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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 Magnetron motion, ω-, due to magnetic field Axial motion, ωz, due to application of an electrostatic harmonic potential Reduced cyclotron motion, ω+, due to coupling of ions magnetic moment to the electric field 2 c 2 2 q c B m 2 z m/q selection Penning trap B z U0 axial (z) magnetron (-) cyclotron (+) ISAC ion beam RFQ cooler & buncher EBIT charge breeder m/q selection Penning trap B 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 ωc. z TRAP DRIFT TUBE MCP ISAC ion beam RFQ cooler & buncher EBIT charge breeder ISOLTRAP: t1/2 = 1 s, δm/m = 1x10-8 t1/2 = 50 ms, δm/m = 5x10-8 m/q selection Penning trap δm m q m N TB m = 100 u, N = 10, 000 2x10-7 1x10-7 -8 5x10 B = 4 T, q = 1 B = 6 T, q = 1 B = 9.4 T, q = 1 -8 dm m 2x10 -8 1x10 5x10-9 -9 2x10 -9 1x10 0.05 0.07 0.01 0.015 0.02 0.03 Observation Time (s) 0.1 ISAC ion beam RFQ cooler & buncher EBIT charge breeder TITAN: t1/2 = 50 ms, δm/m = 1x10-8 m/q selection Penning trap δm m q m N TB m = 100 u, N = 10, 000 2x10-7 1x10-7 -8 5x10 B = 4 T, q = 1 B = 6 T, q = 1 B = 9.4 T, q = 1 -8 dm m 2x10 -8 1x10 5x10-9 B = 4 T, q = 10 -9 2x10 -9 1x10 B = 4 T, q = 20 B = 4 T, q = 30 B = 4 T, q = 50 0.05 0.07 0.01 0.015 0.02 0.03 Observation Time (s) 0.1 ISAC ion beam RFQ cooler & buncher EBIT charge breeder m/q selection Motivation for mass measurements Three areas where TITAN can contribute: Weak interaction studies Atomic and Nuclear Mass Models Stellar Nucleosynthesis Penning trap ISAC ion beam RFQ cooler & buncher EBIT charge breeder m/q selection Penning trap Weak Interaction Studies Vud from mean Ft value and muon decay strength: Vud2 Vus2 Vub2 0.9967 0.0014 Vud 0.9738 0.0004 d w Vud Vus Vub d sw Vcd Vcs Vcb s b V w td Vts Vtb b 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 e.g. 74Rb, t1/2 = 50 ms, required δm/m = 1x10-8 current δm/m = 5x10-8. ISAC ion beam RFQ cooler & buncher EBIT charge breeder m/q selection Penning trap Weak Interaction Studies Vud from average Ft value 2 2 2 V V V ud us ub 0.9967 0.0014 and muon decay strength: Vud 0.9738 0.0004 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 e.g. 74Rb, t1/2 = 50 ms, required δm/m = 1x10-8 current δm/m = 5x10-8. ISAC ion beam RFQ cooler & buncher EBIT charge breeder m/q selection Atomic and Nuclear Mass Models Penning trap ISAC ion beam RFQ cooler & buncher EBIT charge breeder Stellar Nucleosynthesis 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-, rand 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 m/q selection Penning trap RFQ cooler & buncher e--beam EBIT charge breeder B m/q selection Penning trap axially: electron beam space charge 50 m ISAC ion beam longitudinally: electrodes trap potential Ut 450 V RFQ cooler & buncher ISAC ion beam EBIT charge breeder m/q selection Penning trap V Ion Beam 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 Standard quadrupolar geometry focuses in one direction and defocuses in the other ( x2 y 2 ) V 2 r0 2V 2V E x 2 x, E y 2 y r0 r0 m/q selection Penning trap ISAC ion beam RFQ cooler & buncher EBIT charge breeder m/q selection Penning trap 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 m/q selection Penning trap 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 m/q selection Penning trap By segmenting the structure we can also apply a longitudinal field and hence create bunches ISAC ion beam RFQ cooler & buncher EBIT charge breeder m/q selection Penning trap 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 Sine-Wave Vs Square Wave: What is required? Sine-Wave q<0.908 Stable, q≈0.4 best. 4 zeV q , 2 2 m r0 Square-Wave q<0.712 Stable, q≈0.3 best. 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 ≤ 3 MHz @ 400 Vpp, r0 = 10 mm Experimental Viability: Sine Wave 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: Square-Wave No lower limit on frequency, upper limit determined by energy dissipation in MOSFETs Experimental Viability: Square-Wave Energy dissipation is determined by the capacitance of the RFQ Systems have previously been developed that can run at up to Vpp = 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 Vpp = 400V, f = 1 MHz (m ≥ 65) Improvements underway to try and expand to Vpp = 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 The Square-Wave Driver The Square-Wave Driver Properties of the RFQ from Analytic Considerations Meissner equations determine ions motion in square-wave-driven trap: t 2 x 2 y . 2qx 0, 2qy 0, 2 2 2 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 = 0.712 the motion becomes unbound Properties of the RFQ from Analytic Considerations In Phase Space Micro-motion distorts ideal harmonic ellipse Acceptance defined as area of harmonic ellipse whose maximum distorted amplitude = r0 Acceptance varies as a function of q with a maximum at q ≈ 0.3 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: u 1 s kT , v mkT . m Can use information from ellipses to convert from σx and σv as a function of phase/time to σx-SHM and σv-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 m 2 E ps s rmax ze For Cylinder: I Esc , 2 0 r Vd For Sphere: Esc Q 4 0 R 2 Space Charge Limit Continuous, Vd = 1000 m/s Bunched, t = 1 ms In continuous mode Imax ≈ 2 μA, @ q = 0.39 In bunched mode Imax ≈ 30 nA, @ q = 0.33 Modeling Buffer-gas Cooling: Viscous Drag Drift Velocity related to electric field by: Vd kE Acceleration due to electric field countered by deceleration due to scattering: eE eE e Vd aE , ad m m m k 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 250 k m2s 1V 1 200 150 100 50 2000 4000 6000 Vd 8000 m s 10000 12000 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 14000 Modeling Buffer-gas Cooling: Viscous Drag v v m ini k (v) m ini dv R k (v)dv, tc e vtherm v e 0 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: cm 2b 1 rm b V (r ) 2 r Ecm 2 1 2 dr r2 Relate this to energy loss in lab frame: mi2 mg2 2mi mg Esc cos( cm ) 2 2 Ein (mi mg ) (mi mg ) 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 r0 =10 mm, L = 700 mm, Vpp = 400 V Segmented into 24 pieces with longitudinal potential previously shown Transfer of beam with Cooling time approx. 2 x 98% efficiency 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 90o Switch polarity to bend in opposite direction Apply equal voltages to electrodes for undeflected path Four-Way Switch Minimum value for h = 0.4 r0 x2 y2 V 2 r0 V independent of r0 but dependant on h and ion energy We took h = 0.15 r0 For ion energy = 30 keV, V =21.1 kV. Strength of electric field determines size of the steerer: Emax 2V r0 We took r0 = 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 rms 4 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 εrms = 3 p mm mrad @ 2.5 kV x 2 . . x 2 xx 2 Experimental Setup Experimental Setup Experimental Setup: Injection 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 Experimental Setup: RFQ Installed and SquareWave successfully applied to the rods Beam passed through RFQ and detected at the RFQ exit Experimental Setup: Extraction 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 squarewave 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.