Ion traps. Daniel Rodríguez Departamento de Física Aplicada Universidad de Huelva. March 2007 Santiago de Compostela, Spain

Transcription

1 Ion traps Daniel Rodríguez Departamento de Física Aplicada Universidad de Huelva March 2007 Santiago de Compostela, Spain

2 Outline Fundamentals of ion traps. Ion traps at Radioactive Ion Beam facilities. Cooling. High-precision experiments in nuclear physics.

3 Fundamentals of ion traps

4 Why ion traps? Extended preparation. Extended interactions. Extended reaction periods. Which leads to Effective non-destructive (re)-use of rare species. Easy manipulation of trapped particles. Selection by q/m separation. Accumulation and bunching. Cooling. Charge breeding. Polarization. Increase of luminosity, signal/noise..

5 Why ion traps? Prominent argument: Δt Δ E h Storage Δt Δυ 1 Resolving power

6 Applications FUNDAMENTAL TESTS CPT,QED, Parity violation CVC CHEMISTRY NUCLEAR PHYSICS Nuclear binding energies Decay studies ATOMIC PHYSICS, MOLECULAR & CLUSTERS Laser, microwave, Life-times PLASMA PHYSICS Ordered structures METROLOGY Kilogram, fine structure constant Frequency standards ION BEAM MANIPULATION Cooling beam bunching New accelerator, decelerator concepts Accumulation Ultra-high mass separation

7 Trapping of charged particles Required: 3-dimensional potential minimum. Force acting towards a center. + Convenience: a) F ~ -r (Harmonic oscillator) b) Rotational symmetry Consequences: From a) F= e Φ r Φ = ax + by + cz ΔΦ=0 Laplace equation Rotational symmetry around z-axis a b c=0 THERE IS NOT 3-DIMENSIONAL CONFINEMENT WITH ELECTRSOTATIC FIELDS

8 Confinement with RF fields: Paul traps Equipotential lines are hyperboloids of revolution. Φ= Φ 0 r 2 2z 2 2r z y x Ф 0 z 0 r 0 Φ = Φ(t) Paul trap

9 Confinement with RF fields: Paul traps Potential: Φ= U 0 V 0 cos ω RF t r 2 2z 2 2r Equation of motion (Mathieu equation): d 2 u dτ a 2qcos 2τ u=0 u=r,z 2 τ=ω RF t /2 a z = 8eU 0 mr 2 0 ω = 2a 2 r RF q z = 4eV 0 mr 2 0 ω =2q 2 r RF

10 Confinement with RF fields: Paul traps Stable solution for certain values of a,q: Ion trajectories: u t = A c 2n cos β 2n ω RF t /2 B c 2n sin β 2n ω RF t /2 β=β a,q c 2n =c 2n a,q 0 β 1 If a, q<<1 c 2n n 1 0 u t = A 1 q 2 cosωt cos ω RF t

11 Confinement with RF fields: Paul traps Fundamental frequencies of the ion motion: ω u, n t = n 1 2 β u ω RF ω u,0 t = 1 2 β u ω RF = 1 2 a u 1 2 q 2 u ω RF Time-average potential depth: D u = m 8 ω 2 RF r β u

12 Stability diagrams: Paul traps 2 a z 0 β z β r q z

13 Stability diagrams: Paul traps Optimum trapping conditions in Paul traps a z a z q z q z Theory Laser fluorescence

14 Several configurations: Paul traps

15 Paul traps r Ring #3 Ring #4 z PulsedC. Ring #3 Ring #1 Ring #2 Ring #4 V RF cos( ω RF t) V dip cos ω dip t or V quad cos ω quad t 10 mm V RF V dip cos ω dip t or V quad cos ω quad t cos( ω RF t) Ring #1,2 V RF = 130 V pp ν RF = 1.15 MHz Storage time Excitation time

16 Oscillation frequencies Counts ν z ν RF -2ν z ν z Secular frequency /khz

17 Excitation frequencies: Paul traps Excitation frequency / khz Li + ν RF =1.15 MHz ν RF -ν z ν RF -2ν z V RF / a.u. Excitation frequency /khz Na + ν RF =650 khz ν RF +ν z ν RF -ν z ν RF -2ν z V RF / a.u.

