CERN-THESIS-2015-389 //2015 eeomn fnwinsprto ehiusfrshort-lived for techniques ion-separation new of Development uldsadtefis asmaueet of measurements mass first the and nuclides ahmtshNtrisncatihnFakultät Mathematisch-Naturwissenschaftlichen rs-oizAntUiesttGreifswald Ernst-Moritz-Arndt-Universität ragn e kdmshnGae eines Grades akademischen des Erlangung n o i t a t r e s s i d l a r u g u a n I otr e Naturwissenschaften der Doktors risad 2 koe 2015 Oktober 22. Greifswald, der der zur nWolgast in 27.07.1982 am geboren Rosenbusch Marco von vorgelegt 52 , 53 K Dekan: Prof. Dr. Klaus Fesser

1. Gutachter: Prof. Dr. Lutz Schweikhard

2. Gutachter: ......

Tag der Promotion: ...... Contents

1 Introduction 11

2 The mass as a fundamental observable of a nucleus 15 2.1 Separation energies and nuclear shell gaps...... 16 2.2 Other observables...... 18

3 The ISOLDE facility at CERN and the ISOLTRAP setup 21 3.1 The ISOLDE facility...... 21 3.2 Penning-trap mass spectrometry at ISOLTRAP...... 22 3.3 Multi-reflection time-of-flight mass separation and spectrometry at ISOLTRAP...... 27

4 A new method of ion separation in Penning traps 31

5 Space-charge effects in multi-reflection time-of-flight mass separators 35 5.1 Investigation of space-charge effects in multi-reflection devices...... 35 5.2 Avoiding space-charge effects in multi-reflection devices...... 38

6 The neutron shell effects at N = 32 and N = 34 41

7 Conclusion and Outlook 45

8 Bibliography 47

9 Cummulative thesis articles 59 9.1 Author contributions...... 59 9.2 Buffer-gas-free mass-selective ion centering in Penning traps by simulta- neous dipolar excitation of magnetron motion and quadrupolar excitation for interconversion between magnetron and cyclotron motion...... 60 9.3 Ion bunch stacking in a Penning trap after purification in an electrostatic mirror trap...... 68 9.4 Towards Systematic Investigations of Space-Charge Phenomena in Multi- Reflection Ion Traps...... 78 9.5 Delayed Bunching for Muti-Reflection Time-of-Flight Mass Separation. 89 9.6 Probing the N = 32 Shell Closure below the Magic Proton Number Z = 20: Mass Measurements of the Exotic Isotopes 52,53K ...... 99

10 Publications 107 10.1 Peer-reviewed publications...... 107 10.2 Miscellaneous, non-reviewed publications...... 111

3 Contents

11 Erklärung 113

12 Curriculum vitae 115

13 Acknowledgments 117

4 List of Figures

2.1 Average binding energy per nucleon for stable nuclei...... 16 2.2 Neutron separation energies in the calcium region...... 17 2.3 Two neutron separation energies in the calcium region...... 18 2.4 Empirical two-neutron shell gaps in the calcium region...... 19 2.5 E(2+) energies and B(E2) transition probabilities in the Ca chain... 19

3.1 Sketch of the ISOLDE facility at CERN...... 21 3.2 Sketch of the ISOLTRAP setup...... 23 3.3 Penning traps and particle motion...... 24 3.4 Time-of-flight ion-cyclotron resonance technique...... 25 3.5 Resonant mass-centering in a preparation Penning trap...... 26 3.6 MR-ToF MS, schematic view...... 28 3.7 Mass resolving power of an MR-ToF MS compared to Penning traps.. 29

4.1 Schematic view of magnetron and cyclotron radius for SIMCO excitation 32 4.2 Mass spectrum at A=156 obtained by SIMCO excitation...... 33

5.1 MR-ToF MS setup at Greifswald...... 36 5.2 Peak coalescence in an MR-ToF MS...... 37 5.3 Energy transfer between ion clouds in MR-ToF MS...... 38 5.4 Delayed bunching in MR-ToF MS...... 39

6.1 Energy of the first (2+) excited state in the Ca region...... 42 6.2 Phenomenological interpretation of the N = 32 effect in the Ca chain.. 43

5

Nomenclature

A Atomic mass number

BE binding energy

Di empirical two-nucleon shell gap, i = n, p

M(Z,N) measured atomic mass of an element with Z protons and N neutrons

ME mass excess

N neutron number

R mass resolving power

Si separation energy for nucleons, i = n, 2n, p, 2p, . . .

TRF duration of a radio-frequency (RF) excitation

Ublock electric potential applied to block ions by the counter-field method

Ugen signal amplitude from a frequency generator

Z proton number

∆νi full width at half maximum of the signal response as a function of the applied frequency of a radio-frequency excitation, i = c, -, +, z = cyclotron, magnetron, reduced cyclotron, axial

∆m mass difference for calculation of the binding energy or full width at half maximum of a measured signal on the mass scale

∆t full width at half maximum of a measured signal as a function of the ions’ time of flght

Π parity of a nuclear state

δνi measurement uncertainties of eigenfrequencies in a Penning trap, i = c, -, +, z = cyclotron, magnetron, reduced cyclotron, axial

δm measurement uncertainty of the mass u atomic mass unit, u = 1.660 538 921(73) × 10−27 kg = 931.4940598(57) MeV/c2 [NIS13]

νnlj single-particle (shell-model) orbit of a neutron with main quantum number n, orbital angular momentum l and total angular momentum j

7 Nomenclature

νRF frequency of an applied radio-frequency (RF) excitation to stored ions

νi resonance frequencies in a Penning trap, i = c, -, +, z = cyclotron, magnetron, reduced cyclotron, axial

πnlj single-particle (shell-model) orbit of a proton with main quantum number n, orbital angular momentum l and total angular momentum j

AX isotope of element X with mass number A

−1 c0 speed of light in vacuum, c0 = 299 792 458 m s [NIS13] m mass

−31 2 me electron rest mass, me = 9.109 382 91(40) × 10 kg = 0.5109989461(31) MeV/c [NIS13]

−27 2 mn neutron rest mass, mn = 1.674 927 351(74) × 10 kg = 939.5654133(58) MeV/c [NIS13]

−27 2 mp proton rest mass, mp = 1.672 621 777(74) × 10 kg = 938.2720813(58) MeV/c [NIS13] q electric charge

CERN European Organization for Nuclear Research

FT-ICR Fourier-transform ion-cyclotron resonance

GPS general purpose separator of ISOLDE

HRS high-resolution separator of ISOLDE

ICR ion-cyclotron resonance

ISOLDE Isotope Separator OnLine - facility at CERN

J total angular momentum quantum number of a many-particle state j total angular momentum quantum number of a single-particle state l orbital angular-momentum quantum number

MR-ToF MS multi-reflection time-of-flight mass separator/spectrometer

MS mass spectrometry / mass spectrometer / mass separator n main quantum number

PT Penning trap

PT-MS Penning-trap mass spectrometry

RF radio frequency

8 Nomenclature

RFQ radio-frequency quadrupole

ToF time of flight

ToF-ICR time of flight ion-cyclotron resonance

9

1 Introduction

The experimental detection of massive positively-charged atomic centers by E. Ruther- ford in 1911 [Rut11] marks the birth of modern atomic- and nuclear physics. At the same time, the invention and development of new mass-spectrometric methods paved the way for first insights into subatomic properties. The first two groundbreaking events by measuring atomic masses were the discovery of the whole-number rule, i.e. that stable isotopes of the same element were found to have mass distances close to one atomic-mass unit, and the discovery of more than one stable isotope of neon and other light elements with even proton numbers, both by J.J. Thompson and F.W. Aston [Tho13; Ast19; Ast20]. In the late 1920’s, the refinement of mass spectrometric techniques allowed an accuracy of one part in 10000 by Aston, which revealed deviations from the whole-number rule, interpreted as “packing fraction” [Ast27]. The measured masses were always found to be lighter than the sum of masses of their constituents. This was consistent with Einstein’s theory of equivalence between mass and energy, where the mass difference between a compound system and the sum of its constituents (∆m) is reflected in its binding energy (BE) by the relation BE = ∆mc2, with c being the speed of light. After the discovery of the neutron by J. Chadwick in 1932 [Cha32], modern nuclear physics became a research field by its own. One of the first important achievements in nu- clear theory was the semi-empirical mass formula published by C.F. v. Weizsäcker [Wei35] following the idea of nuclei being similar to a liquid drop by G. Gamow. Later, the systematic determination of nuclear masses triggered the first formulation of the nuclear shell model by M. Goeppert-Mayer and J.H.D. Jensen [May48; May49]. This was the most crucial breakthrough for nuclear physics as it explained the appearance of proton/neutron numbers with specific “magic” properties by introduction of a strong spin-orbit coupling (growing with increasing angular momentum). At that time, nuclear mass measurements had been performed mostly for stable isotopes, because the short half lives of unstable species complicated the measurements, even if their production was already possible. In 1951, a new age of experimental nuclear physics was commenced by coupling a uranium oxide target bombarded with fast neutrons (produced in a cyclotron) directly to an isotope separator [Kof51]. This new method gave access to isotopes of much shorter half life as compared to the limits reached by all indirect production techniques used before. This fast extraction technique (called “on-line” technique) was installed for the first time at the ISOLDE facility at CERN in Geneva and made accessible for user experiments from 1967 on [ISO], which enabled the discovery of many new nuclides and the measurement of their properties. One of the major results of on-line measurements of atomic masses in the following years was the observation of deviations of trends of the nuclear binding energy from the predictions of the nuclear shell model. These deviations were later attributed to previously unknown residual nucleon-nucleon

11 1 Introduction

interaction manifesting in neutron rich/deficient nuclei. Perhaps the most important discovery was that in very neutron-rich nuclides with magic neutron number the typical signature for magicity (an enhanced binding with respect to the neighboring isotopes) can be significantly reduced. Given that magic nuclei were described in the shell model as corresponding to closed nuclear shells, this discovery was interpreted as a "shell quenching", meaning that the energy gap giving closed-shell nuclei their "magical" prop- erties was being reduced by some component of the nucleon-nucleon interaction. One of the most famous regions of the nuclide chart for the occurrence of shell quenching is the so-called island of inversion around the neutron number N = 20 and around the proton number Z = 11 (first information has been provided by mass spectrometry [Thi75]), where a vanishing of the N = 20 shell gap takes place, together with an inversion in energy of the 1d3/2 and 1f7/2 orbitals (see e.g. [Sch11] for an overview and further references). As a consequence of such experimental findings from mass spectrometry and other experimental techniques taking place at radioactive ion-beam facilities, the subject of "shell evolution" in exotic nuclei has become a major subject of theoretical and experimental research, leading to continuous developments of the nuclear shell model (see [Cau05] for a more recent review). Systematic studies of exotic nuclei with high precision are nowadays applied to vari- ous physics areas like nuclear shell-structure physics, nuclear astrophysics and parti- cle physics [Bla13; Sch06]. During the last decades of the 20th century, novel tech- niques evolved in the field of mass spectrometry based on particle storage in Penning traps [Bro86]. In Penning-trap mass spectrometry, two detection techniques of major importance have been developed, Fourier-transform ion-cyclotron resonance (FT-ICR) detection [Com74; Mar00] and time-of-flight ion-cyclotron resonance (ToF-ICR) detec- tion [Grä80; Kön95] (see chapter 3.2). In 1987, the first Penning-trap on-line mass measurements with the spectrometer “ISOLTRAP” installed at the ISOLDE facility at CERN (Switzerland) have been reported [Bol87; Klu13]. Other Penning-trap systems have been built at facilities worldwide, where today’s actively employed Penning-trap mass spectrometers for radionuclides are ISOLTRAP [Muk08] at ISOLDE/CERN in Geneva/Switzerland [Kug00], JYFLTRAP [Äys08] at IGISOL in Jyväskylä/Finnland, SHIPTRAP [Blo13] at GSI in Darmstadt/Germany, TITAN [Ett13] at ISAC/Triumf in Vancouver/Canada, CPT [Sav06] at ANL near Chicago/USA, LEBIT [Rin13] at MSU in East Lansing/USA and TRIGA-TRAP [Smo12] at the TRIGA research reactor in Mainz/Germany. One of the main challenges for such experiments (especially at ISOL facilities) is that contaminating species are produced and delivered together with the ions of interest (see chapter3). These species can have very similar masses to that of the ions of interest, which is the case for isobars (molecular or atomic ions of same mass number A) and nuclear isomers with sufficient life time (long-lived excited states of the same nucleus). Two important devices for cleaning of contaminants are presently applied at ISOLTRAP, a buffer-gas filled Penning trap [Sav91] and a multi-reflection time-of-flight mass separator/spectrometer (MR-ToF MS) [Wol90]. In 2010, an MR-ToF MS has been installed at ISOLTRAP. It was the first of such devices used for removal of isobaric con- taminants [Wol12a; Wol13a] at an on-line experiment, and for direct mass measurements of short-lived isotopes [Wie13; Ros15a] (latter publication: cumulative thesis article). The objectives of this thesis are, on the one hand, new developments for mass-spectrometric

12 separation of contaminant ions, i.e. isolating chosen ions of interest from other species by application of ion-trapping devices [Ros12a; Ros13; Ros14; Ros15b] (cululative the- sis articles). On the other hand, direct mass measurements of the most neutron-rich potassium isotopes have been carried out. These measurements confirm for the first time the neutron-shell effect at the neutron number N = 32, which has been measured recently for calcium isotopes [Wie13], also for the open-proton-shell nucleus 51K[Ros15a].

13

2 The mass as a fundamental observable of a nucleus

As direct consequence of the interpretation of a system’s energy loss in special relativity, the mass of a bound system allows extracting its total binding energy. The knowledge of the mass of a nucleus provides thus the energetic sum of all interactions of its constituents, including nuclear forces and electromagnetic forces of proton-proton interactions. For nuclear forces that appear as a residual of the strong interaction taking place between the constituents of nucleons, the obtained binding energies are large enough (several MeV) that already a mass uncertainty of δm/m ≤ 10−3 is sufficient to measure their effects (achieved by early mass spectrometers). Also for different metastable nucleon configurations of the same nucleus (long-lived isomeric states), the mass difference to the ground state is in many cases still large enough to be quantified with modern mass spectrometers reaching uncertainties of δm/m < 10−6. This has been achieved for the first time by Penning-trap measurements at ISOLTRAP [Bol92] (see also [Sta13] as a recent study of nuclear isomers). For an atom with a nucleus consisting of Z protons and N neutrons, the atomic binding energy BE(Z,N) (regarded as positive quantity) is given by:

2 BE(Z,N) = (N · mn + Z · mp + Zme − M(Z,N)) · c , (2.1) where mn is the neutron rest mass, mp the proton rest mass, me the electron rest mass, and M(Z,N) is the measured mass of the atom. For the classification of nuclei in data tables, the value of the mass excess ME(Z,N) is used rather than the binding energy. The mass excess denotes a comparison of the measured mass to an integer multiple of the atomic mass unit u, which is 1/12 of the mass of a neutral 12C atom, and is defined by: ME(Z,N) = M(Z,N) − Au, (2.2) where A = Z + N is the atomic mass number. Analyzing binding energies reveals nuclear properties and serves as input as well as benchmark for nuclear models [Lun03]. A look at the measured binding energy per nucleon (BE(Z,N)/A) of the stable elements already provides evidence of an underlying structure and allows some conclusion of the general nature of nuclear forces. In Figure 2.1, the average binding energies per nucleon for the most abundant stable elements are shown. The saturation of the average binding energy for medium-mass nuclei and its decrease for larger numbers of nucleons shows the finite range of the nuclear forces (nucleons interact only with other nucleons in a small neighborhood) and the effect of electric repulsion between the protons in heavy elements, respectively. The visible peaks of binding energy for 4He, 14C and 16O can be interpreted in terms of two effects, which are the enhanced binding of symmetric (N = Z) nuclei on one hand, and on the other

15 2 The mass as a fundamental observable of a nucleus

62Ni 9 16O 12C 8 4He 56Fe 7 235U 6 238U 5 4

3 3H 3He 2 1 2H 1H Average binding energy per nucleon (MeV) 0 0 50 100 150 200 250 Mass number Figure 2.1: Average binding energy per nucleon as a function of the number of nucleons for the most abundant stable elements up to uranium (data taken from [Wan12]).

hand the nuclear shell effects for the magic numbers 2 and 8 in case of 4He and 16O. To provide a much clearer picture of shell effects, differential quantities like separation energies are used.

2.1 Separation energies and nuclear shell gaps

Specific information about nuclear structure can be obtained when finite-difference formulas (also called “mass filters”) are applied to the binding energies of neighboring nuclides. A first example of such mass filters is the one-nucleon separation energy (Sn for neutrons, and Sp for protons). It is the comparison of the ground-state binding energies of two adjacent isotopes/isotones and provides the energy which is required to remove a nucleon from the system:

Sn(Z,N) = BE(Z,N) − BE(Z,N − 1) (2.3) 2 = (mn + M(Z,N − 1) − M(Z,N)) · c

Sp(Z,N) = BE(Z,N) − BE(Z − 1,N) (2.4) 2 = (mp + me + M(Z − 1,N) − M(Z,N)) · c

From the neutron/proton separation energy, the magnitude of the odd-even staggering in isotopic chains can be extracted (see Fig. 2.2). This provides information about the binding energy of two paired nucleons (pairing energy), although it does not directly reflect the pairing energy because the difference in binding of systems with a missing (or added) nucleon contains also contributions from all other nucleons.

16 2.1 Separation energies and nuclear shell gaps

Sc 16 Ca K 14 Ar

12

10

8

6

Neutron separation energy (MeV) 4

18 20 22 24 26 28 30 32 Neutron number Figure 2.2: Neutron separation energy as a function of the neutron number around the proton- magic calcium chain (data taken from [Wan12]).

In order to gain information about nuclear shell structure while suppressing the odd- even staggering, two-nucleon separation energies can be used (S2n for neutrons and S2p for protons), where only every second isotope/isotone neighbor is taken into account:

S2n(Z,N) = BE(Z,N) − BE(Z,N − 2) (2.5) 2 = (2mn + M(Z,N − 2) − M(Z,N)) · c

S2p(Z,N) = BE(Z,N) − BE(Z − 2,N) (2.6) 2 = (2mp + 2me + M(Z − 2,N) − M(Z,N)) · c

This quantity usually undergoes a smooth decrease with the nucleon number, until for a certain number of nucleons (called magic) it exhibits a sudden drop. Two-nucleon separation energies thus serve as a valuable mass filter for detecting magic numbers. This is exemplified for the calcium isotopes in Fig. 2.3. While a generally decreasing trend is measurable with increasing neutron number between N = 22 and N = 28, which in the shell model corresponds to a filling of the ν1f7/2 orbit (referring to neutrons with main quantum number n = 1, angular momentum l = 3, and total angular momentum j = 7/2), a sharp drop of S2n is visible between N = 28 and N = 30. In the shell model, magic numbers correspond to closed-shell configurations, which are separated by a large energy gap from the shell higher in energy. At N = 28 the ν1f7/2 shell is filled, so at N = 30 the two additional neutrons occupy a shell higher in energy (ν2p3/2) from which they can be removed with smaller expenses of energy. An additional mass filter, which measures the magnitude of the drop of two-nucleon separation energies is the empirical two-nucleon shell gap: Dn(Z,N) as two-neutron shell gap and Dp(Z,N) as two-proton shell gap.

17 2 The mass as a fundamental observable of a nucleus

Sc 30 Ca K Ar 25

20

15

10 Two-neutron separation energy (MeV)

18 20 22 24 26 28 30 32 Neutron number Figure 2.3: Two-neutron separation energy as a function of the neutron number around the proton-magic calcium chain (data taken from [Wan12]).

Dn(Z,N) = S2n(Z,N) − S2n(Z,N + 2) (2.7) = 2BE(Z,N) − BE(Z,N − 2) − BE(Z,N + 2) = (M(Z,N + 2) + M(Z,N − 2) − 2M(Z,N)) · c2

Dp(Z,N) = S2p(Z,N) − S2p(Z + 2,N) (2.8) = 2BE(Z,N) − BE(Z − 2,N) − BE(Z + 2,N) = (M(Z + 2,N) + M(Z − 2,N) − 2M(Z,N)) · c2

The empirical two-nucleon shell gap reflects the derivative of the two-nucleon separation energies, where closed-shell configurations can be identified by large values as shown in Fig. 2.4. On the other hand, very small positive or even negative values of the two- nucleon shell gap can represent a (sometimes unexpected) contribution to the binding energy from nuclear-structure effects other than shell closures, which occurs, e.g., in the region above the Kr isotopic chain due to nuclear deformation [Del06; Nai10]. Beside the discussed mass filters, also other finite difference formulas, which employ several binding energies, are used in nuclear physics. A thorough treatment of finite-difference formulas can be found in [Man14].

2.2 Other observables

In order to find an unambiguous and consistent picture of nuclear structure, the analysis of complementary nuclear data is of great importance. Although nuclear-structure

18 2.2 Other observables

9 Sc Ca 8 K Ar 7 6 5 4 3 2 1 Empirical two-neutron shell gap (MeV) 0 16 18 20 22 24 26 28 30 32 Neutron number Figure 2.4: Empirical two-neutron shell gap as a function of the neutron number around the proton-magic calcium chain (data taken from [Wan12]). effects are reflected in separation energies, the same effect can receive different physical interpretations. In regions of collective effects as for example the A ≈ 100 region [Man13] and the trans-lead region [Kre14], a drop of separation energies can be caused by a sudden decrease of the energy due to other nuclear correlations than a closed-shell configuration. From hyperfine atomic transitions charge radii, spins, magnetic moments and electric quadrupole moments can be extracted, which are used to analyze shell-level ordering, occupations and nuclear deformation [Pap13; Ney05]. The investigation of nuclear decay and internal transitions (e.g. by γ-spectroscopy with

4.0 0.05 ) 0.04 2 3.0 b 2 e (

/ MeV 0.03 /

) 2.0 ) + 0.02 2 2 E ( (

E 1.0 0.01 B

16 18 20 22 24 26 28 30 Neutron number

Figure 2.5: Excitation energies E(2+) of the first (2+) excited state and transition probabilities B(E2) as a function of the neutron number in calcium isotopes (data taken from [Ram01]).

19 2 The mass as a fundamental observable of a nucleus

post-accelerated beams [Dup11]) provides excitation-level schemes and branching ratios (probability distribution for decay channels). One of the most important observables for nuclear structure studies obtained from γ-spectroscopy is the energy gap E(2+) between the ground state and the first excited J Π = 2+ state (total angular momentum J, parity Π) of even-even nuclei. Furthermore, the reduced quadrupole transition probability between the two states, the B(E2) value, plays an important role in deducing the collectivity of the ground-state configuration. In the search for new magic numbers in unstable nuclides both quantities play a very important role which is complementary to the one of the binding energies. A closed-shell configuration is identified by a significantly increased E(2+) (see chapter6) accompanied by a small transition probability B(E2). In figure 2.5, the E(2+) and B(E2) values are shown for the Ca chain from N = 18 to N = 28. For the “traditional” magic numbers, N = 20 and N = 28, particularly large excitation energies are observed while the transition probabilities are low, reflecting small correlations of the valence nucleons. An opposite behavior compared to closed-shell systems can be found in nuclei where collective effects play a major role. For example typical indications for nuclear deformation are small excitation energies of the (2+) state with large B(E2) transition probabilities. This is caused by the emergence of levels at low excitation energies by collective rotational and vibrational modes.

20 3 The ISOLDE facility at CERN and the ISOLTRAP setup

3.1 The ISOLDE facility

At the ISOLDE facility at CERN (see Fig. 3.1) exotic nuclides are produced by pulses of up to 3 · 1013 protons with a kinetic energy of 1.4 GeV (accelerated by the “Proton- Synchrotron Booster” of CERN) impinging, e.g., on a heated uranium carbide tar- get [Kug00]. The impact of the proton beam causes several types of nuclear reactions with the uranium nuclei in the target, where three types are dominantly present:

ISOLDE facility at CERN

HRS

HRS - target

GPS - target

ISOLTRAP plaorm GPS protons from PS-Booster of CERN

Figure 3.1: Sketch of the ISOLDE facility for nuclear research at CERN. The ISOLTRAP experiment is located at the central beamline of the experimental hall.

• Nuclear fragmentation: a fast non-thermal high-energy reaction on time scales of 10−23 s, where the nucleus is directly split into fragments by the collision [Lyn87]

• Nuclear spallation: an excitation of the nucleus to high energy levels in a time scale of 10−22 s, and subsequent de-excitation by thermal evaporation of nucleons in the order of 10−16 s [Cam81]

21 3 The ISOLDE facility at CERN and the ISOLTRAP setup

• Nucleon induced fission: protons or neutrons with energies of a few MeV induce nuclear fission. Secondary nucleons with appropriate energies are either produced by reactions in the target or can be purposely produced by shooting the proton beam on a so-called proton-to-neutron converter [Got14] to favour the production of neutron-rich nuclei.

The production of different isotopes depends on the reaction cross sections, which in turn depend on the interplay between the reactions mentioned above and radioactive decay. However, in general the production of isotopes is non-selective, which leads to a distribution of the products over all mass regions below (and equal to) the initial mass of uranium. Due to this circumstance the ions of interest have to be selected in subsequent processes. The exotic species and all other (much more abundant) free molecules and atoms dif- fuse out of the heated target in neutral electric state (and positively charged in case of alkalies) and further diffuse through a small tube referred to as transfer line. A pre-selection of elements can be obtained by the temperature of transfer line and target and by the material of the transfer line (e.g. SiO2 for adsorption of alkali metals). The neutral atoms have to be ionized after diffusing out of the transfer line, where, e.g., a plasma ion source can be used for non-selective ionization [Sun92]. An element-selective ionization can be performed by use of the resonant-ionization laser ion source of ISOLDE (RILIS) [Mar13], where a suppression of all products except surface ionized elements can be achieved. For the first stage of mass selection the beam is accelerated to 30 − 60 keV and guided through one of two available magnetic separators: “general purpose separator” (GPS) or “high-resolution separator” (HRS), where each of the separators is connected to an independent target. The maximum mass resolving power of the HRS is about R = m/∆m = 5000, which is sufficient to isolate products at a certain atomic mass num- ber A, but most of the isobars, i.e. ions with same mass number (including molecules), have to be purified by the users, to which the ion beams are guided by ion-optical elements in so-called beamlines.

