Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Bale, Jeffrey Charles
Master of Science - MSc
University of British Columbia
TRIUMF is currently undergoing a major expansion of its capabilities to produce exotic ion beams for experiments. In this thesis, I review a portion of the new infrastructure that I helped to design, the CANadian Rare-isotope facility with Electron-Beam ion source’s Radio Frequency Quadrupole buncher and cooler. The portion that I was responsible for was the injection optics into this buncher and cooler. The studies found a solution to exceed the acceptance requirements of the device, 15 mm mrad by a factor of five, resulting in an acceptance of 67±7 mm mrad for masses of ions as low as 15 AMU, as well as 72±7 mm mrad for masses above 30 AMU. These results came about from simulating both the length of a tapered region in the injection optics, as well as the angle of the taper region with respect to the beam axis The optimal design of the tapered region was have a length of 50 mm at an angle of 4⁰. In addition to these simulations, energy spread investigations were conducted. These studies resulted in a maximum loss of 14% of the acceptance of the device when the delivered beam has an energy spread of 25%. In addition to the design of the injection optics for the buncher and cooler, mass measurements of several short-lived isotopes at Triumf’s Ion Trap for Atomic and Nuclear science were analysed. All of the investigated masses have reduced uncertainties when compared to previous values in the Atomic Mass Evaluation of 2012. Mass excesses for ³¹ ³²Na were found to be 12246(14) keV and 18638(37) keV, respectively, with uncertainties being half of the smallest of those currently published in AME. Mass excess of ²⁹ ³⁴ ³⁵Al were shown to be -18207.77(37) keV, -3000.5(29) keV, and -223.7(73) keV. The mass excess of ³⁴Al has also confirmed the two-neutron separation energy cross over with ³³Mg to be 15(10) keV at a N=21. These nuclear physics studies are discussed in context of the so-called island of inversion and nuclear correlation energy.
Bunching, Cooling, and Measuring of Radioactive Isotopesfor Nuclear PhysicsbyJeffrey Charles BaleBSc, Applied Physics, Simon Fraser University 2014A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)April 2016c© Jeffrey Charles Bale, 2016AbstractTRIUMF is currently undergoing a major expansion of its capabilities to pro-duce exotic ion beams for experiments. In this thesis, I review a portion of thenew infrastructure that I helped to design, the CANadian Rare-isotope facilitywith Electron-Beam ion source’s Radio Frequency Quadrupole buncher and cooler.The portion that I was responsible for was the injection optics into this buncherand cooler. The studies found a solution to exceed the acceptance requirementsof the device, 15 mm mrad by a factor of five, resulting in an acceptance of67±7 mm mrad for masses of ions as low as 15 AMU, as well as 72 ±7 mm mradfor masses above 30 AMU. These results came about from simulating both thelength of a tapered region in the injection optics, as well as the angle of the taperregion with respect to the beam axis The optimal design of the tapered region washave a length of 50 mm at an angle of 4◦. In addition to these simulations, energyspread investigations were conducted. These studies resulted in a maximum loss of14% of the acceptance of the device when the delivered beam has an energy spreadof 25%.In addition to the design of the injection optics for the buncher and cooler,mass measurements of several short-lived isotopes at Triumf’s Ion Trap for Atomicand Nuclear science were analysed. All of the investigated masses have reduceduncertainties when compared to previous values in the Atomic Mass Evaluation of2012. Mass excesses for 31,32Na were found to be 12246(14) keV and 18638(37)keV, respectively, with uncertainties being half of the smallest of those currentlypublished in AME. Mass excess of 29,34,35Al were shown to be -18207.77(37) keV,-3000.5(29) keV, and -223.7(73) keV. The mass excess of 34Al has also confirmedthe two-neutron separation energy cross over with 33Mg to be 15(10) keV at aiiN=21. These nuclear physics studies are discussed in context of the so-called islandof inversion and nuclear correlation energy.iiiPrefaceChapter 1: Figures 1.1, 1.2, and1.3 are used with permissions from References [39],[1] and [2].Chapter 2: All figures were created by myself.Chapter 3: Figure 3.4 is used with permission from Reference [13].Chapter 4: Figures 4.1, 4.24.3, 4.4, 4.5, 4.6, 4.7, 4.9 are used with permissionsfrom References [54], [19] [3], [24], [70], [49], [49], and [48]. Figure 4.8 wascreated by myself.Chapter 5: Figures 5.1, 5.2, 5.3, and 5.4, as well as Table 5.1, and portions of thetext are taken from a paper currently being written, from a paper I am first authoron. The paper was co-authored by the following people who aided in analysis,preparation, and presentation: M. Alanssari ,A. A. Kwiatkowski, C. Andreoiu, U.Chowdhury, J. Even, A. Finlay, D. Frekers, A. T. Gallant, G. Gwinner, R. Klawitter,B. Kootte, D. Lascar, K. G. Leach, E. Leistenschneider, A. Lennarz, A. J. Mayer,B. E. Schultz, D. Short, D. Lunney, and J. Dilling.Chapter 6: All text was created by myself.ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix1 Introduction and Motivation . . . . . . . . . . . . . . . . . . . . . . 11.1 The Nuclear Shell Model . . . . . . . . . . . . . . . . . . . . . . 11.2 Motivation of High Accuracy and High Precision Mass Measure-ments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.3 An ARIEL Overview . . . . . . . . . . . . . . . . . . . . . . . . 32 Principles of Ion Traps . . . . . . . . . . . . . . . . . . . . . . . . . 72.1 Paul Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Penning Traps . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 CANadian Rare-isotope facility with Electron-Beam ion source Ra-dio Frequency Quadrupole Buncher and Cooler . . . . . . . . . . . 16v3.1 Introduction to Emittance and Acceptance . . . . . . . . . . . . . 173.1.1 Acceptance Calculations . . . . . . . . . . . . . . . . . . 193.2 Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.3 Injection Optics Design . . . . . . . . . . . . . . . . . . . . . . . 213.3.1 Immersion Lens Simulations . . . . . . . . . . . . . . . . 223.3.2 Taper Electrode Angle Simulations . . . . . . . . . . . . 243.3.3 Taper Electrode Length Simulations . . . . . . . . . . . . 253.3.4 Energy Spread Simulations . . . . . . . . . . . . . . . . . 274 Introduction to the Isotope Separator and ACcelerator (ISAC) andTRIUMF’s Ion Trap for Atomic and Nuclear science (TITAN) . . . 324.1 Rare Isotope Beam Facilities . . . . . . . . . . . . . . . . . . . . 324.1.1 TRIUMF’s Resonant Ionization Laser Ion Source (TRILIS) 334.2 The TRIUMF Facility and ISAC . . . . . . . . . . . . . . . . . . 344.3 TRIUMF’s Ion Trap for Atomic and Nuclear Science (TITAN) . . 364.3.1 TITAN’s RFQ Buncher and Cooler . . . . . . . . . . . . 364.3.2 TITAN’s EBIT . . . . . . . . . . . . . . . . . . . . . . . 384.3.3 TITAN’s MPET . . . . . . . . . . . . . . . . . . . . . . . 404.4 Time-Of-Flight Mass Measurements in Penning Traps . . . . . . . 404.4.1 Dipole Cleaning . . . . . . . . . . . . . . . . . . . . . . 424.4.2 Sources of Uncertainties . . . . . . . . . . . . . . . . . . 435 Atomic Mass Measurements of Na and Al Isotopes . . . . . . . . . . 475.1 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485.2 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . 58Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60viList of TablesTable 5.1 Each of the nuclides measured in this paper is presented here,alongside the ion that was used as its reference, the excitationtime in MPET Tex, the ratio R, (see Equation 5.2), mass ex-cesses ME from both this work and literature, as well as thetwo-neutron separation energy S2n. For 31,32Na and 35Al wecompare to Atomic Mass Evaluation (AME) [12] and for 29,34Althe more recent values in reference [52]. We also used themass measurements of 27,32,33Al in [52] to calculate the S2n. Allspecies presented in this experiment had a charge state of +1.In the case of 29Al, a 100-300-100 ms Ramsey excitation [43]was used. This table also presents the combined results of the50, 71, 100 ms excitation time of 34Al. . . . . . . . . . . . . . 50viiList of FiguresFigure 1.1 The chart of nuclides covers the ranges of all known possibili-ties of protons and neutrons. The black, central region displaysthe stable nuclides, where the yellow region indicates unstablenuclides. The dashed lines depict the stable magic numbers ofprotons and neutrons, where the coloured lines represent theo-retical two-neutron and two-proton driplines. This figure wastaken with permission from reference [39]. . . . . . . . . . . 2Figure 1.2 The exterior of the new Advanced Rare IsotopE Laboratory(ARIEL) building at TRIUMF, currently under development.This picture was taken with permission from the TRIUMFhome page [1]. . . . . . . . . . . . . . . . . . . . . . . . . . 4Figure 1.3 Schematic of ARIEL 1) The electron gun strips electrons fromthe ion beam, and gives them an initial kick of energy. 2) Theelectrons proceed to the e-linac where they are accelerated viaRF cavities to 50 MeV. 3) Magnets steer the electron beaminto the target hall. 4) The electron beam strikes the target pro-ducing photons that shatter atomic nuclei in the target, creatingisotopes. 5) Isotopes are sorted by charge and mass in the massseparator magnets. 6) Isotopes are sorted by charge and massin the mass separator magnets. 7) A future beamline will bringprotons from the TRIUMF cyclotron into ARIEL. This Figurewas taken used with permission from a private communica-tion [2]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6viiiFigure 2.1 Schematic of a three-electrode, one-dimensional trap. Eachelectrode is a hollow cylinder, the outer electrodes have a com-mon bias, higher than that of the center electrode. This voltagescheme will confine positively charged ions along the electrodeaxis. To trap negative ions, the voltages will be reversed withthe center electrode at the highest potential. . . . . . . . . . . 8Figure 2.2 Schematic of a quadrupole that enables trapping of chargedparticles in two-dimensions The voltage on each pair (red orblue) is 180◦ out of phase with the other pair. This creates arotating saddle-point potential, which prevents the ions fromescaping in the transverse direction. . . . . . . . . . . . . . . 9Figure 2.3 As the quadrupole structure shown in Figure 2.2 is undergo-ing its time-varying potential, it creates a rotating saddle po-tential. When the correct parameters are used, this rotatingsaddle-point is responsible for confinement in two-dimensions. 10Figure 2.4 A schematic of a Penning trap. The use of a grounded hyper-bolic ring electrode with either end capped with positive DCbiased hyperbolic end-caps allows trapping along the z direc-tion. By adding a homogeneous magnetic field parallel to thesame axis, ion trapping is possible in three-dimensions. Thisconfiguration comes very close to providing a parabolic trap-ping potential along the z axis. It should be noted that for anideal Penning Trap 2z0 = r0. . . . . . . . . . . . . . . . . . . 12Figure 2.5 This diagram shows the calculated trajectory of the three eigen-motions of an ion present in a Penning trap. The first motionalong the zˆ, shown in red, is due to the axial motion ωz, the sec-ond is a faster motion at the reduced cyclotron frequency, ω+shown in blue, and the final, slowest motion is at a magnetronfrequency ω−, is shown in black. . . . . . . . . . . . . . . . . 15ixFigure 3.1 In order to find the emittance of the beam at a particular crosssection, each ion’s position, as well as its current angle thatits velocity is making with the beam axis is plotted on twoseparate axes. . . . . . . . . . . . . . . . . . . . . . . . . . . 18Figure 3.2 Left: A non-cut acceptance ellipse with prominent filaments.Center: A post-cut acceptance ellipse with the majority of fil-amentation removed. Notice that the cuts are not perfect, andwhat is left is a dog-bone shape. Right: The superimposedprocessed data from the eight phases, each colour representingdifferent phase. Bottom Row: A more typical acceptance el-lipse shape without the dog-bone appearance as it undergoescutting and fitting. Note: The central images have a differ-ent scale due to rotation transformations used to enable bettercutting of filaments. . . . . . . . . . . . . . . . . . . . . . . . 