18 Confinement with RF fields: Mass filters Equipotential lines are hyperbolae. Φ= Φ 0 x2 y 2 r x y z x y + Φ / Φ / 2 - Φ / r Φ / 2 Φ = Φ(t) RFQ

19 Confinement with RF fields: Mass filters Potential: Φ= U 0 V 0 cos wt x2 y 2 2r 0 2 Equations of motion (Mathieu equations): + 2 d 2 x d 2 t ω RF 4 a 2q cos ω RF t x=0 Φ 0 t =U V cosω RF t 2 d 2 y d 2 t ω RF 4 a 2q cos ω RF t y=0 d 2 z d 2 t =0 Φ 0 t = U V cos ω RF t

20 Stability diagrams: Mass filter a x, y 1 0 x - s t a b l e q= 2eV mr ω RF a= 4eU mr ω RF 5 x / y - s t a b l e q x, y 0, 4 0, 3 0, 2 x - s t a b le b x = 1 b y = 0 ( c ) - 5 0, 1 x / y - s t a b l e y - s t a b l e 0, y - s t a b l e a - 0, 1-0, 2-0, 3-0, 4 0, 0 0, 1 0, 2 0, 3 0, 4 0, 5 0, 6 0, 7 0, 8 0, 9 1, 0 q

21 Ion motion in Paul traps u 0.4 mm q=0. 3 t Secular motion u sec t =u sec cos ω sec t qω RF ω sec = 2 2 V eff = qv 4u 0 2 u2 u q=0.908 Micromotion u mic t = q 2 u sec cos ω mic t 0.4 mm t = ω n± q mic 2 2 ω RF n=1,2..

22 Confinement with Magnetic fields: Penning traps Equipotential lines are hyperboloids of revolution. B V = V 0 2d 2 z 2 r 2 2 d 2 = 1 2 z 2 0 r B + z y x V 0 z 0 r 0

23 Different geometries: Penning traps B B End cap End cap Correction electrode Correction electrode V 0 r 0 z 0 Ring electrode V 0 Ring electrode Correction electrode Correction electrode End cap End cap

24 Confinement with magnetic fields: Penning traps Electric field: E r = V 0 2d 2 r B E z = V 0 d 2 z + Equations of motion: m d2 z dt 2 =q E z m d2 r dt 2 =q E r d r dt B u=x iy 2 u du iω c dt ω z 2 d2 u dt =0 u t =u 2 0 e iωt

25 Ion motion: Penning traps B z + r Axial motion Reduced cyclotron motion Magnetron motion ω z= QΦ 0 md 2 ω = 1 2 [ ω c ω c 2 2ω z 2 ] ω = 1 2 [ ω c ω c 2 2ω z 2 ] ω c = ω c Q B m = ω ω + + ω ω z ω ω 2 ω z 2 ω 2 =ω c 2

26 Ion motion: Penning traps R R R R 2 ω ω z = ω z ω

27 Several configurations: Penning traps

28 Landau levels of ions in a Penning trap 3 Energy of the harmonic oscillators E=ħ ω n 1 2 ħ ω z n z 1 2 ħ ω n MAGNETRON MOTION IS UNSTABLE n + n z n - Reduced Cyclotron motion Axial motion Magnetron motion

29 Ion traps at radioactive beam facilities. Cooling

30 Production and separation of exotic nuclei Spallation + 1 GeV 201 Fr Fragmentation + + ISOL method In-flight method 11 Li X n p Fission Cs Y 5 MeV/u Fusion evaporation + In-flight method 80 Zn 208 Pb

31 Production and separation of exotic nuclei F res = q E v B = 0 v B : v = E B fusion a few 100 kev/u detector Z target wheel primary a few MeV/u Intensity of the primary beam from UNILAC: 2-5 * ions/s Mass of the projectile: Target: e.g. Pb, Bi Target thickness : 0.5 N

32 Advantages of ion traps SHIP TRAP B Production and separation of heavy elements Long storage time Precise manipulation of the ion motion Pure and cool ensembles of transuranium nuclides at rest Small phase space or at low and well defined energies. Investigations of nuclear, atomic and chemical properties in high precision experiments

