Simulation and Off-line Testing of a Square-wave- driven RFQ Cooler and Buncher for TITAN Mathew Smith: UBC/TRIUMF ISAC Seminar 2005

Overview The TITAN project The need for a cooler and buncher Square-wave vs sine-wave Simulations RFQ test stand Experimental setup and status Summary and outlook

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection magnetron (-) cyclotron (+) axial (z) Magnetron motion, ω -, due to magnetic field Axial motion, ω z, due to application of an electrostatic harmonic potential Reduced cyclotron motion, ω +, due to coupling of ions magnetic moment to the electric field

Dipole excitation prepares ions in pure ω - state Application of quadrupolar excitation couples ω - to ω +. Extracting ions through magnetic field converts radial energy into longitudinal energy Ion time of flight spectrum can be used to obtain ω c. ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection ISOLTRAP: t 1/2 = 1 s, δm/m = 1x10 -8 t 1/2 = 50 ms, δm/m = 5x10 -8

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection TITAN: t 1/2 = 50 ms, δm/m = 1x10 -8

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection Weak interaction studies Atomic and Nuclear Mass Models Stellar Nucleosynthesis Motivation for mass measurements Three areas where TITAN can contribute:

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection V ud from mean Ft value and muon decay strength: Q-Values needed for superallowed 0 + ->0 + beta emitters with A > 54 Combined with half-lives and branching ratios this will help extend the number of well known Ft values Weak Interaction Studies e.g. 74 Rb, t 1/2 = 50 ms, required δm/m = 1x10 -8 current δm/m = 5x10 -8.

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection V ud from average Ft value and muon decay strength: Q-Values needed for superallowed 0 + ->0 + beta emitters with A > 54 Combined with half-lives and branching ratios this will help extend the number of well known Ft values Weak Interaction Studies e.g. 74 Rb, t 1/2 = 50 ms, required δm/m = 1x10 -8 current δm/m = 5x10 -8.

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection Atomic and Nuclear Mass Models

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection Production of all the heavy elements (A ≥ 7) take place via nuclear reactions in the stars In order to understand the complex chains of nuclear reactions that can take place inside a star (e.g. the s-, p-, r- and the rp- processes) it is necessary to know the masses of the nuclei involved Such chains involve a large number of short-lived nuclei which lie close to the proton and neutron drip lines Stellar Nucleosynthesis

B e - -beam axially: electron beam space charge 50  m trap potential U t  450 V longitudinally: electrodes ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection EBIT cannot accept a continuous beam Low emittance needed in order to traverse magnetic field efficiently Therefore, we need to cool and bunch the ISAC beam

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection Standard quadrupolar geometry focuses in one direction and defocuses in the other

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection However, it has long been known that by placing a series of quadrupoles together a net focusing force can be obtained

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection Alternatively, we can use RF- potential to alternate the orientation of the focusing and defocusing directions

ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection By segmenting the structure we can also apply a longitudinal field and hence create bunches

Thermalization of ion beam via interaction with a buffer gas Thermalization in three dimensions leads to loss of beam Counter longitudinal energy loss via the application of an accelerating electric field Ions disperse radially due to scattering of forward momentum Use RFQ ion trap to provide a force to counteract the dispersion Hence, a gas-filled RFQ can be used to cool an ion beam ISAC ion beam RFQ cooler & buncher EBIT charge breeder Penning trap m/q selection

Sine-Wave Vs Square Wave: What is required? The magnitude of V determines the depth of the psuedopotential This determines the traps acceptance, its transfer efficiency and its space-charge limit. Thus, it is desirable to have V as large as possible If V is fixed ω must be able to vary in order to trap a wide range of masses 7 ≤ m ≤ 235 u, 0.4 ≤ f ≤ V pp, r 0 = 10 mm Sine-Wave q<0.908 Stable, q≈0.4 best. Square-Wave q<0.712 Stable, q≈0.3 best.

Inductor has limited bandwidth Driving off resonance causes core to heat up distorting induced wave However, used in all other experimental systems so the technology is proven Experimental Viability: Sine Wave

Experimental Viability: Square-Wave No lower limit on frequency, upper limit determined by energy dissipation in MOSFETs

Energy dissipation is determined by the capacitance of the RFQ Systems have previously been developed that can run at up to V pp = 1 kV at up to 1 Mhz However, these have only been use to drive 3-d Paul traps or small quadrupole mass filters, C ≈ 25 pF The RFQ required for TITAN is significantly larger than a 3-d trap and has capacitance on the order of C ≈ 1500 pF Square-Wave not possible with current MOSFETs? Experimental Viability: Square-Wave

KICKER group at TRIUMF already had the solution to the capacitance problem By stacking MOSFETs it is possible to reduce the energy dissipated by each chip First system designed and tested V pp = 400V, f = 1 MHz (m ≥ 65) Improvements underway to try and expand to V pp = 800 V, f = 3 MHz Other benefits include: equations of motion simpler than sinusoidal case, possibility to use frequency scanning methods or varying duty cycle to filter impurities Experimental Viability: Square-Wave

The Square-Wave Driver

Properties of the RFQ from Analytic Considerations Meissner equations determine ions motion in square-wave-driven trap: Analytic solution shows a simple harmonic macro-motion perturbed by a coherent micro-motion As q increases so does the amplitude of the micro-motion until at q = the motion becomes unbound

