2.8. The obtained positions are indicted by vertical bars with the principal quantum number n of the recombined Rydberg electron written above first few bars. In the investigated energy range △n = 0 recombination resonances are observed in the recombination spectra of B-like C, while △n = 0 and △n = 1 recombination resonances are observed in B-like Ne spectra. For △n = 1 type DR of B-like Ne, calculations are in progress at the time of thesis writing and not available for direct comparison. So we let this part of the experimental data to discuss in paper VII. For △n = 0, the DR peaks corresponding to two 2 2 1 2 2 series 2s2p ( DJ)nl and 2s2p ( PJ)nl [59] are prominent in both spectra’s. Towards high collisions energies, the outer electron will be attached into pro- gressively high Rydberg states. The corresponding DR resonances positions get closer to each other producing a pile up near the series limit (see e.g. Fig. 4.4). Before reaching the detector, recombined ions/atoms pass through the strong magnetic field in the charge separating dipole magnet after the cooler section. Because of this field, the weekly bound Rydberg electrons are field-ionized that leads to an ncutoff above which all the recombined states are ionized and not detected by the detector. A rough estimate for the ncutoff above which the Rydberg electrons are no longer bound is given by ( ) 3 1/4 10 Q ncuto f f = 6.2 × 10 , (4.6) vi × Bd where Q is the ion charge, vi is the stored ion velocity and Bd is the magnetic field density in the dipole magnet. The estimated value of ncutoff for B-like C, Ne and Be-like F measurements are 8, 21 and 17, respectively. Some of the ions/atoms formed in states higher than ncutoff may decay radiatively below ncutoff during the flight time between the electron cooler and the critical field region of the dipole magnet. These ions/atoms survive their passage through the dipole magnet without being field-ionized and will be detected by the detector. Their contribution can be observed in the experimentally derived spectrum above the energy associated with the field-ionization limits (see Fig. 4.4 & 4.8). The calculated recombination cross sections were obtained in the multi- configuration Breit-Pauli (MCBP) approximation, using AUTOSTRUCTURE

1The closed He-like 1s2 state is ignored in writing the electron conﬁguration

44 code. Details of the MCBP calculations have been reported by Badnell et al. [73]. In figure 4.3 and 4.4 our experimentally derived rate coefficients are compared with the AUTOSTRUCTURE calculations. From comparison of the theoretical and experimental intensities of B-like C for the n=4-8 resonances in figure 4.3 it is apparent that the theoretical intensities are too high for the 2D-series and too low for the 2P-series. If the theoretical intensities for the resonances in 2D-series is multiplied with a scaling factor of 0.45, then the theoretical intensities for the n=4-8 resonances become comparable to the experimental intensities. Similarly, if a scaling factor of 0.5 and 1.3 is applied to the resonances in the 2S and 2P-series, respectively, a good agreement between theory and experiment is found in the energy region between 11 and 13.5 eV. For B-like Ne an overall good agreement can be observed between calculated and experimental results above 10 eV. Below this energy the agreement is poor between both the spectra in DR resonance intensities and energy positions. The dotted lines in figure 4.3 and 4.4 show the AUTOSTRUCTURE results for principal quantum number n up to 1000, used to account for the field- ionization in the experiment. DR into states with n > 1000 is expected to give a negligible contribution to the rate coefficients. Hereafter the field affected recombination data will be designated as ncutoff and data up to n = 1000 will be termed as field-ionization-free spectra. For astrophysical and laboratory plasma applications, the recombination rate coefficients are mostly needed as function of plasma electron temperature [31]. To obtain the plasma rate coefficients at a plasma temperature, Tplasma ∼Te the experientially derived energy dependent merged-beams recombination rate coefficients α(E), were convoluted with a Maxwell-Boltzmann energy distribution of electrons in a plasma at the corresponding temperatures: ∫

α(Te) = α(E) f (E,Te)dE, (4.7) where f (E,Te) is the Maxwell-Boltzmann energy distribution of the electrons and is given by ( ) 2E1/2 E f (E,T ) = exp − , (4.8) e 1/2 3/2 π (kBTe) kBTe where kB is the Boltzmann constant, E and Te are energy and mean electron temperature, respectively. The plasma DR rate coefficients for B-like C ions, obtained from the experimentally derived energy dependent rate coefficients are shown in figure 4.5, along with the theoretical data from literature and our AUTOSTRUCTURE calculations. As discussed in previous section, that the experimental recombination rate coefficients are affected due to field-ionization of high Rydberg