19Figure 3.3 To describe the emittance of the beam beyond simply the area,the Twiss parameters may be utilized as described in Equa-tion 3.1. Here, the graphical representation of the Twiss pa-rameters is shown with√βε defined as the half width of thebeam,√γε as the half width of the divergence, and α describ-ing the orientation of the ellipse. γ is found by γ = 1+α2β . . . . 20Figure 3.4 The CANadian Rare-isotope facility with Electron-Beam ionsource (CANREB) Radio-Frequency Quadrupole (RFQ) systemis comprised of three distinct regions. The first being the in-jection optics, and the latter two being the RFQ section, andthe ejection optics. For details concerning the RFQ section, aswell as the ejection optics, refer to the CANREB design docu-ment [13] from which this figure was taken with permission. . 22Figure 3.5 A schematic of a three component Einzel lens. This Einzellens consists of three hollow, cylindrical electrodes, with theouter two (shown in blue) have the same bias, and a differentbias is applied to the central electrode (shown in green). . . . 23xFigure 3.6 This figure depicts the electric field, as well as example iontrajectories of the Einzel lens in Figure 3.5. The red lines areequipotential lines, the blue lines are ion trajectories (movingfrom the top left to bottom right), and the brown grid is thecross section of the three Enzel lenses. In this simulation, thepotential is caused by biasing the two outer lenses biased iden-tically, and at a lower potential than the center electrode. Thisfigure was produced using Simion 8.1. . . . . . . . . . . . . . 24Figure 3.7 Ion trajectories, shown in blue, are focused as they pass throughthe immersion lens, shown as a brown grid, as they travel fromthe top left towards the bottom right. This figure was producedusing Simion 8.1. . . . . . . . . . . . . . . . . . . . . . . . . 25Figure 3.8 This figure describes a sample scan of acceptance simulationsas a function of immersion lens biases from 0 V-55 kV. Thisparticular set of simulations were carried out with a taper sec-tion of 150 mm long with an angle of 0◦. . . . . . . . . . . . 26Figure 3.9 A rendered drawing of the section between the some injectionoptics (top right) and the cooling region (bottom left). Thisparticular image is from the 150 mm Taper section with an an-gle of 2◦. In this figure, the beam enters from the upper rightand travels towards the bottom left. . . . . . . . . . . . . . . 27Figure 3.10 A diagram of a funnel with a disperse substance being pouredinto the top, and leaving the funnel after being redirected. . . . 28Figure 3.11 These images are a sampling of simulations with the same ionsto show the effect of the taper angle. The ions in these imagesenter from the top. Left: a taper section with an angle of 0◦,causes many ions to miss the point of entry. Center: an angleof 9◦ manages to capture additional ions that would have oth-erwise have escaped. Right: an angle of 90◦ allows nearly allof the would-be ions to escape the device. Note: The positionand angle spread of the incoming ions was chosen to be muchlarger than the acceptance of the device in order to fully traceout the acceptance of the device. . . . . . . . . . . . . . . . . 29xiFigure 3.12 This figure displays a sample of the acceptance simulations in-vestigating the angle dependence. This set of data came fromsimulating a taper section of 150 mm length, with an immer-sion lens bias of 55 kV. As can be seen, there is clearly an angledependence that peaks near the 2◦ case. . . . . . . . . . . . . 30Figure 3.13 This figure depicts a typical acceptance plot as a function of ta-per angle, immersion lens bias, as well as mass. Similar accep-tances to these plots may also be reached by different anglesand biases of different length taper sections. The ion’s energyin these simulations was 200 eV. . . . . . . . . . . . . . . . . 31Figure 3.14 This figure summarizes the ion energy spread investigations.Energies both 50 eV above and below the ideal 60 keV energywere used at different angles for both mass 15 Atomic MassUnit (AMU) and 30 AMU. . . . . . . . . . . . . . . . . . . . . 31Figure 4.1 Green: Elements that have been delivered at TRIUMF vialaser ionization. Blue: Elements that are currently undergoingtesting at TRIUMF for their feasibility with laser ionization.Grey: Elements that are theoretically possible via laser ion-ization, but have yet to be tested at TRIUMF. This figure is anupdated version of that in reference [55], obtained through aprivate communication [54], and used with permission. . . . . 34Figure 4.2 Schematic of Isotope Separator and ACcelerator (ISAC) beamproduction and separation. The proton beam from the maincyclotron impinges on the ISAC target, resulting in a varietyof isotopes. After the newly created isotopes are extractedfrom the ion source, they undergo two phases of mass separa-tion, with the second being the High Resolution Mass Sepera-tor (HRMS). At this point, the mass separated beam is deliveredto the various experiments in the ISAC experimental hall. Thisschematic is taken with permission from Reference [19]. . . . 35xiiFigure 4.3 Schematic of the TRIUMF’s Ion Trap for Atomic and Nuclearscience (TITAN) set-up which consists several sections. TheRFQ (Section 4.3.1) receives the beam from ISAC for bunch-ing and cooling. The second, and optional stage is chargebreeding in the Electron Beam Ion Trap (EBIT) (Section 4.3.2).Thirdly, the ions will enter Measurement Penning Trap (MPET)(Section 4.3.3) for excitation. Finally the ions will strike anMulti-Channel Plate (MCP) to enable mass determination viathe Time-Of-Flight (TOF) technique (Section 4.4). This figurewas taken with permission from the publicly available TITANhome page [3]. . . . . . . . . . . . . . . . . . . . . . . . . . 37Figure 4.4 The schematic of the TITAN RFQ which consists of 24 elec-trodes forming a potential well. As the continuous beam en-ters the RFQ it undergoes collisions with the helium buffer gas.This causes the ions to lose kinetic energy to the buffer gasas they fall deeper into the potential well. Upon extraction, thelast several electrodes change their potential to allow the newlycooled bunched beam to exit. This figure was based on that inreference [24] . . . . . . . . . . . . . . . . . . . . . . . . . . 38Figure 4.5 The TITAN EBIT consists of a potential well where the ions arestruck by an incoming electron beam. The electron beam stripsoff additional electrons from the ions, thus increasing the ionscharge state. Confinement during the charge breeding processis done through a parallel magnetic field, and electrostaticlybiased electrodes. This image is courtesy of M. Simon. . . . . 39Figure 4.6 Normalized radial energy as a function of injection time andexcitation time. Here ∆νRF represents the phase that the ionenters the penning trap, and TRF represents the excitation time.This figure uses TRF = k◦pi . This figure was used with permis-sion from reference [49]. . . . . . . . . . . . . . . . . . . . . 42xiiiFigure 4.7 The solid line represents the theoretical TOF of on and off cy-clotron resonance excitation from Equation 4.6. The dashedline is the superimposed energy due to excitation. This figurewas used with permission from reference [49]. . . . . . . . . 43Figure 4.8 In order to apply dipole cleaning, two electrodes opposite fromeach other (in this case blue and red) undergo a time-varyingpotential 180◦ out of phase from one another. In the case ofTITAN, the electrodes that apply this electric field are slices ofthe so-called compensation electrode in MPET. . . . . . . . . 44Figure 4.9 The solid line represents the extrapolation of the cyclotron fre-quency spanning from 0 to 25 ions trapped simultaneously.This fit was based on the shown data using a least squares fit.This figure was taken from reference [48] for an analysis of36Ar+. This figure was used with permission from reference [48]. 46Figure 5.1 TOF spectrum of 34Al with an excitation time of 100 ms. Hereνc ≈ 1670813 Hz. The solid curve is the analytic fit [49]. . . . 49Figure 5.2 A sample of mass measurements with the horizontal lines cen-tred around the AME indicating the 1σ confidence level. Ascan be seen our new value, TITAN 2015, disagrees with AMEby 1.4σ . Values taken from [46, 61, 69, 76] . . . . . . . . . . 52Figure 5.3 TOF resonance simulations for 34Al for the ground state andisomer with various differences in their masses, and yield ra-tios. The leftmost vertical line represents the νc of the isomer,and the rightmost vertical line represents the νc of the groundstate, νc ≈ 1670813 Hz A: a difference of 100 keV and an iso-mer ratio of anywhere from 50% to 0% of trapped ions. B: adifference of 200 keV was simulated. C: a difference of 300 keV. 55xivFigure 5.4 Two-neutron separation energies comparing the experimentalresults with those from literature, including an expanded viewof the N = 21 crossover. Solid circles represent values takenfrom AME [12], open circles represent values determined byTITAN measurements, triangles represent energies determinedusing both AME and TITAN measurements together, and linesrepresent theoretical values [52]. Note that theoretical calcula-tions for Na have yet to be calculated. . . . . . . . . . . . . . 56xvGlossaryThroughout the thesis many acronyms were used. For simplicity, and convenience,each one is defined hereAC Alternating CurrentAME Atomic Mass EvaluationAMU Atomic Mass UnitARIEL Advanced Rare IsotopE LaboratoryBNG Bradbury Nielsen GateCANREB CANadian Rare-isotope facility with Electron-Beam ion sourceCPET Cooler PEnning TrapCW Continuous WaveEBIS Electron Beam Ion SourceEBIT Electron Beam Ion TrapFWHM Full Width Half MaxHRMS High Resolution Mass SeperatorIR InfraredISAC-TRIUMF Isotope Seperator and ACcelerator at TRIUMFxviISAC Isotope Separator and ACceleratorISAC1 Isotope Separator and ACcelerator facility 1ISOL Isotope Separator On-LineMCP Multi-Channel PlateME Mass ExcessMPET Measurement Penning TrapNSCL National Superconducting Cyclotron LaboratoryPPB Parts Per BillionPPS Particles Per SecondPTMS Penning Trap Mass SpectrometryRF Radio FrequencyRFQ Radio-Frequency QuadrupoleRIB Rare Isotope BeamRILIS Resonant Ionization Laser Ion SourceRMS Root Mean SquareSOI Species of InterestSHM Simple Harmonic MotionSRF Superconducting Radio FrequencyTITAN TRIUMF’s Ion Trap for Atomic and Nuclear scienceTOF Time-Of-FlightTOF-ICR Time-Of-Flight Ion Cyclotron ResonanceTRILIS TRIUMF’s Resonant Ionization Laser Ion SourcexviiUV UltraVioletVOS Valley Of StabilityxviiiAcknowledgementsI would like to thank Brad Barquest for his continuous support throughout theentirety of the CANREB project. Ania Kwiatkowski and Julia Even for taking thetime in assisting me in publishing my first paper. Aaron Gallant, for always findingthe time to discuss PTMS with me. Jens Dilling for being a supportive supervisor.Douglas Bryman for being an excellent second reader. Corina Andreoiu and MartinSimon, for inspiring me as an undergrad to become a grad student. Carlie Deans,for taking the time out of her day, no matter how busy, to make one last edit beforeI send something out. And finally, Chris, for always being there with a beer.Thank you all,CheersxixChapter 1Introduction and MotivationIf I have seen farther it is by standing on the shoulders of Giants.