Properties of the RFQ from Analytic Considerations

In Phase Space q = 0.3 Micro-motion distorts ideal harmonic ellipse Acceptance defined as area of harmonic ellipse whose maximum distorted amplitude = r 0 Acceptance varies as a function of q with a maximum at q ≈ 0.3

Temperature Micro-motion is coherent and therefore doesn’t contribute to the temperature of the ions in the trap Temperature of an ion cloud in a harmonic potential can be defined in terms of the standard deviation in position and momentum space: Can use information from ellipses to convert from σ x and σ v as a function of phase/time to σ x -SHM and σ v -SHM and hence define temperature

Space-Charge Limit Can use amplitude of harmonic motion combined with secular frequency to define the depth of the psuedopotential Use simple model for the beam to get an idea of the space charge limit In continuous mode consider beam to be an infinitely long cylinder In bunched mode consider bunch to be a perfect sphere For Cylinder: For Sphere:

Space Charge Limit Continuous, Vd = 1000 m/sBunched, t = 1 ms In continuous mode I max ≈ 2 q = 0.39 In bunched mode I max ≈ 30 q = 0.33

Modeling Buffer-gas Cooling: Viscous Drag Drift Velocity related to electric field by: Acceleration due to electric field countered by deceleration due to scattering: Need mobility, k, as a function of drift velocity At low energies (E < 10 eV) data exists, for higher energies must extrapolate either using tabulated values for (n,6,4) potentials or MC simulation

Modeling Buffer-gas Cooling: Viscous Drag Cesium in helium extrapolation by MC method Cesium in nitrogen extrapolation using tabulated values Using this model we can calculate range and cooling times However, it tells us nothing of the final properties of the cooled ions as all ions are treated equally

Modeling Buffer-gas Cooling: Viscous Drag Cesium in 2.5x10 -2 mbar Helium Range fits with length of RFQ predetermined to be 700 mm Cooling times on order of 400 μs fits well with 50 ms lifetimes Range, etc., will vary depending on weight of ion of interest Can adjust range and cooling time by varying pressure of the buffer-gas, or using heavier gas

Modeling Buffer-gas Cooling: Monte Carlo Use ion-atom interaction potential to calculate scattering angle in center of mass frame: Relate this to energy loss in lab frame: Runs in SIMION or separately in C Test by using to recreate experimental results for the mobility of ions in the gas

Modeling Buffer-gas Cooling: Monte Carlo Lithium in helium perfect agreement Cesium in helium some small discrepancies Li + -He interaction potential well known with ab-initio calculations possible Cs + -He simple (8,6,4) potential used. Much disagreement about the proper form in the literature

Modeling Buffer-gas Cooling: Monte Carlo RFQ defined in SIMION r 0 =10 mm, L = 700 mm, V pp = 400 V Segmented into 24 pieces with longitudinal potential previously shown Transfer of beam with 98% efficiency Cooling time approx. 2 x longer than that from drag model

Modeling Buffer-gas Cooling: Monte Carlo Ions initialized in trap with T = 800 K Cooled for 500 μs and then data recorded in 0.02 μs intervals for 10 μs Plot of temperature as a function of q shows the effects of RF-heating Space-charge not yet included so represents a minimum possible temperature

Test Setup

Injection Optics Simulated 88% efficiency limited by radius of quadrupoles

Four-Way Switch Use quadrupolar field to bend ions through 90 o Switch polarity to bend in opposite direction Apply equal voltages to electrodes for un- deflected path

Four-Way Switch Minimum value for h = 0.4 r 0 V independent of r 0 but dependant on h and ion energy We took h = 0.15 r 0 For ion energy = 30 keV, V =21.1 kV. Strength of electric field determines size of the steerer: We took r 0 = 17 mm, E ≈ 2.5 kV/mm

Extraction Optics

Extraction Methods In absence of buffer-gas expect all bunches to have the same longitudinal and transverse emittances First extraction method releases ions with a small energy spread and large time of flight spread Second method reduces time of flight spread but increases energy spread

Simulated Beam Properties Buffer-gas heats beam so emittances not constant Kicking the ions hard out of the trap reduces time of flight spread and increases energy spread ε rms = 3 p mm 2.5 kV..

Experimental Setup

Experimental Setup: Injection

Beam through four-way switch with approx. 75% efficiency Beam into RFQ with approx. 25% efficiency Currently trying to diagnose source of loses Beam charging isolators in switch?

Experimental Setup: RFQ

Installed and Square- Wave successfully applied to the rods Beam passed through RFQ and detected at the RFQ exit

Experimental Setup: Extraction

Extraction optics installed MOSFET switch developed at McGill used to switch RFQ dc bias Belhke 60 kV switch used to pulse drift tube Testing of drift tube pulser underway

Summary and Outlook Detailed simulations of cooling process in a square- wave driven RFQ carried out Based on simulations system designed and built Square-wave driver capable of driving large capacitive loads at high voltage and high frequency developed and tested Testing of the system underway. Emittance rig is being built so as to compare the actual beam properties to simulation TITAN platform now installed in proton hall RFQ will be installed ready for the delivery of the EBIT at the end of the summer

Thanks Jens Dilling, Joe Vaz, Laura Blomeley and the rest of the TITAN group. Co-op Students: Robert Cussons, Ori Hadary, Amar Kamdar, George Yuan. Triumf Support: M. Good, H. Sprenger, M. McDonald, R. Dube, R. Baartman, Controls Group, Design Office, KICKER Group, Machine Shop, Vacuum Group.