3.2 Penning-trap mass spectrometry at ISOLTRAP

The ISOLTRAP setup [Muk08; Kre13a] has been installed more than 25 years ago and was the first on-line Penning-trap mass spectrometer for radionuclides worldwide [Bol87; Sto90; Klu13]. From the first tests on, further developments of the setup have been performed permanently. The challenges for radionuclides that have to be addressed are:

• the short half-lives of the ions of interest

• the large ratio of contaminant ions to ions of interest

• a small mass difference between contaminant ions and ions of interest

The aim of developments is thus the reduction of the time required for mass-over-charge separation (as well as the mass-measurement process by itself) to access new nuclides

22 3.2 Penning-trap mass spectrometry at ISOLTRAP

device used for mass measurement ToF detector

device used for mass separation precision Penning trap auxiliary device for mass measurements

magnet 2 preparation Penning trap for mass separation and cooling interface for laser ablation reference ion source or detectors for ion source decay spectroscopy magnet 1 MR-ToF MS for mass separation or direct mass measurements HV platform

ISOLDE 60 keV ion beam pulsed cavity

ND:YAG 532nm

RFQ cooler and buncher for creation of cooled ion pulses ToF detector or from continous beams ion gate

Figure 3.2: Sketch of the ISOLTRAP setup with its four main parts: A radio-frequency quadrupole (RFQ) cooler and buncher, a multi-reflection time-of-flight mass separa- tor/spectrometer, a cylindrical Penning trap for mass separation, and a hyperbolic Penning trap for high-precision mass measurements. See text for details. with shorter half-lives, the increase of the upper limit of the reachable resolving power for mass-over-charge separation, and the reduction of the measurement uncertainty reached in a limited time for precision measurements. Note that for reasons of simplicity, equally-charged ions are considered in the following explanations and the expression “mass separation” will be used rather than “mass-over-charge separation”. The setup presently consists of four main devices as shown in Fig. 3.2: A radio-frequency quadrupole (RFQ) ion trap for cooling and bunching of the ion beam from ISOLDE, a multi-reflection time-of-flight mass separator/spectrometer (MR-ToF MS) for mass separation and also for direct mass measurements, and two Penning traps, which are a cylindrical Penning trap for mass separation (and ion preparation) and a hyperbolic Penning trap for high-precision mass measurements. The radioactive ions are delivered by ISOLDE as a quasi-continuous beam for a chosen time interval, which varies between microseconds and seconds and depends on the beam intensity. The ions are captured, cooled and bunched in the RFQ ion trap by a helium buffer gas. The resulting discrete ion package is forwarded to the MR-ToF MS, either for mass separation as a preparatory step for the usage of the Penning traps, or for direct mass measurements by time-of-flight detection at a ToF detector behind the device. In case of performing Penning-trap measurements, the purified ions from the MR-ToF MS are forwarded to the (buffer-gas filled) preparation Penning trap for further cooling and to provide a second stage of mass separation. The cooled and purified ions are then

23 3 The ISOLDE facility at CERN and the ISOLTRAP setup

a) b) Upper End Cap

Ring Electrode

Lower End Cap Homogeneous Magnec Field Correcon Electrodes

Figure 3.3: Penning traps and the motion of a stored particle: a) schematic view of a Penning trap and 3D-cut of the precision Penning trap of ISOLTRAP showing the most important parts; and b) trajectory of a stored particle in an ideal Penning trap for illustration of the three motional modes.

transferred to the precision Penning trap, where the cyclotron frequency is determined. Magnetic-field calibration is achieved by alternating measurements of the ions of interest and of well-known stable ions taken from the reference ion source. Up to 2010, Penning-trap mass spectrometry (PT-MS) was used exclusively. A Pen- ning trap consists of an axial quadrupolar electric field (with cylindrical symmetry) in superposition with an axial magnetic field as shown in the left part of Fig. 3.3, which is often realized by two end-cap electrodes with a ring electrode in between, all of hyperbolic geometry, and correction electrodes to compensate the limited electrode sizes and other geometrical deviations. In a Penning trap, stored charged particles move with three different motional modes (see right part of Fig. 3.3): a radial magnetron motion at magnetron frequency ν− (mass independent at leading order), a radial cyclotron motion with the reduced cyclotron frequency ν+ (mass dependent), and an axial motion with the axial frequency νz (mass dependent) [Bro86]. Due to the usage of strong magnetic fields of superconducting magnets, the oscillatory eigenmotions of the ions typically fulfill the relation ν−  ν+, where the sum of both eigenfrequencies is the cyclotron frequency νc of the particle with mass m and charge q in the magnetic field B: ν− + ν+ = νc = qB/(2πm). In Penning-trap mass spectrometry, radio-frequency (RF) excitations in the radial plane can be used for manipulation of the particles’ radial motions (also axial RF excitations are possible), where a segmented ring electrode is needed. An excitation using an oscillating dipole field can be used to increase/decrease the motional amplitude of one of the eigenmotions. For example a diplolar excitation at frequency ν+ in the radial plane and in phase with the ion’s motion will increase the cyclotron radius of the ion. An RF excitation with a quadrupolar field geometry in the radial plane couples the two radial eigenmotions, which leads to a periodical interconversion of the motional amplitudes into each other in the resonant case, i.e. when νRF = νc [Bol90]. In the recent years, also an octupolar excitation scheme for the interconversion of the radial eigenmotions has been investigated and applied at different Penning-trap experiments [Rin07; Eli11; Ros12b; Kre13b] but is not yet widely used because of non-linear field properties and the necessity of an eight-fold split ring electrode of the Penning trap. For mass measurements the resonant conversion from initially pure magnetron to cy- clotron motion is used to probe the match between the frequency of the (quadrupolar)

24 3.2 Penning-trap mass spectrometry at ISOLTRAP

14 460 out of resonance 12 in resonance 440 420 10 400 8 380 6 360 340 4

Average time of flight 320 Number of detected ions 2 300 0 280 200 300 400 500 600 700 800 -4 -3 -2 -1 0 1 2 3 4 Time of flight from Penning trap to detector / µs Excitation frequency - 1066697 Hz

Figure 3.4: Time-of-flight ion-cyclotron resonance measurement: time-of-flight spectrum of 85Rb ions for non-resonant (red) and resonant (blue) quadrupolar excitation (left part), and (right part) average time of flight as a function of the excitation frequency and fit to the data (solid line).

RF excitation and the cyclotron frequency of the ion. The cyclotron radius obtained after the excitation, and thus the radial energy of the oscillation with high (ν+) fre- quency, depends on the distance between the excitation frequency and the cyclotron frequency of the ion. When the ions are then ejected slowly from the trap and are leaving the homogeneous region of the magnetic field, an axial acceleration in the strong magnetic-field gradients takes place, which is based on the initial radial energy of the ions. The ions that experience a resonant conversion to cyclotron motion in the trap (and have thus the maximum achievable radial energy) will have the shortest flight time to an ion detector outside the magnet [Grä80](see left part of Fig. 3.4). Scanning the frequency around the expected cyclotron frequency of the ions of interest results in a resonance profile, where the center frequency is determined through a data fit (right part of Fig. 3.4). This method is called time-of-flight ion-cyclotron resonance detection (ToF-ICR). The resolving power of the frequency spectrum is determined by the observation time (excitation time of ions of interest TRF ) for the cyclotron-frequency measurement, R = ∆m/m = ∆νc/νc ≈ 1.25νcTRF , according to the Fourier limit of the quadrupolar RF excitation [Bol01]. The reachable measurement uncertainty is typically two orders of magnitude lower than the inverse resolving power 1/R due to efficient use of data fits, and is reaching δm/m ≤ 10−8 at ISOLTRAP [Kel03]. A further widely-used method for mass measurements should be noted: In Fourier- transform ion-cyclotron resonance detection (FT-ICR), the image current induced by the oscillating ions is amplified, where the signal provides the eigenfrequencies (and sidebands) by Fourier transformation [Mar92; Sch92]. While with the ToF-ICR method mentioned above, single-ion counting is possible with room-temperature Penning traps, the FT-ICR method can not always be applied for on-line experiments, i.e. when dealing with rare and short-lived species. This is because the number of ions necessary to overcome the thermal noise of the trap electrodes and the amplifier is usually not acces- sible. However, single ion detection by FT-ICR is well possible when the Penning trap

25 3 The ISOLDE facility at CERN and the ISOLTRAP setup and detection system is on cryogenic temperatures (see e.g. [Sch12]), but the required preparation and cooling times for the ions mostly exceed the lifetime of the short-lived species of interest today. Nevertheless, the usage of cryogenic systems at radioactive ion-beam facilities will gain attention in the near future. Another novel measurement method gives direct access to the motional phase of the stored ions by ejecting them towards a position-sensitive detector. This phase-imaging ion-cyclotron resonance (PI-ICR) technique provides an order of magnitude higher resolving power and also a lower uncertainty for cyclotron-frequency measurements as compared to ToF-ICR or FT-ICR detection [Eli13; Eli15]. This success has been intro- duced at the SHIPTRAP experiment at GSI/Darmstadt. It is currently implemented but not yet available at ISOLTRAP. A Penning-trap mass measurement can only provide accurate values when a pure ion ensemble is present in the precision Penning trap [Wol13b]. A removal of all unwanted masses is thus required as a preparatory step. Either the wanted ensemble of ions is transferred to a subsequent device after mass separation, or, in very difficult cases, the ensemble has to be purified in the same ion trap where the precision measurement takes place. In the first case, the preparation Penning trap of ISOLTRAP is used, where contaminant a) b)

Figure 3.5: Illustration of the ion motion for mass-selective cooling in a buffer-gas filled Penning trap: a) magnetron radius (ρ−) and cyclotron radius (ρ+) as a function of the time for resonant quadrupolar excitation, and b) corresponding ion trajectory in the radial plane of the Penning trap (pictures from [Ros09]). species are suppressed while the ions of interest can be transmitted to the next device. To this end a mass-selective centering of the ions of interest is performed [Sav91]: A dipolar RF excitation in the radial plane of the trap excites the magnetron motion at the frequency ν− of all ions (mass independent at leading order) to increase the magnetron radius up to several millimeters, which is larger than the radius of a small central aperture in the end-cap electrode. After that, a resonant radial quadrupolar RF excitation at the cyclotron frequency νc of the ions of interest converts the magnetron motion of only the selected mass into the (much faster) cyclotron motion. The dissipation of energy by buffer-gas collisions decreases the cyclotron radius within (typically) a

26 3.3 Multi-reflection time-of-flight mass separation and spectrometry at ISOLTRAP few tens to hundreds of milliseconds (see Fig. 3.5), which depends on pressure and mass of the buffer-gas atoms and ions. Finally, the ions of interest are at sufficiently small distances from the radial trap center so that they can be extracted through the central hole from the trap. All other ions collide with the electrodes, are neutralized, and lost as in contrast to the cyclotron radius the magnetron radius is increased by dissipation (energy decreases with increasing radius). The limit typically reached for mass separation by buffer-gas filled traps is a resolving power of R = 105, which is less than achievable in a high vacuum environment due to the damping of the ions’ motion [Kre08; Geo11]. In the precision Penning trap, mass separation can be performed in a high vacuum environment (no buffer gas), i.e. in the absence of damping forces. This can be necessary for isobars very close in mass or for long-lived isomeric states delivered as contaminants from ISOLDE. However, at ISOLTRAP, the ions of interest need to be preserved in the same trap for a subsequent mass measurement (see also [Ero12], where ions have been sent back to the preparation trap). A dipolar excitation can be used to address the reduced cyclotron frequency of each contaminating ion species as a narrow-band ejection method. If many different contaminating species are stored in the same trap, the application of this narrow-band method can be challenging. To eject an entire region of ions in that way, complicated waveforms are required to address all unwanted ions at once. A new excitation method has been developed within the work in this thesis to solve this issue (see chapter4).

3.3 Multi-reflection time-of-flight mass separation and spectrometry at ISOLTRAP

A multi-reflection time-of-flight mass separator/spectrometer has been developed at the University of Greifswald and has been installed at ISOLTRAP in 2010 [Wol13c]. The aims of this development are to reach a sufficient mass separation for ion purification in a shorter time than possible before [Wol12a; Wol13a], and to perform direct mass mea- surements of isotopes with previously inaccessible half lives and production rates [Wie13; Ros15a; Ata15] (second publication: cumulative thesis article, see chapter6). The concept of multi-reflection time-of-flight mass spectrometry is based on conventional time-of-flight mass spectrometry (ToF-MS), where the performance of the experiments profits from a long flight path (long flight time) of charged particles from a source to a detection device [Wil55]. The mass resolving power of such MR-ToF MS systems is nowadays typically R = m/∆m = t/(2∆t) > 105 and can be reached in time ranges of tens of milliseconds, where t is the total time of flight of the ions and ∆t the full width at half maximum of the ion signal as a function of the time of flight. An MR-ToF MS consists of two electrostatic mirrors facing one another, where each mirror typically consists of a couple of ring-shaped electrodes as indicated in the left part of Fig. 3.6 (other geometries are possible). The two mirrors are spatially separated by a field-free region. The maximum electric potential of the mirrors (regarded as positive here) exceeds the kinetic energy of the ions, which causes repeated reflections and enables thus axial confinement. The accessible flight path in such a device is thus

27 3 The ISOLDE facility at CERN and the ISOLTRAP setup

ion

mirror electrodes field-free region mirror electrodes

Figure 3.6: Left part: schematic view of an MR-ToF MS (top) and technical drawing of the electrode stack of ISOLTRAP’s MR-ToF MS (bottom). A pulsed drift tube is mounted in the center and is used for injection and ejection of ions (in-trap lift [Wol12b; Wie15]).Right part: a Bradbury-Nielsen ion gate (top) is used for mass separation, i.e. a pulsed wire grid enabling deflection of ions when biased and transmission when grounded. For mass measurements, time-of-flight spectra can be recorded at a ToF detector, which can be moved into the beamline at the position of the Bradbury-Nielsen gate. Parts of picture modified from [Wol13b]. theoretically of arbitrary length. The required radial confinement is achieved by the shape of the mirror potentials, which causes a periodic re-focusing towards the radial center of the device for ion bunches (or beams) with sufficient kinetic energy (no storage possible for particles at rest). This can be realized by, e.g., a large negative potential (i.e. opposite to the confinement potential) applied to one of the electrodes of each mirror. Assuming an initial ion cloud which consists of different ion species and has a small spa- tial distribution compared to the dimensions of the device (ensured by the RFQ buncher from which the ions are delivered), a spatial separation between the species takes place while the ions are reflected forth and back, because of the different mass-over-charge ratios m/q of the ions and their common kinetic energies. This separation, and thus the resolving power, increases with the total time of flight. During the trapping time, a synchronization of ions with the same mass but slightly different kinetic energies (distributions of typically a few percent of the total kinetic energy) is necessary to keep the ToF distribution for each species constant and thus to avoid a defocusing. To this end, the potential shape at the mirrors must be adjusted to create an adequate relation between the duration of a revolution and the kinetic energy ∂Trev of equal-mass ions Trev(Ekin), which is ≈ 0 and corresponds to a dispersion-free ∂Ekin transport [Wol12b; Ros15b]. This suggests that the final ToF distribution depends only on the initial one. In practice, however, further ToF aberrations due to the transversal expansion of the beam grow with increasing number of revolutions. At ISOLTRAP, up to a few thousand revolutions are used. In order to perform mass separation (purification) as a preparatory step for a Penning- trap measurement, the ions are ejected from the MR-ToF MS after the resolving power has become sufficient to enable the selection of the ions of interest. For selection the ions are guided through a Bradbury-Nielsen gate [Bra36; Pla08; Bru11; Wol12a], which deflects all unwanted species and transmits the wanted ions (by switching off the deflec-

28 3.3 Multi-reflection time-of-flight mass separation and spectrometry at ISOLTRAP

Figure 3.7: Theoretical mass resolving power as a function of the observation time for ISOLTRAP’s precision Penning trap (B = 5.9 T, solid line) and the MR-ToF MS (dashed line) for a singly-charged ion of Mass A = 100. Picture taken from [Wol13b]. tion field for a short time) to the subsequent preparation Penning trap (see right part of Fig. 3.6). Mass measurements can be carried out in a similar way. The ions are ejected after a chosen number of revolutions and detected by an ion detector, which can be moved into the beamline and is then located at the position of the Bradbury-Nielsen gate. In that way, the total flight time can be measured, reaching measurement uncertainties of about two orders below the inverse resolving power, i.e. down to δm/m = 10−7 at ISOLTRAP. For short storage times, the resolving power of the apparatus is linearly increasing, because the bunch width ∆t can be kept approximately constant. Due to the presently unavoidable increasing time spread from transversal aberrations as mentioned above, a saturation occurs for longer storage times (see Fig. 3.7) and the maximum resolving power is an order of magnitude lower than that of a Penning-trap mass measurement with an observation time in the order of a second. In the linear region, the possible resolving power exceeds that of the Penning trap of ISOLTRAP by an order of magnitude and is thus highly preferable for nuclides with half lives below 100 ms. In such short-lived cases, the longer measurement duration in a Penning-trap can lead to an unacceptable ion loss by radioactive decay to reach the same measurement uncertainty [Wol13b]. The fast increasing resolving power of an MR-ToF MS as compared to a Penning-trap measurement can be understood by referring again to [Eli13] (see chapter 3.2), where the phase of the ion in the Penning trap is determined by the PI-ICR method. An MR-ToF MS provides the phase sensitivity of the ion’s motion in a natural way with the only difference that instead measuring the ions’ phase after a fixed time as in a Penning trap, the time for a fixed phase is measured in an MR-ToF experiment.

29

4 A new method of ion separation in Penning traps

As described in chapter 3.2, high-precision purification of the ions of interest from contaminant species may require a high-vacuum Penning trap in order to reach the wanted mass separation. Although more time consuming, the resolving power can exceed that of the mass-selective centering in buffer-gas filled Penning traps or that of an MR-ToF MS (refers to state-of-the-art devices). This is necessary if the ions are accompanied by very close lying isobars or nuclear isomers, where observation/excitation times in the order of seconds in a Penning trap must be used to detect a mass difference between the stored ions (if possible at all). The invention of mass-selective centering in a buffer-gas filled Penning trap [Sav91] provided the first way to achieve a broadband ejection of all contaminant ions while selecting only a single species for being recovered from the trap by RF excitation at one chosen frequency. A quadrupolar RF field converts the initial magnetron motion of the wanted ions into cyclotron motion which is cooled in a helium buffer gas (see Fig. 3.5). To avoid the transmission of all unwanted species, the magnetron motion of all ions is increased beforehand to a radius larger than the exit hole by use of a dipolar excitation at the magnetron frequency. Due to the fact that only the wanted ions are moved to the radial trap center, only a single specific frequency has to be irradiated, which addresses the ions of interest. Unfortunately the buffer-gas environment leads to a reduced resolving power, which is due to a broadening of the resonance in the presence of damping effects [Geo11]. In a high-vacuum environment, this is not the case. The selected contaminants can be removed from the trap by a dipole excitation on the mass-dependent reduced cyclotron frequency ν+ of a certain contaminating species, where the resolving power depends only on the duration of the excitation pulse according to the Fourier limit (up to the limits of field imperfections). However, there is a bottleneck (and, thus, disadvantage) of this procedure: In case of multiple contaminant species all frequencies have to be addressed, either one after another (which is time consuming) or simultaneously by superposition of several signals. In most cases the contaminant species are unknown, where a single-pulse procedure covering an entire continuous region of frequencies for broadband ejection is needed, which provides a single gap for the ions of interest to keep them in the trap. This poses a particular challenge and was a long-standing problem in the past. The first successful approach to solve this problem was the creation of a complex wave- form that has to be calculated beforehand and delivers the wanted excitation scheme by Fourier transformation from frequency to time domain. The application of the signal in the time domain results in a dipole excitation at all frequencies in a limited region with a gap in the center for the wanted ion specie. The phases of the single waves are adapted in a way that the amplitudes in the time domain are not diverging by the demand of

31 4 A new method of ion separation in Penning traps

magnetron radius for non-resonant excitaon

cyclotron radius for resonant excitaon

magnetron radius for resonant excitaon Distance from trap axes radius of exit hole

Excitation time Figure 4.1: Schematic view of the magnetron and cyclotron radius for SIMCO excitation. The resonantly excited ions return to the trap axes and can be extracted from the trap through an exit hole (grey shaded region) while non-resonantly excited ions are radially ejected from the trap. Picture: remake from cumulative-thesis article [Ros12a].

close lying frequencies. This method is called stored wave-form inverse Fourier-transform (SWIFT) technique [Noe83; Far91; Gua96]. In practice, it is (unfortunately) difficult to create an arbitrarily large frequency region for ejection of contaminants and to obtain a high resolving power (i.e. a narrow frequency gap for the ion of interest) at the same time. In this doctoral thesis, an excitation technique has been developed which solves this issue in a natural way. It is based on the simultaneous superposition of a dipolar and a quadrupolar RF field. A dipolar excitation at the magnetron frequency of all ions increases the magnetron radius while, only for the mass of interest, a quadrupolar excitation at the cyclotron frequency νc converts this increasing magnetron motion into a cyclotron motion at the same time. Due to this simultaneous procedure, the wanted ions first leave the radial trap center and move to a larger radius, but return to the trap axis later and can be detected after extraction through a central hole in the end cap of the trap or, alternatively, can be further stored for subsequent measurements (see Fig. 4.1). This is not the case for all other (non-resonantly) excited ions, which are consequently (broadband) ejected from the trap due to the dipolar excitation. The method has been named “simultaneous magnetron and resonant conversion (SIMCO) excitation” [Ros12a] (cumulative thesis article). In parallel to the developments of this principle and the experimental implementation, a general analytical description of azimuthal excitation schemes for Penning-traps could be developed by M. Kretzschmar, which includes this combined excitation [Kre12; Kre13b]. In Figure 4.2, the response of the ion signal after 800 ms of SIMCO excitation is shown, where the frequency of the quadrupolar excitation is varied in the vicinity of the cyclotron frequencies of 156Eu and 156Dy ions delivered from ISOLDE. This measurement shows

32 90 80 70 60 50 40 30 156Eu 156Dy

Number of detected ions 20 10 0 4 4.5 5 5.5 6 6.5 7 7.5 8 Excitation frequency - 580880 / Hz

Figure 4.2: Number of detected ions extracted from the precision Penning trap as a function of the quadrupolar excitation frequency used for the SIMCO excitation scheme (lines to guide the eye). the successful separation of the two (close lying) isobars, which require a resolving power of at least R ≈ 350000 to be distinguished by full width at half maximum and are thus very challenging for state-of-the-art devices. The resolving power achieved in this measurement is about R = 600000. In conclusion, the new SIMCO excitation scheme provides a significant improvement for ion purification in a high-vacuum Penning trap, because only the knowledge of a single frequency is required and a broadband ejection of all contaminants is enabled in a natural way, previously only possible in a buffer-gas environment. A high-vacuum environment provides a higher possible resolving power. It also allows the treatment of species that explicitly prohibit contact with buffer-gas atoms as, e.g., highly-charged ions. A limit of the performance of SIMCO excitation is given by the relatively large radii that the wanted ions obtain during the excitation before they are moving back to the center, where field inhomogeneities farther away form the trap axes can shift the ions’ eigenfrequencies so that the re-centering process may be incomplete.

33

5 Space-charge effects in multi-reflection time-of-flight mass separators

Multi-reflection time-of-flight mass spectrometry is a fast and efficient method for mass separation providing resolving powers on the order of 105 with a processing time on the order of 10 ms [Wol13b]. It can be used for separation of different ion species and as a mass spectrometer by its own. In this chapter, the main focus will be on the purpose of ion separation/purification, which can be performed by use of a Bradbury Nielsen gate behind the MR-ToF device as discussed in chapter 3.3. In most of the cases, the ions of interest are accompanied by contaminant ions, which exceed the number of delivered ions of interest by far. This is due to the fact that the cross sections of producing very exotic ions in the target (and of their release from the target structure) is by far lower than for ions closer to stability. Unfortunately, for mass separation processes which are performed with any kind of ion trap, the success can be critically harmed by the Coulomb interactions between the stored ions. If the number of simultaneously stored ions in a trapping device is large, the ion-ion interaction becomes non-negligible and the trajectories of the ions are modified to a measurable extend. The separation/measurement precision which is required determines the maximum number of ions allowed simultaneously in the device, e.g. for measurements −12 of cyclotron frequencies in a Penning trap with a precision of δνc/νc < 10 , only single particles are allowed in the trapping device [Ulm15]. Not only the bare number of ions but also their spatial ion distribution (characterized, e.g. by the mean distance between the ions) determines to which extend the wanted process in the storage device is disturbed.

5.1 Investigation of space-charge effects in multi-reflection devices

For multi-reflection devices, the complex dynamics of ion motion under strong influence of Coulomb interactions (space-charge effects) is not fully understood at present. Pio- neering work on space-charge effects in MR-ToF MS has been performed a decade ago at the Weizmann institute in Israel, where the so called “self-bunching effect” has been discovered. This effect refers to a (counterintuitive) increase of ion density when strong repulsive Coulomb forces are present. Self bunching emerges as an interplay between the cloud expansion, which would happen by exclusively considering the Coulomb forces between the ions, and the dispersion of revolution time as a function of the ions’ kinetic energy (in longitudinal flight direction) ∂Trev/∂Ekin [Ped01; Ped02; Str03; Fro12; Ros13]. This effect can be exploited for mass-spectrometric purposes [Zaj03].

35 5 Space-charge effects in multi-reflection time-of-flight mass separators

However, for efficient mass separation addressing different ion numbers to be processed, self bunching is of disadvantage, because the conditions for the mirror potentials would have to be adjusted for every case to obtain the wanted trajectories. Furthermore, the situation becomes unfeasible when the masses of the different ions are close to each other like in case of isobars. Ions of different masses can be permanently confined in the initial ion cloud that consists of a mixture of different species. This effect is called “peak coalescence”, an expression originating from Penning-trap mass

UHV valve electron source MCP detector and mirror electrodes deceleration mesh linear Paul trap (previously 3D Paul trap) movable faraday cup in-trap lift

ionization and MR-ToF MS transport section detection chamber preparation section

U = 0V U = Ublock U ≈ -2000V

+

+ MCP +

kinec energy à mesh1 mesh2

Figure 5.1: Top: sketch of the MR-ToF MS setup at Greifswald. Ions are produced by electron- impact ionization of neutral gas in a linear Paul trap and cooled by an additional background of neutral helium atoms. The ions are then ejected and transported to the MR-ToF MS with a kinetic energy of about 2 keV and captured in the MR-ToF MS by use of an in-trap lift [Wol12b], where the kinetic energy during trapping in the MR-ToF MS is about 1 keV. Upon ejection from the MR-ToF MS, the ions can be detected by a micro-channel plate detector or a Faraday cup [Ros15b] (cumulative-thesis article). Bottom: illustration of the application of the counter- field method to measure the energy distribution of the ions. The number of detected ions is measured while the positive voltage Ublock of a deceleration section (two metal meshes) is increased until all ions are blocked. Due to the complex field distribution of metal grids [Ber89] the obtained spectrum is only a map of the real distribution of kinetic energies, where a shift of the center to higher energies (by up to 50 eV for this system) and an additional broadening of the distribution occurs in the spectra.

36 5.1 Investigation of space-charge effects in multi-reflection devices spectrometry, where different signal peaks obtained from FT-ICR measurements were found to merge to one, when many ions were present [Nai94; Han97; Bol09; Vla12], see also [Her11] for investigations in ISOLTRAP’s preparation Penning trap. For MR-ToF MS, peak coalescence has been investigated analytically within a one- dimensional model [Bol11]. Later on, this effect could be generated and observed using an MR-ToF setup operated at the University of Greifswald (see top of Fig. 5.1): Two ion 12 16 + 14 + species, C O and N2 , have been produced in a Paul trap [Maj04] and forwarded to an MR-ToF MS for mass separation. Time separated signals have been detected by shooting the ions to a ToF detector after 1.6 ms trapping time in the MR-ToF MS as shown in the top spectrum of Fig. 5.2, where the Coulomb interactions between the ions are still negligible. The number of ions stored in the Paul trap (thus in the MR-ToF MS) could be controlled by the amplitude of the guiding field in the Paul trap using a control voltage Ugen to feed an RF-amplification system. While increasing the number of initial ions in the Paul trap to a few thousand, a merging of the two signals has been observed resulting in a single ion signal (see bottom spectrum of Fig. 5.2)[Sch14]. Earlier investigations for peak coalescence have been performed in [Ros13] (cumulative- thesis article), where generation of peak coalescence has been performed at this setup for the first time. Additionally, peak coalescence has been reproduced by many-particle simulations using a modification of a simulation code, originally written for Penning traps, which employs a graphics card for calculations of ion-ion interactions [Van11]. Note that the terminology used in [Ros13] is slightly different from that used in [Ros14]

Ugen = 1.40V 0.2 0.1 CO+ N2+ 0

Ugen = 1.48V 0.2 0.1 CO+ N2+ 0

Ugen = 1.56V 0.2 ion signal / V 0.1 CO+ N2+ 0

Ugen = 1.64V 0.2 0.1 mixture 0 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 time of flight / µ s

Figure 5.2: ToF spectra, i.e. the ion signal as a function of the time of flight [Sch14]. The ions have been produced in a Paul trap and have been forwarded to an MR-ToF MS. At low ion numbers (top spectra), the two ion species with close-lying masses are separated in time of flight. For large ion numbers, the signals are not separated (bottom spectrum).

