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 Belike 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.
7
List of papers
This thesis is based on the following papers, which are referred to in the text
by their Roman numerals.
I
II
III
IV
V
VI
VII
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
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
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
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
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
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
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 summarize 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
2
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Electron-ion collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
13
17
2.1 Electron-ion recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
17
17
18
20
20
22
2.1.1 Radiative recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.1.2 Dielectronic recombination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Electron-impact ionization and excitation . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Electron-impact ionization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.2 Electron-impact excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 Measurements at the Refrigerated Electron Beam Ion Trap . . . . . . .
3.1 Introduction and operation of EBIT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 R-EBIT control and data acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3 Gas injection system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4 Experiments and data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.1 Highly charged sulfur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Highly charged argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.1 Highly charged sulfur . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5.2 Highly charged argon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 Measurements at the CRYRING ion storage ring . . . . . . . . . . . . . . .
4.1 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2 Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.1 Recombination of B-like C and Ne . . . . . . . . . . . . . . . . . . . . . . . . . .
4.2.2 Recombination of Be-like F VI . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 Acknowledgement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
25
25
27
29
29
30
32
33
33
36
39
40
42
42
48
51
55
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 explosion 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 considerable 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 substantially to the line emission and ionization balance in plasmas [3]. DR, in
particular is a dominant recombination channel and therefore has been the subject of intense study since many decades. The importance of this mechanism
in plasma was not appreciated until Burgess correctly estimated its significance 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 demonstrated 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 hightemperature 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 : X q+ + 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
Kramers
σRR
(n, Ee ) = 2.105 × 10−22
Ry2 Z 4
cm2 .
nEe (n2 Ee + RyZ 2 )
(2.3)
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
ZC
Ze f f = (ZC + ZI ) for ZC ≥ ZI ≥
,
(2.4)
2
2
and
√
ZC
Ze f f = ZC ZI for
≥ ZI ≥ 1,
(2.5)
2
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 : X q+ + 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),
18
(2.7)
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:
ERyd (nl) = 13.6
Q2
[eV ],
n2
(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 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 intrashell 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:
σ DR (E) =
S
Γ/2
,
π ((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=
σ DR (E)dE =
Aa (d → i)Σ f Arad (d → f )
h̄3 π 2 gd 1
,
2me gi Eres Σk Aa (d → k) + Σ f Arad (d → f )
(2.10)
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
Σk Aa (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+1)+
−
X q+ + e−
+ e−
1 (Ee ) → X
1 (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:
X q+ + 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:
X q+ + e− → [X q+ ]∗ + e− → X (q+1)+ + 2e− .
(2.14)
-21
2
Cross section (cm )
1,0x10
-22
5,0x10
-23
1,0x10
0
2
4
6
Electron Energy/I
P
8
10
[keV]
Figure 2.2: EII cross section vs electron energy/IP for 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:
Lotz
= 4.5 × 10−14
σEII
N ln(u + 1) 2
Ee
cm , u =
− 1,
2
I p (u + 1)
Ip
(2.15)
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:
X q+ + e− → [X q+ ]∗ + e−
→ X q+ + 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.
VR
σEIE
= 2.36 × 10−13
fi j ḡ
[cm2 eV 2 ],
Ee Ei j
(2.17)
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 ḡ is the effective Gount factor. At energies close to the
excitation threshold the value of g is ∼ 0.2 and at Ee >2Ei j , ḡ = 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:
X q+ + e− → [X (q−1)+ ]∗∗ → [X q+ ]∗ + 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].
23
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 µ m diameter as it advances through the
drift-tube assembly. Beam steering, to compensate for small mechanical misalignments 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
3T
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 11 cm−3
Ion density
10 9 cm−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 figure 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 ionrecombination 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 acquire 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 amplifier 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 Lilike 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 purpose.
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 55 Fe radioactive source. The Kα and
Kβ characteristic x-ray lines of Mn produced by the 55 Fe 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 channelenergy conversion factor.
After having calibration for the photon energy axis, it is rather straightforward 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 55 Fe 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:
I KLn
SKLn = RR σ RR ∆EW (90◦ ) fions ,
(3.2)
I
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 xray 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:
Rq (E) = ne ve Σq Nq σqDR (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, σqDR (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 KRR 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. Figure 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
1
SKLn =
,
(3.4)
2
m1 Z + m2 Z −2
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
constant with Z and Ee ∝ Z2 . 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.
35
50
Experiments
Theory
40
Resonance Strength [10
-20
2
cm eV]
H-like KLL
30
20
10
0
0
20
40
60
80
100
Atomic Number [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
m1 and m2 with values 1.95×1015 and 6.90×1020 in units of cm−2 eV −1 , 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 simplification 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 inves36
L-K
L-RR
3,2
3,0
Electron Energy [keV]
KLN
2,8
KLM
2,6
2,4
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 Blike 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 D5/2 )1 , 2s2 2p2 (2 D3/2 ),
2s2 2p2 (2 S1/2 ), 2s2 2p2 (2 P3/2 ) and 2s2 2p2 (2 P1/2 ) resonances do not explain
the centroid of the observed peak. Underestimated contributions of
1s2s2 2p2 (2 S1/2 ) and 1s2s2 2p2 (2 P3/2 ) resonances might be the reason for this
discrepancy.
