Electron - Ion Recombination Data for Plasma Applications: Results from Electron Beam Ion Trap and Ion Storage Ring

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Electron - ion recombination data

for plasma applications

Results from Electron Beam Ion Trap and Ion Storage Ring Safdar Ali

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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

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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 measure-ments. 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 ar-gon are compared with the calculations performed with a distorted wave ap-proximation.

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 coeffi-cients 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}

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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 con-trol 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 C I

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 re-combining 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

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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.

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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 interstel-lar 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, excita-tion, de-excitaexcita-tion, and electron-ion recombination [3].

Carbon, neon, silicon, sulfur and argon are among the most abundant ele-ments 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 ra-diation 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 inter-stellar 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 struc-ture, elemental composition, energy balance, temperature distribution etc, of these astrophysical objects.

It has been observed recently that HCIs are not only found in hot astro-physical 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 ex-istence 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].

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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 fu-sion plasma applications. For example, these are present in fufu-sion 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 prop-erties 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, ex-citation and recombination. Therefore, to understand the complete behaviour of plasma, each physical process need to be studied separately. Especially, re-combination processes such as radiative rere-combination (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 the-oretically 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

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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 mea-surements 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 elec-trons 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 bar-ium 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

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high resolution recombination measurements. High energy resolution of stor-age rings enables to measure very low-energy DR resonance positions with extreme precision [40]. Accurate low-energy DR resonance positions and in-tensities are very important in order to derive reliable plasma recombination rate coefficients (see for example section 4.2.1), required for plasma applica-tions. 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 investi-gated 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 be-haviour 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 en-ergy 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 de-scription 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 analy-sis 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.

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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 colli-sions 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 reso-nant 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 pro-cess in which a free electron recombines with an ion, emitting expro-cess energy in the form of a photon:

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

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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 σKramers RR (n, Ee) = 2.105× 10−22 Ry2Z4 nEe(n2Ee+ RyZ2) cm2. (2.3) Where Ryis the Rydberg constant, n is the principal quantum number of the

re-combined ion. The Kramers formula gives accurate cross sections for electron capture into high n states. For recombination into low-n states the above for-mula 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], Ze f f = 1 2(ZC+ ZI) for ZC≥ ZI≥ ZC 2 , (2.4) and Ze f f = √ ZCZI for ZC 2 ≥ ZI≥ 1, (2.5)

where ZCis 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:

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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

cal-culated by a simple hydrogenic formula:

ERyd(nl) = 13.6

Q2

n2[eV ], (2.8)

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 cap-tured 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.

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In the isolated resonance approximation, which ignores the interference be-tween close lying resonances, the DR cross section associated with an inter-mediate doubly excited state can be expressed as:

σDR_{(E) =} S

π

Γ/2

((Ee− Eres)2+Γ2/4)

, (2.9)

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

S = ∫ σDR_{(E)dE =} ¯h3π2 2me gd gi 1 Eres Aa(d→ i)ΣfArad(d→ f ) ΣkAa(d→ k) + ΣfArad(d→ f ) , (2.10) where gi and gdare the multiplicity of the initial target state and that of

inter-mediate doubly excited states, respectively. Aa(d→ i) is the rate of

autoion-ization from doubly excited state d to i, ΣfArad(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

Xq++ e−₁(Ee)→ X(q+1)++ e−1(E1) + e−2(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

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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) 0 2 4 6 8 10 1,0x10 -23 5,0x10 -22 1,0x10 -21 C r o s s s e c t i o n ( c m 2 ) Electron Energy/I P [keV]

Figure 2.2: EII cross section vs electron energy/IPfor producing Ar18+from Ar17+,

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:

σLotz EII = 4.5× 10−14 N I2 p ln(u + 1) (u + 1) cm 2_{, u =}Ee Ip − 1, (2.15)

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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 ioniza-tion 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 in-teraction 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}−_{+ h}_ν. _(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 exci-tation (dEIE) cross section depends on the incident electron energy Eeand the

atomic structure of the target ions. The cross section for this process is max-imum as kinetic energy of the free electron becomes equal to the excitation energy of the atomic system.