37 5 Space-charge effects in multi-reflection time-of-flight mass separators

0.5 1 block. volt. = 1900V

CO+ N+ 0 2 0.5 0.5 N+ CO+ block. volt. = 2005V 2

CO+ 0 Normalized area 0 0.5 block. volt. = 2055V 0.02 CO+ 0 Detector signal / V 0.5 0.01 block. volt. = 2105V N+ CO+

Derivative 2 0 0 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 -100 -50 0 50 100 150 Time of flight after ion ejection / µ s Blocking voltage - 2000 V

Figure 5.3: Left: ion signal as a function of the time of flight at different voltages Ublock for the blocking mesh (see text). Right: integrated and normalized ion signals as a function of Ublock, and first derivative of each cure for estimation of the kinetic-energy distributions (picture taken from [Sch14] and modified). Note that the obtained signal voltages from Fig. 5.2 and this figure depend on the detector parameters and can not be compared. and [Ros15b]. Additionally, the setup presented in [Ros13] contains a 3D Paul trap instead of the linear Paul trap presented in [Ros15b] and in Fig. 5.1. Furthermore, a significant energy transfer between two separated (intense) ion clouds occurs as a consequence of Coulomb interaction. This energy transfer has been observed in a condition where many ions were present in the MR-ToF MS, but where the ion 12 16 + 14 + species could still be resolved without peak coalescence ( C O and N2 as described above). The distribution of the kinetic energy of each ion species could be measured using a deceleration (metal) mesh in front of the detector (see bottom of Fig. 5.1), biased with the voltage Ublock, to block ions that have a lower kinetic energy than necessary to penetrate the mesh (counter-field method). In the left part of Fig. 5.3, one can see that 14 + the N2 ions are blocked for lower voltages Ublock as compared to the other species, even if the initial energy distributions given by the prior processes in the Paul trap are equal. A more extensive measurement, shown in the right part of Fig. 5.3, reveals an energy gap of about 100 eV (i.e. 10 percent of the total kinetic energy) between the ion species due to the Coulomb interactions during separation (not observed for low numbers of ions).

5.2 Avoiding space-charge effects in multi-reflection devices

The examples discussed above show that for on-line experiments, where successful mass separation is crucial, space-charge effects must be avoided. However, avoiding too many ions in the device at the same time complicates experiments that suffer from a particularly large abundances of contaminant ions, i.e. > 103 times more abundant

38 5.2 Avoiding space-charge effects in multi-reflection devices contaminants as compared to the ions of interest. In such cases, only very few separation cycles (with the maximum allowed number of ions) will provide an ion of interest as the probability is too low. At ISOLTRAP, the mass-measurement procedure in the precision Penning-trap has a duration in the order of a second. If, e.g., only every 100th cycle delivers an ion of interest, less than one event would be expected per minute and the mass measurement might not be successful after the limited on-line time provided by ISOLDE. In order to improve on such situations and to be able to handle strongly contaminated a)

ion mixture injecon

b)

isochronous transport

c)

switching to + + N2 CO bunching mode

d)

ejecon aer bunching

Figure 5.4: Sketch of the sequence of the delayed-bunching procedure: a) injection of the ion mixture as a defocused beam, b) isochronous transport of the ion distribution, c) enabling bunching mode to re-focus the ion cloud, and d) ejection of the separated ions after finishing the bunching procedure. ion beams, a new experimental method has been introduced that exploits more efficiently the fast separation process of the MR-ToF MS, which takes two orders of magnitude less time than the complete cycle: Before each mass measurement in the precision Penning trap (in the future also in parallel with the mass measurement in the precision trap), the beam from ISOLDE is taken several times (instead of only once) by rapid repetitions of the capture and separation cycle of the MR-ToF MS. The purified ions are forwarded

39 5 Space-charge effects in multi-reflection time-of-flight mass separators to the Preparation Penning trap where they are captured, accumulated (stacked) and cooled. The collected pure ensemble can then be forwarded to precision trap. This method of ion-bunch stacking has become possible by installation of a “heavy-duty” high-voltage switch, and by adjustment of the electrostatic potentials of the preparation Penning trap to enable multiple ion captures (partly opening of the trap for injection without loss of previously stored particles). By use of a hundred stacking cycles for each cycle of the precision-trap procedure, the total cycle duration increases by only a factor of two. Thus, this method increases the possible number ratio between contaminant ions and ions of interest by up to two orders of magnitude [Ros14] (cumulative thesis article). Another possibility to avoid space-charge effects has been investigated in the framework of a new idea of how to separate more simultaneously stored ions than achieved with the conventional MR-ToF MS method [Ros15b] (cumulative-thesis article). The new method makes use of the adjustable ToF-energy dispersion of the system. It allows to inject and trap a wide spatial distribution (see Fig. 5.4 a) of ions in axial direction (thus large ∆t) instead of the usual compressed cloud with small time distribution ∆t, while still enabling a high resolving power with short ion bunches at the end of the process. A wide spatial distribution means in turn a low ion density and, thus, a reduction of Coulomb-interaction strength. Intuitively, a large time spread ∆t of the ions means a low resolving power, but the new method makes use of the adjustable ToF-energy dispersion of the MR-ToF MS by a sudden change of the mirror potentials to bunch the ions (i.e. compressing the clouds and reducing the time spread): First, a dispersion-free transport (same revolution time for all ions of same mass) is performed. After a trapping time of choice, i.e. when the spatial difference of the centers of masses of the ion clouds (for different species) has grown larger than the minimal distribution achieved after the bunching (see Fig. 5.4 b/c), the mirror potentials are switched to “bunching mode” and the different ion clouds are compressed to small bunches at their center of mass (Fig. 5.4 d). When the minimum time spread is reached, the ions can be ejected as separated bunches.

40 6 The neutron shell effects at N = 32 and N = 34

The shell model is the central paradigm of nuclear physics today. Nuclei that exhibit certain special properties, such as an enhanced binding energy (relative to the average of their neighbors) or large energy gaps in the excitation spectrum are referred to as “magic nuclei” which in the shell model are associated to a closed-shell configuration. The con- cept of closed-shell configuration assumes that the protons and neutrons are orbiting in an effective potential, which can approximately be described by an independent-particle model. In this model, due to the presence of a large energy gap between closed nuclear shells, there is a minimal coupling of single-particle states at low energy. The isotopic chain of calcium with the magic proton number Z = 20 is one of the most important test benches for studying neutron shell effects as well as effective proton- neutron and neutron-neutron interactions. Between the neutron numbers that allow bound states for Ca isotopes are two of the “traditional” magic numbers, namely 20 and 28. The two isotopes 40Ca and 48Ca are thus prominent examples for so called “doubly-magic nuclei” which have closed shells for each of the two nucleon types according to the shell model. The experimental study of magic nuclei and, more important in recent research, the evolution of their properties with the isospin (proton-to-neutron asymmetry) provides valuable input for the understanding of nuclear forces (see [Sor08] for a review). In recent years experiments revealed an isospin-dependent weakening (or even vanishing) of the special properties of magic nuclei, which in the shell model was associated to the reduction of shell gaps [War04]. On the other hand, new nucleon numbers can determine the emergence of “magic” nuclear properties, where the neutron number N = 32 for Ca isotopes is such a case. The first experimental indication of special properties at N = 32 for Ca isotopes was found in 1985. The first excited (J Π = 2+) state of 52Ca was populated by beta decay of 52K (produced at ISOLDE). The excitation energy E(2+) of this state was measured by gamma-ray detection following the internal decay to the ground state [Huc85]. The measured E(2+) value was found to represent a local maximum in the Ca chain after the prominent shell closure at N = 28. The ν2p3/2 orbit (referring to neutrons with main quantum number n = 1, orbital angular momentum of l = 1 and total angular momentum j = 3/2) is completely occupied. This behavior of the E(2+) energy could thus be interpreted in the simple shell model as a surprisingly large gap above the ν2p3/2 orbit, contrary to the expectations of a small energy gap between the ν2p3/2 + filled at N = 32 and the following neutron orbit, ν1f5/2. In Fig. 6.1 the E(2 ) values in the vicinity of the calcium chain are shown. The effect for proton magicity is clearly visible, and significant large values for 48Ca, 52Ca, and 54Ca. The measurement of the increased E(2+) value of 54Ca is a recent achievement and can be interpreted as a new

41 6 The neutron shell effects at N = 32 and N = 34

26 4

3.5 24 Cr 3

22 Ti 2.5 / MeV )

2 + 20 Ca 2 ( E Proton number 1.5 18 Ar 1

16 0.5 22 24 26 28 30 32 34 36 38 Neutron number Figure 6.1: Energy of the first (2+) excited state as a function of the neutron number and the proton number in the vicinity of 52Ca.

shell closure also at N = 34 [Ste13]. A prominent shell-closure-like effect at N = 32 for calcium was confirmed for the first time by mass measurements of the ground state of 53,54Ca in 2013. A shell gap of 52 Dn ≈ 4 MeV has been measured, pointing to a new doubly magic nucleus Ca [Wie13]. Now, a first investigation of the N = 32 shell effect below the Z = 20 proton core was performed by mass measurements of exotic potassium isotopes, namely 52,53K[Ros15a] (cumulative-thesis article). Due to the very short half-life of 53K of only 30 ms, this mass measurement is a remarkable achievement of the ISOLTRAP experiment. The new measurements provide an important test of the quality of the N = 32 effect, be- cause potassium has an open proton shell, where, in addition, due to the odd number Z = 19 even an unpaired proton is present. In such systems, proton correlations become active and can create states at low excitation energies. The main reason for low-energy excitations is that the energy to break up a nucleon pair is not required. While such configurations can lead to a vanishing of the shell gap, the result of these mass measure- 51 ments was a Dn = 3.1(1) MeV shell gap for K. This is a smaller value than measured for 52Ca, but still proves a strong persistence of the N = 32 neutron-shell effect below Z = 20, which is a behavior known for traditional magic numbers. Thus, the obtained results support the hypothesis of 52Ca being a closed-shell nuclide. A phenomenological interpretation of the large shell gap at the neutron numbers N = 32 and N = 34 can be found in the shell-model picture by the effect of an attractive tensor force [Ots05] between the π1f7/2 proton orbit and the ν1f5/2 neutron orbit. A tremendous increase of the ν1f5/2 single-particle energy takes place when increasing the neutron-to-proton asymmetry by the removal of protons from the π1f7/2 orbit [Ste13] as shown in Fig. 6.2. In the standard nuclear shell model, the ν1f5/2 orbit is located 60 between the ν2p3/2 orbit (filled at N = 32) and the ν2p1/2 orbit, e.g. in the case of Fe which is close to stability. Above N = 32 the next neutrons would occupy the ν1f5/2

42 ν 1 f5/2 ν 1 f5/2 π ν π ν π ν π ν 2p1/2 2p1/2 2p1/2 2p1/2 2p1/2 2p1/2 2p1/2 2p1/2 (N = 34) π ν π ν π π 1 f5/2 1 f5/2 1 f5/2 1 f5/2 1 f5/2 1 f5/2

(N = 32) π ν π ν π ν π ν 2p3/2 2p3/2 2p3/2 2p3/2 2p3/2 2p3/2 2p3/2 2p3/2

π1 f7 2 ν1 f7 2 π1 f7 2 ν1 f7 2 π1 f7 2 ν1 f7 2 π1 f7 2 ν1 f7 2 / / / / / / / / (N = 28) 60Fe (Z = 26) 58Cr (Z = 24) 56Ti (Z = 22) 54Ca (Z = 20)

Figure 6.2: Schematic view of the change in single-particle energies from 60Fe to 54Ca. The weakening of the phenomenological tensor interaction strength is indicated by thinning of the green arrows. The final configuration provides large shell gaps for both 52Ca and 54Ca. Picture: remake from [Ste13]. orbit accompanied by a small shell gap. However, when approaching the Ca chain, the π1f7/2 proton orbit is less occupied and eventually completely empty, which leads to an absence of the attractive interaction. The increase in energy is sufficient for a prominent shell effect for both, N = 32 and N = 34. An alternative reproduction of the experimental findings for Ca isotopes has been obtained with an interaction derived in chiral effective field theory, including a direct treatment of three-nucleon (3N) forces [Hol12; Hag12]. This approach played already a central role for the explanation of the neutron drip line at 24O[Ots10]. Three-nucleon forces are expected to play an important role in low-energy nuclear physics due to the fact that nucleons are not point-like particles. Chiral effective field theory is a framework in which many-body forces arise naturally from the expansion of the nuclear interaction [Bog10]. Approaches with phenomenological (entirely) two-body forces are however still very popular and benefit from a long tradition. It is also thought that in calculations with phenomenological two-body interactions including tensor forces, the latter effectively encode the physics arising from the neglected 3N degrees of free- dom [Ste13]. For example, an impressive reproduction of two-neutron separation energies from 52Ca to 54Ca could be obtained by many-body perturbation theory using 3N forces based on chiral effective field theory. However, the same properties can still be well reproduced by phenomenological two-body interactions [Wie13; Ste13]. The effect of the tensor interaction was also studied in the framework of mean-field theory, in order to improve the description of the properties of neutron-rich nuclei. It was shown through Skyrme-Hartree-Fock-Bogoliubov calculations that the effect of tensor forces depends strongly on the way how the interaction strength is fitted to the existing nuclear data [Gra14]. This issue has been illustrated for the measured potassium isotopes, where a too small empirical shell gap was obtained at N = 28 and N = 32, when a tensor force was taken into account. In turn, ab initio Gorkov-Green function calculations beyond N = 32 performed with an interaction deduced in chiral effective field theory and including 3N forces, reproduce a significant shell effect for 53K, although the empirical shell gap is overestimated (see [Ros15a], cumulative thesis article). Recent measurements of the g-factor of 51Ca have revealed a value which is not of single-particle type as would be expected considering a prominent shell closure N = 32 (which is the case, e.g., for 47Ca at the N = 28 shell closure) [Rui15]. The reproduction

43 6 The neutron shell effects at N = 32 and N = 34 of the experimental values requires including cross-shell excitations (see also [Isa11]), i.e. a mixed wave function with partial occupancy of other shells that are higher in energy than ν1p3/2. These findings point to a nuclear structure of more complexity than assumed by a bare closed-shell configuration in 52Ca. The situation has to be further clarified by measurements of other observables, e.g. B(E2) values that are presently only known up to 50Ca [Val09], or charge radii and magnetic moments beyond 52Ca.

44 7 Conclusion and Outlook

In this thesis, the first on-line mass measurements of the isotopes 52,53K have been performed. These measurements by multi-reflection time-of-flight mass spectrometry with the ISOLTRAP setup at ISOLDE/CERN are linked to previously measured masses of exotic Ca isotopes, which had shown an unexpected large neutron-shell gap at the neutron number N = 32 for the magic proton core Z = 20 [Wie13]. The new measure- ments provide the first exploration of the N = 32 neutron-shell closure below the proton number Z = 20. With a measured empirical two-neutron shell gap of about 3 MeV for 51K, the N = 32 gap is smaller as compared to that of 52Ca, which measures about 4 MeV, but is still significantly present. This confirms that the nuclear shell effect mea- sured for calcium isotopes is not a phenomenon purely raised by its closed-proton-shell configuration, but is also present in potassium isotopes that possess an open proton shell and an unpaired proton. The second main objective of this thesis was the development of new techniques for efficient mass separation in Penning traps and multi-reflection devices, because the success of nuclear mass measurements with high precision depends crucially on the purity of the ion ensemble. The two main difficulties that have been addressed are, first, when the masses of the ions of interest and the masses of contaminant ions are very similar, and second, when the contaminant ions are predominantly present in the beam from ISOLDE. For the removal of contaminant ions in a high-vacuum Penning trap with high resolving power, a new technique for mass separation has been developed. A simultaneous appli- cation of a dipolar radio-frequency field at the magnetron frequency of all ions (mass independent at leading order) and a quadrupolar radio-frequency field at the cyclotron frequency (highly mass dependent) of a chosen ion species provides a new way of ion purification. The result is that the magnetron radius of all ions is increased by the effect of the dipolar excitation, and, at the same time, the quadrupolar excitation leads to a conversion of the radial eigenmotions for the chosen species. The consequence of this simultaneous process is that the wanted ions move back to the trap axes while all other ions are radially ejected from the trap. The advantage of the new method is the simultaneous ejection of all unwanted species in a high vacuum, which otherwise have to be addressed by a dipolar excitation at different frequencies, or by use of complex waveforms if a broadband ejection is required. A comparable (general) broadband ejection as achieved by the new method was previously only achieved in buffer-gas filled Penning traps. Further technical developments were performed with ISOLTRAP’s multi-reflection time- of-flight mass separator. The goal was to improve on situations when dealing with highly contaminated beams from ISOLDE during on-line Penning-trap measurements. In such cases, the number of events obtained in a limited time can be very low for the reason that only a limited number of ions, which predominantly consist of contaminant

45 7 Conclusion and Outlook

ions, can be stored and separated in the multi-reflection device at a given time to avoid non-negligible Coulomb interactions between the ions. The situation at ISOLTRAP has been significantly improved by a more efficient use of the separation cycle of the multi-reflection device. The mass-separation cycle is by far shorter (on the order of 10 ms) than a Penning-trap mass measurement (on the order of seconds). Thus, the separation in the multi-reflection device has been decoupled from the Penning-trap mass measurement and is repeated rapidly, while the purified ions are accumulated, stored, and cooled in the preparation Penning trap of ISOLTRAP. The collected ions of interest can then be transferred to the precision-measurement trap. This method increases the possible ratio of the number of contaminant ions to ions of interest by up to two orders of magnitude, i.e. the ratio of the corresponding process durations. Additionally, space-charge problems in multi-reflection devices have been investigated by setting up an off-line apparatus at Greifswald. The dynamical effects of ions in multi-reflection devices under non-negligible Coulomb interactions have been investigated in order to search for possibilities for improvements on such situations. This resulted in a new method of manipulating the ion densities in the device. The ions move in a cloud with large spatial extend for the major part of the trapping time and can later be compressed to small bunches for high-resolution mass separation. Proof-of-principle measurements have been performed with a low number of stored ions, where successful isobar separation has been demonstrated.

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57

9 Cummulative thesis articles

9.1 Author contributions

Ros12: Buffer-gas-free mass-selective ion centering in Penning traps by si- multaneous dipolar excitation of magnetron motion and quadrupolar exci- tation for interconversion between magnetron and cyclotron motion, M. Rosenbusch, K. Blaum, Ch. Borgmann, S. Kreim, M. Kretzschmar, D. Lunney, L. Schweikhard, F. Wienholtz and R.N. Wolf, Int. J. Mass Spectrom. 325-327, 50-57 (2012) M. R. and L. S. invented the method, M. R. performed the measurements and evaluated the data, M. K. performed calculations for the presented paper. M. R. and L. S. prepared the manuscript. The manuscript was edited by all coauthors.

Ros14: Ion bunch stacking in a Penning trap after purification in an elec- trostatic mirror trap, M. Rosenbusch, D. Atanasov, K. Blaum, Ch. Borgmann, S. Kreim, D. Lunney, V. Manea, L. Schweikhard, F. Wienholtz and R.N. Wolf, Applied Physics B 114, 147-155 (2014) M. R., V. M., R.N. W. and F.W. invented the method. R. W. and F. W. installed the hardware for voltage switching presented in the paper. M. R., V. M., R.N. W. and F. W. performed the measurements, M. R. evaluated the data, V. M. performed the calculations presented in the paper. M. R., L. S. and R.N. W. prepared the manuscript. The manuscript was edited by all coauthors.

Ros13: Towards systematic investigations of space-charge phenomena in multi-reflection ion traps, M. Rosenbusch, S. Kemnitz, R. Schneider, L. Schweikhard, R. Tschiersch and R.N. Wolf, AIP Conf. Proc. 1521, 53-62 (2015) M. R and, R.N. W. set up the apparatus, M. R. prepared and performed the mea- surements, M. R. performed the presented many-particle simulations, S. K. installed the simulation hardware and libraries, M. R. and L. S. prepared the manuscript. The manuscript was edited by all coauthors.

Ros15b: Delayed bunching for muti-reflection time-of-flight mass separa- tion, M. Rosenbusch, P. Chauveau, P. Delahaye, G. Marx, L. Schweikhard, F. Wienholtz and R.N. Wolf, AIP Conf. Proc. 1668, 050001 (2015) M. R. invented the method and performed the measurements, M. R. and L. S. prepared the manuscript. The manuscript was edited by all coauthors.

59 Ros15a: Probing the N = 32 Shell Closure below the Magic Proton Number Z = 20: Mass Measurements of the Exotic Isotopes 52,53K, M. Rosenbusch, P. Ascher, D. Atanasov, C. Barbieri, D. Beck, K. Blaum, Ch. Borgmann, M. Breitenfeldt, R.B. Cakirli, A. Cipollone, S. George, F. Herfurth, M. Kowalska, S. Kreim, D. Lunney, V. Manea, P. Navrátil, D. Neidherr, L. Schweikhard, V. Somà, J. Stanja, F. Wienholtz, R.N. Wolf and K. Zuber Phys. Rev. Lett. 114, 202501 (2015) M. R., D. B., Ch. B., R.B. C., S. K., D. L., V. M., D. N., J. S., F. W. and R.N. W. performed the experiment. M. R. and F. W. performed the data analysis. C. B., A. C., P. N. and V. S. performed the GGF calculations. V. M. performed the DFT calculations, M. R., K. B., L.S., C. B. and V. S. prepared the manuscript. The manuscript was edited by all coauthors.

Obige Angaben werden bestätigt.

9.2 Buffer-gas-free mass-selective ion centering in Penning traps by simultaneous dipolar excitation of magnetron motion and quadrupolar excitation for interconversion between magnetron and cyclotron motion, Int. J. Mass Spectrom. 325-327, 50-57 (2012)

60

International Journal of Mass Spectrometry 325–327 (2012) 51–57

Contents lists available at SciVerse ScienceDirect

International Journal of Mass Spectrometry

j ournal homepage: www.elsevier.com/locate/ijms

Buffer-gas-free mass-selective ion centering in Penning traps by simultaneous

dipolar excitation of magnetron motion and quadrupolar excitation for

interconversion between magnetron and cyclotron motion

a,∗ b,c b b,d e f

M. Rosenbusch , K. Blaum , Ch. Borgmann , S. Kreim , M. Kretzschmar , D. Lunney ,

a a a

L. Schweikhard , F. Wienholtz , R.N. Wolf

a

Institut für Physik, Ernst-Moritz-Arndt-Universität, 17487 Greifswald, Germany

b

Max-Planck-Institut für Kernphysik, 69117 Heidelberg, Germany

c

Physikalisches Institut, Ruprecht-Karls-Universität, 69120 Heidelberg, Germany

d

CERN, 1211 Geneva 23, Switzerland

e

Institut für Physik, Johannes Gutenberg-Universität, 55099 Mainz, Germany

f

CSNSM/IN2P3, Université de Paris Sud, 91405 Orsay, France

a r t i c l e i n f o a b s t r a c t

Article history: A new excitation scheme of the radial ion-motional modes is introduced for Penning-trap ion-cyclotron-

Received 13 April 2012

resonance experiments. By simultaneous dipolar excitation of the magnetron motion and resonant

Received in revised form 13 June 2012

quadrupolar excitation for the conversion between magnetron motion and cyclotron motion, a mass-

Accepted 13 June 2012

selective recentering of the ions of interest is performed while all other (contaminant) ions are ejected

Available online 23 June 2012

from the trap. This new technique does not rely on the application of a buffer gas as presently used [G.

Savard, St. Becker, G. Bollen, H.-J. Kluge, R.B. Moore, Th. Otto, L. Schweikhard, H. Stolzenberg, U. Wiess,

Keywords:

Physics Letters A 158 (1991) 247] and will thus prevent charge-exchange reactions and damping of the

Penning trap

motion that decreases mass resolving power.

Simultaneous excitation

© 2012 Elsevier B.V. All rights reserved.

Mass-selective ion centering

1. Introduction selection, all ions are first excited with a dipolar field to a large mag-

netron radius. The ions of interest are then excited resonantly with

High-resolution mass separation is essential for many mod- a quadrupolar field at the sum of the magnetron and the reduced

ern rare-ion experiments. Together with the ions of interest, ion cyclotron frequency. Thus, their magnetron motion is converted to

sources typically deliver a mixture of other species. However, a cyclotron motion, which is damped by buffer-gas collisions. This

pure ensemble is often crucial for the accuracy of the experimental brings the ions of interest back to the trap axis whereas all others

results. In particular, mass-selective ion centering in Penning traps move even further out as the damping of their magnetron motion

by a combined application of quadrupolar excitation and buffer-gas leads to larger magnetron radii [1,9]. The presence of a buffer gas

cooling [1] has long been the method of choice. It reaches resolving has the advantage that the ions’ phase space can be reduced down

5

powers on the order of R = 10 [2,3], and is routinely employed as a to the temperature of the gas during the separation process. How-

preparatory step for precision Penning-trap mass measurements of ever, the very presence of buffer gas limits the achievable resolving

short-lived nuclei [4,5]. It has also been quickly transferred to the power of this technique [3,10].

field of (Fourier transform) ion cyclotron resonance (FT-ICR) mass Many experiments, e.g., in nuclear spectroscopy [11,12] or mass

spectrometry [6] where it is now used for analytical applications measurements of short-lived radionuclei [4,5] necessitate isomer-

[7,8]. ically pure ion ensembles. The preparation of such ion ensembles

6

The success of Penning-trap experiments lies in the ability to can require resolving powers of more than R = 10 , which is only

carefully manipulate the trapped-ion motion. Three eigenmodes achievable under ultra-high vacuum conditions. In addition, for

can be distinguished: the trapping motion in the axial direction experiments where the quality of the vacuum plays a central role

and in the radial plane the cyclotron and the (lower-frequency) (e.g., experiments with highly charged ions), buffer-gas-free sepa-

magnetron motion. In the standard method of buffer-gas assisted ration techniques are needed.

Buffer-gas-free ion selection in Penning traps can be performed

by dipolar excitation of the cyclotron motion, however the corre-

∗ sponding reduced cyclotron frequencies of all contaminants must

Corresponding author.

E-mail address: [email protected] (M. Rosenbusch). be identified. While there are elegant solutions in the form of the

1387-3806/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.ijms.2012.06.008

52 M. Rosenbusch et al. / International Journal of Mass Spectrometry 325–327 (2012) 51–57

2. Theoretical background

The motion of an ion with mass m and charge q in a Penning trap

is composed of three independent modes, an axial oscillation at the

frequency z = ωz/2 and two radial circular modes, the magnetron

motion with the magnetron frequency − = ω−/2 (magnetron

radius −) and the cyclotron motion with the reduced cyclotron

frequency + = ω+/2 (cyclotron radius +) [17]. The SIMCO exci-

tation combines two effects: A radial dipolar excitation at the

magnetron frequency, i.e., d = ωd/2 = − increases the magnetron

radius of all ions. A quadrupolar excitation (frequency q = ωq/2)

at q = c = ωc/2 = q · B/(2m) = + + − results in a conversion of the

radial motional modes into each other [9,10,18]. Both oscillatory

fields are applied at the same time. The duration of this combined

excitation will be called t0.