33 But Radioactive ion sources provide exotic nuclei at very high energies. The exotic nuclei are delivered with non-ideal ion optical properties. Large transverse emittance Large energy spread ( E). Large time structure ( t). ε trans,x =π Δ x Δθ x E t E θ θ x t x x

34 Ion manipulation and cooling Resistive cooling. Buffer-gas cooling (collisional cooling). Laser cooling. Sideband cooling. Radiative cooling (for cyclotron motion of electrons). Adiabatic cooling. Evaporative cooling. Sympathetic cooling (by second ion species). Stochastic cooling.

35 Basics: cooling The phase-space density of a system is conserved in the absence of dissipativ forces Δp x Δp y Δp z ΔxΔyΔz= constant The evolution of the system can be described separately in each direction The phase space can be divided in three action diagrams. Δp u Δu= constant u=x,y ΔEΔt= constant Collisions of ions with buffer gas atoms or molecules Can reduce the area of the action diagrams (emittance). Universal. Any ion can be practicable. Fast. Within less than 1 ms. Easy implemented. Confinement of the ions is needed Electromagnetic forces can provide this confinement.

36 Buffer-gas cooling V r = C r n V r = A r 4 E t = m ion m gas m ion +m gas nσv E 2 Viscous drag E t = 2e Km E

37 Mobility versus collisions α E = m ion m gas m ion +m gas nσv 2 K c = 2e m 1 α E 6000 K [ m 2 / V sec ] E ion kt gas Damping model E ion >> kt gas Collisional model Ar + ions in He at 10-3 mbar Ion energy [ ev ]

38 Coupling of ion traps to RIB facilities In-Flight method ions = 20 kev/u MeV/u ISOL method E ions = kev Penning/ Paul traps Gas-filled stopping chamber E ions ~ e V RFQ buncher E ions ~ e V

39 In-flight: the gas-filled stopping chamber Gas flow + RF + DC fields Detector Nozzle Extraction RFQ DC voltage cage Entrance window Beam from SHIP Funnel To the SHIPTRAP Buncher

40 Gas flow VARJET

41 RF+DC fields SIMION

42 Photos

43 ISOL-method: the RFQ buncher V RF cos ω RF t+π V RF cos ω RF t Injected ions Extracted ion bunch U DC Buffer gas Ion bunch Trapping Ion cooling in buffer gas. Ion extraction in short bunches with low emittance. Ion collection and accumulation. Ejection z

44 Time constant τ [ ms ] d 2 u sec dt 2 δ du sec dt Ion energy [ ev ] 2 q2 ω RF u 8 sec =0 Ar + ions in He at 10-3 mbar τ sec =4τ E

45 Cooling Radial motion x z x x=a 1 y t Effect of the buffer gas on the radial motion x t x=a 2

46 Bunching: SHIPTRAP A potential well is needed in the axial direction Fast cooling in transverse direction. Enough length to reduce the axial energy. Transport of the ions (axial electric field). Inclined electrodes. Segmentation of the RFQ. V RF cos ω RF t+π V RF cos ω RF t A. Loboda et al. Eur. J. Mass Spectrom. 6, 531 (2000) Extracted ion bunch Injected ions Extracted ion bunch U DC Buffer gas Ion bunch Trapping R.B. Moore et al. Ejection z

47 A potential well is needed in the axial direction Fast cooling in transverse direction. Enough length to reduce the axial energy. Transport of the ions (axial electric field). 100 Injected ions Bunching: SHIPTRAP Segmentation 60 of the RFQ. COUNTS V RF cos ω RF t+π V RF cos ω RF t FWHM = 510 ns FWHM = 1.5 µs FWHM = 260 ns Inclined electrodes. A. Loboda et al. Eur. J. Mass Spectrom. 6, 531 (2000) FWHM = 1.01 µs Extracted ion bunch FWHM = 230 ns Extracted ion bunch U DC COUNTS R.B. Moore 0 et al Buffer gas 50 Ion bunch Trapping Ejection z