— Sir Isaac Newton (1676)1.1 The Nuclear Shell ModelMatter is a fundamental part of our universe, and its study has been on going forthousands of years in different forms. Today’s investigations of matter have pro-gressed so far that we are no longer content at simply studying the atoms that makeup the world around us, but we are creating more and more exotic and short-livedspecies that have long since departed our world. How we have come to classifyatoms is now both by the number of protons Z, their number of neutrons N, andtheir energy states. We have moved far from the standard periodic table that peoplelearn about in secondary school and, in fact, have had to produce a much largerand more comprehensive view of what matter is consists of. The current option ofchoice to describe the atomic constituents of matter is the chart of nuclides, suchas that in Figure 1.1. The chart of nuclides includes all known possibilities of com-binations of different proton and neutron configurations. In general, the centralregion of the chart contains the more stable of the proton-neutron combinations,with the species further out from this Valley Of Stability (VOS) being less stable.However this trend of decreasing life times further out from the VOS does occur,there are local regions of higher stability. These regions of enhanced stability arise1Figure 1.1: The chart of nuclides covers the ranges of all known possibil-ities of protons and neutrons. The black, central region displays thestable nuclides, where the yellow region indicates unstable nuclides.The dashed lines depict the stable magic numbers of protons and neu-trons, where the coloured lines represent theoretical two-neutron andtwo-proton driplines. This figure was taken with permission from refer-ence [39].from the closure of nuclear shells, and occur at so-called magic proton and neutronnumbers[45, 56, 57].1.2 Motivation of High Accuracy and High PrecisionMass MeasurementsThe discovery of the enhanced stability of nuclei with magic proton and neutronnumbers paved the way for the postulation of the nuclear shell model [45, 56,57]. The nuclear shell model gives robust results to describe properties of nucleialong the VOS. However, when moving away from the valley of stability, the well-known magic numbers seem to disappear while new magic numbers appear [47,71]. In 1975, it was found that the N = 20 neutron shell closure disappears inneutron rich Na isotopes, and this has since become known as one of the islands ofinversion [73]. In recent years, this N = 20 island of inversion has been shown to2rise from a non-standard filling of the sd and p f energy levels [71]. This modifiedorder of energy level occupation is caused by large gains in correlation energy dueto the excitation of neutron pairs into the p f orbital. By studying regions wherethese features are prominent [72], as well as those regions with extreme neutron-to-proton ratios, it’s possible to gain further insight into nuclear structure [11].Through this, we can further investigate the details of the shell model, and canidentify new, possible features that have previously gone undetected. Examplesof such are the recent measurements that showed that the inversion of the shellsof N = 20 and N = 28, are in fact, a single island connected via neutron rich Mgisotopes [29, 35].One of the most efficient ways to investigate features of nuclear structure,including binding energies and two-neutron separation energies, is through massmeasurements. Mass measurements are a versatile and powerful tool which pro-vide access to the combined effects of all interactions inside the atom. This makesmass measurements an integral part of nuclear-structure investigations and the ex-ploration of new regions of the chart of nuclides (e.g. [47]).There are multiple approaches to performing mass measurements where eachof the various approaches reach different degrees of precision and accuracy. Al-though each technique has its advantages, the resultant precision that arises fromtechniques may be insufficient for scientific objectives. The Time-Of-Flight (TOF)mass excess determinations of 32Na [38, 46, 61, 69, 76], for example, span a rangeof 2.5 MeV with uncertainties varying from 0.1 MeV to 1.3 MeV. The size of thisspread hinders reliable conclusions on the underlying structure. More reliable re-sults can be delivered via the more accurate and precise method of Penning TrapMass Spectrometry (PTMS) [14]). Indeed, the uncertainties of the mass measure-ments via PTMS in this thesis (see Chapter 5) are a factor of 3.2 times smaller thanthat of the smallest, previously mentioned uncertainties [12].1.3 An ARIEL OverviewAs time progresses, more exotic beams are required in order to study new andinteresting physics. In order to help meet the requirements of these ever increas-ing demands TRIUMF is currently building the Advanced Rare IsotopE Labora-3Figure 1.2: The exterior of the new ARIEL building at TRIUMF, currentlyunder development. This picture was taken with permission from theTRIUMF home page [1].tory (ARIEL) (1.2) to not only reach further into more extreme neutron-proton ra-tios, but also to expand the capabilities of the Isotope Seperator and ACceleratorat TRIUMF (ISAC-TRIUMF) to performing three simultaneous experiments[58].Upon completion ARIEL will allow investigations of isotopes relevant for the fieldsof of Nuclear Physics, Astrophysics, Nuclear Medicine, and Material Science thathave previously been inaccessible.The new ARIEL facility will utilize a 50 MeV 10 mA Continuous Wave (CW)linear electron accelerator, as well as the CANadian Rare-isotope facility withElectron-Beam ion source (CANREB). The second beamline will take advantageof a currently inactive beamline driven by the world’s largest cyclotron[4] accel-erating protons to 500 MeV with a current of 100 µ A[58]. ARIEL consists ofSuperconducting Radio Frequency (SRF) cavities that brings the electron beam to450 MeV, followed by a target station where photo-fission occurs. After photo-fission, radioactive isotopes are created and undergo mass separation at the CANREBHigh Resolution Mass Seperator (HRMS), followed by a Radio-Frequency Quadrupole(RFQ) buncher and cooler (discussed in Chapter 3). The RFQ’s purpose is to pack-age the CW beam into discrete packets, as well as to decrease the beam’s energyspread. After extraction from the RFQ the beam may be sent into the Electron BeamIon Source (EBIS) where charge breeding, increasing the charge state of ions, mayoccur. Finally, the radioactive beam will be filtered with a Nier Spectrometer [30]and sent to ISAC-TRIUMF where the various experiments are located. Using ARIELin conjunction with the Isotope Separator On-Line (ISOL) technique at Isotope Sep-arator and ACcelerator (ISAC) (see Chapter 4) will for not only allow for a fartherreach from the VOS, but enable an additional two beamlines to service the ISACexperimental halls. This will be accomplished by extending a currently unusedbeamline from the cyclotron, and transporting it alongside ARIEL and adding it’sown target station for the ISOL technique, as shown in Figure 1.3.5Figure 1.3: Schematic of ARIEL 1) The electron gun strips electrons from theion beam, and gives them an initial kick of energy. 2) The electrons pro-ceed to the e-linac where they are accelerated via RF cavities to 50 MeV.3) Magnets steer the electron beam into the target hall. 4) The electronbeam strikes the target producing photons that shatter atomic nuclei inthe target, creating isotopes. 5) Isotopes are sorted by charge and massin the mass separator magnets. 6) Isotopes are sorted by charge andmass in the mass separator magnets. 7) A future beamline will bringprotons from the TRIUMF cyclotron into ARIEL. This Figure was takenused with permission from a private communication [2].6Chapter 2Principles of Ion TrapsAn RFQ buncher and cooler is a three-dimensional trap that confines charged par-ticles (in our case ions) as they undergo buffer gas collisions and are grouped intobunches. In order to understand the mechanisms behind the RFQ, we must firstcover the theory behind its predecessor, the linear Paul trap, which confines ions intwo-dimensions.2.1 Paul TrapsThe force from an electric field or magnetic field acting on a charged particle isdescribed by Equation 2.1 [22]. In this equation, F is the force acting on an ionwith a charge of q moving with a velocity v, in an electric field E, and a magneticfield B. This force is known as the Lorentz Force, and this is what enables theconfinement of ions.~F = q(~E +(~v×~B)) (2.1)Using this equation, one-dimensional confinement may be accomplished simplyby using three electrodes to create a potential well (Figure 2.1). This confinementis possible by having the outer two hollow cylindrical electrodes, at a matchingvoltage higher than that of the inner electrode. This will create a potential well thatwill capture positively charged ions. In order to confine negatively charged ions,the potentials would have to be reversed.7Figure 2.1: Schematic of a three-electrode, one-dimensional trap. Each elec-trode is a hollow cylinder, the outer electrodes have a common bias,higher than that of the center electrode. This voltage scheme will con-fine positively charged ions along the electrode axis. To trap negativeions, the voltages will be reversed with the center electrode at the high-est potential.In this configuration, a charged ion will repelled by the outer two electrodes,and attracted to the central electrode. Thus, the ion is subjected to one-dimensionalconfinement. Two-dimensional confinement requires creating a two-dimensionalpotential well. However, this entails having a charge distribution or an electrode atthe potential minimum. Having an electrode at the potential minimum would causeany trapped ions to collide with it, and as such would defeat the purpose of the trap.In order to trap charged ions in two-dimensions, we need a potential minimum infree-space. As the Earnshaw Theorem shows, it is impossible for a charged particleto remain stable in a purely static electric field [74]. However, it is still possible totrap an ion in free-space if we take advantage of time-dependent electric fields. Thesimplest way to accomplish time-dependent electric field, is to apply a sinusoidallyoscillating field to a quadrupole electrode configuration. In this configuration, twopairs are 180◦ out of phase with each other, as shown in Figure 2.2. Using thisconfiguration correctly allows us to produce an overall restoring force.As the two electrode pairs are exactly half an oscillation period out of phase, an8Figure 2.2: Schematic of a quadrupole that enables trapping of charged par-ticles in two-dimensions The voltage on each pair (red or blue) is 180◦out of phase with the other pair. This creates a rotating saddle-pointpotential, which prevents the ions from escaping in the transverse direc-tion.ion will experience both an attraction, and a repulsion in different directions. As thecharged ion is attracted to two of the electrodes, it will move towards one of them.If the applied voltages change quickly enough, the ion will be repelled by the sameelectrode before the ion collides with the electrode, and move towards one of theelectrodes of the opposite polarity. This field oscillation causes an overall focusingeffect [31] in two-dimensions, and results in a rotating saddle-point, as shown inFigure 2.3. The time averaged potential that an ion experiences due to the switchingelectrodes is known as the pseudo-potential, and is shown in Equation 2.2 [16].Vpseudo(r) =eV 2RF4mr40ω2RFr2 (2.2)Thus, this pseudo-potential, Vpseudo, is dependent on the ion’s radial distance,denoted as r, the distance the electrodes are spaced from the beam axis, r0, the ion’smass, m, the ions charge, e, the frequency of oscillation applied to the electrodes,ωRF , and the applied peak to peak voltage of the electrodes, VRF . Although onecan apply an arbitrary pseudopotential according to Equation 2.2, not all parametercombinations will yield desirable results. Qualitatively, if ωRF is not large enough,9Figure 2.3: As the quadrupole structure shown in Figure 2.2 is undergoing itstime-varying potential, it creates a rotating saddle potential. When thecorrect parameters are used, this rotating saddle-point is responsible forconfinement in two-dimensions.it is easy to picture the ions rolling down the saddle-point and out of the trap beforethe electrodes are able to switch their polarity, and force the ion back towards thecenter. In order to determine which sets of parameters can yield stable motion, onestarts with the equation of motion of a ion in the centre of a quadrupole potential[62]. The solution of Laplace’s Equation for a linear quadrupole (Equation 2.3)resembles stable Simple Harmonic Motion (SHM) in one direction, and unstableSHM in the other [22].