]

10 -1 s 3 cm -12

0,1 Rate Coefficients [10

3 4 5 6

10 10 10 10

Tem perature [K] Figure 4.5: Plasma DR rate coefficients for C II as a function of temperature. The ncutoff plasma rate coefficients obtained from the experimental spectrum is shown by the black solid line. The grey area represents our measured field-ionization-free rate coefficients. The field-ionization-free AUTOSTRUCTURE calculation results are shown by the dash-dot line. The calculated DR rate coefficients is shown from the literature, and is given as following: filled triangles [74], filled squares [75], filled circles [76], open squares [77], open and filled stars (for n=2-6 and n=2-500 states, respectively) [78], open triangles [79]. ) -1 s 3

100 cm -12

10 Rate Coefficients (10 Coefficients Rate

3 4 5 6 7

10 10 10 10 10

Temperature (K) Figure 4.6: As in Fig. 4.3 but for B-like Ne. The calculated DR rate coefﬁcients from [74] are shown with stars, from [80] with circles, from [81] with squares and from [82] with triangles.

46 states in the recombined ions. In order to obtain field-free plasma recombination rate coefficients, the field affected part of the experimental spectrum is estimated using the AUTOSTRUCTURE calculations. It can be seen from figure 4.5 that ncutoff DR and scaled field-free DR plasma rate coefficients have same values up to plasma temperature of ∼104 K, above this temperature DR into high-n states, above ncutoff, starts to contribute and change the resulting DR plasma rate coefficients.

1 1

a b

0,8

0,8 ] ] -1 -1 s 0,6 s 3 3

0,6 cm cm

0 m eV -10 0 m eV -10 0,4

10 m eV

+50 m eV

0,4

50 m eV

+100 m eV

100 m eV

+150 m eV

0,2

0,2 Rate Coefficients [10 Rate Coefficients [10

3 4 5 3 4 5

10 10 10 10 10 10

Tem perature [K] Tem perature [K]

Figure 4.7: The black solid lines represents the experimental ncutoff rate coefficients results for F VI. (a) The dash, dot and dash-dot curves show experimental rate coefficients obtained by changing the resonance energy positions by +50, +100 and +150 meV, respectively. The plasma rate coefficients in (b) is obtained by taking various low-energy cut as depicted in figure.

As can be seen from figure 4.5 that below ∼ 2×104 K, the data from the literature shows a wide spread in DR plasma rate and strongly disagree with our experimental results. This might be due to inaccurate calculations of the low-energy DR resonance strengths and energy positions. At very low-energy the DR rate coefficients are very sensitive to the slight variations of the resonance intensities and positions. A slight variation in the intensity or a few meV shift in the DR resonances energy positions can change the magnitude of the resulting plasma DR rate coefficients to a large extent. The effect of energy shift on the resulting plasma rate coefficients is highlighted in figure 4.7(a), where we shift the experimentally obtained resonance energy positions by +50 meV, +100 meV and +150 meV. The energy shift of +50 meV decreases the low-temperature DR plasma rate coefficients by 21% at 103 K, while a shift of +100 meV and +150 meV decrease the value to 47% and 66%, respectively at this temperature. In order to estimate the effect of low-energy DR resonances on the plasma rate coefficients, several low-energy ranges of the merged-beam spectrum were removed. The resulting spectra were then used to obtain the temperature dependent plasma rate coefficients, identified by the corresponding label in figure 4.7(b). The exclusion of energy range between

47 10 meV and 100 meV decreases the plasma rate coefficients between 4-51% at 103 K. The temperature dependent total field-free-recombination rate coefficients of B-like Ne are shown in figure 4.6 along with the the calculated results from literature. Below ∼105 K, only the calculated results of Altun et al. [74] are close to our experimental data. The rate coefficients of Nahar [80](containing RR+DR rate) are quite high compared to our experimental data, while the rate coefficients results of Shull & Steenberg [81] show lower values than our experimentally derived results. Above ∼105 K the calculations show the same behaviour as that our experimental data. In this temperature range the experimental rate coefficients are lower than the calculations because the contributions for states above n≥21 are not added yet to the experimental △n = 1 recombination resonances spectrum. Therefore, at the moment no possible conclusion can be drawn from the comparison.