σV R

EIE= 2.36× 10−13

fi jg¯

EeEi j

[cm2eV2], (2.17)

where Ei jis the excitation energy, Eeis 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 ex-cited state (see figure 2.3(b)). For this process to occur at least one electron

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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 ex-cited 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].

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3. Measurements at the Refrigerated

Electron Beam Ion Trap

The Electron Beam Ion Trap (EBIT) is one of the unique laboratory instru-ments 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 ob-serving 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 sys-tem 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

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(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 sur-rounded 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 poten-tial of +30 kV. The magnetic field produced by the superconducting magnet compresses the electron beam to 70µm 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 sep-arately 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 form-ing 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 num-ber 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 ex-periments. 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 super-conducting magnet and the reversed magnetic field of the collector magnet. At the entrance of the collector a suppressor electrode is used to prevent sec-ondary electrons from being accelerated back into the trap and electron gun region. On the exit of the collector a negatively biased electrode called extrac-tor is located. This electrode helps to guide the ions from EBIT during ion

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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 35µ m Max. central current density 4 kA/cm2

Trap length 2 cm

Electron density 1011cm−3

Ion density 109cm−3

3.2 R-EBIT control and data acquisition

A schematic diagram of the data taking scheme used for electron-ion recom-bination 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 pro-gram controls the potentials of the electron gun anode and focus, transition,

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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 cur-rent, 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 de-creases/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.

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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 continu-ous 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 pro-duction 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 de-creases 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

experi-ments.

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.

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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, SH2gas was injected into the trap

region using a ballistic gas injection system in pulse mode as discussed in sec-tion 3.3, through one of the ports of the R-EBIT. Following the injecsec-tion, 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 breed-ing 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 ve-locity 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.

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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 ef-fect 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 a55Fe radioactive source. The Kα and Kβ characteristic x-ray lines of Mn produced by the55Fe 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

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Figure 3.5: Calibration lines and fit used for the SiLi-detector channel-energy conver-sion. The lines are produced by irradiating Si, Cl, and Ti with55Fe 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: SKLn=I KLn IRRσ RR_∆EW(90◦_{) f} ions, (3.2)

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,}_σRR _{is the}

theo-retical RR cross section of H-like sulfur ions, and fionsis 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 PRRis 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 breed-ing, probbreed-ing, 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 ac-quired X rays data were published in the JINST journal (paper I).

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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 calcu-lated data was adjusted using the following formula:

Rq(E) = neveΣqNqσqDR(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

trapped ions with a charge state q interacting with the electrons,σ_qDR(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 Nqwere 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 exci-tation 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

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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-K-RR, respectively. The resonances that appear along the L-K-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 chan-nels 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 theo-retical calculations convolved with 24 eV FWHM of the electron beam. Both results show a good agreement in resonances energy positions and intensi-ties. 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 com-pare 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

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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

SKLn= 1

m1Z2+ m2Z−2

, (3.4)

where Z is the atomic number and m1 and m2 are fitting parameters. In

de-riving the above formula following scaling were used, Ar ∝ Z4, Aa remains constant with Z and Ee ∝ Z2. By using our DR resonance strengths results

of sulfur and silicon in this formula, together with the previous experimen-tal 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 fig-ure 3 of the same paper.

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0 20 40 60 80 100 0 10 20 30 40 50 H-like KLL Experiments Theory R e s o n a n c e S t r e n g t h [ 1 0 -2 0 c m 2 e V ]

Atom ic Num ber [Z]

Figure 3.8: DR resonant strengths vs atomic number for H-like iso-electronic se-quence. The data points with vertical dotted lines are our results of S15+_{and Si}13+

ions. The other experimental and calculated data points are H-like ions of O7+_from

[60], Ti21+ _{from [61], C}5+_{, O}7+_{, Si}13+_{, S}15+ _{from [62], from Ge}31+_{, Se}33+_,Kr34+

from [63] and U91+from [64]

For KLL DR resonant strength of H-like ions, we obtain the fitting parameters

m1 and m2 with values 1.95×1015and 6.90×1020 in units of cm−2eV−1,

re-spectively. 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 elec-tron energy is shown in figure 3.9. The horizontal and vertical axis represents the projectile electron energy and the X rays energy, respectively. DR reso-nances 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

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inves-2,5 3,0 3,5 4,0 4,5 5,0 2,0 2,2 2,4 2,6 2,8 3,0 3,2 KLN KLM

Photon Energy [keV]

E l e c t r o n E n e r g y [ k e V ] KLL L-K L-RR

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 ad-justed 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.