Φ=Φ02r20(y2− x2) (2.3)Here, Φ is the potential experienced by the ion, Φ0 is the potential difference acrossthe electrode structure, r0 is the spacing of the electrodes from the central axis,and x and y represent the position of the ion in the transverse plane. The secondorder differential equations used to describe the transverse motion in the x and ydirections are standard equations for SHM described in Equations 2.4 through 2.6with Φ oscillating in time according to Equation 2.7.d2xdt2−ω2x = 0 (2.4)d2ydt2+ω2y = 0 (2.5)10ω2 =eΦ0mr20(2.6)Φ0 =VRF cos(ωRFt) (2.7)Due to time dependence, Equations 2.4 to 2.7 do not have closed form solu-tions. Thus, another technique to analyse them is needed. With substitutions andmanipulation they may be made to take the form of Equation 2.8, known as theMathieu Equation. In this equation, ξ is a generic variable that may represent ei-ther x or y. In addition to ξ , two substitutions are used and defined in Equations 2.9and 2.10. Here, q is known as the Mathieu stability parameter.d2ξdτ2+2qcos(2τ)ξ = 0 (2.8)q =2eVRFmr20ω2RF(2.9)τ =ωRFt2(2.10)The condition for stable trapping is q< 0.908 [16]. The ions will undergo two typesof motion inside the trap. The first is a slower macro-motion which occurs due tothe pseudo-potential, and the second is a faster micro-motion due to the drivingfrequency. By using Equations 2.9 and 2.10, and defining Vpseudo =mω2macror22 , weobtain Equations 2.11 and 2.12.ω2macro =q2ω2RF8(2.11)ω2macro =2emr20Vpseudo(r0) (2.12)Extending a two-dimensional Paul trap in the third direction, it’s possible toconfine ions radially while travelling down the z axis. This type of trap is knownas a linear Paul trap [37], and commonly referred to as an RFQ due to the fact thatit operational frequency is typically in the same range as radio-waves (MHz). See11Figure 2.4: A schematic of a Penning trap. The use of a grounded hyper-bolic ring electrode with either end capped with positive DC biased hy-perbolic end-caps allows trapping along the z direction. By adding ahomogeneous magnetic field parallel to the same axis, ion trapping ispossible in three-dimensions. This configuration comes very close toproviding a parabolic trapping potential along the z axis. It should benoted that for an ideal Penning Trap 2z0 = r0.Section 4.3.1 for more information on the uses of an RFQ.2.2 Penning TrapsIn this section, the theory behind the hyperbolic Penning trap will be discussed.It was this variety of trap that was used to produce the measurements presented inChapter 5. The hyperbolic Penning trap consists of a hyperbolic ring electrode, twohyperbolic caps with a DC bias, and a homogeneous magnetic field (Figure 2.4).Using this configuration, three-dimensional confinement is possible. The additionof the magnetic field will cause an ion with a component of its velocity perpendic-ular to the z-axis to move in a circular pattern in the x and y directions, while theDC bias will confine the ion along the z axis (axes defined in Figure 2.4).An ideal hyperbolic Penning trap’s electric field [9] takes on the form of Equa-tion 2.13, where z and r are the longitudinal and radial distances between the centerof the trap, VDC is the end-cap bias voltage. The characteristic length, d0, is furtherdefined as shown in Equation 2.14. It should also be noted that for an ideal Penning12trap, the longitudinal and radial distances are related by 2z0 = r0.V(z,r) =VDC2d20(z2− r22) (2.13)d0 =√z202+r204(2.14)Using this potential, and transferring into a cylindrical co-ordinate system, theforce that an ion will undergo is simply:F = m~a =−qVDCd20(~z−~r2)−qB~˙r× zˆ. (2.15)Separating the radial (r) and axial (z) motions, we obtain Equations 2.16 and 2.17.z¨ =−qVDCmd20z (2.16)r¨ =qVDC2md2o~r− qBm~˙r× zˆ (2.17)Once again, by inspection it is clear that ions exhibit SHM in the axial direction.Rewriting this to solve for the oscillating frequency in the axial direction, we obtainωz as shown in Equation 2.18.ωz =√qVDCmd20(2.18)As the cyclotron frequency [41] is given by Equation 2.19, we may combine itwith Equations 2.17 and 2.18 to obtain the radial equation of motion as presentedin Equation 2.20.ωc =qmB (2.19)~¨r =ω2z2~r+ωc~˙r× zˆ (2.20)Rewriting Equation 2.20 into Cartesian co-ordinates, Equations 2.21 and 2.2213are obtained.~¨x−ωcy˙− ω2z2x = 0 (2.21)~¨y−ωcx˙− ω2z2y = 0 (2.22)Defining a general co-ordinate u = x+ iy these two equations may be combinedinto a single relation as shown in Equation 2.23.u¨ =−iωcu˙+ ω2z2u (2.23)Solving for the eigen-frequencies of Equation 2.23 leads to Equation 2.24.ω± =ωc2± ωc2√1− 2ω2zω2c(2.24)Rearranging this, we obtain Equations 2.25 to 2.27.ωc = ω++ω− (2.25)ω2c = ω2++ω2−+ω2z (2.26)ω2z = 2ω+ω− (2.27)As ωz is much lower than that of ωc, it is possible to take the Taylor seriesapproximation of Equation 2.24 to obtain Equations 2.28 and 2.29. Here ω− isknown as the magnetron motion, and ω+ is the reduced cyclotron motion, as it isslightly lower than that of ωc.ω− ≈ ω2z2ωc(2.28)ω+ ≈ ωc− ω2z2ωc(2.29)14Figure 2.5: This diagram shows the calculated trajectory of the three eigen-motions of an ion present in a Penning trap. The first motion along thezˆ, shown in red, is due to the axial motion ωz, the second is a fastermotion at the reduced cyclotron frequency, ω+ shown in blue, and thefinal, slowest motion is at a magnetron frequency ω−, is shown in black.Thus, the three eigen motions of an ion in a Penning trap areωz in combination withω− and ω+. This motion is shown in Figure 2.5. For a more thorough derivationof these motions, please consult reference [36].15Chapter 3CANadian Rare-isotope facilitywith Electron-Beam ion sourceRadio Frequency QuadrupoleBuncher and CoolerThe CANREB buncher and cooler is a device that will take the continuous beamof isotopes from ARIEL’s HRMS, lower the energy spread of the beam via buffergas collisions, and bunch the beam into discrete pulses of ions to be sent to thenext stage of CANREB. Although simulations that were done on all the variousregions of the CANREB buncher and cooler, see Figure 3.4, the focus of this chapterwill be on the injection optics. The extraction optics, as well as the bunching andcooling simulations are outside of the scope of this work, but are documented inthe CANREB design document [13].It should be noted that the taper angle section, studied within Sections 3.3.2and 3.3.3, will not be used in the final RFQ design due to several reasons. Thefirst reason is that it was decided that in order to deliver low energy, singly chargedion beams to select experiments in ISAC, the RFQ will have to be able to utilizereverse extraction This means the injected ions will leave through the same opticsas the beam originally entered. This need of reflecting the beam arises from the16optics downstream of the RFQ being designed for non-singly charged ions at higherenergies (10’s of keV as opposed to 100’s of eV). The only other alternative low-energy beam transport without removing the taper-section from the injection opticswould be to add an additional beamline parallel to the existing highly charged ionbeamline. This additional beamline would be designed for the lower energies,however this was deemed infeasible due to both funding and space limitations. Asthe taper-section would not be able to support the reverse extraction from the RFQ,it was decided their added benefits (in the form of an enlarged acceptance) did notoutweigh the additional complications that would arise in delivering the beam toIsotope Separator and ACcelerator facility 1 (ISAC1).3.1 Introduction to Emittance and AcceptanceAn important figure of merit for beam transport is the beam emittance. The beamemittance is found by taking a transverse slice, in the x− y plane of the beam, andrecording each ion’s position (x) and momentum (~P′) on a single graph. In thecase of the axial momentum, ~Paxial , being much greater than that of the transversemomentum, ~Ptrans, the small angle approximation may be used such that the angleof each ion’s trajectory with respect to the beam axis is x′ ≈ PtransPaxial . An exampleof the emittance plot is shown in Figure 3.1 with the area of the spanned regionknown as the emittance of the beam. Because emittance is the area found on a mmvs mrad plot, it has units of mm mrad, however, due to convention a factor of pimay also added into the units of emittance creating an overall unit of pi mm mrad(note this factor of pi is not used within this report). This comes from the fact mostideal emittances are elliptical.Ideally in a transversely symmetric potential, the shape of a beam (in the x,x′phase space) is an ellipsoid, however, beams are not limited to this shape as beamsare known to become filamented with spiralling arms coming off of the body ofthe ellipse (See Figure 3.2). This filamentation is due to higher order effects thatare beyond the scope of this work. In order to avoid over estimating the acceptanceof the device due to including these filimentations, they may be removed. Thisremoval of the filaments is accomplished by rotating the acceptance ellipse, andthen removing the arms. The rotation of the ellipse is used to allow for more17Figure 3.1: In order to find the emittance of the beam at a particular crosssection, each ion’s position, as well as its current angle that its velocityis making with the beam axis is plotted on two separate axes.precise cutting away of the arms, without removing sections of the main body ofthe ellipse.When discussing a component it is common to refer the largest possible emit-tance it can accept as the acceptance of the device. In order to describe the beam’sorientation as well as its phase space area, Twiss parameters [28] are used. TheTwiss parameters based on the half-width of the emittance in both x and x′ direc-tions, as well as the orientation in the x,x′ phase space. To describe the emittanceof the beam beyond simply the area, the Twiss parameters may be utilized as de-scribed in Equation 3.1. A graphical representation of the Twiss parameters areshown in Figure 3.3. In order to quantitatively find if a beam is either converg-ing (narrowing) or diverging (widening), α , as defined in Equation 3.4 may beused. If α > 0 the beam is converging, if α < 0 the beam is diverging, and fi-nally if α = 0 the beam section may be described as either a waist (minimum)or anti-waist (maximum). Throughout the simulations these values were calcu-lated via Equations 3.2-3.4 with ε being defined as the emittance of a Root MeanSquare (RMS).18Figure 3.2: Left: A non-cut acceptance ellipse with prominent filaments.Center: A post-cut acceptance ellipse with the majority of filamen-tation removed. Notice that the cuts are not perfect, and what is left isa dog-bone shape. Right: The superimposed processed data from theeight phases, each colour representing different phase. Bottom Row: Amore typical acceptance ellipse shape without the dog-bone appearanceas it undergoes cutting and fitting. Note: The central images have a dif-ferent scale due to rotation transformations used to enable better cuttingof filaments.