The electric field strength Ed of the dipolar field is combined with

other quantities into a dipole coupling parameter C = qEd/2mω1

−1 2 2

= =

(dimension s ), where ω1 ωc − 2ωz ω+ − ω−. Similarly,

Fig. 1. Magnetron (red solid line) and cyclotron radius (red dashed line) as a func-

tion of time for on-resonance SIMCO excitation (see text); linear increase of the the strength of the quadrupolar field is represented by a coupling

−1



magnetron radius (blue dotted line) in the off-resonance case. The green shaded parameter g with dimension s , which is proportional to the volt-

region indicates the radius of the aperture of the endcap electrode.

age Vq (see Section 3) and also incorporates factors related to the

trap geometry [19]. In case of quadupolar excitation only, exactly

on resonance (ωq = ωc) an initially (t = 0) pure state of magnetron

motion is converted into a state of pure cyclotron motion when the

excitation has acted with strength g for a time tconv = /2g. This

notch excitation [13,14] and the SWIFT technique (Stored Wave-

time is called the ‘conversion time’ for a given g. If the field contin-

form Inverse Fourier Transform) [15], the contaminants have to

ues to act until t = 2tconv the cyclotron motion will be reconverted

be known unless exceedingly large frequency ranges have to be

into magnetron motion, and so on. Vice versa, we can decide that

covered. In contrast, the buffer-gas assisted selection addresses all

the quadrupolar field acts for a time t0. Then we adjust the strength

contaminant ions in parallel, since the magnetron frequency is (to

of the field to g(t0) = /2t0 to obtain the conversion of a pure mag-

first order) mass independent.

netron state into a pure cyclotron state of motion after time t0.

The present work introduces a buffer-gas-free mass-selective

When we double the field strength to g(t0) = /t0 the initial mag-

centering technique, which is based on the same principle, namely

netron motion will be converted into pure cyclotron motion after

magnetron excitation of all ions and resonant quadrupolar exci-

time t0/2 and it will be reconverted into magnetron motion after

tation of the ions of interest. However, instead of a sequential

time t0.

application of these two excitation modes, they are performed

Starting with an arbitrary initial magnetron radius −(t) =

t=0

simultaneously. Fig. 1 illustrates the resulting radii of the ion

−(0) ≥ 0 and with a zero initial cyclotron radius +(t) =

motions: for all ions that are off-resonance with respect to their t=0

+(0) = 0, the evolution of magnetron and cyclotron radius at the

conversion frequency the magnetron radius increases linearly as a 

time t during SIMCO excitation is given by [16]

function of time. In contrast, the magnetron motion of ions with 

on-resonance conversion frequency is simultaneously converted 2g ω t − i + i

R i ωRt ωRt

+(t) = −i sin −(0) + ie C (e 2 I+ − e 2 I−)

to cyclotron motion. Thus, the magnetron motion is reduced back ωR 2

to zero while the cyclotron radius increases up to a maximum of    (1a)

 

twice the magnetron maximum. If the simultaneous excitation is  

continued, the magnetron radius goes through another cycle while

the cyclotron radius is also reduced back to zero. Thus, the on- ωRt ı ωRt

−(t) = cos − i sin −(0)

resonance ions are brought back to the trap axis while all other

2 ωR 2

ions have been excited to a large magnetron radius. When the  

    

ions of interest are ejected axially through an aperture of the end-  ı − i ı + i

+ i ωRt ωRt

 ie C 1 + e 2 I+ + 1 − e 2 I−

cap electrode, they are separated from the off-resonance ions that ωR ωR

     have larger magnetron radii and are not transmitted through the (1b) aperture. 



This new procedure of SImultaneous Magnetron and resonant

−

Here ı = ωq ωc is the detuning of the angular excitation fre-

COnversion (SIMCO) excitation removes the necessity of the fric-

quency ωq with respect to the resonance frequency ωc and ωR =

tional buffer-gas force of the presently applied procedure. It can be

2 2

= +

implemented easily and behaves robustly with respect to the initial 2R 4g ı is the Rabi frequency, i.e., the frequency of a full

ion position of the ion cloud. As described below, off-line experi- motional cycle of the system in the absence of dipolar excitation of



ments have been performed at ISOLTRAP, where resolving powers the magnetron motion. The initial phase of the magnetron motion

5

exceeding R = c/ = 7 × 10 have been achieved with an excita- − is combined with the initial phase of the dipolar field d and the

tion duration below 350 ms at a cyclotron frequency c of about angle of the dipolar field direction (with = 0 for an excitation in

− −

1 MHz, where is the full-width at half-maximum (FWHM) of the x-direction) into a total phase = d − . The functions I+

the resonance curve (ion counts as a function of the quadrupolar- and I− are defined by:

excitation frequency). Before these measurements are presented t

(Section 4), Section 2 gives an overview of the results of a theoret-  iωt 1 iωt

I(t, ω) = dt e = (e − 1), (2a)

ical study [16] followed by the experimental setup and procedure iω

(Section 3). 0

M. Rosenbusch et al. / International Journal of Mass Spectrometry 325–327 (2012) 51–57 53

ı + ωR

I+ = I t, ω − ω− − , (2b) d 2 2  

ı ωR

I− = I t, ω − ω− − − . (2c) d 2 2

 

In the following, only the case ωd = ω− will be considered, i.e.,

2 i − (ωR ı)t I+ = (e 2 − 1) (3a)

i(ωR − ı)

2 − i +

(ωR ı)t

I− = − (e 2 − 1) . (3b)

i(ωR + ı)

2.1. On-resonance excitation for −(0) = +(0) = 0

For on-resonance excitation (ı = 0), the expression for the Rabi

2 2

= =

+ =

frequency simplifies to ωR 2R 4g ı 2g and the Eqs.

(1a) and (1b) become

 Fig. 2. Magnetron (solid line), cyclotron radius (dashed line) and sum of radii (dotted

line) as a function of the excitation time for on-resonance SIMCO excitation. (a) One

i 2C

=

+(t) = −i sin(gt) · −(0) + e · (1 − cos(gt)) (4a) complete motional period with t0 4tconv and g = 4/2t0. (b) Two complete motional

g

=

periods within the same time tconv t0/8, corresponding to g = 8/2t0. (c) Three

  motional periods t0 = 12tconv and g = 12/2t0. All curves are normalized to 2Ct0/,

 2C 

i the maximal cyclotron radius of (a).

−(t) = cos(gt) · −(0) + ie · sin(gt) . (4b)  g 

 

If the ion starts on the axis of  the Penning trap, i.e., 2.2. Off-resonance excitation for +(0) = −(0) = 0

 i 

−(0) = +(0) = 0, the phase factors e become irrelevant and the

Eqs. (4a) and (4b) further simplify to In Fig. 3 the radii are shown as a function of q for SIMCO exci-

tation. In Fig. 3a the excitation duration is such that in resonance

2C

= −

+(t) (1 cos(gt)) (5a) ( = ) one complete motional period is performed. In case of off-

g q c

resonance excitation, both radii are increasing significantly (thus

2C also the sum), i.e., the ions are ejected radially from the trap.

−(t) = sin(gt) . (5b)

g If a stronger quadrupolar excitation is used and, e.g., two com-

  plete motional periods are performed within the excitation time as

Both radii oscillate between zero and the maximum values given

  shown in the Fig. 3b, the width of the resonance increases for the

by

magnetron radius, whereas for the cyclotron radius it remains very

2C similar. However, note that there are off-resonance frequencies

max(−(t)) = , (6a)

±

g ı = 3/t0, where the ions are also recentered. Thus, this com-

bination of excitation amplitude and duration is, in general, not

4C

suitable for broad-band ejection of contaminant ions. However, max(+(t)) = , (6b)

g

an increased number of conversion periods may be preferable in

certain situations as shown in Section 4.

which depend on the strength of the quadrupolar excitation as

If a further period is added (three motional periods) as shown

compared to the dipolar excitation. The maximum of the sum of

in Fig. 3c, the ions can be ejected in a broader frequency region

the two radii, i.e., the maximum extension of the ion trajectory

around the center frequency if the strength of the dipolar excitation

from the trap axis is given by

√ C

max((t)) = max(−(t) + +(t)) = (1 + 2)2 . (6c)

g

In Fig. 2a the evolution of the radial motional modes for on-

resonant SIMCO excitation is shown for a complete motional

period.

After 2tconv the cyclotron radius reaches the maximum value

(4C/g = 2Ct0/) and after 4tconv the ion returns back to trap axis.

This situation (t/tconv = 4 of Fig. 2a) will be considered as the end

of one complete motional period in the sense of SIMCO excitation.

When the coupling constant is doubled (g → 2g), while keeping the

excitation time t0 constant, the period is divided by two (Fig. 2b),

i.e., in the same absolute excitation time t0 the full motional period

is performed twice. If the strength of the dipolar excitation is kept

the same, the maxima of the radii (max((t)) ∝ C/g) are reduced

by a factor of two, i.e., by the factor that the coupling constant is

increased. In order to achieve the same radii while changing the

excitation strength g, the strength of the dipolar field has to be

scaled as well to keep C/g constant. An increase of quadrupolar exci-

Fig. 3. Magnetron (solid line), cyclotron radius (dashed line), and sum of the two

tation strength by a factor of three as compared to Fig. 2a leads to

radii (dotted line) as a function of the normalized frequency detuning ı/2t0 at the

a three times shorter motional period (Fig. 2c), and so forth.

end of the excitation time (t = t0) for (a) g = 4/2t0, (b) g = 8/2t0, and (c) g = 12/2t0.

54 M. Rosenbusch et al. / International Journal of Mass Spectrometry 325–327 (2012) 51–57

Fig. 5. Magnetron (solid line), cyclotron radius (dashed line), and sum of radii (dot-

Fig. 4. Magnetron (solid line), cyclotron radius (dashed line), and sum of radii (dot-  

ted line) as a function of the normalized frequency detuning ı/2t at the time t = t

ted line) as a function of the excitation time for on-resonance SIMCO excitation 0 0

for initial conditions as in the top of Fig. 4 and for (a) g = 4/2t0, (b) g = 8/2t0, (c)

with = − /2 (top) and = 0 (bottom), both with the same initial magnetron radius

g = 12/2t0. Scaling of radii as in Fig. 3.

(coupling parameter: g = 4/2t0).

3. Experimental setup and procedure

is sufficient. Also in this case, the ions are recentered ( = 0) at other

The SIMCO excitation has been investigated experimentally

frequencies q =/ c, but these frequencies are farther away from

with the precision Penning trap of the ISOLTRAP experiment. The

the center frequency as compared to Fig. 3b, i.e., ı = ±16/t0 (not

ISOLTRAP setup, in particular the sections made use of in the

in the figure). The resolving power is still close to that of the other

present study, has been reviewed recently and details can be

two cases. Note that the amplitudes of the radii are similar for all

found in Ref. [20]. The hyperbolic trap electrodes have dimensions

the resonances shown in Fig. 3. This is achieved by adjusting the

0 = 13.00 mm (ring) and z0 = 11.18 mm (endcaps) with central end-

strength of the dipolar excitation for n SIMCO cycles by Cn = nC0

cap bores of 1 mm radius for injection and ejection of the ions. The

with respect to that of the quadrupolar excitation, i.e., C/g = const

magnetic field is about B = 5.9 T and the effective trapping-potential

(see Section 2.1). 85 +

depth at the trap center was U0 = 8.4 V. Singly charged Rb ions

are delivered to this trap as a clean ensemble from the prepara-

tion Penning trap of ISOLTRAP and are captured in flight [21]. The

2.3. Extension to finite initial magnetron radii, −(0) ≥ 0

initial position is reproducible and results in a defined magnetron

radius and phase −. The phase d of the dipolar excitation can be

In a more realistic description, the ions are no longer initialized

adjusted accordingly [22] to achieve = − /2.

on the trap axes, i.e., an initial magnetron radius has to be consid-

The ring electrode is split into four segments (see Fig. 6). The

ered. In this case, the phase of the dipolar excitation is no longer

dipolar magnetron excitation with frequency − and voltage ampli-

automatically = − /2. In Fig. 4, the evolution of the radii is shown

tude Vd is applied to ring segment 1 and the inverted signal to ring

for two cases of the dipolar excitation phase and −(0) = C/g =/ 0.

segment 3. The quadrupolar conversion excitation with frequency

This initial magnetron radius is one fourth of the maximal cyclotron

q and voltage Vq is applied on ring segments 1 and 3 (added to

radius (see Section 2.1), which represents a considerably large value

dipolar signal), and the inverted signal on ring segments 2 and 4.

for realistic injections into the Penning trap.

The inversion and addition of the signals is realized using two lin-

The top of Fig. 4 shows the case of dipolar excitation in phase

ear fan-in/fan-out devices (LeCroy 428F). For the dipolar excitation

with = − /2. The evolution of the radii is different as compared

a frequency generator (Stanford Research Systems DS345) in the

to Fig. 2a, where the decrease to a radius of zero (± = 0) of the

so-called burst mode is used with a well-defined initial phase d

two radial modes is now asynchronous. The sum of radii cannot be

and fixed number of magnetron oscillations Nmag defining the exci-

= 

decreased to zero, but at the time t t the sum of radii reaches

0 tation time. The signal for the quadrupolar excitation (frequency

a minimum value (zero magnetron radius, finite cyclotron radius)

generator: Agilent 33250A) is applied at the same time using a high-

smaller than the sum at the beginning of the excitation. Thus, this

frequency switch. For a negligibly small initial cyclotron radius [23],

scenario can nonetheless be exploited for the application of the

this second frequency generator does not require synchronization



SIMCO excitation scheme. The time t is the most suitable moment

0 with the experimental sequence.

to stop the excitation. In the bottom of Fig. 4 an example for = 0 is

In order to analyze the radial position of the ions after excitation

shown (initial magnetron radius as in top). In this particular case,

they are ejected through the central aperture of the detector-side

the sum of the two radii cannot be decreased. An extended discus-

endcap, pass a system of drift tubes and hit a microchannel-plate

sion for different phases is beyond the scope of the present work

(MCP) detector. Ions with radial positions larger than the radius of

but can be found in the theoretical study of Ref. [16]. So far, the case

the exit hole are lost as they hit the electrode during ejection. The

= − /2 has been found to be the only scheme of practical interest.

dipolar-excitation voltage V is chosen high enough that all ions

 d

Fig. 5 shows the resonances for t = t in case of conditions as in

0 are lost that do not experience a resonant quadrupolar excitation

the top of Fig. 4. The resonance shapes are similar to those discussed

(for the present experiment even up to one order of magnitude

above (Fig. 3). The difference to the ideal case (of −(0) = 0) is a

higher). In the realistic case of deviations from the ideal trajectory

slight increase of the maximal radii during the motion and the fact

(trap imperfections etc.) and a non-zero initial magnetron radius,

that a small residual cyclotron radius remains even at the center

the voltage Vq for the quadrupolar excitation at a fixed excitation

frequency (ı = 0).

c time t0 has to be optimized. To this end, the quadrupolar-excitation

M. Rosenbusch et al. / International Journal of Mass Spectrometry 325–327 (2012) 51–57 55

Fig. 7. Normalized ion count as a function of the excitation frequency q. Top:

Nmag = 100, g ≈ 4/2t0. Bottom: Nmag = 200, g ≈ 4/2t0. Solid lines to guide the eye.

are not excited beyond the radius of the aperture. The trapping

fields deviate more and more from the ideal values as the ions move

further away from the trap axis.

For Nmag = 400, i.e., at the longest investigated excitation time

of t0 ≈ 327 ms, the use of one SIMCO conversion period (g ≈ 4/2t0)

(by dividing the excitation voltages by two as compared to the mea-

surements with Nmag = 200) did not show any further increase in

resolving power. Increasing, in addition, the voltage of the dipo-

Fig. 6. Technical scheme for the realization of the SIMCO excitation. Signals for

dipolar and quadrupolar excitation are superimposed at ring segment 1 and 3. lar magnetron excitation led to a loss of ions. Most probably the

limit in SIMCO excitation duration and resolution observed in the

present study is due to the frequency shift mentioned above: if this

frequency is set to the cyclotron frequency of the ions of interest

shift exceeds the Fourier width of the excitation, the on-resonance

(q = c) and the voltage Vq is adjusted for the maximum ion count,

condition is no longer fulfilled during the whole excitation period.

so that g is in the vicinity of 4/2t0, 8/2t0, . . .. Alternatively, the

 However, a workaround has been found by adding another exci-

→

excitation time for a fixed voltage can be optimized t0 t0 (see

tation period, i.e., by going to g ≈ 8/2t0. Fig. 8 shows a scan of the

Fig. 4) with a constant value of Vq.

quadrupolar excitation voltage for a fixed voltage of the dipolar

excitation. As a first step the ions have been brought back by use of

4. Results and discussion

≈

two complete periods with g 8/2t0 due to the smaller maximum

radius during the motion, where only a few ions have been detected

The performance of the SIMCO excitation has been investigated

≈

for g 4/2t0 (see Eq. (5)). As a second step the dipolar excitation

with respect to resolving power and ion efficiency, i.e., the number

voltage has been increased as long as high efficiencies could still be

of ions of interest detected in resonance after the excitation step

retained. This optimization resulted in the SIMCO resonance data

compared to the number of ions without any excitation. After opti-

shown in Fig. 9a and b. Fig. 9a shows a scan across a somewhat wider

mization of both excitation voltages Vd and Vq and the frequency of

frequency range, where the secondary peaks expected from Fig. 3b

the quadrupolar excitation, an efficiency above 90% was achieved

for all excitation times investigated (discussed in detail below).

In order to determine the resolving power for ion separation,

the frequency of the quadrupolar excitation has been scanned in

85 +

the vicinity of c of the ion of interest (only Rb in trap) while

monitoring the number of ions detected Nion(q). The resulting dia-

gram shows the so-called “count-rate resonance” from which

(FWHM) is determined.

For Nmag = 100, 200, 400 magnetron periods (excitation times

at − = 1078 Hz : 92 ms, 185 ms and 327 ms, respectively), count-

rate resonances have been taken. Fig. 7 shows the resonances for

Nmag = 100 and 200.

For both resonances the data have been taken under condi-

tions of Fig. 2a, i.e., one SIMCO conversion period. The FWHM of

the resonances are = 3.5 Hz for Nmag = 100, and = 2.5 Hz for

Nmag = 200. Note that the center frequencies of the resonances are

not the same. A possible explanation for this frequency shift is the

very large radius to which the ions are excited as compared, e.g.,

Fig. 8. Normalized ion count as a function of the quadrupolar excitation voltage Vq.

to the radii used for precision mass measurements, where the ions Solid line to guide the eye.

56 M. Rosenbusch et al. / International Journal of Mass Spectrometry 325–327 (2012) 51–57

Table 1

Summary of the experimental results: excitation times, FWHM of the frequency scans, resolving power for c ≈ 1 MHz, and further remarks on the type of excitation (periods,

strength) and measurement conditions.

Excitation time (ms) FWHM of resonance curve (Hz) Resolving power for c = 1 MHz Remarks

5

92 3.5 2.8 × 10 1 SIMCO period, g ≈ 4/2t0

5

185 2.5 4.0 × 10 1 SIMCO period, g ≈ 4/2t0

5

327 1.4 7.1 × 10 2 SIMCO periods, g ≈ 8/2t0, larger ion count

5

327 1.2 8.3 × 10 3 SIMCO periods, g ≈ 12/2t0

respectively. Furthermore, the limits for the maximum load of ions

[24] will be investigated for these scenarios.

Additionally, the applicability of the SIMCO excitation for preci-

sion mass measurements is still to be studied. For such an approach

the excitation parameters will have to be carefully chosen such that

the motional radii are kept as small as possible in order to avoid

the frequency shifts mentioned above. Combining the method of

simultaneous excitation with other recent innovations such as the

Ramsey [19,25–27] or the octupolar excitation [28–31] approaches

are also to be addressed.

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≈

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3

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European Physics Journal A 35 (2008) 1.

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[21] H. Schnatz, G. Bollen, P. Dabkiewicz, P. Egelhof, F. Kern, H. Halinowsky, L.

of the experimental parameters almost all ions have been recen-

Schweikhard, H. Stolzenberg, Nuclear Instruments and Methods A 251 (1986)

tered at the quadrupolar resonance frequency. Resolving powers in 17.

5

×

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P. Schmidt, L. Schweikhard, Journal of Physics B 36 (2003) 921.

behaves robustly with respect to the initial ion position in the trap

[23] M. Kretzschmar, International Journal of Mass Spectrometry 309 (2011) 30.

and with a load of a few hundred trapped ions as shown in the

[24] L. Schweikhard, K. Blaum, A. Herlert, G. Marx, European Journal of Mass Spec-

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[25] S. George, S. Baruah, B. Blank, K. Blaum, M. Breitenfeldt, U. Hager, F. Herfurth,

Further studies will be performed to test the applicability for

A. Herlert, A. Kellerbauer, H.-J. Kluge, M. Kretzschmar, D. Lunney, R. Savreux,

ion separation in case of different ion species, which require either

S. Schwarz, L. Schweikhard, C. Yazidjian, Physical Review Letters 98 (2007)

low or very high resolving powers, e.g., isotopes and isobars, 162501.

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Spectrometry 262 (2007) 33. ters 107 (2011) 152501. 9.3 Ion bunch stacking in a Penning trap after purification in an electrostatic mirror trap, Applied Physics B 114, 147-155 (2014)

68 Appl. Phys. B (2014) 114:147–155 DOI 10.1007/s00340-013-5702-0

Ion bunch stacking in a Penning trap after purification in an electrostatic mirror trap

M. Rosenbusch • D. Atanasov • K. Blaum • Ch. Borgmann • S. Kreim • D. Lunney • V. Manea • L. Schweikhard • F. Wienholtz • R. N. Wolf

Received: 2 July 2013 / Accepted: 16 October 2013 / Published online: 22 November 2013 Ó Springer-Verlag Berlin Heidelberg 2013

Abstract The success of many measurements in analyt- particular for the number of ion bunches captured as a ical mass spectrometry as well as in precision mass function of the ions’ lifetimes and the parameters of the determinations for atomic and nuclear physics is handi- experiment. capped when the ion sources deliver ‘‘contaminations’’, i.e., unwanted ions of masses similar to those of the ions of interest. In particular, in ion-trapping devices, large 1 Introduction amounts of contaminant ions result in significant system- atic errors—if the measurements are possible at all. We Electrostatic multi-reflection ion traps [1–3] are one of the present a solution for such cases: The ions from a quasi- most recent developments for ion trapping. Several of these continuous source are bunched in a linear radio-frequency- devices have been constructed that cover a wide spectrum quadrupole ion trap, separated by a multi-reflection time- of applications ranging from cluster physics [4–9], of-flight section followed by a Bradbury–Nielsen gate, and molecular physics [10–13], electron collisions [14], high- then captured in a Penning trap. Buffer-gas cooling is used resolution mass separation [15–17] to precision mass to damp the ion motion in the latter, which allows a spectrometry like recent direct mass determinations in repeated opening of the Penning trap for a stacking of nuclear-physics experiments [18, 19]. mass-selected ion bunches. Proof-of-principle demonstra- The two latter applications exploit the mass-spectro- tions have been performed with the ISOLTRAP setup at metric advantages of multi-reflection devices, i.e., a mass ISOLDE/CERN, both with 133Cs? ions from an off-line ion resolving power R ¼ m=Dm ¼ t=2Dt increasing with the source and by application to an on-line beam of 179Lu? time-of-flight (ToF) t of stored ion bunches with a bunch ions contaminated with 163Dy16O? ions. In addition, an length Dt. If several ion species with individual mass-to- optimization of the experimental procedure is given, in charge ratios m/q are trapped simultaneously, the increas- ing differences in ToF while performingpffiffiffiffiffiffiffiffiffi multiple reflec- tions (revolution time: T / m=q) allow for mass M. Rosenbusch (&) L. Schweikhard F. Wienholtz separation with high resolving power, which then facili- R. N. Wolf tates an effective purification of ions for subsequent Institut fu¨r Physik, Ernst-Moritz-Arndt-Universita¨t, 17487 Greifswald, Germany experimental steps. With these multi-reflection time-of- e-mail: [email protected] flight mass separators (MR-ToF MS), resolving powers in excess of R = 105 can be reached within time scales in the D. Atanasov K. Blaum Ch. Borgmann S. Kreim order of ten milliseconds [13, 15–19]. Max-Planck-Institut fu¨r Kernphysik, 69117 Heidelberg, Germany Recently, a particularly high interest came from nuclear- physics experiments at radioactive ion beam facilities, S. Kreim where a fast and efficient separation of the ions of interest CERN, 1211 Geneva 23, Switzerland from simultaneously delivered isobaric contaminants is D. Lunney V. Manea required. However, cleaning at high resolving powers CSNSM/IN2P3, Universite´ de Paris Sud, 91405 Orsay, France means, in turn, a high sensitivity to Coulomb interactions 123 148 M. Rosenbusch et al. between the trapped ions. This leads to a limitation with In the 1990s, the accumulation and buffer-gas cooling of respect to the maximum number of ions that can be pro- charged-particle bunches in a Penning trap have been cessed simultaneously [20]. If this number is exceeded, the demonstrated, e.g., in case of gold clusters [32], with purification is not effective, i.e., the ions of interest cannot rubidium ions in the preparation Penning trap of the be separated. On the other hand, decreasing the total ISOLTRAP setup [26], and, more recently, such accumu- number of ions at a given time is inefficient, in particular if lations have been employed at JYFLTRAP [33]. However, the experimental steps after the purification are much more in the present investigation, we purify the ion bunches in an time-consuming than the purification steps. Only very few MR-ToF MS before they enter the Penning trap to be ions of interest can then be investigated during the limited accumulated. time of an on-line experiment. In the following, the ISOLTRAP setup and event For example, precision mass measurements of short- sequence for the new stacking method are described and lived nuclides in Penning traps [21, 22] suffer from such demonstrated with off-line and on-line measurements. In contamination scenarios. At the ISOLTRAP mass spec- addition, the realization of the high repetition rate of the trometer at ISOLDE/CERN [23, 24], beam purification stacking loop is described in detail. Finally, the optimal methods have been developed and studied since more than number of stacking loops for mass measurements of short- two decades [25–28]. The ISOLTRAP setup employs a lived nuclei as a function of the ions’ half-life, release time linear radio-frequency-quadrupole (RFQ) ion trap for from the production target, and durations of the experi- bunching of the quasi-continuous on-line ISOLDE ion mental procedures is investigated. beam [29], a recently installed MR-ToF MS [17], and a preparation Penning trap for mass-selective buffer-gas cooling [25] as devices for beam preparation and purifi- 2 Experimental setup and procedure cation. The actual mass spectrometry is performed in a precision Penning trap by use of the time-of-flight ion- All measurements have been performed with the ISOL- cyclotron-resonance (ToF-ICR) method [30, 31]. Recently, TRAP setup at ISOLDE/CERN. The components relevant the MR-ToF MS at the ISOLTRAP setup has reduced the for the present study are shown in Fig. 1 and are described ion-separation time by an order of magnitude for resolving briefly in the following. powers similar to that of the preparation Penning trap At ISOLDE, radioactive atoms are produced by impact which, previously, was the purification device of choice. of 1.4-GeV protons on a thick target, released by thermal In the following, a method is introduced, where the ion diffusion, ionized, accelerated, and delivered as a 30–60- purification phase, using the RFQ and MR-ToF MS, is keV quasi-continuous ion beam for durations controlled by decoupled from all further processes of the ToF-ICR mea- the ‘‘ISOLDE beamgate’’ [34]. When reaching the ISOL- surement cycle. In this new experimental sequence multiple TRAP setup, the ions are electrostatically decelerated to a ion bunches, each purified by the MR-ToF device, are few eV and injected into a radiofrequency quadrupole accumulated and cooled in the preparation Penning trap, (RFQ) for accumulation, buffer-gas cooling, and bunching. comparable to the use of an accumulation RFQ, as previ- After the ejection of ion pulses from the RFQ toward the ously suggested [15]. In contrast to an RFQ approach, MR-ToF MS, the (potential) energy of the ions is adjusted however, the present method allows to use the Penning trap from the HV-potential of the RFQ to the ground potential as a second high-resolution cleaning stage for further sup- of the ISOLTRAP setup by a pulsed HV drift tube. The pression of contaminations. This new approach improves ions are then captured in the MR-ToF MS by use of an in- the performance of the ISOLTRAP setup significantly, in trap lift [35] and trapped until a sufficient separation particular in the cases where the ions of interest have half- between the ions of interest and the contaminants is lives larger than the duration required for the ion separation achieved. Subsequently, the ions are ejected toward a in the MR-ToF MS, but where the ions come at low pro- Bradbury–Nielsen gate (BNG) [17, 36], which deflects the duction rates relative to a high amount of accompanying contaminating ions in closed mode, whereas the ions of contaminations. The fast ion separation in the MR-ToF MS interest are transmitted toward the preparation Penning trap is repeated several times and acts as a pulsed ion source for in open mode. In the preparation Penning trap, mass- the preparation Penning trap, to which the purified ion selective resonant buffer-gas cooling can be applied bunches are transferred for accumulation (stacking). This (duration typically 100–500 ms) to remove, e.g., residual procedure multiplies the number of ions of interest available contaminants and to cool and center the ions, before they for the subsequent ToF-ICR detection by the number of are transported to the precision Penning trap (not shown in applied accumulation steps (stacking loops), while the total Fig. 1). The mass measurement is then performed via duration of the ToF-ICR measurement cycle is only determination of the cyclotron frequency with the ToF-ICR increased by a small fraction of this factor. technique (duration typically 100 ms to 1 s). In general, 123 Ion bunch stacking in a Penning trap 149

to precision Penning trap

MCP detector

preparation Penning trap reference B = 4.7T ion source HV platform

RFQ cooler and buncher pulsed MR-TOF BN drift mass separator beam tube gate

ISOLDE ion beam

Fig. 1 Sketch of the horizontal beamline and the preparation Penning trap of the ISOLTRAP setup

Fig. 2 Flow diagram of one ToF-ICR measurement cycle, which consists of several stacking loops and the further processing of ions in the Penning traps: a final cleaning in the preparation Penning trap and ToF-ICR detection using the precision Penning trap

ToF-ICR resonance measurements consist of several (tens MR-ToF-MS ? BNG purification, and the capture in the of) cycles where different excitation frequencies of a preparation Penning trap for accumulating the mass- quadrupolar RF field are used to probe the influence on the selected species by lowering the voltage at the injection- motion of the ions in the measurement Penning trap. The side end-cap electrode (Fig. 3a). After the end-cap elec- resonance curve consists of the mean time-of-flight of the trode is activated again, the ions thermalize due to buffer- ions after ejection from the trap toward a micro-channel gas collision at typically p & 10-4 mbar, resulting in a plate detector as a function of the excitation frequency [31, reduction of the axial ion motion amplitudes (Fig. 3b) 37]. while performing the next stacking cycle. Therefore, ions The new event sequence of the experimental cycles is can be injected again by lowering the end-cap electrode characterized by a repetitive structure with the duration without losing the previously captured ion bunches tloop (see Fig. 2). This loop comprises the RFQ bunching, (Fig. 3c) and are cooled as well (Fig. 3d). In case of

123 150 M. Rosenbusch et al.