1 1s
38
state is ignored in writing the electron configuration
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 Laboratory 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 preaccelerated 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
Emax = 96 × 2 [MeV /amu],
(4.1)
A
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
Ee =(me /2)v2 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 experiences from the electron beam during the energy scan. This force tends to
decrease the velocity difference between electron and ion beam. The corre41
sponding change in ion velocity vi as a function of time is obtained by
dvi
η li
=
Fz (t),
dt
Mi LR
(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 circulate 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 + Mi c2 + me c2 )2
(4.4)
1
]
)2 2
(√
√
2
2
2
2
−
Ei + 2Mi c Ei + Ee + 2me c Ee
− (Mi c2 + me c2 ),
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:
α (E) =
R(E)γ 2
,
Ni ne ( LliR )
(4.5)
√
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 9.049.32 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
42
1200
900
2
2
600
2 2
2s2p ( S)nl
Rate Coefficients (10
-12
cm
3
s
-1
)
2s2p ( P)nl
300
80
2
2
2s2p ( D)nl
60
40
20
0
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.
400
-1
s )
500
7
8
9
2 4
2s2p ( P ) nl
Rate Coefficients (10
-12
cm
3
6
2 2
J
2s2p ( P )nl
J
4
80
4
5
5
6
7
6
8
7
8
2 2
2s2p ( D )nl
60
J
40
20
0
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
series 2s2p2 (2 DJ )nl 1 and 2s2p2 (2 PJ )nl [59] are prominent in both spectra’s.
Towards high collisions energies, the outer electron will be attached into progressively 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
)1/4
(
Q3
ncuto f f = 6.2 × 1010
,
vi × Bd
(4.6)
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 multiconfiguration Breit-Pauli (MCBP) approximation, using AUTOSTRUCTURE
1 The
44
closed He-like 1s2 state is ignored in writing the electron configuration
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 2 D-series and too low for the 2 P-series. If the theoretical intensities for
the resonances in 2 D-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 2 S and 2 P-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 fieldionization 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, T plasma ∼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
(
)
2E 1/2
E
f (E, Te ) = 1/2
exp −
,
kB Te
π (kB Te )3/2
(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 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
45
]
-1
Rate Coefficients [10
-12
cm
3
s
10
1
0,1
10
3
10
4
10
5
10
6
Temperature [K]
100
Rate Coefficients (10
-12
cm
3
-1
s )
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].
10
1
103
104
105
106
107
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
0,8
b
-1
cm s
3
0,6
+50 meV
+100 meV
+150 meV
0,2
10
3
10
4
Temperature [K]
0,6
-10
0 meV
0,4
Rate Coefficients [10
Rate Coefficients [10
-10
3
cm s
-1
]
]
0,8
10
5
0 meV
10 meV
0,4
50 meV
100 meV
0,2
10
3
10
4
10
Temperature [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
5
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
excited states 2s2p (3 PJ )nl and 2s2p (1 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
be seen clearly in the 2s2p (1 P1 )nl series. It is also interesting to see that the
strength of DR peaks belonging to 2s2p (1 P1 )nl series increases towards the
series limit, while decreases in case of 2s2p (3 PJ )nl type of DR resonances
with no observable pile up structure near the series limit. The radiative decay
of the 3 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
sharp decrease of the DR strength along the 3 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
the metastable 3 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
48
60
1
2s2p( P )
1
50
3
Rate Cofficients [10
-10
cm s
3 -1
]
70
2s2p( P )
J
40
4
3
2
1
0
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
of 103 -106 K. The derived total (DR+TR) ncutoff (n ≤ 17) plasma rate coefficients are shown in figure 4.9a, along with the previous experimental results
49
1
1
a
Rate Coefficients [10
Rate Coefficients [10
-10
-10
3
3
cm s
cm s
-1
-1
]
]
b
0,1
0,01
10
0,1
0,01
3
10
4
10
Temperature [K]
5
10
6
10
3
10
4
10
5
10
6
Temperature [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 AUTOSTRUCTURE 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 electronion 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 Refrigerated 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 Blike 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 SuperEBIT (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 anpassningsparametrar. 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 överennsstämmelse, förutom en liten skillnad på 9 eV i fall av Be-liknande joners resonansposition. Anledningen till denna diskrepans kan bero på en underskattning av bidragen från några av resonanserna i beräkningarna.
53
Från CRYRING-mätningarna har koefficienterna för rekombineringshastigheten 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 forskningsområden. 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 högZ-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 precisionsmasspektrometern 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, wholehearted 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 Comission of Pakistan (HEC) and Swedish Institute (SI) for administrating the funding. My special thanks to Swedish Research council (VR) and Stockholm University 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.
56
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