ε = γx2 + 2αxx′ + βx′2 (3.1)γ =var(x′)ε(3.2)β =var(x)ε(3.3)α =−covar(x,x′)ε(3.4)3.1.1 Acceptance CalculationsAs the RFQ provides a time varying potential to trap ions in the transverse di-rections, xˆ and yˆ, ions entering the RFQ at different points during the Radio Fre-quency (RF) cycle, will encounter different fields. In order to ensure an accurate ac-19Figure 3.3: To describe the emittance of the beam beyond simply the area, theTwiss parameters may be utilized as described in Equation 3.1. Here,the graphical representation of the Twiss parameters is shown with√βεdefined as the half width of the beam,√γε as the half width of thedivergence, and α describing the orientation of the ellipse. γ is foundby γ = 1+α2β .ceptance simulation of a CW beam, the ions were simulated at eight evenly spacedRF phases from 0◦ to 360◦ during the RF cycle. The acceptance of each of thesephases was viewed individually, and any large filaments were removed such that90 % of the fitted ellipse was filled with the fitting program (See Figure 3.2). Theacceptance plots in this report include results of the averaged acceptance of theeight phases that the ions were simulated to enter the RFQ.After each phase was processed and was cut individually, the area of over-lapping acceptance ellipses was calculated. Thus the overlapping acceptance isthe minimum acceptance that can be guaranteed. Due to the nature of the cutting20and averaging process, the average acceptance of the eight different phase injec-tion will always be higher than the overlapping acceptance. Occasionally a singlephase may skew the overlapping acceptance by being small enough to dominatethe fit. In order to account for this situation when it occurred, the emittance of eachphase were averaged together. The reported averaged Twiss parameters arise fromaveraging them across all eight phases.3.2 RequirementsThe requirements of the CANREB RFQ [13] are to maximize the efficiency of injec-tion, extraction, and cooling of a CW beam, into an Alternating Current (AC) beam.More specifically, the RFQ must be capable of handling a beam of ions with a massrange from 15 Atomic Mass Unit (AMU) to 250 AMU. Although the exact injectionenergy spread is unknown, it was decided that if a simulated energy spread range of±50 eV could be transported without significant (> 50%) efficiency drops, the RFQshould meets specifications. In addition to this, the acceptance of the device mustbe, at a minimum, 15 mm mrad. In order to ensure that these requirements weremet, multiple investigations were carried out for the injection region including theimplementation of an immersion lens (Section 3.3.1) as well as a taper region withboth the taper’s angle (Section 3.3.2), and its length (Section 3.3.3).3.3 Injection Optics DesignAs mentioned previously, in order to maximize the normalized acceptance of theRFQ, simulations of the injection optics were carried out for both the immersionlens (Section 3.3.1) and taper section (Sections 3.3.2 and 3.3.3). In order to opti-mize both the immersion lens biasing, the tapered section’s angle, as well as thetaper section’s length, two of the three variable had to be held constant as the thirdwas investigated. The results of these simulations are discussed in the followingsections.21Figure 3.4: The CANREB RFQ system is comprised of three distinct regions.The first being the injection optics, and the latter two being the RFQsection, and the ejection optics. For details concerning the RFQ section,as well as the ejection optics, refer to the CANREB design document [13]from which this figure was taken with permission.3.3.1 Immersion Lens SimulationsIn order to understand how the immersion lens focuses the beam, one first has tounderstand the physics of the Einzel lens [8] from which it is derived. The use of anEinzel lens in beamlines is quite common for focusing in both transverse directionsand consists of three hollow, cylindrical electrodes that the ions will sequentiallytravel through. (see Figure 3.5). The outer electrodes of the Einzel lens are heldat the same potential while the central cylinder is biased separately. The potentialdifferences between the cylinders produces a focussing field. However, due tothe fact that electric fields are conservative, the normalized emittance must remainconstant, thus increasing the angular spread of the beam (Section 3.1. The useof an Einzel lens allows the rotation of the emittance of a beam from one of oneoccupying a large spatial spread and little angular spread, to one of a large angularspread with a small spatial spread. This conversion from spatial spread into angularspread can be seen in Figure 3.6.In the case of the CANREB RFQ it was decided that an entire Einzel lens wouldnot be needed, and as such only two of the three electrodes were incorporated(shown in Figure 3.7).This modified Einzel lens is known as an immersion lens [5] and has the advan-tage of bringing the beam to a different potential. Thus, upon exiting the immer-sion lens, not only are the ions focused in position space, but they have decreased22Figure 3.5: A schematic of a three component Einzel lens. This Einzellens consists of three hollow, cylindrical electrodes, with the outer two(shown in blue) have the same bias, and a different bias is applied to thecentral electrode (shown in green).their longitudinal speed as they are at a higher potential energy than they origi-nally started. This allows for more effective cooling via buffer gas collisions asthe ions will encounter the gas at lower speeds, and allows the ions to be extractedafterwards with the desired energy by lowering their potential energy.The immersion lens parameter that was investigated was the effect that the lensbiasing had on the acceptance of the CANREB RFQ in conjunction with differentmass ranges. As the Rare Isotope Beam (RIB) is entering the RFQ with an energyof 60 keV the simulated bias ranged from a minimum of 0 V up to a maximum of55 kV. At this point the acceptance of the device was clearly dropping, as shown23Figure 3.6: This figure depicts the electric field, as well as example ion tra-jectories of the Einzel lens in Figure 3.5. The red lines are equipotentiallines, the blue lines are ion trajectories (moving from the top left to bot-tom right), and the brown grid is the cross section of the three Enzellenses. In this simulation, the potential is caused by biasing the twoouter lenses biased identically, and at a lower potential than the centerelectrode. This figure was produced using Simion 8.1.in Figure 3.8. As the simulation’s parameter space included not only lens biasing,but also the length and angle of the taper section, as well as ion masses, only asampling of the simulations will be shown in this thesis.3.3.2 Taper Electrode Angle SimulationsThe following results are an expansion upon the work at National SuperconductingCyclotron Laboratory (NSCL) by Brad Barquest in his PhD thesis [6]. The theorybehind using a tapered section (Figure 3.9) is similar to that of using a funnel (seeFigure 3.10), with the wider the entrance region, the easier to accept the incomingions. If the angle (as shown in Figure 3.10 is 0◦, the funnel simply becomes ahollow cylinder and ions may simply miss the entire entrance. As the taper angle24Figure 3.7: Ion trajectories, shown in blue, are focused as they pass throughthe immersion lens, shown as a brown grid, as they travel from thetop left towards the bottom right. This figure was produced usingSimion 8.1.increases such this cylinder becomes more funnel like, the acceptance is expectedto increase as less ions will miss entrance.This effect was observed in the simulations, however, once they began to betoo large, the acceptance once again decreased. In this analogy, when the angle iscloser to 90◦, the funnel ceases to be a funnel and starts to become a wall with a holein the center. In this case, it is expected that the majority of ions will simply splashagainst the wall and not be redirected and, as such, not successfully be accepted. Tovisualize the effect that the angle has on the acceptance of the RFQ several screenshots of ion trajectories are shown in Figure 3.11 with the ions entering from above,and being accepted towards the bottom.3.3.3 Taper Electrode Length SimulationsWhile in the designing stage of the RFQ it became clear early on that space is at apremium. As such, when designing the device, effort was taken to limit its length25Figure 3.8: This figure describes a sample scan of acceptance simulations asa function of immersion lens biases from 0 V-55 kV. This particular setof simulations were carried out with a taper section of 150 mm longwith an angle of 0◦.when possible. For the injection optics, this meant limiting the length of the tapersection while still maximizing the acceptance of the device. The three electrodesimulated were 150 mm, 100 mm, and 50 mm.As mentioned previously, the acceptance of the device was simulated using theparameter space of length and angle of the taper section, as well as the ion’s mass.Figure 3.13 shows, there is a definite effect on acceptance of lens bias, taper angle,and the ion’s mass. The maximum acceptances of the three taper lengths werecompared by mapping out this parameter space for each one, and it was found thatcomparable acceptances were possible at each length for different angles and lensbiasing. This can be seen from the shorter, 50 mm taper section’s acceptance plot26Figure 3.9: A rendered drawing of the section between the some injectionoptics (top right) and the cooling region (bottom left). This particularimage is from the 150 mm Taper section with an angle of 2◦. In thisfigure, the beam enters from the upper right and travels towards thebottom left.in Figure 3.13. After it was found to be possible for each taper section length tohave comparable acceptances, when the angles were changed, it was concludedthat the shortest length simulated would be used. Thus, it was decided to use the50 mm taper section with an angle of 4◦ at a bias of 45 kV. Using these parameters,an acceptance of 67±7 mm mrad for masses as low as 15 is expected, with anacceptance of 72±7 mm mrad for masses above 30 AMU. This result exceeds thetechnical requirements of 15 mm mrad [13] by a factor of five.3.3.4 Energy Spread SimulationsAs it is practically impossible to have a uniform beam energy, an investigationwas completed to find out the affect the ion energy spread has on the acceptance.It is not well known a priori what the energy spread will be as the ions enter theRFQ. For this reason, the effect of energy spread on the acceptance of the RFQ was27Figure 3.10: A diagram of a funnel with a disperse substance being pouredinto the top, and leaving the funnel after being redirected.investigated within a range of ± 50 eV from the targeted beam energy of 60 keV .This range was chosen as an estimated upper bound on the energy spread basedon the experience obtained from studies of the of the NSCL RFQ [6]. It should bementioned that the RFQ in its entirety was biased to 59.8 keV thus resulting in anion energy of 200 eV upon entry. The energy dependence was investigated usingboth the 100 mm and 50 mm taper length as it was already decided that the 150 mmlength was unnecessarily large.Figure 3.14 displays a typical selection of simulations that were done for angles2◦ to 6◦ for the shorter, 50 mm taper section. From this figure, it is clear that theRFQ was designed for a beam energy of 60 keV to satisfy CANREB requirements,as the largest acceptances are in that row. However, the purpose of these simula-tions was not to confirm the operational target, but to confirm an energy spread of± 50 eV will not be detrimental (loss> 50%) to the acceptance of the RFQ. Thelargest acceptance for both cases is the 4◦ case for both mass 15 AMU and 30 AMU.The results of these simulations shows that applying a±25% energy spread for themass 15 case, only a 4% drop in the acceptance occurred. For the heavier, mass30 AMU simulations, it was found that a ±25% energy spread resulted in a 14%drop in the acceptance of the device. Thus is was shown that the injection optics ofthe CANREB RFQ may handle a 25% energy spread without detrimental loss.28Figure 3.11: These images are a sampling of simulations with the same ionsto show the effect of the taper angle. The ions in these images enterfrom the top. Left: a taper section with an angle of 0◦, causes manyions to miss the point of entry. Center: an angle of 9◦ manages to cap-ture additional ions that would have otherwise have escaped. Right:an angle of 90◦ allows nearly all of the would-be ions to escape thedevice. Note: The position and angle spread of the incoming ions waschosen to be much larger than the acceptance of the device in order tofully trace out the acceptance of the device.29Figure 3.12: This figure displays a sample of the acceptance simulations in-vestigating the angle dependence. This set of data came from simulat-ing a taper section of 150 mm length, with an immersion lens bias of55 kV. As can be seen, there is clearly an angle dependence that peaksnear the 2◦ case.30Figure 3.13: This figure depicts a typical acceptance plot as a function oftaper angle, immersion lens bias, as well as mass. Similar acceptancesto these plots may also be reached by different angles and biases ofdifferent length taper sections. The ion’s energy in these simulationswas 200 eV.Figure 3.14: This figure summarizes the ion energy spread investigations.Energies both 50 eV above and below the ideal 60 keV energy wereused at different angles for both mass 15 AMU and 30 AMU.31Chapter 4Introduction to the IsotopeSeparator and ACcelerator(ISAC) and TRIUMF’s Ion Trapfor Atomic and Nuclear science(TITAN)4.1 Rare Isotope Beam FacilitiesFor many years, TRIUMF has been providing rare and exotic nuclei to variousexperiments in the form of RIBs. The two varieties of RIB production are ’in-flight’facilities [15, 59], such as NSCL or RIKEN, as well as ISOL facilities [65], such asTRIUMF or ISOLDE at CERN.The in-flight technique is accomplished by impinging heavier ion beams intorelatively lighter targets. The beam may then undergo fragmentation and/or fissionand form unstable nuclei. Both of these mechanisms may produce a large range ofisotopes of interest [59], but it may do so at yields too low for many experimentswhen far from the valley of stability. As the initial beam was at relativistic speeds,the daughter nuclei will have the majority of their momenta in the axial direction.32This translates into the RIB to have a narrow angular distribution as x′ ≈ PaxialPt rans theyare transported to experiments.The ISOL technique [65] employed at TRIUMF consists of using a high energyproton beam at 500 MeV impinging on a many-layered target, in the case of Chap-ter 5 UCx was used as this target. Once the high intensity proton beam (100 µA)hits with the target, it breaks the target nuclei into a range of both stable and un-stable isotopes. These isotopes will then diffuse towards the ion source where theyare ionized, and subsequently extracted into the beamline. Once the nuclei arriveat the ionization region, those with an ionization energy below 6 eV will be surfaceionized [10]. Species whose ionization energy is above 6 eV, such as alkaline earthmetals and transition metals with ionization energies up to 9 eV [10], may be laserionized (See Section 4.1.1 for additional information). Although the ISOL methodmay produce higher yields than the in-flight technique, it can suffer due to chem-istry effects as the nuclei produced are nearly at rest, and may chemically interactbefore emerging from the target.4.1.1 TRIUMF’s Resonant Ionization Laser Ion Source (TRILIS)As not all ionization energies for Species of Interest (SOI) are below 6 eV, TRI-UMF, as well as many other RIB facilities have had to develop other methods ofionization. A popular choice of accomplishing this is using a Resonant Ioniza-tion Laser Ion Source (RILIS). TRIUMF’s Resonant Ionization Laser Ion Source(TRILIS) utilizes three TiSa lasers which may operate between 680 nm to 990 nm at10 kHz [55]. Through the use of of frequency doubling, tripling, and quadruplingTRILIS may produce a large portion of both UltraViolet (UV) and Infrared (IR)wavelengths [7, 44, 63]. By utilizing these lasers, step-wise excitation of specificelements is possible (see Figure 4.1 for what is possible at TRIUMF). In the caseof aluminium two lasers of wavelengths 308 nm and 309 nm are used to excite theatom from its split ground state. Once it’s excited a non-resonant laser of 532 nmis used once again excite the aluminium atom into a state that is prone to ioniza-tion [54].33Figure 4.1: Green: Elements that have been delivered at TRIUMF via laserionization. Blue: Elements that are currently undergoing testing at TRI-UMF for their feasibility with laser ionization. Grey: Elements that aretheoretically possible via laser ionization, but have yet to be tested atTRIUMF. This figure is an updated version of that in reference [55], ob-tained through a private communication [54], and used with permission.4.2 The TRIUMF Facility and ISACTRIUMF uses the ISOL technique with a 100 µA and 500 MeV proton beam im-pinging on a target. The device accelerating the proton beam is TRIUMF’s cy-clotron, the largest in the world [4]. After the production of the desired isotopesionization must occur, and the unwanted species are rejected before being deliveredto an experiment. This is done through a magnetic dipole mass separator, whichfilters out the undesired species via their charge over mass ratio (q/m). However,as a limit of the HRMS’s resolution being approximately δmm ≈ 2500 [34], isobarsthat are too close in mass to the SOI will still be present, and may, dependingon experiment specific sensitivities, need to be cleaned out prior to experiments. Aschematic of ISAC including the target and mass separators are shown in Figure 4.2.34Figure 4.2: Schematic of ISAC beam production and separation. The protonbeam from the main cyclotron impinges on the ISAC target, resultingin a variety of isotopes. After the newly created isotopes are extractedfrom the ion source, they undergo two phases of mass separation, withthe second being the HRMS. At this point, the mass separated beam isdelivered to the various experiments in the ISAC experimental hall. Thisschematic is taken with permission from Reference [19].354.3 TRIUMF’s Ion Trap for Atomic and Nuclear Science(TITAN)TRIUMF’s Ion Trap for Atomic and Nuclear science (TITAN) is a mass spectrom-etry experiment located at ISAC-TRIUMF, in Vancouver, Canada, and makes fulluse of the RIB produced at TRIUMF by utilizing a high-precision hyperbolic Pen-ning trap, as discussed in Section 2.2. In addition to the Penning trap, TITAN hastwo additional traps that are currently in use, including TITAN’s RFQ buncher andcooler, as well as the Electron Beam Ion Trap (EBIT). An overview of the TITANset-up is shown in Figure 4.3. Please note that the Cooler PEnning Trap (CPET),where cooling of the ions will occur, has yet to be implemented in the beamline.4.3.1 TITAN’s RFQ Buncher and CoolerAfter delivery of the RIB from ISAC to TITAN 4.3, the beam will first enter TITAN’sRFQ buncher and cooler [24]. The purpose of the RFQ is to take the continuous RIBfrom ISAC and form it into discrete bunches of ions with a decreased emittance.This is accomplished via helium buffer gas collisions (see Figure 4.4). AlthoughISAC is designed to provide beam of ions with a kinetic energy in the range of12 keV to 60 keV [24], the beam’s energy may be changed by simply by raisingthe RFQ’s bias and converting the desired portion of the beam’s kinetic energy intopotential. When the ions enter the RFQ they begin transferring their kinetic energyinto the buffer gas via collisions. In order to ensure that the ions do not simply stopdue to the loss of all their kinetic energy, a decreasing electric field is applied overthe course of the first 23 electrodes, dropping a total of 6.6 V (see Figure 4.4). Thisdecreasing electric field will cause the positively charged ions to move towards theextraction optics, and as such this field is commonly refereed to as a drag field.When it is time for extraction, the last electrode’s (# 24) potential is lowered to-26.6 V while electrode # 22’s potential is increased to +13.4 V. This allows theaccumulated ions at the bottom of the potential well to be extracted as a singlebunch, while the ions currently entering the RFQ are blocked and are not allowedto exit.As the theory of trapping transversely in an RFQ was described in Section 2.1,simply a reference to the operational parameters will be mentioned here. The36Figure 4.3: Schematic of the TITAN set-up which consists several sections.The RFQ (Section 4.3.1) receives the beam from ISAC for bunching andcooling. The second, and optional stage is charge breeding in the EBIT(Section 4.3.2). Thirdly, the ions will enter MPET (Section 4.3.3) forexcitation. Finally the ions will strike an MCP to enable mass determi-nation via the TOF technique (Section 4.4). This figure was taken withpermission from the publicly available TITAN home page [3].37Figure 4.4: The schematic of the TITAN RFQ which consists of 24 electrodesforming a potential well. As the continuous beam enters the RFQ itundergoes collisions with the helium buffer gas. This causes the ions tolose kinetic energy to the buffer gas as they fall deeper into the potentialwell. Upon extraction, the last several electrodes change their potentialto allow the newly cooled bunched beam to exit. This figure was basedon that in reference [24]TITAN RFQ has a total length of 700 mm with an r0 of 11 mm, and is operatedat a Helium pressure of approximately 0.01 mbar. The RF parameters are such thatthe VPP is 400 V and driven by a square wave at 1.2 MHz.Once the beam exists the RFQ after being cooled and bunched, it may be steeredto either the EBIT where it may be charge bred, or it may pass through the BradburyNielsen Gate (BNG) for further mass filtering [23], then enter the MPET.4.3.2 TITAN’s EBITIn the case where additional precision is needed, the EBIT may be used to charge-breed ions into higher charged states [53]. As both electric and magnetic forcesdepend on the charge of an ion this is an efficient means of increasing the precisionof mass measurements. The exact relation of the uncertainty in mass measure-ments at TITAN is shown by Equation 4.1 with q representing the charge state, Bthe magnetic field, m the ion’s mass, and N being the number of ions detected.mδm≈ TRFq√Nm(4.1)38Figure 4.5: The TITAN EBIT consists of a potential well where the ions arestruck by an incoming electron beam. The electron beam strips off ad-ditional electrons from the ions, thus increasing the ions charge state.Confinement during the charge breeding process is done through a par-allel magnetic field, and electrostaticly biased electrodes. This image iscourtesy of M. Simon.The EBIT consists of an electron gun, a collector, and electrodes to provide apotential well along the axis, as well as a superconducting magnet to provide amagnetic field. The radial confinement of the ions is provided by the magneticfield parallel with the beam axis, as shown in Figure 4.5. In addition to radialconfinement, the ions must be trapped axially during the charge breeding process.This is accomplished by using cylindrical electrodes to form a potential well. Thebottom of this well is where the ion cloud forms and charge breeding occurs. Thecharge breeding is brought about by an electron beam, emitted from an electron-gun, typically operating at, 5 keV with a current of 400 mA [53]. When the electronbeam encounters the ion cloud, it may knock off additional electrons from theions, thus increasing the charge state of the ions. Once charge breeding has beenaccomplished, the wall of the potential well is lowered, and the charge bred andbunched beam will be extracted towards MPET for mass measurement.It should be noted that charge breeding of the RIB is typically limited by twofactors. The first limitation is the lifetime of the SOI. While it is true that thelonger the time charge breeding occurs for abunch, a larger portion of the bunchwill be ionized, if the SOI has a short enough lifetime, they may decay away beforeextraction. The second limitation of charge breeding ions is the ionization energy.39As the electron beam has a particular energy, the capability of charge breeding islimited to ionization energies below the e-beam energy.4.3.3 TITAN’s MPETThe MPET is the work-horse behind TITAN as it allows us to make mass measure-ments. The characteristic dimensions of MPET (See Section 2.2) are a r0 = 15 mm,z0 =11.785 mm, and d0 =11.21 mm. As discussed in Section 2.2, axial confine-ment is achieved via two electrostatic endcaps, where radial confinement is accom-plished via a magnetic field. In order to excite the trapped ions from the magnetronmotion to the reduced cyclotron motion, an RF field is applied to the trapping re-gion. It is by exciting the faster reduced cyclotron motion that the mass of theisotopes may be determined via Time-Of-Flight measurements as discussed Sec-tion 4.4.4.4 Time-Of-Flight Mass Measurements in PenningTrapsAt TITAN, ion masses are are determined via the Time-Of-Flight Ion CyclotronResonance (TOF-ICR) technique [49] in which a range of excitation frequencies areapplied to the ion, centred near the expected cyclotron frequency, νc. Whenever ahigher portion of the motion is converted into the reduced cyclotron motion, it willresult in a decreased TOF from MPET to the MCP (See Figure 4.7). This excitationis simply driving by quadrupole RF field within MPET.When the axial confinement is removed and the ions are ejected out of MPET,the ion navigates a magnetic field gradient, and the radial energy is converted intoaxial energy. Thus an ion with a higher reduced cyclotron frequency is ejected witha higher energy, and has a decreased TOF to the MCP.In the case of a ωRF = ωc, the amplitude of the radial motion is defined byEquation 4.2 with ρ representing the radial position, t is the time, k0 is defined byEquation 4.3, r0 is the radius of the ring electrode, and ∆φ = ωRF −ωc.