(a) 12

10 (b) 8

6 (c) 4 number of detected ions (d) 2

0 0246810 number of stacking loops Fig. 3 Potential along the axis of the preparation Penning trap (solid lines). a capture mode during arrival of the first ion bunch: trap Fig. 4 Average number of detected ions after ejection from the (partially) opened for injection of purified ions, b trapping mode: preparation Penning trap as a function of the number of stacking storage of ions and cooling of ion motion by buffer gas (indicated by loops. Solid line linear fit to the data. Dashed line expected increase in dashed line) between capture events, c capture mode during the ions for ideal transfer, capture, cooling, and storage in the preparation arrival of another ion bunch, and d cooling of next ion bunch Penning trap medium-mass ions of m & 100 u, the time required for a previous HV switch that was connected to the pulsed drift sufficient reduction of their kinetic energy is on the order of tube was tested with up to ten stacking loops. The number 10 ms. This allows a repetition rate of up to 100 Hz for the of ions accumulated in the preparation Penning trap as a stacking loop structure. After repeating the loop n times function of the number of stacking loops was measured by (duration: n 9 tloop), the accumulated purified ions ejecting the ions toward a micro-channel plate (MCP) undergo a final high-resolution cleaning step (mass selec- detector. For a substantially higher throughput of purified tive buffer-gas cooling) and the subsequent ToF-ICR ions as compared to a single injection in the preparation detection, where the duration of both last steps will be Penning trap, the stacking loop duration should be signif- called tmeas. The additional cleaning is applied to remove icantly shorter than the typical storage times of ions in the contaminants that may have survived the earlier cleaning preparation Penning trap for mass-selective buffer-gas stage (limited suppression factor of the BNG [17]) or that cooling. However, when the loop length was decreased, may be created during the stacking by charge transfer already a duration of 100 ms (for 10 pulses per second) reactions or in-trap decay [38]. A high repetition rate of the turned out to be too fast for an efficient transport of ions loop sets special demands on the pulsing capability of the due to the recovery time of the HV switch (see Fig. 4). This HV-pulsed drift tube. Thus, the corresponding switching leads to inadequate transport energies of the ions on their system had to be upgraded (for details see Sect. 4). way through the system, which causes ion losses. As a result, the number of ions obtained when adding additional stacking loops is not the product of loop number 3 Experimental results times the number of ions obtained in the first loop as marked by the dashed line. Instead, the average ion number In the following, several results from both off-line tests and as a function of number of loops increases only by a on-line applications of the MR-ToF MS/Penning trap stacking fraction of the initial ion bunch (solid line). method are described. In particular, initial tests with the existing hardware (Sect. 3.1) showed that a faster high-voltage 3.2 Performance with the new HV switch system switch for the drift tube behind the RFQ was essential for the implementation of the stacking method. The new switch The performance of the stacking scheme after exchanging improved the performance significantly (Sect. 3.2). the HV switch was tested with an on-line beam of 179Lu?

ions (half-life of t1/2 = 4.59 h) from ISOLDE, contami- 3.1 Tests with the old HV switch system nated with stable 163Dy16O? ions. The contaminants were more abundant than the ions of interest, 179Lu?, by a factor The first tests of ion stacking at the ISOLTRAP setup were of 1,300. The ion losses due to decay were negligible performed with 133Cs? ions from an off-line alkali refer- because of the long half-life. In every stacking loop, a ence ion source (see Fig. 1). The performance of the mixture of about 1,200 ions (calculated with 30 % 123 Ion bunch stacking in a Penning trap 151 detection efficiency)—of both 179Lu? and 163Dy16O?— accumulations, where 12 average counts (about 40 ions) was injected in the MR-ToF MS for purification. Note that per ejection from the preparation Penning trap have been this means that on average in every loop only about one achieved compared to 0.3 counts with only one stacking single ion of interest is leaving the MR-ToF MS. The loop, i.e., a single capture event per measurement cycle. 179 ? overall length of the stacking loop was tloop = 52 ms, A ToF-ICR resonance of Lu was recorded (see bottom where the major part was used as waiting time of 30 ms in part of Fig. 5) by use of the new accumulation scheme with order to slow down the repetition rate to roughly 20 Hz. In 50 stacking loops per ToF-ICR measurement cycle. The principle, the stacking loop can run with a repetition fre- mass-selective buffer-gas cooling and the ToF-ICR detec- quency of several hundred Hertz; however, the ISOLDE tion lasted tmeas = 890 ms including further excitation and beamgate limited the repetition rate in this case. The cooling times in the preparation Penning trap, transfer opening time of the ISOLDE beamgate was 1 ms, the times, and 400 ms of quadrupolar RF-excitation in the cooling and bunching time in the RFQ was set to 5 ms, and precision Penning trap. Thus, the duration of one ToF-ICR 16 ms were chosen for the ion bunch separation in the MR- measurement cycle including the 50 stacking loops was 50

ToF MS, by far exceeding the needed resolving power of tloop ? tmeas = 3.49 s. For comparison, the time needed for m/Dm & 8,000. The average number of detected ions as a an equivalent measurement without ion stacking (using 50 function of the number of stacking loops is shown in the measurement cycles) would have been 50 (tloop ? top part of Fig. 5. tmeas) = 47.6 s. Thus, the reduction in measurement time Up to n = 20 injections, i.e., for about one second, the due to the stacking method was a factor of about 13. The count rate increases linearly with the number of accumu- total time of data taking for the measurement of the reso- lations. For more than 20 stacking loops, the increase in the nance (40 frequency steps) with sufficient statistics was number of ions slows down (solid line). This change of the 35 min. If the measurement had been performed in the slope may be due to radial losses of trapped ions whose conventional way without stacking, more than 7 h would motion is damped by buffer-gas collisions including an have been required. increase in the magnetron motion. This ion loss could be avoided with an adequate quadrupolar RF-excitation dur- ing the sequence of stacking loops. However, even without 4 Realization of the fast-loop repetition such a recentering [32], the ion number available for the ToF-ICR detection was increased by a factor of 40 for 50 For an effective application of the stacking method, all electrically switched beamline elements have to be oper- ated at switching frequencies of several tens or hundreds of Hertz. In general, this requirement poses no problem for low-voltage modules requiring only moderate precision, e.g., for the RFQ extraction pulse or the capture pulse of the preparation Penning trap. However, the switching module of the HV drift tube (see Fig. 1) had to be replaced to implement the new accumulation method. This pulsed drift tube transfers the ions from the RFQ on

the URFQ = 60 kV high-voltage platform to considerably lower kinetic energies in the ground-potential beamline. To

this end, the ‘‘high potential’’ UH of the drift tube has a value only somewhat (about 3.1 kV) lower than the high- voltage platform when the ions are ejected. Once the ions are inside, the voltage on the drift tube is switched to ground potential. Thus, when the ions leave the tube, their remaining energy is qUtransfer ¼ q ðURFQ UHÞ, i.e., around 3.1 keV, which is the transfer energy to the MR-ToF MS and the preparation Penning trap. The module used so far for the switching of the drift tube Fig. 5 Top Average number of detected ions after ejection from the (combination of two Behlke HTS MOSFET 650) provides preparation Penning trap as a function of the number of stacking either only a fast (*10 to 100 ns) rising or only a fast falling loops. Solid line to guide the eye; dashed line linear extension from edge, while the corresponding other edge is considerably the data at low loop numbers. Bottom ToF-ICR resonance of 179Lu? recorded by use of the new stacking scheme. Solid line fit to the slower. Due to the need for a load resistor RL (see Fig. 6)in resonance curve the range of some 100 MX, sufficiently recharging the load 123 152 M. Rosenbusch et al.

which does not become critical for the application. On the low-voltage (i.e., ground) side, the impedance is matched

to the load by integrating a RSL = 175 X series resistor. This value was chosen to achieve critical damping. A fast but over-shoot and ringing-free edge transient is essential because any voltage fluctuation will modulate the energy of the ions when they leave the pulse drift tube. Furthermore, an over-shoot increases the voltage across the switching module, which can cause damage if the maximum oper- ating voltage is exceeded. The time constant of the falling

edge has been determined to sfall & 21 ns and the time 10 sfall & 210 ns to discharge the pulsed drift tube to less -5 than 5 9 10 UH \ 5 V is short enough for the required passage time of the lightest ions investigated at the Fig. 6 Simplified scheme of the previous switching circuit for the ISOLTRAP setup. The power supply connected to the pulsed drift tube switching circuitry (Heinzinger PNChp ± 60 kV, 10 mA) 5 has a specified stability of DUdrift\10 UH=8 h, a peak-to- 5 peak ripple of DUpp\10 UH; and a temperature coeffi- 5 cient of DUtemp\10 UH=K. No noticeable voltage drift was observed, which would have resulted in a change of the capture and transport efficiency of the preparation Penning trap. The complete high-voltage switching cir- cuitry is installed in a radio-frequency-sealed grounded copper cage. The system has been operated with voltages up to 50 kV and frequencies of several hundred Hertz. With the available heat exchange rate of the liquid-cooling system, no significant temperature increase could be observed even at high switching voltages and rates. Fig. 7 Sketch of the new switching circuit for the pulsed drift tube capacitance CL (in the range of some 100 pF) takes some 100 ms. A significant reduction of the load resistor is 5 Optimization of the stacking parameters impossible due to power-dissipation considerations and the current provided by the high-voltage supplies. For a particular measurement, the optimal number of stacking To overcome this limitation, the switching system has loops depends on the properties of the ions of interest and of been replaced by a push–pull module. The power to be the contaminants. The lifetime s ¼ t1=2=lnð2Þ of the ions of provided by the voltage supply and therefore to be dissi- interest is the most important parameter and competes with pated by the resistances in the switching system is the storage times in the ion traps. Short half-lives, for exam- 2 P ¼ fCL UH, where f is the repetition rate. At a nominal ple, exclude long accumulation times, since the number of voltage of UH ¼ URFQ Utransfer ¼ 56:9 kV, a total load ions stagnates quickly with increasing number of stacking capacitance of about CL = 300 pF and a switching rate of loops. This number has to be chosen such that the final number f = 100 Hz, the required power dissipation is P & 100 W, of purified ions in a given measurement time is maximal. which cannot be achieved by air-convection cooling with- To calculate the number of ions per ToF-ICR mea- out increasing the temperature of the switch considerably. surement cycle, the number of ions which reach the prep- To avoid the excessive heating, a liquid-cooled switch aration Penning trap after each stacking loop is integrated (Behlke HTS 651-10-GSM, 65 kV, 100 A peak current) over the opening time of the ISOLDE beamgate (tbg) has been installed (see Fig. 7). The high-voltage side is including the decay of the radioactive ions. The ions of the buffered by a CB = 500 nF oil-filled capacitor, keeping the next stacking loop are added by use of the same integral to voltage drop below 0.1 % of the nominal value. A series the ions already stored taking into account the decay loss of resistor of RSH = 5kX on the high-voltage side reduces the latter during the last loop period tloop. After n loops, the the current in case of a discharge or failure on the output measurement is continued by mass-selective buffer-gas while it is connected to the high side. Furthermore, it cooling and ToF-ICR detection which together last for reduces the oU=ot transient speed of the positive edge, but tmeas. The number of ions at the end of a ToF-ICR 123 Ion bunch stacking in a Penning trap 153 measurement cycle with n repetitions of the stacking loop t IðtÞ¼I0esr : ð3Þ can be expressed by: The quantity s , the time constant of the release, is in N n; t ; t ; t r ð bg loop measÞ general different from the lifetime of the ion species. Thus, ðk1ZÞtloopþtbg in addition to the exponential function of the radioactive Xn ðnkÞt ðkt tÞ tmeas loop loop ¼ e s e s IðtÞe s dt; decay also that of the ion release enters as factor in the k¼1 argument of the integral. The ion number of a cycle is: ðk1Þtloop

ðk1Þt þt ðk1ZÞtloopþtbg Zloop bg Xn  Xn nt ntloop tmeas loop t tmeas t t ¼ e s e s IðtÞesdt; Nðn; tbg; tloop; tmeasÞ¼e s e s I0esr esdt k¼1 k¼1 ðk1Þtloop ðk1Þtloop

k 1 t t ðk1ZÞtloopþtbg ð ZÞ loopþ bg Xn nt Xn ntloop tmeas loop t tmeas tðÞ1 1 ¼ e s e s IðtÞesdt: ð1Þ ¼ e s e s I0 e sr s dt: ð4Þ k¼1 k¼1 ðÞk1 tloop ðk1Þtloop The ion number per time interval I(t) includes all ion losses The integral has a closed solution and Eq. (4) simplifies within the ISOLTRAP setup. This may also include time thus to: nt dependent ion losses independent of the delivered beam. tmeas loop ssr Nðn; tbg; tloop; tmeasÞ¼e s e s I0 If one to a few events per ToF-ICR measurement cycle sr s can be achieved, a further increase in the number of hiXn1 1 1 1 1 tbgðÞ ktloopðÞ stacking loops is not required. In more challenging cases, e s sr 1 e s sr : where the latter cannot be achieved, one needs to optimize k¼0 the number of ions per cycle length: ð5aÞ

Nðn; tbg; tloop; tmeasÞ As the sum over the terms depending on k is reduced to Qðn; tbg; tloop; tmeasÞ¼ : ð2Þ ntloop þ tmeas a geometric series, the number of ions per cycle length (Eq. 2) can be written as: So far no approximations have been introduced, as all hi ssr t 1 1 further complications can be described by I(t). In the Qðn; t ; t ; t Þ¼ I e bgðÞs sr 1 bg loop meas s s 0 following, the same experimental conditions are assumed r nt nt tmeas loop loop for each stacking loop. Two cases will be discussed in more e s e sr e s 1 1 : detail, which are of practical interest for the operation of tloop e ðÞs sr 1 ntloop þ tmeas the ISOLTRAP setup at ISOLDE, where radionuclides are ð5bÞ produced by subjecting targets to pulsed proton beams. Considering only the terms that are functions of the 5.1 Short half-lives and synchronization number of stacking loops n, the optimal number of loops is with the proton pulses the solution of the equation: ! ntloop ntloop d e sr e s In case the half-life of the ions of interest is considerably ¼ 0 dn ntloop þ tmeas shorter than the time between two proton pulses, it is  favorable to synchronize the experiment with the proton ntloop ntloop þ tmeas ntloop ntloop þ tmeas e s þ 1 e sr þ 1 ¼ 0; impact on the target. I(t) is correlated to the proton impact s sr and contains the time-dependent release characteristics of ð6Þ the ions of interest from the target (see e.g. [39, 40]). A typical release curve has a fast rise compared to a slower which can be solved numerically. The optimal number of falling component, where the corresponding time constants stacking loops is a function of the lifetime of the ions of are determined by the chemical properties of the element in interest, as well as of the lengths of the loop time, the time question, as well as by the half-life of the ions of interest. It for the Penning trap processes, and the release time. is convenient to set a delay after each proton impact before the start of the cycle to hinder the intake of contaminating 5.2 Long half-lives and no synchronization ions released faster from the target than the ions of interest. with the proton pulses In this situation, one usually probes the falling side of the release curve, which can be approximated with a single Consider now that the release time of the ions of interest is in time constant as: the order of or even longer than the time between two proton 123 154 M. Rosenbusch et al.

MR-ToF MS and the preparation Penning trap. The fast separation of ions provided by the MR-ToF MS reduces the on-line beam time for measurements of heavily contami- nated ion beams significantly by repetitive stacking of purified ions in the preparation Penning trap. Depending on the ions of interest, the required experimental time can be reduced by more than an order of magnitude as compared to the use of cycles without accumulation loops. In order to lower the ion energy from 30 or 60 keV as delivered by ISOLDE to the transfer energy of about 3 keV between the ISOLTRAP components at repetition rates of up to several Fig. 8 Ion number per cycle length (normalized to the maximum of each curve; maxima vary by orders of magnitude) as a function of the 100 Hz, a new high-power switch has been installed and number of stacking loops for two different life times of the ions of tested. The new method is most efficient for cases of interest. Left sr = 300 ms, right continuous production nuclides with half-lives above several seconds produced with only low yields but accompanied by high numbers of pulses on the ISOLDE target, which is in the order of a contaminating ions. second. In this case, there is no advantage in synchronizing the loop with the proton pulses and I(t) can be regarded as Acknowledgments This work was supported by the German Fed- being a statistical distribution, i.e., a mean beam current I0.In eral Ministry for Education and Research (BMBF) (Grants No. Eq. (3), this is represented by an infinite release time 05P12HGCI1, 05P12HGFNE and 06DD9054), the Max-Planck Society, the European Union seventh framework through ENSAR (sr !1). In this case, Eqs. (5a, 5b) thus simplifies to: (Contract No. 262010), and the French IN2P3. We acknowledge the nt hitmeas loop support of the ISOLDE Collaboration and technical teams. We thank tbg e s 1 e s s Rudi Henrique Cavaleiro Soares, Baudouin Bleus and Mike Barnes Qðn; tbg; tloop; tmeasÞ¼I0s e 1 tloop : e s 1 ntloop þ tmeas from the CERN TE-ABT group for discussions and advice on the ð7Þ installation of the new HV switch system. The analog of Eq. (6) then reads: ntloop þ tmeas ntloop References þ 1 ¼ e s ; ð8Þ s 1. H. Wollnik, M. Przewloka, Int. J. Mass Spectrom. Ion Process. which, again, can be solved numerically. 96, 267–274 (1990) To provide a numerical example, a beam is considered 2. D. Zajfman, O. Heber, L. Vejby-Christensen, I. Ben-Itzhak, M. 55 which allows a maximum beamgate period of tbg = 1msdue Rappaport, R. Fishman, M. Dahan, Phys. Rev. A , R1577– to a high yield of contaminating ions. In addition, times of R1580 (1997) 3. W.H. Benner, Anal. Chem. 69, 4162–4168 (1997) 9 ms in the RFQ and 10 ms in the MR-ToF MS are assumed 4. A. Naaman, K.G. Bhushan, H.B. Pedersen, N. Altstein, O. Heber, which sum up to tloop = 20 ms. The time tmeas is set to 500 ms M.L. Rappaport, R. Moalem, D. Zajfman, J. Chem. Phys. 113, (200 ms cooling in preparation Penning trap and 300 ms in 4662 (2000) precision Penning trap), and the release-time constant is 5. Y. Toker, O. Aviv, M. Eritt, M.L. Rappaport, O. Heber, D. Schwalm, D. Zajfman, Phys. Rev. A 76, 053201 (2000) assumed to be sr = 300 ms. The evolution of Eqs. (5a, b)fora 6. O. Aviv, Y. Toker, M. Errit, K.G. Bhushan, H.B. Pedersen, M.L. lifetime of s = 100 ms (domination of radioactive decay) and Rappaport, O. Heber, D. Schwalm, D. Zajfman, Rev. Sci. In- s = 500 ms (stronger influence of chemical release) is shown strum. 79, 083110 (2008) in the left part of Fig. 8. Note that the case s \ s implies a 7. M. Lange, M. Froese, S. Menk, J. Varju, R. Bastert, K. Blaum, r J.R. Crespo Lo´pez-Urrutia, F. Fellenberger, M. Grieser, R. von further production of the nuclide of interest by radioactive Hahn, O. Heber, K.-U. Ku¨hnel, F. Laux, D.A. 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123 9.4 Towards Systematic Investigations of Space-Charge Phenomena in Multi-Reflection Ion Traps, AIP Conference Proceedings, 1521, 53-62 (2013)

78 Towards Systematic Investigations of Space-Charge Phenomena in Multi-Reflection Ion Traps

M. Rosenbusch1, S. Kemnitz2, R. Schneider1, L. Schweikhard1, R. Tschiersch1, R. N. Wolf1

1Institut für Physik, Ernst-Moritz-Arndt-Universität, 17487 Greifswald, Germany 2Fakultät für Informatik und Elektrotechnik, Universität Rostock, 18059 Rostock, Germany

Abstract. A multi-reflection time-of-flight mass spectrometer has been set up for systematic studies of Coulomb effects of stored ion bunches. We report preliminary experimental results and simulations of peak coalescence of time-of-flight signals as a function of the number of simultaneously trapped ions. Keywords: multi-reflection ion traps, time-of-flight mass spectrometry, space-charge effects PACS: 07.75.+h, 82.80.Rt, 85.30.Fg

INTRODUCTION

The multi-reflection ion trap (MR-IT) is a recently developed storage technique for mass spectrometry with ion bunches and short beams with kinetic energies in the range of a few hundreds of electronvolts to a few kiloelectronvolts [1-3]. For the axial confinement the ions are reflected back and forth by two concentric electrostatic mirrors facing one another. The transverse confinement is achieved with electrostatic lenses in front of the mirrors, resulting in a periodic focusing of the ions. MR-IT devices can be used for ion storage only [2,4] or for an additional mass spectrometric analysis or separation [5-10]. While performing multiple revolutions the individual species are spatially separated due to their flight times corresponding to their mass- over-charge ratios m/q. As an example, the “isobar separator” at the ISOLTRAP mass spectrometer at ISOLDE/CERN reaches mass-resolving powers R=m/m=t/2t in excess of 100,000 in a few tens of milliseconds flight time t [11]. When the number of simultaneously stored ions in an MR-IT increases, the repulsing Coulomb interactions can become non-negligible. At certain ion densities and trapping conditions, a counterintuitive “self-bunching” effect has been observed as reported already about a decade ago [12-14]. This phenomenon was further studied theoretically [14,15] as well as experimentally [16]. The self-bunching enhances stabilization or causes even an increase of ion densities as a function of storage time. It is caused by Coulomb interactions even though the latter are of repulsive nature. An appropriate description has to take into account the electric potential distribution in the ion mirrors as well as the space charge of the ion bunch. The relative position and

Non-Neutral Plasma Physics VIII AIP Conf. Proc. 1521, 53-62 (2013); doi: 10.1063/1.4796061 © 2013 American Institute of Physics 978-0-7354-1144-9/$30.00 53

Downloaded 28 Mar 2013 to 141.53.32.80. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions energy of the individual ions in the bunch enters as a further input parameter in the calculation of their motion. In addition to the importance of the space charge of identical ion species, the interaction of different ion species, i.e. ions of different mass-over-charge ratios, has considerable consequences: As reported from Fourier-Transform Ion-Cyclotron- Resonance mass spectrometry in a Penning trap, different ion species can be caught in the same ion cloud – again counterintuitive – due to the repulsing Coulomb force. In this case the frequency spectrum shows only a single signal instead of the expected different signals corresponding to the individual trapped ion species [17-19]. This peak coalescence has been observed in MR-ITs as well, where different species are not anymore separated in the time-of-flight (ToF) spectra if the mass difference is considerably small, e.g. for isobaric species (same mass number A). This situation has already been discussed in the framework of a one-dimensional model [14,15]. In the following, a new setup is described with which self-bunching and peak- coalescence phenomena are currently studied. Preliminary experimental results are accompanied by simulations. While these combined investigations have been initiated only recently, we hope to shed some more light in the near future on these interesting as well as important effects.

EXPERIMENTAL SETUP AND PROCEDURE

The new apparatus has been set up in order to perform systematic studies of Coulomb interactions in MR-ITs. It consists of three main parts (see Figure 1): 1) a three-dimensional Paul trap with internal electron-impact ionization, followed by a Wiley-McLaren acceleration stage, a pulsed drift tube and ion-optical einzel lenses, 2) the MR-IT, and 3) a microchannelplate (MCP) detector.

FIGURE 1. Sectional view of the experimental setup consisting of a Paul trap with an electron-beam source for ionization, an MR-IT and an MCP detector (for detail see text).