4.2.2 Recombination of Be-like F VI The experimental F VI merged beam recombination rate coefficients are shown in figure 4.8, in the electron-ion collisions energy range of 0-24 eV. In this energy range △n = 0 resonances are observed in the experimental spectrum which corresponds to the capture of free electrons to some nl states, with the simultaneous excitation of a 2s2 core electron, forming doubly 3 1 excited states 2s2p ( PJ)nl and 2s2p ( P1)nl. With the increase of kinetic energy, the free electron is attached into (increasingly) higher n states for the same excitation of core electron. As a result the resonance energy position get close to each other forming a pile up structure near the series limit, as can 1 be seen clearly in the 2s2p ( P1)nl series. It is also interesting to see that the 1 strength of DR peaks belonging to 2s2p ( P1)nl series increases towards the 3 series limit, while decreases in case of 2s2p ( PJ)nl type of DR resonances with no observable pile up structure near the series limit. The radiative decay 3 of the PJ core is dipole forbidden, which implies that the radiative decay necessary to complete DR is forced to take place through the decay of the Rydberg electrons or via autoinization, instead of a core electron transition. The decay of Rydberg electrons via a radiative cascade decrease rapidly for higher nl states, while the autoionization rate gets larger. This results in a 3 sharp decrease of the DR strength along the PJ resonance series. In the merged-beam experiments, the contamination of the stored ion beam with metastable fraction is an issue of concern in deriving the absolute recombination rate coefficients. Calculations are used in order to estimate the contribution from metastable ions in the experimental spectrum. In the present experiment no DR resonances are observed from the population of 3 the metastable P0 fraction in the primary ion beam. The entire measured spectrum is attributed to the excitation of ground state ions of Be-like F. The non-existence of such metastable ions in the storage ring experimental

2s2p( P ) 60

1 ] -1 s 3

50 cm

2s2p( P )

J -10

1 Rate Cofficients [10

0 5 10 15 20 25

Center of Mass Energy [eV] Figure 4.8: Experimental recombination rate coefficients for F5+ are shown by grey shaded area. The red and blue solid lines show calculated DR and TR rate coefficients for n ≤17, respectively. The dotted line show the calculations for field-ionization free recombination rate coefficients. The vertical bars are same as in Fig. 4.3 and 4.4.

spectra’s is not uncommon. For example Orban et al. [83] did not observed any significant metastable DR strength for △n = 0 type DR of Be-like Ne and Schippers et al [84] also not observed any such DR resonances while measuring recombination of Be-like Mg ions. In Be-like ions, a third resonant recombination channel called trielectronic recombination (TR) is available, in which two bound electrons from 2s state are excited simultaneously to the 2p2 state during the attachment of a free electron to a certain nl Rydberg state. If the newly formed triply excited state stabilizes radiatively below the first ionization threshold, autoionization will no longer be possible and TR is finalized. The TR contribution to experimental spectrum of Be-like F is shown by the blue curve in figure 4.8, predicted by the calculations. The experimentally derived DR rate coefficients results are compared with the AUTOSTRUCTURE calculations shown in figure 4.8. A very good agreement can be seen above 13 eV between the experimentally derived and calculated results. In the energy range of 4 eV to 13 eV some of the DR resonances from calculations are slightly lower in peak intensity than the experimental data. At low energies below 4 eV, the agreement between the two spectra is not satisfactory in both DR resonance energy positions and intensities. The plasma recombination rate coefficients for F VI were obtained by convoluting the recombination spectra from figure 4.8, over a temperature range 3 6 ≤ of 10 -10 K. The derived total (DR+TR) ncutoff (n 17) plasma rate coefficients are shown in figure 4.9a, along with the previous experimental results

1 1

b ] ] -1 -1 s s 3 3 cm cm -10 -10

0,1 0,1

Rate Coefficients [10 Rate Coefficients [10

0,01 0,01

3 4 5 6 3 4 5 6

10 10 10 10 10 10 10 10

Tem perature [K] Tem perature [K]