ρ±(t) = ρ±(0)cos(kot2)±ρ∓(0)ei∆φ sin(k0t2) (4.2)40k0 =VRFq2r201ω+−ω− (4.3)In the case where the ions are injected with a pure magnetron ρ−(0) = ρ0(ρ0 > 0), or pure cyclotron motion, ρ+(0) = 0, the two motions will be convertedcompletely from one form into the other in an excitation time of TRF = pik0 . If anexcitation time of TRF = 2 pik0 is applied to the ion, the ion will be again in its originalstate.However, what if the driving frequency of ωRF 6= ωc? This is known as theoff-resonance case and results in an incomplete conversion from one motion intothe other. The relationship between an ion with an initially pure magnetron motion,and the excitation time is shown in Equation 4.4, and is graphically shown in Fig-ure 4.6 with the Full Width Half Max (FWHM) of the central peak approximately0.8TRF[49].Er ∝4k20sin2(k02TRF) (4.4)As the ion within MPET will have a kinetic energy of approximately Er, as itpasses through the magnetic field, it’s magnetic moment of~µ = Er(ωRF )B eˆ will causeit to experience the axial force shown in Equation 4.5.~F(ωRF ,z) =−~µ(ωRF) ·5~B(z) (4.5)The TOF of an ion between point z0 and z f with an initial total energy of E0, andwith electric and magnetic fields along the axis, of strengths V (z) and B(z) maythen be determined via Equation 4.6 [49].T (ωRF =∫ z fz0(m2[E0−qV (z)−µωRFB(z)] )) 12dz (4.6)By combining Equations 4.4 and 4.6 and setting k0 = piTRF the plot on Figure 4.7.41Figure 4.6: Normalized radial energy as a function of injection time and ex-citation time. Here ∆νRF represents the phase that the ion enters thepenning trap, and TRF represents the excitation time. This figure usesTRF = k◦pi . This figure was used with permission from reference [49].4.4.1 Dipole CleaningAs mentioned previously, the limited resolution of the pre-TITAN mass separatoris δmm = 2500 [34]. While this may be acceptable for some experiments it is in-sufficient to resolve the species of interest from isobaric contaminants. In orderto expel the isobars from the trap as to prevent them from shifting the resonancefrequency [18], dipole cleaning is used.Dipole cleaning is accomplished by applying an electric RF field to the trappedions in MPET. This is implemented by biasing an electrode pair of the four elec-trode slices of MPET 180◦ out of phase from one another (Figure 4.8). The fre-quency chosen is that of the eigen frequency of the unwanted isobars. When asufficiently long excitation time is applied with a high enough amplitude, the mo-tion of the isomer will grow large enough that it will either strike the side of trapor gain enough energy to escape the trap along the axis. Both of these options willeliminate the unwanted contaminant from our TOF spectrum [40].42Figure 4.7: The solid line represents the theoretical TOF of on and off cy-clotron resonance excitation from Equation 4.6. The dashed line is thesuperimposed energy due to excitation. This figure was used with per-mission from reference [49].4.4.2 Sources of UncertaintiesNon-Uniformity of Magnetic FieldAlthough extreme care was taken in the construction of TITAN’s MPET, it is impos-sible to to ensure a idealized magnetic field. This is due to limitations of alignment,the finite size of the solenoid, as well as imperfections in the material itself [20].The frequency shift from these misalignments and material imperfections is givenby Equation 4.7 [17].∆νc = β2[(z2−ρ2+)−ν−νc(ρ2++ρ2−)] (4.7)43Figure 4.8: In order to apply dipole cleaning, two electrodes opposite fromeach other (in this case blue and red) undergo a time-varying potential180◦ out of phase from one another. In the case of TITAN, the electrodesthat apply this electric field are slices of the so-called compensationelectrode in MPET.Here, β2 is the quadrupole coefficient of the magnetic field inhomogeneity, z is theamplitude of the axial oscillation, and ρ− is the radius of the magnetron motion,and ρ+ is the radius of the reduced cyclotron motion. The upper limit of the shiftin cyclotron frequency at TITAN is given by Equation 4.8 with the ∆ representingthe difference in mass (in AMU) between the reference ion, and the SOI.∆RR< 4.3×10−10∆mq(4.8)44Relativistic EffectsAs the trapped ions undergo reduced cyclotron motion, their velocity may enterthe realm where relativistic effects may occur. The velocity of an ion travelling ata radius of ρ+ at a frequency of ω+ is simply V+ = ω+ρ+. When fitting the TOFspectrum, both ρ+ and ω+ are determined. As an example, for the measurement of29Al (see Chapter 5) a radius of approximately 2 mm was found with a frequencyof about 1 960 026 Hz. This produces a velocity of 8× 10−5c, with c being thespeed of light, thus giving us a correction factor of γ ≈ 1.000000003. Using thiscorrection factor to obtain the relativistic mass, the cyclotron frequency is given byEquation 4.9, leading to an effect of 1.6 Parts Per Billion (PPB).ωc(rel) =∆mq(4.9)Ion-Ion InteractionWith the goal of obtaining high-precision and high-accuracy mass measurements,an emphasis must be placed on understanding what has been trapped inside ofMPET. This includes not only ions of similar masses to the SOI, but also the numberof ions that were successfully trapped simultaneously. Through the use of theHRMS and the BNG, the majority of contaminants may be removed before enteringMPET. However if multiple SOI are trapped simultaneously, the center frequencymay still be altered due to Coulomb interactions, as well as a modification of thetrapping potential [66]. In order to compensate for multiple ions being trapped atonce, a count-class analysis [48] may be used.The count-class analysis takes into account not only the number of trapped ionsin MPET but also the efficiency of ion detection. If multiple SOI are trapped at oncewith the same charge state, shifts in the center frequency will be linearly relatedto the number of ions trapped [75]. This is the relation that count-class analysisrelies on. By recording the number of ions detected on the MCP, it’s possible tobin the data in such a way that the cyclotron frequency for a single ion may beextrapolated. Extrapolating the frequency and including detector efficiency is howion-ion interaction is taken into account when reporting mass determinations. Anexample of this relationship for 36Ar+ may be seen in Figure 4.945Figure 4.9: The solid line represents the extrapolation of the cyclotron fre-quency spanning from 0 to 25 ions trapped simultaneously. This fit wasbased on the shown data using a least squares fit. This figure was takenfrom reference [48] for an analysis of 36Ar+. This figure was used withpermission from reference [48].46Chapter 5Atomic Mass Measurements ofNa and Al Isotopes”The most exciting phrase to hear in science, the one that heralds themost discoveries, is not ”Eureka!” but ”That’s funny...”— Isaac AsimovAs the benchmark for accurate and precise mass measurements, PTMS has beenrepeatedly used to uncover deviations from previous measurements, for Na32, oneof the isotopes investigated here, Na32’s values from the TOF technique spans arange of 2.5 MeV with uncertainties varying from 0.1 MeV to 1.3 MeV [38, 46,61, 68, 76]. However, PTMS also has the ability to reveal smaller, novel fea-tures that may have otherwise been looked over due to a lack of resolution. Anexample of one of these features revealed by PTMS is the crossover of the two-neutron separation energy, S2n, found in 33Mg and 34Al, as first discussed at lengthin [52]. When initially discovered, this crossover was considered to be due to inac-curate mass measurements [52]; however, previous mass measurements performedat TITAN [26, 52], as well as this work have further confirmed the crossover. Large-scale nuclear-shell-model calculations [52] indicate that the crossover arises fromlarge gains in correlation energy due to degenerate energy levels. A possible ex-perimental explanation for the seeing this crossover would be the measurement ofan isomer [67] that was erroneously assigned to be the ground state. Additionalmeasurements were required to determine the excitation energy of this theoretical47isomer. This is the motivation of the mass measurements presented in this chapter.In this chapter, I report on PTMS measurements of 31,32Na and 29,34,35Al per-formed at TITAN [33]. Particular attention was given to searching for a recentlydiscovered, long-lived isomer of 34Al [67]. Since the excitation energy is unknown,this may effect the understanding of the reported crossover of the two-neutron sep-aration energies of 33Mg and 34Al [52]. Though an isomer was not observed in thiswork, we have confirmed the previous measurement of the ground-state mass [52]and, thus, the crossover in the two-neutron separation energy.5.1 ExperimentThe measurements presented in this chapter were performed at the ISAC-TRIUMFfacility [32] via the ISOL technique outlined in Chapter 4. The sodium isotopeswere surface-ionized, while aluminium isotopes were ionized via TRILIS [55] (seesection 4.1.1). In this experiment, the determined yields ranged from 75 ParticlesPer Second (PPS) for 34Al, to 2.0×106 PPS with 29Al. The singly charged beam wasmass separated via the dipole magnet spectrometer with R ≈ 2500 [34] and thentransported at 20 keV to the TITAN facility where it underwent further beam prepa-ration followed by the mass measurement itself. The preparation involved the cool-ing and bunching of the beam via the TITAN RFQ (Section 4.3.1), and further massseparation by the use of a BNG, and finally dipole cleaning [40] (Section 4.4.1) topurify the beam. Once cleaned, the TOF-ICR technique [17] (Section 4.4) was usedto determine the cyclotron frequency, νc. As discussed, this frequency is related tothe ion’s mass m, the ion’s charge q, and the magnetic field B of MPET viaνc =12piqmB. (5.1)With the TOF-ICR technique, the ion’s TOF is measured as a function of theexcitation frequency applied to the trap, after which the data are fitted with theanalytic line-shape [49], whose centroid corresponds to the cyclotron frequency,as shown in Figure 5.1. The centroid of this figure corresponds to the cyclotronfrequency of 34Al+. In the case of 29Al, a Ramsey excitation scheme [43, 51] wasapplied with two 100 ms excitation pulses separated by 300 ms.48Figure 5.1: TOF spectrum of 34Al with an excitation time of 100 ms. Hereνc ≈ 1670813 Hz. The solid curve is the analytic fit [49].5.2 Data AnalysisTaking the ratio of frequencies between a reference ion νc,re f , and the isotope ofinterest νc, allows the magnetic field to be cancelled out as in Equation 5.2:R =νc,refνc=qrefq· mmref. (5.2)By using this cancelling out of magnetic fields, the measurements may be cali-brated by bracketing each radioactive ion measurement by reference ion measure-ments. This bracketing allowed for a linear interpolation of the magnetic field tothe time of the radioactive ion’s cyclotron frequency being determined. This ratiois, in principle, independent of the magnetic field, and thus, our primary result. Thefrequency ratios and their statistical uncertainties are shown in Table 5.1.We analysed the data to determine both the systematic and statistical uncer-tainties. Systematic uncertainties [20] including relativistic effects (Section 4.4.2),non-linear fluctuations in the magnetic field (Section 4.4.2), anharmonicities in thetrapping potential, and other mass-dependent effects were found to be negligible )as compared to statistical uncertainties (relative uncertainties of 10−9 vs 10−7).49Species Reference Ion Tex (ms) R METITAN (keV) MELit (keV) S2n (keV)31Na 39K+ 20 1.25636549(62) 12246(14) 12261(23) 657(16)32Na 39K+ 20 1.2168586(15) 18638(37) 18810(120) 5979(38)29Al 23Na+ 100-300-100 0.793281449(10) -18207.77(37) -18209.0(19) 