The Paul trap consists of four disc electrodes made of stainless steel. The two outer electrodes represent the two endcaps and the two inner electrodes form the ring electrode. Each disc has a thickness of 1mm, the inner diameter of the ring electrodes and the endcaps is 10mm and 3mm, respectively. The two ring electrodes are mounted with a gap of 1mm between each other while the distance to the neighboring endcap electrodes is 2mm. The split ring electrode enables to inject an electron beam perpendicular to the axis of the Paul trap into its center. This is used to ionize gas-

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Downloaded 28 Mar 2013 to 141.53.32.80. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions phase atoms and molecules directly in the trap volume, which are injected via a needle valve. The intensity and duration of the electron beam as well as the gas pressure in   the chamber (between 4 410 6 Pa and 1410 3 Pa) determine the number of ions trapped for the subsequent experiment. The guiding radio-frequency (rf) potential is applied to the ring electrodes, while the two endcaps are held on a constant DC potential during trapping. Ejection is achieved by switching both endcap electrodes of the Paul trap, thus creating an electric dipole field that forms the first Wiley-McLaren acceleration stage. The second stage of the acceleration section consists of ten disc electrodes, similar to those of the Paul trap electrodes, with an inner diameter of 10 mm, mounted in distances of 5 mm. A voltage divider connected to the individual disc electrode realizes a quasi-linear potential slope on the axis, which accelerates the ions to their

final transfer kinetic energy of typically Etransfer = 2 keV. The ion-optical section consists of two electrostatic einzel lenses of an inner diameter of 23 mm. They are connected with a cylindrical conductive mesh which acts as a long drift tube. The voltage applied to this tube is pulsed in order to transfer the ions from the negative potential at the end of the second acceleration stage to ground potential, without modifying their kinetic energy. The MR-IT consists of two identical electrostatic ion mirrors, each made of four electrodes. A central electrode, the in-trap lift [20], serves to capture and eject the ions. The total length of the MR-IT is 384 mm with an inner diameter of 40 mm. The in-trap lift consists of two rings, which are connected with a cylindrical mesh. A reduced aperture of 14mm in each ring shields the drift region from electric fields of the mirror electrodes, providing a large undisturbed field-free section for injection and ejection. The mirror electrodes (see Table 1) are made of stainless steel separated by Teflon insulator rings. Mirror 4 has a smaller aperture of 12mm at the outer end for electric shielding of the MR-IT from the adjacent parts of the setup.  4 Ions with a kinetic energy Etransfer q Umax , where Umax is the highest voltage at the mirror electrodes, pass the electrostatic mirror on the entrance side. After the ions entered the activated in-trap lift, it is switched to ground to capture them [20]. The potential of the in-trap lift electrode Ulift while injecting the ions defines their kinetic   4 energy during the subsequent trapping period: Etrapping Etransfer q Ulift . For ion ejection, the in-trap lift voltage is switched back on and the ions can pass the mirror on the detector side. The voltages used for the present measurements are included in Table 1.

TABLE 1. Lengths of the MR-IT electrodes (1-4 from inside to outside) and voltages used for the present measurements Electrode Length Voltage In-trap lift electrode 212 mm Injection: 769 V / Trapping: 0 V mirror electrode 1 26 mm -4270 V mirror electrode 2 16 mm 1345 V mirror electrode 3 10 mm 752 V mirror electrode 4 22 mm 1462 V

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Downloaded 28 Mar 2013 to 141.53.32.80. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions The mirror electrode 1 acts as a negative electrostatic lens and focuses the ions for radial confinement. The potential wall on each side of the MR-IT device is realized with the mirror electrodes 2 to 4. The optimum mirror-electrode potentials were simulated as described in [21]. The in-trap lift electrode is adjusted each time the trapping duration is changed to optimize the time focusing of the ions on the detector [20]. The ions are detected by a 25 mm-diameter MCP detector in chevron arrangement with metal anode (Photonis USA, APD 3025) to analyze the ToF distributions. The data acquisition is performed with an oscilloscope (Tektronix MSO2024) directly connected to the anode of the MCP detector. The vacuum system, incorporating the ion-optical bench on which the experimental setup is attached (Figure 1), consists of several CF100 chambers. The MCP detector is mounted in one of the CF100 chambers, separated by a CF100 gate valve. A pre- vacuum pump (Leybold Trivac-D5E) and two turbo-molecular pumps (Leybold Turbovac 151, Leybold Turbovac 50) evacuate the system. With a gas-mixing system, defined ratios of different gas species can be prepared. The control of the experimental setup (timing sequence, communication with devices, data acquisition) is fully integrated in the ClusterTrap-CS [22,23], based on the control system (CS) framework developed at GSI Darmstadt [24,25]. The time- sequence signals for switching the electrode voltages are generated by an FPGA card (National Instruments NI-7811R) programmed as a pulse-pattern generator [22]. This controls, e.g., the activation and deactivation of the in-trap lift electrode, which is realized via a solid-state MOSFET switch (Behlke HTS 151-03-GSM). The time structure of a measurement cycle is shown in Fig. 2.

FIGURE 2. Schematic time structure of a measurement cycle.

After the ionization period, i.e. the application of the electron beam through the Paul trap (A: between 0.1-100 ms) and a delay (B of typically less than 1ms) follows the ion ejection (C) from the Paul trap, which is synchronized with a given phase of the rf potential. After the ions have passed the acceleration section and the entrance of the ion-optical section (waiting time D, around 3 s for ions with a mass of m28 u), the drift tube in the ion-optical section adjusts the ions’ potential energy to ground (E). Subsequently, the ions are injected through the entrance mirror of the MR-IT into the

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Downloaded 28 Mar 2013 to 141.53.32.80. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions activated in-trap lift (waiting time F) that is switched to ground for a defined storage time (G: up to several milliseconds). At the end of the storage time, the ions are ejected towards the MCP detector and the data acquisition (H) is started simultaneously.

SIMULATION OF COULOMB INTERACTION IN THE MR-IT

Three-dimensional many-particle simulations have been performed using a simulation program that includes realistic trap potentials and a modified particle- particle algorithm for Coulomb interactions suitable for graphics processing units [26]. The calculation of the force on each particle is divided into two parts. The first part F el contains the components obtained from the electric vacuum fields of the MR-IT, c and the second part F contains the Coulomb force. For the particle with number i  and position ri , the force from the electrical vacuum potential in spatial direction  xˆ j ( j 1, 2, 3 ) is: C  S (r (t)) F el (r,t) qD i Txˆ . i, j D  T j E xj (t) U

The Coulomb force for identical-charged particles is derived from

q2 F c  B f i, j  ik, j 4 0 ik ,

where the position-dependent term fik, j for particle k acting on particle i is

x  x  i, j k, j fik, j 3 3  2 B(xi, j xk, j ) j1

 2  Due to the condition fik, j fki, j only half of the ( N N) summands are calculated for N particles. In every time step, the electric-field force is computed on the standard processor

(CPU), whereas fik, j is computed on a graphics card (GPU). A considerable speed- up using the GPU is achieved by parallelizing of stream processors with internal pipelines. The positions of the particles are copied twice into the device memory of the GPU (particles with index i and index k ). The i -positions are divided into groups with the size of each shared memory on the GPU while the k -data sets are divided into groups with the size of the number of pipelines in every stream processor, where in each step of the calculation loop one k -group is copied to all stream-processor registers. Each stream processor calculates the required coefficients for all stored k -

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Downloaded 28 Mar 2013 to 141.53.32.80. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions sets and one of the i -sets. Thus, as many i -sets as the number of stream processors are treated at the same time. For more details see [27]. The integration of the ion motion is performed with the Gear method, a fifth-order predictor-corrector integrator with only one force-computation per time step. A simulation with, e.g., 106 time steps, is performed within a few hours for several thousands of test ions. The program has been developed for simulation of space- charge effects in Penning traps. However, it includes a routine to integrate any rotationally symmetric field and can, thus, be adapted to other ion optics and storage devices. The electric potentials of the MR-IT have been derived with the SIMION software [28] and transferred to the simulation program. The initial trapping energy and diameter of the bunch has been chosen Gaussian distributed with a FWHM of 40 eV around an average of 1 keV and with a FWHM of 1mm on the optical axis, respectively, which is close to the experimental conditions. The propagation of two + + ion bunches with an abundance of 90% N2 and 10% CO was simulated for 5000 ions. The required mass resolving power of the two species is m/ m 2500 , where m is the mass difference and m the mass (mass number of both species: A  28). A scaling factor of the Coulomb force, i.e. using pseudo-particles representing a larger amount of real particles, has been used to reduce the simulation time [29,30]. The + position differences of each ion with respect to an interaction-free N2 reference particle were collected each time the reference particle crossed the center plane between the two ion mirrors. From this, a ToF spectrum was reconstructed. The influence of the Coulomb interaction on the evolution of the ion clouds has been simulated for different scaling factors of the Coulomb interaction. Figure 3 shows selected results for scaling factors of 0, 5, 10, 20, where a factor of 0 and 1 stand for no interaction and the real interaction strength, respectively. In the first case (Fig. 3a) the ions are moving independently without Coulomb forces and a complete separation of both ion clouds is observed. In the second case, the Coulomb-scaling factor is 5 (Fig. 3b), i.e. the ion clouds represent 25,000 interacting ions. The CO+ ions are still separated, but are less focused in time after + + leaving the N2 bunch. The N2 bunch later narrows down to a minimum time width due to self-bunching. For a Coulomb-scaling factor of 10, representing 50,000 ions, (Fig. 3c) many CO+ ions are forced to stay within the initial ion cloud. However, ions from both species are ejected to both sides of the peak. In the fourth case (Fig. 3d), representing 100,000 ions, almost no ions leave the initial cloud. It behaves like a single species with a modified mass, i.e. the peak shifts to lower flight times as + compared to the non-interacting reference ion of N2 . The present analytical models [14, 15] contain important basic ideas and principles, but cannot yet describe the evolution of these complex systems for arbitrary electromagnetic field configurations. Simulations as presented can be used to improve the understanding of many-ion dynamics in ion-optical systems like ToF mass and energy analyzers. Furthermore, simulations can be applied in the design phase of an apparatus to improve its capabilities of handling high-intensity ion beams, which are subject of major concern in existing and future radioactive ion-beam facilities.

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+ + FIGURE 3. Simulated ToF spectra of an initial mixture of CO (red) and N2 (blue) ions (ToF + compared to the non-interacting N2 reference ion). The trapping time increases from top to bottom of every part of the picture (details in picture). The Coulomb scaling factors are a: 0 (no Coulomb interaction), b: 5, c: 10, d: 20.

PRELIMINARY EXPERIMENTAL RESULTS

First experiments have been performed with a mixture of the isobaric ion species + + N2 and CO . After electron-impact ionization inside the Paul-trap volume, the ions were transferred to the MR-IT and stored for approximately 1 ms. This trapping time      is sufficient to reach a resolving power of R m/ m ttrap /2 t 3000 which is

needed to separate the two ion species (ttrap is the trapping time, and t 170 ns is the FWHM of the ion signals in time). Figure 4 shows ToF spectra recorded at three different nitrogen gas pressures at the Paul trap.

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+ + FIGURE 4. ToF spectra of CO and N2 for 1 ms flight time. For low ion numbers (i.e. a pressure of  p  5410 6 Pa at the Paul trap), the species are separated (top). A medium ion number  ( p  6.5410 6 Pa) results in a spectrum (center) where the average ToF of the CO+ ions is shifted

+ 5 + towards the N2 peak. At p  5410 Pa (bottom), the CO peak is no longer visible, i.e. the species are not separated. (For comparison, the initial spectrum (top) is shown in the background of the other spectra.)

+ The number of N2 ions created in the Paul-trap volume is thus varied while the + number of CO ions (presumably produced from fragmentation of residual CO2 gas) stays constant. The signal of the MCP detector was fed directly to the oscilloscope.  No obvious Coulomb effects have been observed for a pressure of ( p  5410 6 Pa), where the two ion peaks are clearly identified after the separation process. When the + + pressure is increased (center), the CO peak is observed to move closer to the N2  peak. At p  5410 5 Pa (bottom), the signal of the CO+ peak completely vanishes (compare lines in the bottom of Figure 4 to inserted background from the top), comparable to the case in Fig. 3c. Since the CO+ ions have a lower mass and have + reached the detector earlier than the N2 ions in the top and middle spectrum, their disappearance cannot be explained by a saturation effect of the detector due to the + + large N2 peak. A significant narrowing of the N2 signal for growing ion numbers, as in the simulations, has not been observed within the present measurements.

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Downloaded 28 Mar 2013 to 141.53.32.80. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions SUMMARY AND OUTLOOK

A new setup for systematic investigations of Coulomb effects in multi-reflection ion traps has been built and tested. It allows the analyses of ToF distribution of the + + ions as demonstrated by the preliminary results from experiments with CO and N2 . A Coulomb-force based effect, the so-called peak coalescence as known from Penning-trap experiments, has been observed. The experimental studies are accompanied by simulations including realistic trap potentials and an algorithm for particle-particle interactions profiting from the high parallelism of a graphics card. The studies will provide valuable systematics concerning the conditions for the appearance of Coulomb effects and will help to further characterize the effects of self- bunching and peak coalescence.

ACKNOWLEDGMENTS

We thank the Federal Ministry of Education and Research (06GF9102, 06GF9101I, 06GF7133 and 06GF7134F) for its financial support.

REFERENCES

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Downloaded 28 Mar 2013 to 141.53.32.80. This article is copyrighted as indicated in the abstract. Reuse of AIP content is subject to the terms at: http://proceedings.aip.org/about/rights_permissions 9.5 Delayed Bunching for Muti-Reflection Time-of-Flight Mass Separation, AIP Conference Proceedings, 1668, 050001 (2015)

89 Delayed Bunching for Multi-Reflection Time-of-Flight Mass Separation

† † M. Rosenbusch∗, P. Chauveau , P. Delahaye , G. Marx∗, L. Schweikhard∗, F. Wienholtz∗ and R. N. Wolf∗∗

∗Institut für Physik, Ernst-Moritz-Arndt Universität Greifswald, 17487 Greifswald, Germany †GANIL, CEA/DSM-CNRS/IN2P3, 14000 Caen, France ∗∗Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany

Abstract. Many experiments are handicapped when the ion sources do not only deliver the ions of interest but also contam- inations, i.e., unwanted ions of similar mass. In the recent years, multi-reflection time-of-flight mass separation has become a promising method to isolate the ions of interest from the contaminants, in particular for measurements with low-energy short-lived nuclides. To further improve the performance of multi-reflection mass separators with respect to the limitations by space-charge effects, the simultaneously trapped ions are spatially widely distributed in the apparatus. Thus, the ions can propagate with reduced Coulomb interactions until, finally, they are bunched by a change in the trapping conditions for high-resolution mass separation. Proof-of-principle measurements are presented. Keywords: nuclear-mass measurements, ion purification, electrostatic ion traps, space-charge effects. PACS: 21.10.Dr,33.15Ta,52.27Jt

INTRODUCTION

The electrostatic multi-reflection ion trap is a recent development for trapping of ion bunches and short ion beams with kinetic energies of 100eV to a few keV [1–3]. Two concentric electrostatic mirrors, separated by a field-free region, are facing one another and confine the ions in longitudinal direction. Transverse confinement is achieved by electrostatic lenses for periodical spatial focusing. While multi-reflection ion traps in general cover a wider spectrum of applications – e.g. cluster physics [4–9], molecular physics [10–13], and electron collisions [14] – the mass-spectrometric advantages, i.e. exploiting the repeated revolutions of ions, were a breakthrough for high- resolution mass separation of short-lived isotopes and for precision mass spectrometry of such exotic species [15–17] (see also [18] for very recent studies). In this context, these devices are called multi-reflection time-of-flight mass separators/spectrometers (MR-ToF MS). In time-of-flight mass spectrometry different ions species are separated in time of flight due to their different mass- over-charge ratios m/q, where m is the mass and q the charge of the ion. In MR-ToF devices the flight path is prolonged significantly enabling high resolving powers R = t/(2∆t) = m/∆m, where t is the time-of-flight (ToF), ∆t the full width at half maximum (FWHM) of the ToF distribution and ∆m the corresponding value on mass scale. With state-of-the-art devices, resolving powers of R 105 are achieved with flight times in the order of 10ms [19–24]. This feature is of particular high≥ interest for nuclear physics experiments at radioactive ion-beam facilities. Here, experiments like high-precision mass measurements, hyperfine structure studies and decay studies benefit from a fast and efficient procedure to isolate the ions of interest [15, 25, 26]. In particular at ISOL facilities, the short-lived isotopes of interest are typically accompanied by isobaric contaminations, i.e. ions with the same mass number A, therefore of very similar masses. Thus, MR-ToF MS devices in combination with Bradbury-Nielsen beam gates (BNG) [19, 27] have enabled previously impossible measurements. A prominent example is the mass determination of 82Zn [15] with the Penning-trap mass spectrometer ISOLTRAP at ISOLDE/CERN. Its MR-ToF MS allowed a separation about an order of magnitude faster in time than the buffer-gas assisted quadrupolar excitation in a Penning trap [28], which was the only high-resolution cleaning device before and can now be used as a second cleaning stage. However, if many ions are stored simultaneously in an MR-ToF MS, space-charge phenomena such as self-bunching and peak coalescence can occur [29–33], which may prevent successful mass separation. In many cases, the abundance of contaminant ions delivered by the source is orders of magnitude larger than that of the ions of interest. Thus, the

Non-Neutral Plasma Physics IX AIP Conf. Proc. 1668, 050001-1–050001-9; doi: 10.1063/1.4923120 © 2015 AIP Publishing LLC 978-0-7354-1315-3/$30.00 050001-1 separation and the subsequent experiment can fail: 1. if too many ions are injected and the maximum ion number below the appearance of detrimental space-charge effects is exceeded. 2. if, on the other hand, the number of ions processed per experimental cycle is reduced to avoid space-charge effects, and the rate of purified ions becomes too low for the measurement, e.g. due to the limited online measurement time. A solution for the second approach has recently been developed at ISOLTRAP at ISOLDE/CERN for cases where the fast purification cycle of the MR-ToF MS can be decoupled from subsequent measurement processes of longer duration. In these situations a Penning trap can be used as temporary accumulator of the purified ions [32]. However, this procedure is limited to nuclides with half-lifes in the order of the re-accumulation time or above. The desired mass separation in MR-ToF MS is enabled by controlling the focusing condition of the ions, which depends on the dispersion of revolution time as a function of the kinetic energy Trev = Trev(Ekin), as shown in Fig. 1: One mainly distinguishes between a non-zero dispersion with positive (negative) slope, i.e. the revolution time increases (decreases) with increasing kinetic energy ∂Trev(Ekin)/∂Ekin > 0(< 0), and a dispersion-free (or "isochronous") transport ∂Trev(Ekin)/∂Ekin 0, meaning a constant revolution time for all energies within a certain interval [23]. The focusing properties of the≈ system can be adjusted by either tuning the mirror electrodes (changing shape of Trev(Ekin), or by varying the mean energy of the ions addressing a region that provides the desired dispersion (changing Ekin), e.g. by use of an in-trap lift [23]. In the present work, we discuss the possibility to increase the number of ions per injection while maintaining mass separation to improve on the first of the two problems mentioned above. In the procedure that is commonly used, in the following simply referred to as “standard procedure”, a “short” ion bunch is provided by the source. During trapping in the MR-ToF MS, this “short” bunch is kept at a fixed ToF-focus by isochronous conditions or is slightly focused with small dispersions to achieve a ToF focus at a subsequent ion detector (or BNG). However, the short bunch width that persists for the complete trapping time means in turn that high ion densities are present leading to space-charge effects that have to be avoided. The new method proposed in this work divides the mass separation process in two phases. First, a “long” ion bunch containing multiple species is created by a pulsed source and trapped for a certain time in the MR-ToF MS. Due to the low ion density caused by the distribution of the ions over a larger volume, space-charge effects are potentially reduced and peak coalescence is less likely to occur. The different ion species start to separate in time due to their m/q, where, however, the species are still overlapping because of the broad ToF-distributions. Second, the focusing condition of the MR-ToF MS is switched “in-flight” to a strong ToF-dispersion of the system to create a time-focus at the detector, leading to a full separation, even with an increased number of ions in the device. ) kin E (

rev ! ! T Trev(Ekin) < 0 Trev(Ekin) > 0 Ekin Ekin

!Trev(Ekin) ≈ 0 Ekin revolution time

kinetic energy Ekin

FIGURE 1. Schematic ToF-energy relation obtained from the mirror potentials.

050001-2 EXPERIMENTAL SETUP AND PROCEDURE

The experiments have been performed at the MR-ToF setup depicted in Fig. 2 [32]. It consists of the following main parts: 1. Ionization and preparation: A radio-frequency quadrupole (RFQ) trap where atomic and molecular ions are produced by electron-impact ionization. 2. Acceleration and transport: After an acceleration stage, a pulsed drift tube is used to adapt the ion energy to the beam-line potential and ion-optical einzel lenses and deflectors to prepare the injection of ions into the MR-ToF MS. 3. MR-ToF mass analyzer, which contains a pulsed drift tube (in-trap lift) between the electrostatic mirrors for injection/ejection of ions and manipulation of the mean energy of the ions for the trapping period [23, 24]. 4. Ion detection: a micro-channel plate (MCP) detector with a multi-channel analyzer for ion counting of low- intensity signals and a Faraday cup (FC) with a low-noise amplifier in case of intense ion bunches, which cannot be detected by an MCP without a deterioration in gain linearity. Further technical details can be found in [32]. Recently, the 3D Paul trap has been replaced by a short segmented linear radio-frequency quadrupole (RFQ) trap. It allows one to adjust the shape of the axial potential for trapping and ejection more freely in order to produce different initial conditions of the ions for the MR-ToF MS trapping period. The RFQ trap has five segment quartets, enclosed by two endplate electrodes. Each of the segments is equipped with an individual LC-resonance circuit to create the necessary radio-frequency amplitudes. The center tap of each inductance is directly biased to the corresponding DC voltage, which also enables a fast switching between trapping- and ejection potentials. Thus, the axial shape of trapping- and ejection potentials can be applied in a more flexible way than before. 3 Since the RFQ uses helium buffer gas at pressures around 10− mbar to cool down the ions’ motional amplitudes, the RFQ trap is housed in a cylinder to allow for differential pumping between the RFQ trap and other parts of the setup. A continuous gas flow with adjustable fractions of helium, carbon monoxide and atmospheric gas is guided into the RFQ trap volume. There, the atoms and molecules are ionized by an axial electron beam from a small filament unit. For the present studies, the confinement conditions for the ions in the RFQ trap have been adjusted to the region at mass + + + + number A 30 for singly charged ions, where CO ,N2 ,N2H , and O2 ions are dominantly present. Subsequently, the ion are≈ thermalized through collisions with the helium buffer gas for 20ms after the electron beam has been blocked. The ions, which have been produced and trapped close to DC-ground potential, are then ejected from the RFQ trap and accelerated into the pulsed drift tube at 2kV. While the ions are passing through, the voltage is switched to ground potential and thus adapts the ion energy− to the beam-line potential. Then the ions enter the MR-ToF MS

;<=%8)"8! !"! !"#$%&#'" ! .:*%-!!! !#"%)$- 4(""#"%!"! !"#-!& -! !"!")!(#$%4!&6 "($!)"%*)'"%!")+

4#8)7"!% 5)")-)9% '+ ($0!")+%"(5!

(#$(,)!(#$%)$- ./01#2%.3 !")$&+#"!%&! !(#$ -!!! !(#$% 6)47!" +"!+)")!(#$%&! !(#$

FIGURE 2. Cut view of the MR-ToF MS setup. For details, see text.

050001-3 (kinetic energy exceeds the mirror potentials) and are captured by use of the in-trap lift technique, where the pulsed drift tube in the center of the MR-ToF MS is switched from 1kV to 0V during the ions’ passage. This enables the storage of the ions, which are reflected back and forth between the mirrors for the desired number of revolutions at a mean energy of about 1keV. + + The CO and N2 ions separate with increasing flight time, the required mass resolving power of R 2500 is reached after a few hundred microseconds, while the FWHM of the ions’ ToF distribution at the detector is≈ about 100ns. In the “standard procedure”, this ToF distribution stays almost constant for the complete trapping period (dispersion-free transport as discussed above). The ion signals can be detected with the MCP detector or the FC. While usually the MCP signal is amplified and discriminated in order to count the ions, this procedure is not applicable at high ion intensities. If too many ions hit the detector in a short time, the single-ion MCP signals are not short enough to be separated and therefore cannot be correctly discriminated anymore. However, the current amplification of the MCP can still be used by reading the analog ToF signal from the anode electrode with an oscilloscope. Furthermore, due to the finite number of micro- channels which have a recharge time in the order of milliseconds after electron emission, i.e. much longer than the ToF differences of the ions, the measured signal drops for ions which arrive later. This leads to distorted signal amplitudes, which do not allow a trustworthy determination of the number of ions from the MCP signal. Instead, the Faraday cup can be used in combination with a low-noise amplifier (Stahl Electronics PR-E3). The calibration of the amplifier is performed by coupling a chosen electric charge to the amplifier. To this end, a low voltage (e.g. 1mV) is coupled with 1pF in series to the amplifier input ( 120pF load capacity between amplifier input and ground replaces the Faraday cup for calibration). With this setup,≈ the amplifier yields a signal of about 1mV for 6000 electric charges.

PEAK COALESCENCE STUDIES

+ + To determine the number of CO and N2 ions necessary for peak coalescence to be observable, the number of ions in the MR-ToF MS has been increased, starting from the point where the two species are still clearly separated. The ions have been produced in equal amounts, injected into the MR-ToF MS and stored for 100 revolutions, which corresponds to a flight time of about 800 µs. In the left bottom of Fig. 3, a ToF spectrum is shown where the number of ions still + + allows a ToF separation of the CO and N2 peaks. On the left top, the averaged corresponding amplified FC signal shows a drop of 2mV, which corresponds to about 12000 ions. The time difference to the MCP spectrum is due to the

1 ion signal at FC 0 ion signal at FC 0 -2 2mV≈ˆ 12000 ions -4 8mV≈ˆ 50000 ions -1 -6 -2 -8 0 0

-200 CO+ N+ -200 mixture signal at oscilloscope / mV 2 signal at oscilloscope / mV

ion signal at MCP ion signal at MCP -400 -400 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 time after ion ejection / µs time after ion ejection / µs

FIGURE 3. Left part: Averaged ion signal at the Faraday cup (top) and averaged time-of-flight signal from the MCP detector (bottom) for a large number of ions that still enables ion separation. Right part: As left part, but with increased number of ions leading to peak coalescence.

050001-4 difference in axial position of the two detection devices. The right part of Fig. 3 shows the FC and MCP signals for a higher number of ions due to an increase of the electron beam intensity in the RFQ trap. This number of ions of about 50000, corresponding to the 8mV-step given by the amplifier at the FC, is now too large for a ToF separation of the two ion species. The examples emphasize that in this particular scenario for about 104 or more simultaneously stored ions, the effects of ion-ion interactions become non-negligible (see also [33]). Closer-lying mass doublets require even higher resolving powers and thus a longer MR-ToF MS storage time. Thus, it can be expected that the ion-number limit for successful separation decreases with decreasing mass difference.