48 LPCTrap Ions per bunch / Accumulation time / ms 4 He + P H2 = mbar an et al. Nucl. Instrum. Methods A 518 (2004) 712. Ion current / a.u. Cooling and bunching of 4 He + ions I incident =75 pa τ E ( 4 He + ) = 1 ms N max = ions/bunch Efficiency = 5 % FWHM ( 4 He + ) = 100 ns P H2 = mbar Storage time / ms 4 He + τ S = 13 ms 80

49 ISOLTRAP, University of Jyväskylä First coupling of traps to radioactive ion beams ISOLDE beam Buncher beam ε ~ 30 π mm ε trans ~ 10 π mm mrad mrad E ~60 kev E ~2.5 kev DC-like Efficiency of 12-15%. ε long ~ 10 evμs An improvement of several orders of magnitude. F. Herfurth et al., NIMA 469, 264 (2001) Highlights 2003 / Ar 72 Kr 74 Rb 98 ms 17.2 s 65 ms 1.8 kev 8.0 kev 4.5 kev ~100 / s ~1000 / s ~500 / s K. Blaum et al., Nucl. Phys. A 746, 305c (2004), private communication Laser spectroscopy IGISOL beam Buncher beam ε ~ 13 π mm ε ~ 3 π mm mrad mrad ΔE ~80 ev ΔE < 1 ev DC-like Δt ~ 5-10 μs Efficiency of 60%. A. Nieminen et al., NIMA 469, 244 (2001) Laser spectroscopy on 175 Hf A. Nieminen et al., PRL 88, (2002) Laser spectroscopy on Zr P. Campbell et al., PRL 89, (2002) Mass measurements Nuclid Halflife Uncertain Yield e 17 Ne 109 ty ~300 ev ~1000 / 22 Na ms 2.6 y 160 ev s ~10 6 / s Nuclid Halflife Uncertain Yield e 104 Zr 1.2 s ty 50 kev ~200 / s S. Rinta-Antila et al., Phys. Rev. C 70, (2004)

50 High precision experiments in nuclear physics

51 + Excitation of the ion motion in Penning traps V t =V cos ω RF t V t =V cos ω RF t V t =V cos ω RF t+π V t =V cos ω RF t+π

52 Buffer-gas cooling in Penning traps Increase of the cyclotron radius when no excitation is applied. Centering of the ions after excitation at ω RF = ω c.

53 he principle of mass measurements in Penning tra External RF quadrupole field with ω RF =ω c =ω +ω ( 1 ) ( 2 ) ( 3 ) I o n s D e t e c t o r 8 t=0 μ= μ min M a g n e t i c f i e l d [ T ] T r a p c e n t e r z = z D e t e c t o r p o s i t i o n 0 z = z ( 1 ), ( 3 ) E n d c u p s ( 2 ) R i n g a n d c o r r e c t i o n e l e c t r o d e s z [ c m ] F z B = µ z t=t RF μ= μ max TOF min μ max ω RF =ω c

54 Time of flight resonance E ( t) = r 1 mrk sin ( ωbtrf ) 0 2 ωb

55 Mass measurements with SHIPTRAP Statistical uncertainty Magnetic field fluctuations 7.3(5) T [min] Mass-dependent uncertainty 1.1(1.7) (m/q) [u] Residual systematic uncertainty ~ Overall uncertainty mass determination of a

56 The measurement sequence

57 rp-process Nucleosynthesis e.g. on accreting neutron stars Explosive hydrogen burning (X-ray bursts) Steady-state burning Evolution of the process depends on pdensity and temperature in stellar environment A s (3 3 ) G e (3 2 ) G a (3 1 ) Z n (3 0 ) R K B S b (3 7 ) r (3 6 ) r (3 5 ) e (3 4 ) T c (4 3 ) M o (4 2 ) N b (4 1 ) Z r (4 0 ) Y (3 9 ) S r (3 8 ) A P R R g d h u S b (5 1 ) S n (5 0 ) In (4 9 ) C d (4 8 ) (4 7 ) (4 6 ) (4 5 ) (4 4 ) C u (2 9 ) N i (2 8 ) C o (2 7 ) F e (2 6 ) M n (2 5 ) 3132 C r (2 4 ) V (2 3 ) 2930 T i (2 2 ) S c (2 1 ) C a (2 0 ) K (1 9 ) 2324 A r (1 8 ) C l (1 7 ) 2122 S (1 6 ) P (1 5 ) S i (1 4 ) A l (1 3 ) 1516 M g (1 2 ) N a (11 ) 14 N e (1 0 ) F (9 ) O (8 ) N (7 ) 9 10 C (6 ) B (5 ) 7 8 B e (4 ) X e (5 4 ) I (5 3 ) T e (5 2 ) Astrophysical observations: elemental abundance, light curves Required nuclear data : Masses (sep. energies, Q-values) β decay half-lives Reaction rates L i (3 ) H e (2 ) 5 6 H (1 ) H.Schatz et al., Phys. Rep. 249, 167 (1998); Int. J. Mass Spectrom. 251, 293 (2006)