Figure 4.9: Plasma recombination rate coefficients of Be-like F as a function of temperature. (a) The black solid line shows our experimental results for total (DR+TR) rate coefficients into states with n ≤ 17. The previous experimental results taken from [85] and [86] are shown by dashed and dotted lines, respectively. (b) The shaded area shows our experimental derived field-ionization-free total plasma rate coefficients. Results of our AUTOSTRUCTUR calculations are given by open squares. The full squares present the data taken from [87]. The open and filled stars show the calculated rate coefficients taken from [86] and [88], respectively. The rate coefficients results from [85] are shown by open triangles. of Dittner et al. [86] and Badnell et al. [85]. Both of these results show a strong disagreement with our experimental results below 2×105 K due to different electron-ion collisions energy ranges and low resolution of the recombination data. Dittner et al. [86] results are for the electron energy range of 8 eV to 28 eV and the data shows only one peak in this energy range due to low-energy resolution. The recombination rate coefficients results of Badnell et al. [85] also does not shows a clear resonance structure as observed in our spectrum, resulting low values of plasma rate coefficients compared to our results. In figure 4.9b our field-ionization-free plasma rate coefficients are compared with the calculated data available in literature and our AUTOSTRUC- TURE results. The field-free rate was obtained using the calculated data for recombination into states with n ≥ 17, similar to that of B-like C ions as discussed earlier. It can be seen from figure 4.9b that at temperature lower than 2×104 K the calculated data shows a wide spread and significantly lower than the experimental results. The rate coefficients from AUTOSTRUCTURE calculations have lower values than our experimentally derived results up to 20% in the temperature range 2×104-106 K. At 103 K the rate coefficients from AUTOSTRCUTUE calculations is 42% higher than our derived plasma rate coefficients. This illustrates the uncertainties in the calculated data associated with low-energy DR resonances as discussed in the previous section.

50 5. Summary and outlook

Extensive experimental and theoretical work has been carried out on electron- ion recombination over the past three decades, as they play a vital role in investigating astrophysical and laboratory plasmas. The aim of this experimental work was to study electron-ion recombination processes for plasmas relevant ions to derive DR cross sections, resonance strengths, plasmas rate coefficients and resonance energies. This was done with the Stockholm Re- frigerated Electron Beam Ion Trap (R-EBIT) and the CRYRING heavy-ion storage ring. Both of these laboratory instruments provide an excellent experimental environment to study electron-ion collision processes, in particular electron-ion recombination, such as radiative recombination (RR) and dielectronic recombination (DR). In this thesis we report the experimental results for sulfur and argon from EBIT measurements and carbon, neon and fluorine from CRYRING measurements. Recombination data for highly charged sulfur is obtained for the first time, no earlier recombination data for sulfur ions have been published so for. We have used two different techniques in order to get reliable atomic physics data for sulfur i.e. by measuring X rays from the trapped ions and by extracting the ions using a TOF method. The later is a newly developed technique by our group [57], which offer complimentary information about the collision processes that take place inside the trap. The spectrum obtained with the TOF method contains the abundance of several charge states, which facilitates the extraction of rate coefficients for different charge states simultaneously. A combination of these two methods also allows to obtain the excitation rate coefficients. The obtained DR resonant strength for H-and He-like sulfur and silicon are used to check the behaviour of a scaling formula for the low Z, H-and He-like iso-electronic sequences [42] and to obtain new fitting parameters. Earlier, this formula was used down to Z=18. The experimental results for KLL DR peak positions of initially He-to B-like argon ions are compared with calculations and found in excellent agreement, except for a small discrepancy of 9 eV in case of Be-like ions resonance position. The reason for this discrepancy might be due to an underestimation of the contributions from some of the resonances in the calculations. From the CRYRING measurements recombination rate coefficients of B- like C, B-like Ne and Be-like F were derived for the first time with high resolution. The derived results are compared with the AUTOSTRUCTUR cal-