HIGH-RESOLUTION FOCUSING BY CONTINUOUS BUNCHING

+ + In order to decrease the ion density during the separation process, CO and N2 ions have been injected with a much broader time-of-flight distribution than for the standard procedure. To this end, the ions are not accelerated to 2keV directly after the ejection from the RFQ trap, but only to 200eV on their way to the pulsed drift tube. Due to their relative energy distribution, which is now higher compared to the standard procedure, the time distribution increases. The ion bunch crosses its time-focus point closer to the RFQ trap and can then expand in space. In order to still achieve the same injection energy into the MR-ToF MS as used for the standard procedure, the kinetic energy of the ions has then been increased to 2keV after the ions’ passage through the first drift tube. This is achieved by switching the first drift tube from 200V to 1800V instead of switching from 2kV to 0V as in the standard procedure. The trapping and ejection potentials− of the RFQ are not changed compared− to the standard procedure. The difference achieved by the longer propagation time of the ions ejected from the RFQ trap is shown in Fig. 4, where the ions were transferred through the MR-ToF MS without being trapped. The spectrum in the upper part of Fig. 4 is obtained with the standard procedure, i.e. injecting a short ion bunch in the MR-ToF analyzer. The spectrum in the lower part has been obtained by the low-energy transport, which results in an FWHM increase of the ToF peaks by a factor of about five. The correlation between the position of an ion in the bunch and its kinetic energy opens the possibility to refocus the ions in the MR-ToF MS at any time by tuning the mirror potentials or by changing the mean energy of the ions by the in-trap lift. To investigate the possibility of refocusing the increased ToF distribution described above, the mirror potentials have been adjusted to a positive time-of-flight dispersion with respect to energy enabling a continuous decrease of the ion bunch width at the position of the detector. The minimal bunch width is reached after 80 revolutions, which corresponds to a flight time of about 640 µs.

250 CO+/N+ 200 2 150 O+ 100 2 + 50 N2H 0 12.5 13 13.5 14 14.5 15 15.5 + + 140 CO /N2 120 + 100 + O N2H 2 number of detected ions 80 60 40 20 0 17.5 18 18.5 19 19.5 20 20.5 time after ion ejection / µs

FIGURE 4. Accumulated ion count of about 1000 experimental cycles (see end of this section) as a function of the time-of- flight after ejection from the RFQ trap with direct transmission to the MCP (no trapping in MR-ToF mass analyzer). Top part: as performed in the standard procedure. Bottom part: with modified procedure to obtain a broader ToF distribution.

050001-5 120 400 350 100 CO+ N+ 2 300 80 250 60 + 200 N2H 150 40 100 + number of revolutions 20 O 2 50 0 5 5.5 6 6.5 7 7.5 time after ion ejection / µs

FIGURE 5. Ion count as a function of the time-of-flight after ejection from the MR-ToF MS and as a function of the revolution number. The width of the ion bunch is reduced continuously until a focus is reached after 80 revolutions. In addition to the main + + + + signals of CO and N2 , the signals from the simultaneously stored N2H and O2 ions appear (indicated by lines) as described in [22] in the context of broad-band MR-ToF mass spectrometry.

A contour plot of this process is shown in Fig. 5: The accumulated ion count is plotted as a function of the ToF after ejection from the MR-ToF MS (abscissa), where the number of revolutions (ordinate) has been increased in steps of + + two. From 60 revolutions on, a separation between CO and N2 becomes visible (black stripe appearing on the left of + the N2 signal) and at 80 revolutions the ToF focus is achieved. This demonstrates that with the continuous-bunching process, a broad initial ion distribution can be focused to achieve a high mass resolving power, while potentially keeping the space-charge effects smaller than in the standard procedure. However in this and the following proof-of- principle studies, the number of ions were restricted to about 10/cycle, where for each spectrum shown in this section and the next one, a few thousand ions have been accumulated in about 1000 experimental cycles.

HIGH-RESOLUTION FOCUSING BY DELAYED BUNCHING

The continuous bunching process discussed above, needs a readjustment of the mirror electrode potentials depending on the number of revolutions the ions should perform. This is not advantageous for the flexibility of the device, since in an online experiment, the available time is restricted. Furthermore, the low ion densities after the injection are only present in the first part of the process. To overcome this, the separation is split in two phases. First, an isochronous storage of the broad initial distribution until the mean ToF difference of the different species is larger than their width after the second phase, which is a fast focusing, induced by a change in ToF-dispersion of the system. Due to the isochronous trapping in the first phase, the individual positions of the ions within the bunch remain unchanged (at a certain position in the MR-ToF MS). Therefore, the revolution number after which the bunch is ejected will not alter the ejection conditions in phase two. Such a fast bunching of the ions can be achieved in only a few revolutions using a strong ToF-dispersion. In Fig. 6, bottom left, the bunch has been refocused in the first 6 revolutions after injection, but due to the trapping time of only about 60 µs (revolution time for fast focusing conditions 10 µs), the mass + + ≈ resolving power is not sufficient to separate CO from N2 . However, in combination with an isochronous storage, high-resolution mass separation can be achieved, as further illustrated in Fig. 6:

1. left top: An ion bunch with broad ToF distribution is injected as discussed for continuous bunching.

050001-6 150 + + 200 + + CO / N2 CO / N2

direct 150 100 + 100 transmission N2H to MCP 100 revolutions 50 50 0 0 17.5 18 18.5 19 19.5 5 5.5 6 6.5 7

+ + + CO / N2 250 N2 600 200 6 150 106 number of detected ions 400 revolutions revolutions 100 200 CO+ 50 0 0 5 5.5 6 6.5 7 5 5.5 6 6.5 7 time after ion ejection / µs

FIGURE 6. Accumulated ion count as a function of the time-of-flight. Left top: after ejection from the Paul trap with direct transmission to the MCP (no trapping in MR-ToF MS). Left bottom: ToF focus after six revolutions and ejection from the MR-ToF MS using a strong positive ToF-energy dispersion. Right top: ToF distribution after isochronous transport for 100 revolutions and + + ejection from the MR-ToF MS. Right bottom: ToF focus with visible mass separation of CO and N2 after 106 revolutions using delayed bunching.

2. right top: The ions are transported dispersion-free for a revolution number of choice, e.g. 100, that would be sufficient to enable mass separation for the standard procedure. 3. right bottom: The mirror potentials are switched to fast focusing (identical to the setting used for the spectrum on the left bottom) when the ions pass through the center drift tube. The spectrum in the right bottom of Fig. 6 demonstrates not only that a ToF focus can be achieved but also the + + successful mass separation of CO and N2 by use of delayed bunching. The adjustment of the mirror voltages has been achieved using high-voltage switches, where the potential can be changed within a few tens of nanoseconds while the ions cross the quasi field-free region between the electrostatic mirrors. This method enables a transport with low axial ion densities over almost the complete trapping period. In addition, the experimental setting is independent of the trapping time as the transport is performed isochronous. This means that in principal the switch of the voltages to the fast-bunching mode can be performed at any time allowing a fast adjustment of the desired resolving power. When comparing the two different spectra in the bottom of Fig. 6, it is obvious that the short ToF focus as obtained after six revolutions is not achieved after the complete delayed-bunching procedure. Two possible reasons are voltage fluctuations during the intended isochronous transport and voltage ripples due to the switching. Time- of-flight aberrations due to the transversal emittance also increase the bunch width. Additionally, only two high- voltage switches were available during the performed measurements, which caused problems for enabling a good radial confinement for the ions in the fast-bunching mode (spatial-focusing lens could not be adjusted) and a fraction of the ions were lost in those last few revolutions.

SUMMARY AND OUTLOOK

For the purpose of reducing space-charge effects for mass separation in MR-ToF MS devices, we have demonstrated two methods for high-resolution focusing that decrease the ion density during the separation process. To this end, the ions are on purpose distributed along the axis. They are focused in time-of-flight to a short distribution at a later time by switching the potentials of the MR-ToF analyzers to appropriate voltages. The procedure reduces the axial ion

050001-7 density for a part of the trapping period and may thus improve the separation of a large number of ions stored at the same time. So far, only few ions per cycle have been used for the present test measurements. Experiments with a larger amount of ions and a comparison with the limits of the standard method are still to be performed. Note that while the present delayed-bunching study was performed by changing the mirror potentials to different values, the method may be simplified by use of the in-trap lift concept. To this end, high-voltage switching of the in-trap lift between at least three different potentials is necessary, but a switch between three values was not available for the present experiment. In any case, the method of delayed bunching seems to be a promising approach to increase the space-charge limit for MR-ToF mass separators.

ACKNOWLEDGMENTS

This work was supported by the german BMBF (Grands No. 05P12HGFNE and 05P12HGCI1)

REFERENCES

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050001-9 9.6 Probing the N = 32 Shell Closure below the Magic Proton Number Z = 20: Mass Measurements of the Exotic Isotopes 52,53K, Physical Review Letters 114, 202501 (2015)

99 week ending PRL 114, 202501 (2015) PHYSICAL REVIEW LETTERS 22 MAY 2015

Probing the N ¼ 32 Shell Closure below the Magic Proton Number Z ¼ 20: Mass Measurements of the Exotic Isotopes 52;53K

M. Rosenbusch,1 P. Ascher,2 D. Atanasov,2 C. Barbieri,3 D. Beck,4 K. Blaum,2 Ch. Borgmann,2 M. Breitenfeldt,5 R. B. Cakirli,2,6 A. Cipollone,3 S. George,2 F. Herfurth,4 M. Kowalska,7 S. Kreim,2,7 D. Lunney,8 V. Manea,8 P. Navrátil,9 D. Neidherr,4 L. Schweikhard,1 V. Somà,10,11,12 J. Stanja,13 F. Wienholtz,1 R. N. Wolf,1,2 and K. Zuber13 1Institut für Physik, Ernst-Moritz-Arndt Universität Greifswald, 17487 Greifswald, Germany 2Max-Planck-Institut für Kernphysik, Saupfercheckweg 1, 69117 Heidelberg, Germany 3Department of Physics, University of Surrey, Guildford GU2 7XH, United Kingdom 4GSI Helmholtzzentrum für Schwerionenforschung GmbH, Planckstraße 1, 64291 Darmstadt, Germany 5Instituut voor Kern- en Stralingsfysica, KU Leuven, Celestijnenlaan 200d, B-3001 Heverlee, Belgium 6Department of Physics, University of Istanbul, 34134 Istanbul, Turkey 7CERN, 1211 Geneva 23, Switzerland 8CSNSM-IN2P3-CNRS, Université Paris-Sud, 91405 Orsay, France 9TRIUMF, 4004 Westbrook Mall, Vancouver, British Columbia V6T 2A3, Canada 10CEA-Saclay, IRFU/Service de Physique Nucléaire, 91191 Gif-sur-Yvette, France 11Institut für Kernphysik, Technische Universität Darmstadt, 64289 Darmstadt, Germany 12ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, 64291 Darmstadt, Germany 13Institut für Kern- und Teilchenphysik, Technische Universität Dresden, 01069 Dresden, Germany (Received 31 December 2014; revised manuscript received 14 March 2015; published 20 May 2015) The recently confirmed neutron-shell closure at N ¼ 32 has been investigated for the first time below the magic proton number Z ¼ 20 with mass measurements of the exotic isotopes 52;53K, the latter being the shortest-lived nuclide investigated at the online mass spectrometer ISOLTRAP. The resulting two- neutron separation energies reveal a 3 MeV shell gap at N ¼ 32, slightly lower than for 52Ca, highlighting the doubly magic nature of this nuclide. Skyrme-Hartree-Fock-Bogoliubov and ab initio Gorkov-Green function calculations are challenged by the new measurements but reproduce qualitatively the observed shell effect.

DOI: 10.1103/PhysRevLett.114.202501 PACS numbers: 21.10.Dr, 21.30.-x, 21.60.De, 21.60.Jz

Since the introduction of the shell concept in nuclear only for even-even species. Two-neutron separation ener- physics, the evolution of the shell structure far away from gies (S2n) are another strong indication—even in the stability is one of the main research efforts. Similarly to case of odd-Z nuclides (such as potassium)—and are atomic electrons, protons and neutrons can be regarded in a obtained from mass measurements [6,7] as performed with simple picture as occupying nuclear orbitals, of varying mass spectrometers like the ISOLTRAP experiment at energy and angular momentum. Nuclides show a spherical ISOLDE/CERN [8]. nature and enhanced stability when these orbitals are filled, Beta-decay studies of 52Ca at ISOLDE published in 1985 leading to the so-called “magic” numbers of nucleons; how- [9] revealed the energy of what was thought to be the first ever, the standard shell picture has been shown to no longer 2þ excited state (confirmed in 2006 [10]) and hinted at an be applicable to some exotic species. As magic numbers enhanced N ¼ 32 shell effect. Recent mass measurements 53;54 disappear going farther from stability, new shell closures arise including Ca revealed a 4 MeV drop in S2n between in consequence, as in the case of the doubly magic oxygen 52 54 24 Ca and Ca yielding a correspondingly large empirical isotope O [1,2]. Such surprising isospin-dependent migra- shell gap [11]. An important test of the strength of the tions of the nuclear quantum states point to the need to N ¼ 32 shell closure comes from neighboring elements – improve the understanding of the nuclear force [3 5]. where proton correlations become active. For the isotopic 2þ High excitation energies of the lowest excited state chains of the heavier even-Z elements titanium (Z ¼ 22), are a traditional clue for closed-shell nuclides, however, þ chromium (Z ¼ 24), and iron (Z ¼ 26), the Eð2 Þ values have a local peak at N ¼ 32 although with an absolute magnitude lower than for 52Ca [12,13]. Their two-neutron Published by the American Physical Society under the terms of separation energies, however, as well as the ones of the the Creative Commons Attribution 3.0 License. Further distri- þ bution of this work must maintain attribution to the author(s) and odd-Z neighbor elements, which have no Eð2 Þ indicator, the published article’s title, journal citation, and DOI. show no significant kink at N ¼ 32—in sharp contrast to

0031-9007=15=114(20)=202501(6) 202501-1 Published by the American Physical Society week ending PRL 114, 202501 (2015) PHYSICAL REVIEW LETTERS 22 MAY 2015

precision Penning trap

reference preparation Penning trap ion source movable MCP detector RFQ cooler and buncher pulsed MR-TOF drift mass separator tube

ISOLDE beam

FIG. 1. Sketch of the part of the ISOLTRAP setup used for the measurements reported here. For details, see the text. the closure of the Z ¼ 20 proton core in calcium, where as oxides, dioxides, sulfides, and hydrides, and of doubly recently also for 54Ca a large Eð2þÞ value has been revealed charged ions have been compared with the observed peaks. [14]. Until now, the region below Z ¼ 20 was unexplored, The only species that would come close are 36;37Sið16OÞþ, as these extremely exotic nuclides could not be produced in that contain short-lived silicon isotopes. However, due to sufficient quantity. the slow chemical release from the target, the probability for In this Letter, we present the first measurement of the short-lived silicon beam components is very low. More masses of 52;53K and, thus, the first investigation of the importantly, it can be excluded as only in the case of A ¼ 52 N ¼ 32 shell closure towards the neutron drip line for would the flight time of 36Sið16OÞþ fit the measured peak; Z<20. The experimental S2n values are compared to the at A ¼ 53, the measured mass deviates by 1000(130) keV predictions of self-consistent ab initio Gorkov-Green from the value of 37Sið16OÞþ [21], which corresponds to a function (GGF) theory. This recent development signifi- time-of-flight difference in the order of 40 ns. cantly extends the reach of calculations based on realistic In 4 h, 12 000 counts were collected for 52K, and in 12 h, interactions, including three-nucleon forces, in particular to 2300 counts for 53K. Note that with a half-life of just open-shell (and odd-Z) nuclei. In contrast, we show that the 30 ms, 52K is the shortest-lived nuclide ever investigated predictions of mean-field calculations with phenomeno- with ISOLTRAP. For mass calibration, stable 39K from the logical interactions are highly dependent on the parameter- ISOLTRAP reference ion source as well as 52;53Cr ions ization of both the particle-particle and particle-hole parts from ISOLDE were used. With the reference-ion masses of the energy functional. To this end, we performed in m1;2 and their corresponding flight times t1;2, the ion mass addition Hartree-Fock-Bogoliubov (HFB) calculations of interest m is determined from its time of flight t by [11] with the Skyrme interactions SLy4 and SLy5 [15], the latter containing a phenomenological tensor term. 1=2 1=2 1=2 1=2 m1=2 ¼ C ðm − m Þþðm þ m Þ=2; ð1Þ The exotic potassium isotopes were studied at ISOLDE/ TOF 1 2 1 2 ’ CERN with ISOLTRAP s multi-reflection time-of-flight where the experimental values are described by the single mass separator (MR-TOF MS) [16,17]. Figure 1 shows the variable C ¼ð2t − t1 − t2Þ=½2ðt1 − t2Þ. Because of the parts of the setup relevant for the present measurements: a TOF radio-frequency quadrupole (RFQ) ion cooler and buncher [18], the MR-TOF MS, and a microchannel plate (MCP) 10000 52Cr+ on-line spectrum A = 52 detector. 1000 52 53 The nuclides K and K were produced by impact of 52 + 100 K 1.4-GeV protons on a uranium carbide target. The atoms 52Ca+ were surface ionized, along with stable chromium isobars. 10 All ions were accelerated to 30 keV, transported via the 1 Number of detected ions ISOLDE magnetic high-resolution mass separator to the 6.090 6.091 6.092 6.093 ToF / ms ISOLTRAP setup [8,19], captured and cooled in the RFQ buncher, and ejected towards the MR-TOF MS. The energy 10000 53Cr+ on-line spectrum A = 53 of the ions was adapted by a pulsed drift tube prior to the 1000 injection into the MR-TOF MS, where in-trap-lift capturing 100 53Ca+ was applied [20]. After several hundred reflections, the ions 53K+ were ejected towards the MCP detector. 10 Figure 2 shows time-of-flight spectra of isobaric ions at 1 mass numbers A ¼ 52 and A ¼ 53. The calcium peaks were Number of detected ions 4.330 4.331 4.332 identified by an element-selective laser-ionization scheme. ToF / ms For TOF signals at longer flight times, there are no known FIG. 2 (color online). Time-of-flight spectra for nuclides at 52;53 isobaric atomic ions except K. The expected flight mass numbers A ¼ 52 (top) and A ¼ 53 (bottom). Vertical lines times of possible molecular ions produced at ISOLDE, such indicate the Crþ fit ranges.

202501-2 week ending PRL 114, 202501 (2015) PHYSICAL REVIEW LETTERS 22 MAY 2015 20 TABLE I. Half-lives T1=2 [21], reference nuclides (Ref. nucl.), 21Sc experimental TOF variable C , and resulting mass-excess TOF 18 Ca (ME) values of the investigated isotopes 52;53K. The mass values 20 of the reference nuclides are taken from Ref. [21]. 16 19K

T C Ar Isotope 1=2 Ref. nucl. TOF ME (keV) 14 18 52K 110(4) ms 39K, 52Cr 0.50295425(256) −17138ð33Þ 12 53K 30(5) ms 39K, 53Cr 0.50306656(799) −12298ð112Þ 10 deviation from Gaussian shape of the intense chromium ion 8 ISOLTRAP, Wienholtz et al. peaks as shown in Fig. 2, the mean flight times have been Two-neutron separation energy (MeV) ISOLTRAP, present data determined from a limited region around the peak maxi- 6 AME2012 mum (as indicated by vertical lines) that cover about 95% Meisel et al. of the measured events. Uncertainties that arise from 26 28 30 32 34 different choices of this region have been investigated Neutronnumber and taken into account. FIG. 3 (color online). Two-neutron separation energies for the The resulting mass excesses ME ¼ M − Au are listed in Z ¼ 18–21 isotopes from the atomic-mass evaluation 2012 Table I, where M is the atomic mass, A is the mass number, (AME2012, open symbols) [21], recent measurements of and u is the atomic mass unit. We note that, in principle, 48;49Ar by Meisel et al. [24], and the ISOLTRAP data (from 52Ca, with its mass well known from recent Penning-trap Ref. [11] and this work). measurements [11,22], would be the second mass reference of choice (in addition to 52Cr) for measuring 52K rather than 39 52 As shown already in Ref. [11] for the calcium isotopes, K from the reference ion source, as Ca appears in the density-functional-theory calculations reproduce the aver- 52 52 same spectrum with K and Cr. In general, such a age S2n trend across N ¼ 28 and N ¼ 32 but do not predict procedure (used here for the first time) is preferred, because the sharp drops associated with the two shell closures. We the MR-TOF data of all three isobaric ions are taken extend this study to Z<20 and perform Skyrme-Hartree- simultaneously, excluding drifts between the measure- Fock-Bogoliubov (Skyrme-HFB) [25] calculations using ments. The mass values from both calibrations are in the HFODD code [26] and interactions of the Skyrme-Lyon agreement. However, the isobaric calibration has a larger family [15], in the spherical approximation. 52 uncertainty due to significantly lower statistics of the Ca The calculations use the SLy4 or SLy5 interactions for 39 as compared to the K signal from the reference ion source. the particle-hole part and a volume delta-pairing interaction In Fig. 3, the two-neutron separation energies S2n ¼ for the particle-particle part of the energy functional, the BðZ; NÞ − BðZ; N − 2Þ, where BðN;ZÞ is the binding latter being defined exclusively by a strength parameter V0. energy of a nuclide with Z protons and N neutrons, of With respect to the SLy4 interaction, SLy5 contains in the isotopic chains from argon to scandium are presented, addition a tensor term. including the present data. The new S2n values show a significant drop from 51K [22] to 53K: about 3 MeV, 49 51 compared to only about 1 MeV from Kto K, clearly 8 ISOLTRAP, Wienholtz et al. ISOLTRAP, present data illustrating the N ¼ 32 shell effect for potassium. The large AME2012 N=32 53 7 AME2012 N=28 uncertainty of the S2n value of Sc (271 keV) [21,23] at N ¼ 32 leaves room for some ambiguity as to whether 6 the S2n values of calcium and scandium cross. Thus, new 5 precision-mass measurements of the corresponding Sc Ca isotopes would be desirable. 4 K Sc In Fig. 4, the empirical two-neutron shell gap 3 S2nðN;ZÞ − S2nðN þ 2;ZÞ is plotted as a function of the proton number for N ¼ 28 and N ¼ 32, including the new Empirical neutron shell gap (MeV) 2 point below the magic proton number Z ¼ 20. A local maximum of the N ¼ 32 shell gap has thus been revealed 18 20 22 24 26 28 30 32 for the proton-magic Z ¼ 20 core. In addition, the plot Proton number shows a similar behavior for both neutron numbers going FIG. 4 (color online). Empirical shell gaps for N ¼ 28 and towards the drip line with lower Z, where the shell gap is N ¼ 32 from the atomic-mass evaluation 2012 (AME2012, open rising up to a maximum at Z ¼ 20 and falling by about symbols) [21] and the ISOLTRAP data (from Ref. [11] and 1 MeV at Z ¼ 19. this work).

202501-3 week ending PRL 114, 202501 (2015) PHYSICAL REVIEW LETTERS 22 MAY 2015

The top panel in Fig. 5 shows the experimental and Thus, new mass calculations have been performed in the computed HFB S2n values for the potassium and calcium ab initio GGF framework [31,37,38] that allow for the isotopic chains. The theoretical S2n are computed for nuclei study of open-shell nuclei. This method is particularly of even neutron number. Self-consistent quasiparticle suited for the present purpose due to the ease of calculating blocking of the odd protons is performed for the potassium odd-even systems, which also makes it a unique tool to isotopes, by using the procedure described in Ref. [27]. investigate neighboring isotopic chains. A strength of the pairing interaction of −200 MeV fm3 In our calculations, the only input are two- and three- reproduces the very smooth S2n trend observed in Ref. [11]. body interactions fitted to properties of systems with It describes correctly the experimental values on average A ¼ 2, 3, and 4, without any further adjustments of the but underestimates the drop at the crossing of the magic parameters. GGF calculations have recently addressed neutron numbers. A reduction of the strength of the pairing the region around Z ¼ 20 [31] and are extended here for interaction (solid lines) leads to a significant improvement the first time beyond N ¼ 32 for potassium. of the description of the experimental S2n trend. The The present calculations made use of two- and three- addition of the tensor term with the SLy5 interaction leads nucleon forces derived within chiral effective field theory at to a change in the wrong direction. However, a recent next-to-next-to- and next-to-next-to-next-to-leading order work [28] has shown that the effect of the tensor term in (N2LO and N3LO), respectively [39,40], extended to the mean-field calculations strongly depends on the way it is low-momentum scale λ ¼ 2.0 fm−1 by means of free-space constrained to experimental data. similarity renormalization-group techniques. The many- In addition to the empirical HFB approach, it is now body treatment is set by a second-order truncation in the possible to perform calculations up to the medium mass GGF self-energy expansion [37]. Model spaces up to 14 region using ab initio methods (see, e.g., Refs. [29–36]). harmonic oscillator shells were employed, and three-body E ≤ 16 interactions were restricted to basis states with 3 max . 20 HFB calculations 18 Infrared extrapolations of the calculated ground state SLy4 SLy5 energies were subsequently performed following 18 -150 MeV fm3 16 -200 MeV fm3 Ref. [41]. We note that, in the present case, this procedure 16 14 is formally defective due to the different truncations of one- 14 12 and three-body model spaces. Nevertheless, we find that 12 10 19K 20Ca the trend expected from Ref. [41] is qualitatively repro- 10 8 duced, although with larger extrapolation uncertainties. 8 Experimental 6 This is in agreement with other calculations [35].Asan 6 4 example, we obtain binding energies of 439.52(0.71) MeV ISOLTRAP, Wienholtz et al. 51 53 4 ISOLTRAP, present data 2 for K and 443.31(0.85) MeV for K. This overbinding of AME2012 about 0.7 MeV=A is a general feature of currently available 20 18 chiral interactions, and it is a constant effect through- 18 16 out the whole isotopic chain that cancels in separation 16 14 energies [31,35,36]. 47;49;51;53 48;50;52;54 14 12 GGF results for S2n of K and Ca are 12 10 shown in the bottom panel in Fig. 5 and are all resulting 19K 20Ca Two-neutron separation energy (MeV) 10 8 from the infrared extrapolation. Different sources of uncertainty affect the present theoretical results (see 8 6 Refs. [31,38] for a detailed discussion). In particular, this 6 4 method breaks particle-number symmetry (like HFB 4 Gorkov-Green function theory, Ca 2 Gorkov-Green function theory, K theory) and generates the correct expectation values for 26 28 30 32 34 the proton and neutron numbers only on average, with a Neutron number finite variance. However, the associated errors are expected to cancel with good accuracy for energy differences (such FIG. 5 (color online). Two-neutron separation energies for the as S2n). The uncertainties indicated in Fig. 5 are uniquely isotopic chains of potassium (left axes) and calcium (right axes); those originating from the extrapolation fit and range note the shifted scales. Open symbols, data from Ref. [21]; filled between 0.4 and 1.5 MeV with increasing mass number. symbols, calcium data from Ref. [11] and new mass data from S In general, GGF calculations are in fair agreement with this work. Top: With 2n values from HFB calculations using the S 53 SLy4 (green lines) and the SLy5 (red lines) interaction, with measured 2n, with the mismatch at K being on the order 3 51 53 volume-type delta pairing of strength V0 ¼ −150 MeV fm of the truncation error. The significant drop from Kto K 3 (solid lines) or V0 ¼ −200 MeV fm (dashed lines). Bottom: is qualitatively reproduced but overestimated by theory, With S2n values obtained from ab initio Gorkov-Green function which also leads to an overestimation of the empirical shell theory (see the text for details). gap for potassium. In contrast to the N ¼ 28 gap, which is

202501-4 week ending PRL 114, 202501 (2015) PHYSICAL REVIEW LETTERS 22 MAY 2015 quantitatively better reproduced, the overestimation of the [4] O. Sorlin and M.-G. Porquet, Nuclear magic numbers: New N ¼ 32 gap emerges as a common feature of ab initio features far from stability, Prog. Part. Nucl. Phys. 61, 602 calculations in this mass region (see also [35]). The present (2008). measurements therefore constitute an important test for the [5] O. Sorlin and M.-G. Porquet, Evolution of the N ¼ 28 shell ongoing developments of chiral interactions and ab initio closure: a test bench for nuclear forces, Phys. Scr. T152, methods. 014003 (2013). In summary, direct mass measurements performed with [6] K. Blaum, J. Dilling, and W. Nörtershäuser, Precision atomic physics techniques for nuclear physics with radio- ISOLTRAP’s multi-reflection time-of-flight mass separator N ¼ 32 active beams, Phys. Scr. T152, 014017 (2013). show that the neutron-shell closure at extends below [7] Special issue, edited by L. Schweikhard and G. Bollen, the closed proton shell Z ¼ 20. The empirical gap is about Ultra-accurate mass spectrometry and related topics, Int. J. 1 MeV weaker than for calcium, indicating the stabilizing Mass Spectrom. 251, 85 (2006). effect of the Z ¼ 20 proton core and highlighting the doubly [8] M. Mukherjee et al., ISOLTRAP: An on-line Penning trap magic nature of 52Ca. Mean-field calculations for K and Ca for mass spectrometry on short-lived nuclides, Eur. Phys. J. show that interactions with effective parameters, although A 35, 1 (2008). leading to more easily accessible calculations, depend on the [9] A. Huck, G. Klotz, A. Knipper, C. Miehé, C. Richard-Serre, G. Walter, A. Poves, H. L. Ravn, and G. 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Wolf et al., On-line separation of short-lived nuclei by Alliance Program (Contract No. HA216/EMMI), the United a multi-reflection time-of-flight device, Nucl. Instrum. Kingdom Science and Technology Facilities Council (STFC, Methods Phys. Res., Sect. A 686, 82 (2012). Contracts No. ST/L005743/1 and No. ST/L005816/1), and [17] R. N. Wolf et al., ISOLTRAP’s multi-reflection time-of-flight the Natural Sciences and Engineering Research Council of mass separator/spectrometer, Int. J. Mass Spectrom. 349–350, Canada (NSERC, Contract No. 401945-2011). GGF calcu- 123 (2013). lations were performed by using HPC resources from [18] F. Herfurth et al., A linear radiofrequency ion trap for GENCI-CCRT (Contracts No. 2014-050707 and accumulation, bunching, and emittance improvement of No. 2015-057392) and the DiRAC Data Analytic system radioactive ion beams, Nucl. Instrum. Methods Phys. at the University of Cambridge (BIS National E-infrastruc- Res., Sect. 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Hoffman et al., Evidence for a doubly magic 24O, [22] A. T. Gallant et al., New Precision Mass Measurements Phys. Lett. B 672, 17 (2009). of Neutron-Rich Calcium and Potassium Isotopes and [3] D. Warner, Not-so-magic numbers, Nature (London) 430, Three-Nucleon Forces, Phys. Rev. Lett. 109, 032506 517 (2004). (2012).