58 rp-process end-points The Sn-Sb-Te cycle ( γ,a ) 105T 104S e b 106T 105S e b 107T 106 e Sb 108T 107S e b ( p,γ) 103S n 102In 104S n 103In 105S n 106S n β+ A s (3 3 ) G e (3 2 ) G a (3 1 ) Z n (3 0 ) R K B S b (3 7 ) r (3 6 ) r (3 5 ) e (3 4 ) T c (4 3 ) M o (4 2 ) N b (4 1 ) Z r (4 0 ) Y (3 9 ) S r (3 8 ) A P R R g d h u S b (5 1 ) S n (5 0 ) In (4 9 ) C d (4 8 ) (4 7 ) (4 6 ) (4 5 ) (4 4 ) C u (2 9 ) N i (2 8 ) 105 C o (2 7 ) F e (2 6 ) M n (2 5 ) 3132 C r (2 4 ) V (2 3 ) 2930 T i (2 2 ) S c (2 1 ) C a (2 0 ) K (1 9 ) 2324 A r (1 8 ) C l (1 7 ) 2122 S (1 6 ) P (1 5 ) S i (1 4 ) A l (1 3 ) 1516 M g (1 2 ) N a (11 ) 14 N e (1 0 ) F (9 ) O (8 ) N (7 ) 9 10 C (6 ) B (5 ) 7 8 B e (4 ) 104In X e (5 4 ) I (5 3 ) T e (5 2 ) In L i (3 ) H e (2 ) 5 6 H (1 ) H.Schatz et al., PRL 68, 3471 (2001)

59 Measurements along the rp-process Xe(54) # I(53) # # # # Te(52) # # Sb(51) # # # # # # Sn(50) # # # In(49) # # # # Cd(48) # # # # 60 Ag(47) # # # # 58 Pd(46) # # # # # 56 Rh(45) # # # # # # 54 Ru(44) # # # # # # 52 SHIPTRAP Tc(43) # # # # # Mo(42) # # # ANL # Nb(41) # # J YFL Zr(40) # #

60 Mass measurements with ISOLTRAP

61 Mass measurements with ISOLTRAP

62 Mass measurements with ISOLTRAP

63 Astrophysics: The mass of Kr 72 calculations Sr 74 50# ms β (γ,p) (p,γ) + Rb 73 <27 ns β (γ,p) (p,γ) + Kr 72 Effective lifetime /s Network 10 ISOLTRAP AME s β Temperature /GK ME(73Rb, Sr) using Coulomb shifts from Brown et al. PRC 65 (2002) 5802 Proton capture rates as in Schatz et al. PRL 86 (2001) D. Rodríguez et al., PRL 93 (2004)

64 In-trap decay: mass spectrometry Decay in the buffer-gas-filled preparation trap produced at ISOLDE X Y + e+ not produced at ISOLDE Make more radioactive species available Nearly simultaneous ωc measurement of mother and daughter nuclei Test candidate: 37 Ar 50 X A Z A Z-1 0 Y e+ Y X A Z-1 A Z-1 A Z Y X A Z -50 e e+ X A Z K cm A Z-1 e+ A Z z (mm) X A Z e+ 100