51 culations. At high energies, an overall good agreement is found between experimentally derived rate coefficients and calculations. Plasma recombination rate coefficients of all these ions were obtained by convoluting the energy dependent recombination spectra with a Maxwell-Boltzmann distribution in the temperature range of 103-106 K. The different calculations available in literature show a wide spread at temperatures below ∼ 104 K. The strong deviation between different calculations and the experimental results are due to inaccurate calculations, since DR resonance strengths and energy positions of the doubly excited states are very sensitive to the electron correlation effects in low-energy region below 3 eV. The limitation of the electron beam energy of the R-EBIT to 30 keV restricts studies of HCIs to light up to medium-Z ions. In order to study HCIs of high Z elements, we have upgrade the R-EBIT to a high energy version, called Super- EBIT (S-EBIT) with an electron beam energy of 260 keV, for charge breeding of any stable element up to bare uranium. The new EBIT version includes a vibration free cryogenic system, fast switchable high-voltage operations, and an improved ion injection and extraction system. Besides this upgrade, an external ion source such as MEVVA (Metal Vapour Vacuum Arc) [89] and a CHORDIS (Cold or Hot Reflex Discharge Ion Source) [90] have been installed for injecting low q ions into the S-EBIT. The S-EBIT facility will open up a new window for several research areas. Future experiments extend the study of nano-capillaries and nano-tubes by using HCIs delivered from the S-EBIT. The S-EBIT facility will be used in future for electron-ion collisions studies of HCIs for high Z elements, important for laboratory and astrophysical plasmas applications. The HCIs delivered by S-EBIT will also open up a new window for precision mass measurements. In mass spectrometry with Penning traps the precision increases linearly with the charge of the ion, which is exploited by the precision Penning trap mass spectrometer SMILETRAP [91].

52 Svensk Sammanfattning

Omfattande experimentella och teoretiska studier har utförts på elektron-jon rekombinationer under de senaste tre decennierna, eftersom de spelar en viktig roll i studiet av astrofysikaliska och laboratorie-plasma. Syftet med detta experimentella arbete var att studera elektron-jon-rekombinationsprocesser för joner relevanta för plasmaaplikationer samt att härleda DR-tvärsnitt, resonansstyrkor, plasmahastighetskoefficienter och resonansenergier. Detta har gjorts med Stockholms EBITen, R-EBIT (Re-frigerated Electron Beam Ion Trap), och CRYRING, en lagringsring för tunga joner. Båda dessa laboratorieinstrument ger en utmärkt experimentell miljö för att studera elektron-jon kollisionsprocesser, i synnerhet elektron-jon rekombination, såsom strålande rekombination (RR) och tvåelektronsrekombination (DR). I denna avhandling redovisar vi de experimentella resultaten för svavel och argon från EBIT-mätningar och kol, neon och fluor från CRYRING-mätningar. Rekombinationsdata för högt laddat svavel erhålls för första gången, inga experimentella rekombinationsdata för svaveljoner har tidigare publicerats. Vi har använt två olika metoder för att få tillförlitliga atomfysikaliska data för svavel, genom att mäta röntgenstrålning från fångade joner och genom att mäta flygtiden (TOF) för extraherade joner. Den senare metoden är en teknik som nyligen utvecklats av vår grupp [57] och som erbjuder kompleterande information om de kollisionsprocesser som äger rum inne i fällan. Det spektrum som erhålls med TOF-metoden innehåller information om förekomsten av olika laddningstillstånd, vilket främjar en simultan extraktionen av hastighetskoefficienter för olika laddningstillstånd. En kombination av dessa två metoder möjliggör också erhållandet av koefficienterna för excitationshastighet genom elektron kollision. Den erhållna DR-resonansstyrkan för H- och He-liknande svavel och kisel används för att kontrollera uppförandet hos en skalningsformel för låga Z hos H- och He-liknande iso-elektroniska sekvenser [42] och för att få nya anpass- ningsparametrar. Tidigare har denna formel använts ner till Z = 18. De experimentella resultaten för KLL DR topp-positioner för He- till B-liknande argonjoner har jämförts med beräkningar och har funnits vara i utmärkt öv- erennsstämmelse, förutom en liten skillnad på 9 eV i fall av Be-liknande jon- ers resonansposition. Anledningen till denna diskrepans kan bero på en under- skattning av bidragen från några av resonanserna i beräkningarna.