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[23] H. L. Crawford et al., β decay and isomeric properties of [32] G. Hagen, T. Papenbrock, D. J. Dean, and M. Hjorth-Jensen, neutron-rich Ca and Sc isotopes, Phys. Rev. C 82, 014311 Medium-Mass Nuclei from Chiral Nucleon-Nucleon Inter- (2010). actions, Phys. Rev. Lett. 101, 092502 (2008). [24] Z. Meisel et al., Mass Measurements Demonstrate a Strong [33] C. Barbieri and M. Hjorth-Jensen, Quasiparticle and quasi- N ¼ 28 Shell Gap in Argon, Phys. Rev. Lett. 114, 022501 hole states of nuclei around 56Ni, Phys. Rev. C 79, 064313 (2015). (2009). [25] P. Ring and P. Schuck, The Nuclear Many-Body Problem, [34] G. Hagen, M. Hjorth-Jensen, G. R. Jansen, R. Machleidt, Texts and Monographs in Physics (Springer, New York, 2000). and T. Papenbrock, Evolution of Shell Structure in Neutron- [26] N. Schunck, J. Dobaczewski, J. McDonnell, W. Satuła, J. A. Rich Calcium Isotopes, Phys. Rev. Lett. 109, 032502 Sheikh, A. Staszczak, M. Stoitsov, and P. Toivanen, Solution (2012). of the Skyrme–Hartree–Fock–Bogolyubov equations in the [35] H. Hergert, S. K. Bogner, T. D. Morris, S. Binder, A. Calci, J. Cartesian deformed harmonic-oscillator basis.: (VII) hfodd Langhammer, and R. Roth, Ab initio multireference in- (v2.49t): A new version of the program, Comput. Phys. medium similarity renormalization group calculations of even Commun. 183, 166 (2012). calcium and nickel isotopes, Phys. Rev. C 90, 041302 (2014). [27] J. Dobaczewski et al., Solution of the Skyrme–Hartree– [36] S. Binder, J. Langhammer, A. Calci, and R. Roth, Ab initio Fock–Bogolyubov equations in the Cartesian deformed path to heavy nuclei, Phys. Lett. B 736, 119 (2014). harmonic-oscillator basis.: (VI) hfodd (v2.40h): A new [37] V. Somà, T. Duguet, and C. Barbieri, Ab initio self- version of the program, Comput. Phys. Commun. 180, consistent Gorkov-Green’s function calculations of semi- 2361 (2009). magic nuclei: Formalism at second order with a two-nucleon [28] M. Grasso, Magicity of the 52Ca and 54Ca isotopes and interaction, Phys. Rev. C 84, 064317 (2011). tensor contribution within a mean-field approach, Phys. [38] V. Somà, C. Barbieri, and T. Duguet, Ab initio self- Rev. C 89, 034316 (2014). consistent Gorkov-Green’s function calculations of semi- [29] H. Hergert, S. Binder, A. Calci, J. Langhammer, and R. magic nuclei: Numerical implementation at second order Roth, Ab Initio Calculations of Even Oxygen Isotopes with with a two-nucleon interaction, Phys. Rev. C 89, 024323 Chiral Two-Plus-Three-Nucleon Interactions, Phys. Rev. (2014). Lett. 110, 242501 (2013). [39] D. R. Entem and R. Machleidt, Accurate charge-dependent [30] A. Cipollone, C. Barbieri, and P. Navrátil, Isotopic Chains nucleon-nucleon potential at fourth order of chiral pertur- Around Oxygen from Evolved Chiral Two- and Three- bation theory, Phys. Rev. C 68, 041001 (2003). Nucleon Interactions, Phys. Rev. Lett. 111, 062501 (2013). [40] P. Navrátil, Local three-nucleon interaction from chiral [31] V. Somà, A. Cipollone, C. Barbieri, P. Navrátil, and T. effective field theory, Few-Body Syst. 41, 117 (2007). Duguet, Chiral two- and three-nucleon forces along [41] S. N. More, A. Ekström, R. J. Furnstahl, G. Hagen, and medium-mass isotope chains, Phys. Rev. C 89, 061301 T. Papenbrock, Universal properties of infrared oscillator (2014). basis extrapolations, Phys. Rev. C 87, 044326 (2013).

202501-6

10 Publications

10.1 Peer-reviewed publications

• Probing the N = 32 Shell Closure below the Magic Proton Number Z = 20: Mass Measurements of the Exotic Isotopes 52,53K, M. Rosenbusch, P. Ascher, D. Atanasov, C. Barbieri, D. Beck, K. Blaum, Ch. Borgmann, M. Breitenfeldt, R.B. Cakirli, A. Cipollone, S. George, F. Herfurth, M. Kowalska, S. Kreim, D. Lunney, V. Manea, P. Navrátil, D. Neidherr, L. Schweikhard, V. Somà, J. Stanja, F. Wienholtz, R. N. Wolf, and K. Zuber, Phys. Rev. Lett. 114, 202501 (2015)

• Delayed bunching for muti-reflection time-of-flight mass separation, M. Rosenbusch, P. Chauveau, P. Delahaye, G. Marx, L. Schweikhard, F. Wienholtz, R. N. Wolf, AIP Conf. Proc. 1668, 050001 (2015)

• Ion-Bunch Stacking in a Penning Trap after Purification in an Electro- static Mirror Trap, M. Rosenbusch, D. Atanasov, K. Blaum, Ch. Borgmann, S. Kreim, D. Lunney, L. Schweikhard, F. Wienholtz, R.N. Wolf, Appl. Phys. B 114, 147-155 (2014)

• Evolution of nuclear ground-state properties of neutron-deficient iso- topes around Z = 82 from precision mass measurements, Ch. Böhm, Ch. Borgmann, G. Audi, D. Beck, K. Blaum, M. Breitenfeldt, R. B. Cakirli, T. E. Cocolios, S. Eliseev, S. George, F. Herfurth, A. Herlert, M. Kowalska, S. Kreim, D. Lunney, V. Manea, E. Minaya Ramirez, S. Naimi, D. Neidherr, M. Rosenbusch, L. Schweikhard, J. Stanja, M. Wang, R. N. Wolf, K. Zuber, Phys. Rev. C 90, 044307 (2014)

• Competition between pairing correlations and deformation from the odd-even mass staggering of francium and radium isotopes, S. Kreim, D. Beck, K. Blaum, Ch. Borgmann, M. Breitenfeldt, T. E. Cocolios, A. Gottberg, F. Herfurth, M. Kowalska, Yu. A. Litvinov, D. Lunney, V. Manea, T. M. Mendonca, S. Naimi, D. Neidherr, M. Rosenbusch, L. Schweikhard, Th. Stora, F. Wienholtz, R. N. Wolf, K. Zuber, Phys. Rev. C 90, 024301 (2014)

• Isobar separation and precision mass spectrometry of short-lived nu- clides with a multi-reflection time-of-flight analyzer, L. Schweikhard, M. Rosenbusch, F. Wienholtz, R.N. Wolf, Proc. of Sci., 10th Latin Am. Sym. Nucl. Phys. Appl. 011 (2014)

• Collective degrees of freedom of neutron-rich A≈100 nuclei and the first mass measurement of the short-lived nuclide 100Rb,

107 10 Publications

V. Manea, D. Atanasov, D. Beck, K. Blaum, Ch. Borgmann, R.B. Cakirli, T. Eronen, S. George, F. Herfurth, A. Herlert, M. Kowalska, S. Kreim, Yu.A. Litvinov, D. Lunney, D. Neidherr, M. Rosenbusch, L. Schweikhard, F. Wienholtz, R.N. Wolf, K. Zuber, Phys. Rev. C 88, 054322 (2013)

• Mass spectrometry and decay spectroscopy of isomers across the Z = 82 shell closure, J. Stanja, Ch. Borgmann, J. Agramunt, A. Algora, D. Beck, K. Blaum, Ch. Böhm, M. Breitenfeldt, T.E. Cocolios, L.M. Fraile, F. Herfurth, A. Herlert, M. Kowalska, S. Kreim, D. Lunney, V. Manea, E. Minaya Ramirez, S. Naimi, D. Neidherr, M. Rosenbusch, L. Schweikhard, G. Simpson, F. Wienholtz, R.N. Wolf, K. Zuber, Phys. Rev. C 88, 054304 (2013)

• New exploits of the in-source spectroscopy method at RILIS/ISOLDE, B. A. Marsh, B. Andel, A. N. Andreyev, S. Antalic, D. Atanasov, A. E. Barzakh, B. Bastin, Ch. Borgmann, L. Capponi, T. E. Cocolios, T. Day Goodacre, M. Dehairs, X. Derkx, H. De Witte, D. V. Fedorov, V. N. Fedosseev, G. J. Focker, D. A. Fink, K. T. Flanagan, S. Franchoo, L. Ghys, M. Huyse, N. Imai, Z. Kalaninova, U. Köster, S. Kreim, N. Kesteloot, Y. Kudryavtsev, J. Lane, N. Lecesne, V. Liberati, D. Lunney, K. M. Lynch, V. Manea, P. L. Molkanov, T. Nicol, D. Pauwels, L. Popescu, D. Radulov, E. Rapisarda, M. Rosenbusch, R. E. Rossel, S. Rothe, L. Schweikhard, M. Seliverstov, S. Sels, A. M. Sjödin, V. Truesdale, C. Van Beveren, P. Van Duppen, K. Wendt, F. Wienholtz, R. N. Wolf, S. G. Zemlyanoy, Nucl. Instr. and Meth. in Phys. Res. B 317, 550-556 (2013)

• Recent developments of the mass spectrometer ISOLTRAP, S. Kreim, D. Beck, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, T. E. Cocolios, D. Fink, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, U. Köster, M. Kowalska, D. Lunney, V. Manea, E. Minaya-Ramirez, S. Naimi, D. Neidherr, M. Rosenbusch, L. Schweikhard, J. Stanja, F. Wienholtz, R. N. Wolf, K. Zuber, Nucl. Instr. and Meth. in Phys. Res. B 317, 492-500 (2013)

• ISOLTRAP’s Multi-Reflection Time-of-Flight Mass Separator/Spectrometer, R. N. Wolf, F. Wienholtz, D. Atanasov, D. Beck, K. Blaum, Ch. Borgmann, F. Herfurth, M. Kowalska, S. Kreim, Y. Litvinov, D. Lunney, V. Manea, D. Neidherr, M. Rosenbusch, L. Schweikhard, J. Stanja, K. Zuber, Int. J. Mass Spectrom. 349-350, 123-133 (2013)

• Masses of exotic calcium isotopes pin down nuclear forces, F. Wienholtz, D. Beck, K. Blaum, Ch. Borgmann, M. Breitenfeldt, R.B. Cakirli, S. George, F. Herfurth, J.D. Holt, M. Kowalska, S. Kreim, D. Lunney, V. Manea, J. Menendez, D. Neidherr, M. Rosenbusch, L. Schweikhard, A. Schwenk, J. Simonis, J. Stanja, R. N. Wolf, K. Zuber, Nature 498, 346-349 (2013)

• Towards systematic investigations of space-charge phenomena in multi- reflection ion traps,

108 10.1 Peer-reviewed publications

M. Rosenbusch, S. Kemnitz, R. Schneider, L. Schweikhard, R. Tschiersch, and R. N. Wolf, AIP Conf. Proc. 1521, 53 (2013)

• Plumbing Neutron Stars to New Depths with the Binding Energy of the Exotic Nuclide 82Zn, R. N. Wolf, D. Beck, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, N. Chamel, S. Goriely, F. Herfurth, M. Kowalska, S. Kreim, D. Lunney, V. Manea, E. Minaya Ramirez, S. Naimi, D. Neidherr, M. Rosenbusch, L. Schweikhard, J. Stanja, F. Wienholtz, and K. Zuber, Phys. Rev. Lett. 110, 041101 (2013)

• Buffer-gas-free mass-selective ion centering in Penning traps by simul- taneous dipolar excitation of magnetron motion and quadrupolar exci- tation for interconversion between magnetron and cyclotron motion, M. Rosenbusch, K. Blaum, Ch. Borgmann, S. Kreim, M. Kretzschmar, D. Lunney, L. Schweikhard, F. Wienholtz, and R. Wolf, Int. J. Mass Spectrom. 325-327, 51-57 (2012)

• Surveying the N = 40 island of inversion with new manganese masses, S. Naimi, G. Audi, D. Beck, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, M. Kowalska, D. Lunney, E. Minaya Ramirez, D. Neidherr, M. Rosenbusch, L. Schweikhard, R. N. Wolf, and K. Zuber, Phys. Rev. C 86, 014325 (2012)

• Trap-assisted decay spectroscopy with ISOLTRAP, M. Kowalska, S. Naimi, J. Agramunt, A. Algora, D. Beck, B. Blank, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, L.M. Fraile, S. George, F. Herfurth, A. Herlert, S. Kreim, D. Lunney, E. Minaya Ramirez, D. Neidherr, M. Rosenbusch, B. Rubio, L. Schweikhard, J. Stanja, K. Zuber, Nucl. Instr. and Meth. A 689, 102-107 (2012)

• On-line separation of short-lived nuclei by a multi-reflection time-of- flight device, R. N. Wolf, D. Beck, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, F. Herfurth, A. Herlert, M. Kowalska, S. Kreim, D. Lunney, S. Naimi, D. Neidherr, M. Rosenbusch, L. Schweikhard, J. Stanja, F. Wienholtz, K. Zuber, Nucl. Instrum. Methods Phys. Res., Sect. A 686, 82-90 (2012)

• A study of octupolar excitation for mass-selective centering in Penning traps, M. Rosenbusch, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, A. Herlert, M. Kowalska, S. Kreim, G. Marx, S. Naimi, D. Neidherr, R. Schneider, L. Schweikhard, Int. J. Mass Spectrom. 314, 6-12 (2012)

• Static-mirror ion capture and time focusing for electrostatic ion-beam traps and multi-reflection time-of-flight mass analyzers by use of an in-trap potential lift, R. N. Wolf, G. Marx, M. Rosenbusch, L. Schweikhard, Int. J. Mass Spectrom. 313, 8-14 (2012)

109 10 Publications

• Q-Value and Half-Lives for the Double-Beta-Decay Nuclide 110Pd, D. Fink, J. Barea, D. Beck, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, F. Herfurth, A. Herlert, J. Kotila, M. Kowalska, S. Kreim, D. Lunney, S. Naimi, M. Rosenbusch, S. Schwarz, L. Schweikhard, F. Šimkovic, J. Stanja, K. Zuber, Phys. Rev. Lett. 108, 062502 (2012)

• Cadmium mass measurements between the neutron shell closures at N = 50 and 82, Ch. Borgmann, M. Breitenfeldt, G. Audi, S. Baruah, D. Beck, K. Blaum, Ch. Böhm, R.B. Cakirli, R. F. Casten, P. Delahaye, M. Dworschak, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, M. Kowalska, S. Kreim, D. Lunney, E. Minaya-Ramirez, S. Naimi, D. Neidherr, M. Rosenbusch, R. Savreux, S. Schwarz, L. Schweikhard and C. Yazidjian, AIP Conf. Proc. 1377, 332-334 (2011)

• Mass measurements of short-lived nuclides using the Isoltrap prepara- tion Penning trap, S. Naimi, M. Rosenbusch, G. Audi, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Bre- itenfeldt, S. George F. Herfurth, A. Herlert, M. Kowalska, S. Kreim, D. Lunney, E. Minaya-Ramirez, D. Neidherr, L. Schweikhard, M. Wang, Hyperfine Interactions, 199, 231-240 (2011)

• Direct mass measurements of 194Hg and 194Au: A new route to the neutrino mass determination?, S. Eliseev, Ch. Böhm, D. Beck, K. Blaum, M. Breitenfeldt, V.N. Fedosseev, S. George, F. Herfurth, A. Herlert, H.-J. Kluge, M. Kowalska, D. Lunney, S. Naimi, D. Neidherr, Yu. N. Novikov, M. Rosenbusch, L. Schweikhard, S. Schwarz, M. Seliverstov, K. Zuber, Phys. Lett. B. 693, 426-429 (2010)

• Critical-Point Boundary for the Nuclear Quantum Phase Transition Near A = 100 from Mass Measurements of 96,97Kr, S. Naimi, G. Audi, D. Beck, K. Blaum, Ch. Böhm, Ch. Borgmann, M. Breitenfeldt, S. George, F. Herfurth, A. Herlert, M. Kowalska, S. Kreim, D. Lunney, D. Neidherr, M. Rosenbusch, S. Schwarz, L. Schweikhard and K. Zuber, Phys. Rev. Lett. 105, 032502 (2010)

• Approaching the N = 82 shell closure with mass measurements of Ag and Cd isotopes, M. Breitenfeldt, Ch. Borgmann, G. Audi, S. Baruah, D. Beck, K. Blaum, Ch. Böhm, R. B. Cakirli, R. F. Casten, P. Delahaye, M. Dworschak, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, M. Kowalska, D. Lunney, E. Minaya-Ramirez, S. Naimi, D. Neidherr, M. Rosenbusch, R. Savreux, S. Schwarz, L. Schweikhard, and C. Yazidjian, Phys. Rev. C 81, 034313 (2010)

• High-precision Penning-trap mass measurements of heavy xenon iso- topes for nuclear structure studies, D. Neidherr, R. B. Cakirli, G. Audi, D. Beck, K. Blaum, Ch. Böhm, M. Bre- itenfeldt, R. F. Casten, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, M.

110 10.2 Miscellaneous, non-reviewed publications

Kowalska, D. Lunney, E. Minaya-Ramirez, S. Naimi, M. Rosenbusch, S. Schwarz, and L. Schweikhard, Phys. Rev. C 80, 044323 (2009)

• Neutron Drip-Line Topography, E. Minaya Ramirez, G. Audi, D. Beck, K. Blaum, Ch. Böhm, C. Borgmann, M. Breitenfeldt, N. Chamel, S. George, S. Goriely, F. Herfurth, A. Herlert, A. Kellerbauer, M. Kowalska, D. Lunney, S. Naimi, D. Neidherr, J.M. Pearson, M. Rosenbusch, S. Schwarz, L. Schweikhard, AIP Conf. Proc. 1165, 94-97 (2009)

• Preparing a journey to the east of 208Pb with ISOLTRAP: Isobaricpu- rification at A = 209 and new masses for 211−213Fr and 211Ra, M. Kowalska, S. Naimi, J. Agramunt, A. Algora, G. Audi, D. Beck, B. Blank, K. Blaum, Ch. Böhm, M. Breitenfeldt, E. Estevez, L.M. Fraile, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, D. Lunney, E. Minaya-Ramirez, D. Neidherr, B. Olaizola, K. Riisager, M. Rosenbusch, B. Rubio, S. Schwarz, L. Schweikhard, U. Warring, Eur. Phys. J. A 42, 351-359 (2009)

• Discovery of 229Rn and the Structure of the Heaviest Rn and Ra Iso- topes from Penning-Trap Mass Measurements, D. Neidherr, G. Audi, D. Beck, K. Blaum, Ch. Böhm, M. Breitenfeldt, R. B. Cakirli, R. F. Casten, S. George, F. Herfurth, A. Herlert, A. Kellerbauer, M. Kowalska, D. Lunney, E. Minaya-Ramirez, S. Naimi, E. Noah, L. Penescu, M. Rosenbusch, S. Schwarz, L. Schweikhard, T. Stora, Phys. Rev. Lett. 102, 112501 (2009)

10.2 Miscellaneous, non-reviewed publications

• IS518: New mass values of neutron-rich Fr and Ra from ISOLTRAP M. Rosenbusch for the ISOLTRAP collaboration, CERN ISOLDE newsletter 2012 http://isolde.web.cern.ch/sites/isolde.web.cern.ch/files/May%202012.pdf

• Excitation modes for the cooling of the ion motion in Penning traps Diploma Thesis, Institut für Physik, Ernst-Moritz-Arndt-Universität Greifswald

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11 Erklärung

Hiermit erkläre ich, dass diese Arbeit bisher von mir weder an der Mathematisch- Naturwissenschaftlichen Fakultät der Ernst-Moritz-Arndt-Universität Greifswald noch einer anderen wissenschaftlichen Einrichtung zum Zwecke der Promotion eingereicht wurde. Ferner erkläre ich, daß ich diese Arbeit selbständig verfasst und keine anderen als die darin angegebenen Hilfsmittel und Hilfen benutzt und keine Textabschnitte eines Dritten ohne Kennzeichnung übernommen habe.

Greifswald, den 22. Oktober 2015

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12 Curriculum vitae

Hauptstr. 35 Marco Rosenbusch 1509 Rubenow H 0157/74934517 curriculum vitae B [email protected]

Personal Date of birth 27. July 1982. Place of Wolgast, Mecklenburg-Vorpommern. birth Education 1990–1994 Primary school, Wolgast. 1994–1996 Middle school, Wolgast. 1996–2002 Secondary school, Phillip-Otto-Runge-Gymnasium, Wolgast, Abitur. 2002–2003 Basic Military Service, 2. Logistikbataillon 142, Basepohl. Tertiary education, University 2003– Ernst-Moritz-Arndt University of Greifswald, Institute of Physics, Studies August. 2009 Physics/Diploma. Diploma Excitation Modes for the Cooling of the Ion Motion in Penning Traps thesis Diploma “sehr gut” (1.4) grade Advisor Prof. Dr. Lutz Schweikhard, Dr. Magdalena Kowalska, Dr. Gerrit Marx PhD thesis Sept. 2009– Ernst-Moritz-Arndt University of Greifswald, Institute of Physics, PhD student, Workgroup Atom and Molecular Physics, Prof. Dr. Lutz Schweikhard.

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13 Acknowledgments

This page is dedicated to express my thanks to all the people around me who made this work possible. I was never alone when carrying out all the effort, meaningless if at CERN or in Greifswald. This makes every achievement to an achievement of us all. First of all I want to thank Prof. Dr. Lutz Schweikhard for supporting me and my ideas since I joined this work group. Dear Lutz, you always had the patience for my questions and ideas about ions in traps. I feel honored that I was sent to CERN to support this great experiment and enjoyed that I always got the freedom try things out. I also want to thank Prof. Dr. Klaus Blaum for his motivation and all the support during my time in the ISOLTRAP collaboration. I want to thank the people at ISOLTRAP I have known during my time. First I want to thank the people who worked closest to me in the recent years, Dr. Robert Wolf who is a great experimental physicist and contributed massively to all setups I have touched during my research, Frank Wienholtz who supported the evaluation of the mass data and who can manage million things in an unbelievable short time, and Dr. Vladimir Manea who supported all my write-ups and who has nerves of steel for my always repeating questions about nuclear physics. Together with Dinko Atanasov, we are a good team and always found a solution for problems. Many thanks also go to the other people I know and have known at ISOLTRAP: Dr. Dennis Neidherr, Daniel Fink, Dr. Sebastian George, Dr. Pauline Ascher, Dr. Christopher Borgmann, Dr. Christine Böhm and the three group leaders I have had during my time, Dr. Alexander Herlert, Dr. Magdalena Kowalska and Dr. Susanne Kreim. I am glad that I had the chance to meet Dr. David Lunney from the ISOLTRAP collaboration who never said no to a nice beer with me. Of course I will also not forget my favorite two ISOLTRAPers from the old times: Dr. Sarah Naimi and Dr. Martin Breitenfeldt, who became good friends of mine. Many thanks go as well to everybody else in the ISOLTRAP collaboration. It was an honor and a positive experience to work together with you. Thanks to the colleagues from my local institute and workgroup in Greifswald for all the support. Half of my research I did together with you all and I appreciated your society, meaningless if for science discussions or for a nice coffee break outside: Dr. Gerrit Marx, Dr. Franklin Martinez, Steffi Bandelow, Albert Vass, Stephan König, Madlen Müller, Christian Dröhse, Paul Fischer, Markus Wolfram, Dirk Weidermann, and my office community Dr. Birgit Schabinger and Stefan Knauer who is my next-chair neighbor. I thank also Iris D. Passow and Erhardt Eich. Special thanks to Prof. Dr. Ralf Schneider and Stefan Kemnitz for all the comuptational support. Ich möchte der Aikidoschule Greifswald für Gesunde und schöne Jahre danken, besonders Dr. Fred Gebler und Alexander Kupin bei denen ich viel gelerne habe. Ich danke meinen beiden Eltern, Hedwiga und Klaus Rosenbusch, und meiner Schwester, Sindy Rosenbusch, für all den Rückhalt der mir über die Jahre gegeben wurde. Ihr habt mich motiviert und mich bei allen Entscheidungen unterstützt und dafür bin ich euch dankbar.

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