65 Standard Model: search for exotic couplings Nuclear β decay spectrum v H β = c H Nν =+1 Ke,tR H β = ν β Tensor β v c a H ν = 1 dk dt =F ±Z, E C E p E p R pe p ν dk e dt R e R e e ν e 2 t Axial-vector C12V C 2S aa= F= 2 C3 C 2 V ν S C1T C A agt =a=+ 2 3 C3T C 2A Ne Ar (1959) (1959) He V-A(1963) Theory of the Standard Model 6 (Exp - S af =1n (1978) agt = 21 Na 1 3 (2003) 32 Ar (1999) Experimental results n 19 Ne, 23Ne, 21Na 32,33 Ar, 35Ar 37 K, 38mK He p 2R C S0=0 0.2 C T = Fermi fraction x0.8 agt = ± C.H. Johnson et al. Phys. Rev. 132, (1963) 11 F. Gluck et al. Nucl. Phys. A 628 (1998) 493.

66 Standard Model: search for exotic couplings Transparent Paul trap MCP MCPdetector detector 0+ He+ Electron ms βqβ = MeV Telescope ββ Telescope Recoil ion 1+ Li Neutrino Pure Gamow-Teller transition. Maximal recoiling-ion energy 1.4 kev. Any ion produced by the source can b practicable. High rate from SPIRAL ions/s. Easy-to-use device. Easy to place at the low energy beam line of SPIRAL2. Better sensitivity to a. Better control of systematic errors.

67 The LPCTrap facility Surface ion source 6, Li, Na+.. PhD. Thesis G. Darius RFQ trap PhD. Thesis P. Delahaye, A. Méry Diagnostics LIRAT HV Pulsed cavities 3.5 m Paul Trap

68 Performance of the LPCTrap He+ 4 H2 buffer gas RFQ + Pulsed cavity 1 5.6(8)% Transmission RFQ>Trap Pulsed cavity 2 40% Trapping 7.7(8)% Overall efficiency 50(1)% 8.7(8) 10-4 Ar+ He buffer gas 40 RFQ + Pulsed cavity 1 4.8(8)% Transmission RFQ>Trap Pulsed cavity 2 46% Trapping 12(2)% Overall efficiency 25(1)% 6.6(12) Storage time Paul trap He+ 4 Ar (5) ms 595(40) ms D. Rodríguez et al. NIMA 565 (2006) 876.

69 Monte Carlo simulations GEANT4 DSSSD + Scintillator (E,x,y) Control of the systematic effects on the measurements. Pβ, Eβ e- scattering and backscattering. Size of the ion cloud. Electron Phase ofion thecloud RF field. Using the SIMION grid concept to transport ions in GEANT4. Recoil ion SIMION MCP (TOF,x,y) SIMUTIL PR,ER Potential (S. Schwarz) Chart ASCII file.pa# file GEANT4 Electric field GEANT4 User Stepping Action Results compared to SIMION v.7 at energies down to 50 ev.

70 3 5x10 43 Counts Counts 10 4x10 3 3x x10 T =0 K 2 2 Mν =TE ν=-p 900 K ν T =0 K a=-1/3 2 Size All coincidences ofdsssd the Condition in & Scint ion cloud EDSSSD / MeV Kinematics properties x Mν M /MeV / MeV ν ETotal / MeV Paul trap parameters: VRF =150 V. νrf = 1.15 MHz. Detectors resolution: Time of flight ->400 ps. Position MCP->120 μm. Energy Scintillator->10%. Energy DSSSD->1%. Position DSSSD->1 mm.

71 The time of flight of the recoil ions Monte Carlo fit to the time-of-flight distribution of the recoil ions. Size of the ion cloud. RF Phase x10 T =0 K T = 900 K T = 1800 K T = 3600 K a = -1/ x10 3 6x x x No RF RF phase π /2 RF phase 3π /2 T= 900 K a =-1/3 3 5x10 Counts Counts 8.0x Time of flight / ns 4x10 3 3x10 3 2x10 3 1x Time of flight /ns

72 Experimental results July RF phase Counts Time of flight /ns The main disturbance in the time-of-flight distribution arises from the RF field ts < 25 ms Counts Counts 500 Size of the ion cloud ts > 25 ms Experimental results Simulations Time of flight /ns Arbitrary phase T = 900 K Time-of-flight /ns 1000