17153.51(37)34Al 39K+ 50 1.14610225(44) -2999(12) -2990.0(72) 8042(15)34Al 39K+ 71 1.14610245(24) -3004.4(67) -2990.0(72) 8048(11)34Al 39K+ 100 1.14610227(12) -2999.5(34) -2990.0(72) 8042.8(93)34Al 39K+ 50,71,100 1.14610230(11) -3000.5(29) -2990.0(72) 8043.7(92)35Al 39K+ 50 1.11325817(25) -223.7(73) -220(70) 7869(10)Table 5.1: Each of the nuclides measured in this paper is presented here, alongside the ion that was used as its reference,the excitation time in MPET Tex, the ratio R, (see Equation 5.2), mass excesses ME from both this work andliterature, as well as the two-neutron separation energy S2n. For 31,32Na and 35Al we compare to AME [12] andfor 29,34Al the more recent values in reference [52]. We also used the mass measurements of 27,32,33Al in [52] tocalculate the S2n. All species presented in this experiment had a charge state of +1. In the case of 29Al, a 100-300-100 ms Ramsey excitation [43] was used. This table also presents the combined results of the 50, 71, 100 msexcitation time of 34Al.These systematic uncertainties were typically two orders of magnitude smallerthan statistical (relative uncertainties of 10−9 versus 10−7), and thus were insignif-icant. The uncertainty stemming from ion-ion interactions (Section 4.4.2) wasdetermined via a count-class analysis [48] whenever yields allowed. This countclass analysis takes into account the detector efficiency (40±20%), as well as thenumber of ions detected in the same measurement. The count-class analysis ex-trapolates using this information to determine the cyclotron frequency of a singleion in the trap. Moreover, reference measurements of 39K+ or 23Na+ were alter-nated with the radioactive mass measurements. These calibration measurementswere within one standard deviation of Atomic Mass Evaluation (AME) and hadcomparable uncertainties to those of our radioactive ion measurements.5.3 ResultsUsing the frequency ratio in Equation 5.2, the atomic masses of the species mea-sured were extracted using the AME mass value of the reference [12], as well as theelectron binding energy (BE) [50], and the mass of the electron (me), this relationto the atomic mass is defined asm = R ·mref−BE−me. (5.3)As the SOI in this experiment were singly charged, the amount of energy to re-move a single electron BE, compared to the measurement’s statistical uncertainty,was negligible and could be ignored. A convenient way to describe masses is bythe difference between an atom’s mass and the number of present nucleons. Thisquantity is refereed to as the Mass Excess (ME) of the atom, and is defined byEquation 5.4 where the mass is in units of AMU, and A is the number of nucleonspresent in atom.ME = (Mass−A)×931.49432 MeV (5.4)The resulting ME values are presented in Table 5.1 alongside the literature values.MEes of 31Na and 32Na were found to be 12246(14) keV and 18638(37) keV,respectively. The uncertainties of these new measurements are half of the smallestcurrently published in AME. While our measurement of 31Na is 0.6σ from the51Figure 5.2: A sample of mass measurements with the horizontal lines centredaround the AME indicating the 1σ confidence level. As can be seen ournew value, TITAN 2015, disagrees with AME by 1.4σ . Values takenfrom [46, 61, 69, 76]values in AME, we find a deviation of 1.4σ for 32Na, as shown in Figure 5.2.The TITAN-measured mass excesses for 29,34,35Al are listed in Table 5.1. Thoseof 29,34Al agree with our prior measurements [52] within a 1 σ and 2 σ uncertain-ties, but also have lower uncertainties. The ME value of 35Al presented in Table 5.1agrees with AME [12] and has an improved precision by a factor of ten over the pre-vious values determined via the TOF technique [38, 46, 61, 68, 76].During the experiment and data analysis, we paid special attention to 34Al dueto the possible presence of a long-lived isomer [67]. Such an isomer could havebeen produced in the ISAC production target and delivered simultaneously with52the ground state. To identify the constituent species in the beam we turned thelaser ionization of 34Al on and off. Note that due to Doppler broadening in theionization region, both the ground state of 34Al and its isomer would be ionizedwith the same laser-excitation scheme. Stable 31PH+3 accounted for at least 75%of the surface-ionized beam. Thus, more than 90% of the beam at the MPET MCPproduced with laser ionization, was 34Al+. The stable 31PH+3 was identified via itsνc in the MPET.If an isomer were present during the mass measurements, a second resonancefeature would be visible in its TOF distribution (see for ex. [42]). In the analysis,we attempted to fit the data with a fitting function for both a single and double res-onance; however, no second resonance was observed. Therefore, only one specieswas identified. In an effort to clarify which nuclear state of 34Al was being mea-sured, we used multiple ν excitation times as the isomer and ground state havevery different half-lives with the isomer’s being 26(1) ms [67] and the ground stateof 56.3(5) ms [60]. The various excitation times used were 50 ms, 71 ms, and100 ms. Due to variations in the ISAC yields, as well as data being taken for 34intermittently with other elements, it was not possible to normalize the count ratesbetween the various measurements of 34Al. These variations in yield were observedto change from a fraction of surface-ionized 34Al+ to surface-ionized contaminantions of ≈ 12% at the start of the experiment to ≈ 3% at the end of the experiment,and as such a comparison of the count rates could not be used to distinguish theratio of the ground-state to the isomer if a mixture were present. A linear extrap-olation of count rates for 34 was not possible due to a 48 hour period between thefirst round of measurements of 34Al with an excitation time of 100 ms, and thesecond round with the excitation time of 50 ms. This gap was due to taking mea-surements of our other SOI. However, as the shortest excitation time was nearlytwice the half-life of the short lived isomer, a maximum of 14% of those deliveredfrom the target station would survive long enough to be observed. This drop inthe number of detected isomers is even more apparent with the longer excitationtime of 100 ms with a maximum of 4% of the original isomer yield possibly beingmeasured, further lowering our ability to detect it.In order for TITAN to observe a separation of two species at a difference ofFWHM with the longest excitation, 100 ms, the mass difference would need to53be as large as 200, keV. At this point, a second TOF resonance would be consid-ered fully resolved. An illustration of fitting with an isomer present is shown inFigure 5.3 for various isomer to ground state ratios, as well as mass differences.However, as the short excitation scheme used would reduce the quantity of the iso-mer to 14% of its original value, we do not expect a yield sufficient to distinguishit from the 34Al ground state.As no second resonance was observed, and since the isomer yield could beat most 14% of our total 34Al yield, it was concluded that only the ground statewas in fact, the species measured. The only other known isomeric state [64] wasobserved via a Coulomb excitation experiment, and its half-life is of the order ofnanoseconds.The measured mass excess of 34Al agrees with that of TITAN’s previous mea-surement of −2990.0(72) keV [52], but with a smaller uncertainty due to betterstatistics. Using this updated mass excess, two-neutron separation energies werefound to overlap for 33Mg and 34Al. The two-neutron separation energy tabulatedin Table 5.1 is defined asS2n(N,Z) =−m(N,Z)+m(N−2,Z)+2mn. (5.5)Thus, with our observations, the two-neutron separation energy crossover of 33Mgand 34Al at N = 21 is confirmed with an overlap of 15(10) keV.The importance of the aluminium masses derives from their transitional na-ture as they border the island of inversion. In addition to agreeing with previousmeasured mass values, the 29,34,35Al values presented here support large-scale nu-clear shell model calculations [52], the values of Mg were obtained from [25].In these predictions, 34,35,36Al have mixed sd and p f nuclear orbitals. The rel-ative gains in correlation energy peak at N = 21,22 for the aluminium isotopes,which can be seen in the trend of the two-neutron separation energy flatteningfrom 34Al to 36Al. Figure 5.4 shows this for Al, and Mg for the N = 19− 21 re-gion, and shows the an overlap at N = 21. This overlap is known as the crossoverat N = 21. The present TITAN measurements are in agreement with this flatten-ing of the 34,35Al two-neutron separation energy. This is significant as the currentAME value of 36Al [12] does not agree with this flattening. The TOF mass mea-54Figure 5.3: TOF resonance simulations for 34Al for the ground state and iso-mer with various differences in their masses, and yield ratios. The left-most vertical line represents the νc of the isomer, and the rightmostvertical line represents the νc of the ground state, νc ≈ 1670813 Hz A:a difference of 100 keV and an isomer ratio of anywhere from 50% to0% of trapped ions. B: a difference of 200 keV was simulated. C: adifference of 300 keV.55Figure 5.4: Two-neutron separation energies comparing the experimental re-sults with those from literature, including an expanded view of theN = 21 crossover. Solid circles represent values taken from AME [12],open circles represent values determined by TITAN measurements, tri-angles represent energies determined using both AME and TITAN mea-surements together, and lines represent theoretical values [52]. Notethat theoretical calculations for Na have yet to be calculated.56surements of 36Al currently span ≈ 0.3 MeV with uncertainties at a maximum of≈ 0.4 MeV [46, 61, 68, 76]. A discrepancy of approximately 0.5 MeV with the lit-erature value [12] would bring the measured mass in agreement with the calculatedvalue and strongly support the predicted gains in correlation energy[52].This correlation energy would be due to a neutron pair crossing the N=20 shellgap, and occupying close lying orbitals in the p f shell [21]. This is also knownas a two-particle-two-hole excitation. The new state is now constructed of thetwo-particle-two-hole excitations may then lead to a lowering of the ground stateenergy, leading to the flattening of the 21−23Al two-neutron separation energy.57Chapter 6Conclusions and OutlookIn this thesis, I have presented my results of simulations and designs of the newCANREB buncher and cooler. The results of the simulations have shown that thedesign is adequate for the specified requirements. This includes being capable ofhandling a mass range from 15 to 250 AMU, as well as an energy spread of 50 eV.In addition to this, the acceptance of the device is a factor of five times larger thanthose outlined in the design document [13], thus creating a tool that would facilitatetuning of the beamline.In addition to aiding ARIEL in the process of providing a larger range of iso-topes to the scientific program at TRIUMF, I have presented mass measurements ofspecies that are currently available at ISAC. These mass measurements of 31,32Na,as well as 29,34,35Al help aid our understanding in the region of the island of inver-sion [27], and have joined TITAN’s previous mass measurements of the island ofinversion now spanning 29−32Na, 29−34Mg, and 29−35Al. The flattening of the S2nfrom 34Al to 36Al is supported by our investigations, and support the predictionsof large correlation gains in 34,35Al [52]. Although extensive efforts were used inthe search for an isomer of 34Al, none was observed. This supports the claims inReference [52] of a crossover in the two-neutron separation energy of the 33Mgand 34Al ground states.Although the measurements presented in this paper aid in our understandingof the island of inversion, more measurements must be carried out to further ourunderstanding of the inversion mechanism itself. Spin-parity measurements will58play a role in investigating the inversion mechanism, and as such spectroscopicinformation is still needed. 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Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Bunching, cooling, and measuring of radioactive isotopes for nuclear physics
Text