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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 res-onances 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 KLL peak. The calculated intensities for 2s2_2p2₍2_D

5/2)1, 2s22p2(2D3/2),

2s22p2(2S1/2), 2s22p2(2P3/2) and 2s22p2(2P1/2) resonances do not explain

the centroid of the observed peak. Underestimated contributions of 1s2s2_2p2₍2_S

1/2) and 1s2s22p2(2P3/2) resonances might be the reason for this

discrepancy.

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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:

Emax= 96×

Q2

A2[MeV /amu], (4.1)

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 temper-ature 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

Ee=(me/2)v2 compresses the electron momentum spread to reduce the

tem-perature 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 effec-tive length of 80 cm [68]. The ion cooling takes place by repeated Coulomb interactions between the constantly refreshed low-temperature electrons and

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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 re-combined species.

hot ions as they pass through the cooler about a million times per second dur-ing their circulation in the rdur-ing. 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 approxi-mately 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 cir-culating 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 elec-tron 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

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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 cen-tral 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 cor-rection 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

Uspis 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

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corre-sponding change in ion velocity vias a function of time is obtained by dvi dt = η Mi li LR Fz(t), (4.3)

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]:

ECM = [ (Ei+ Ee+ Mic2+ mec2)2 (4.4) −(√E_i2+ 2Mic2Ei+ √ E2 e + 2mec2Ee )2]12 − (Mic2+ mec2),

where ECM is the center-of-mass energy, Ei is the drag force corrected ion

energy, Ee is the space charge corrected electron energy, Miis the mass of the

ion, and meis the mass of the electron.

The experimental DR rate coefficients, α(E), are derived from the back-ground subtracted count rate recorded in each channel:

α(E) = R(E)γ2

Nine(_Lli_R)

, (4.5)

whereγ = 1/√1−β2_{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 ex-periment was very poor and they did not observe any discernible resonance structure. In order to provide high resolution experimental DR data, we have

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0 3 6 9 12 15 0 20 40 60 80 300 600 900 1200 2s2p 2 ( 2 S)nl 2s2p 2 ( 2 D)nl R a t e C o e f f i ci e n t s ( 1 0 -1 2 cm 3 s -1 )

Center of Mass Energy (eV)

2s2p 2

( 2

P)nl

Figure 4.3: Recombination rate coefficients spectrum of B-like C up to the 2s2p2 (2PJ)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 indi-cate 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.

0 5 10 15 20 25 30 0 20 40 60 80 400 500 4 5 6 7 8 4 5 6 7 8 6 7 8 9 2s2p 2 ( 4 P J ) nl 2s2p 2 ( 2 D J )nl 2s2p 2 ( 2 P J )nl R a t e C o e f f i ci e n t s ( 1 0 -1 2 cm 3 s -1 )

Center of Mass Energy (eV)

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performed recombination measurements for B-like carbon and neon ions, us-ing the CRYRING heavy-ion storage rus-ing.

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 Ne}4+ _{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 ob-served 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 series 2s2p2(2DJ)nl1and 2s2p2(2PJ)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

ncuto f f = ( 6.2× 1010 Q 3 vi× Bd )1/4 , (4.6)

where Q is the ion charge, viis 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 de-tector. Their contribution can be observed in the experimentally derived spec-trum 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 1_{The closed He-like 1s}2_{state is ignored in writing the electron configuration}

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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 reso-nances in figure 4.3 it is apparent that the theoretical intensities are too high for the2D-series and too low for the2P-series. If the theoretical intensities for the resonances in2D-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 the2S and2P-series, respectively, a good agreement be-tween theory and experiment is found in the energy region bebe-tween 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 agree-ment 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 coefficientsα(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 f (E, Te) = 2E1/2 π1/2_(k BTe)3/2 exp ( − E kBTe ) , (4.8)

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 exper-imentally 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 recom-bination rate coefficients are affected due to field-ionization of high Rydberg

Electron - Ion Recombination Data for Plasma Applications: Results from Electron Beam Ion Trap and Ion Storage Ring