53 Från CRYRING-mätningarna har koefficienterna för rekombinering- shastigheten av B-likt C, B-likt Ne och Be-likt F med hög upplösning extraherats för första gången. De härledda resultaten har jämförs med AUTOSTRUCTUR beräkningar. Vid höga energier har en övergripande god överensstämmelse funnits mellan experimentella hastighetskoefficienter och beräkningar. Plasmarekombinationshastighets-koefficienter av alla dessa joner erhölls genom att konvolutera det energiberoende rekombinationsspektrat med en Maxwell-Boltzmann fördelningen inom temperaturområdet 103-106 K. Beräkningar tillgängliga i litteraturen visar en stor spridning vid temperaturer under ∼ 104 K. Den stora avvikelsen mellan olika beräkningar och de experimentella resultaten beror på felaktiga beräkningar, eftersom DR-resonans styrkor och energipositioner för dubbelt exciterade tillstånd är mycket känsliga för elektronkorrelationeseffekter i lågenergiområdet under 3 eV. Begränsningen av elektronstrålens energi för R-EBIT till 30 keV begränsar studier av högt laddade joner (HCI) till låg- och medelhöga Z. För att kunna studera HCI av element med höga Z har vi uppgraderat R-EBIT till en högenergi version, kallad super-EBIT (S-EBIT) med en elektronstråle på 260 keV, för laddningsförädling av alla stabila elementet upp till naket uran. Den nya EBIT-versionen innehåller ett vibrationsfritt kryosystem, ett snabbt omkopplingsbart högspänningssystem och ett förbättrat joninjektion- och jonextraktions-system. Förutom denna uppgradering har externa jonkällor, så som MEVVA (Metal Vapour Vacuum Arc) [89] och CHORDIS (Cold eller Hot Reflex Discharge Ion Source) [90], installerats för att injicera lågt laddade joner in i S-EBIT. S-EBIT anläggningen kommer att öppna ett nytt fönster för flera forskning- sområden. Framtida experiment förväntas utökar studier av nano-kapillärer och nano-rör med HCI levererade från S-EBIT. S-EBIT anläggning kommer i framtiden att användas för elektron-jon kollisionsstudier av HCI för hög- Z-element, viktiga för laboratorie- och astrofysikaliska plasmaapplikationer. De HCI som levereras av S-EBIT kommer också att öppna ett nytt fönster för precisions-massmätningar. I masspektrometri med Penningen fällor ökar precisionen linjärt med laddningen av jonen, vilket utnyttjas av precisions- masspektrometern SMILETRAP [91].

54 6. Acknowledgement

I would like to take this opportunity to thank all those people who spent their time and shared their knowledge and experience with me during my study. First of all I would like to express my profound appreciation and sincere gratitude to my supervisor Reinhold Schuch for giving me an opportunity to work in his research group. His excellent support, valuable inputs, whole- hearted cooperation and constructive criticism make possible the completion of this work. I also thank him for his patience to correct my mistakes in writing, especially the use of definite and indefinite articles. I greatly acknowledge the financial support from Higher Education Comis- sion of Pakistan (HEC) and Swedish Institute (SI) for administrating the fund- ing. My special thanks to Swedish Research council (VR) and Stockholm Uni- versity for extending my financial support for the last eight months. My eternal gratitude and thanks goes to Istvan Orban, with whom I have spent a lot of time in the EBIT-Lab. He guided me during the experiments as well as during the data analysis for which I have disturbed him a lot. I am very grateful to Sebastian Bohm for his help and support during the first year of my PhD. My sincere thanks goes to Stanislav Tashenov for having very good time during experiments, discussion about data analysis, and to help out me while writing articles. I wish to thanks Sultan Mahmood, for having invaluable discussions about data analysis and articles. I also enjoyed his company a lot while walking to home in the evening. I am grateful to Jan Weimer for his help and support while working in the EBIT-Lab. Thanks to Peter Glans for his quick response to all my questions and giving constructive comments on the manuscripts. I would like to thank Matthias Hobein, Yao Ke and Tareq Ali Mohamed for reading my thesis and giving useful comments. I would like to thank all my PhD colleagues Nadeem Akram, Hongqiang Zhang, Patrik Skog, Andreas Solders for their help and support and having a good time together. I would like to offer my deepest regards and gratitudes to my parents/brothers/sisters for their unflagging love and support throughout my life.

55 Last, but deﬁantly not least, my special thanks goes to my beloved wife Sidra Safdar for her patience, encouragement, understanding and having long discussions about my and her own research work.

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