Q UADRUPOLE A NALYZERS AND I ON T RAPS I. ermk, CGC Instruments, - PowerPoint PPT Presentation

Q UADRUPOLE A NALYZERS AND I ON T RAPS I. Č ermák, CGC Instruments, Chemnitz, Germany, www.cgc-instruments.com Presentation Outline Physics of electrodynamic multipoles Ion Guides and Traps • Focusing in 2D or 3D • Ion-storage setups, measurement sequences • Particle trajectories • Resulting spectra • Potentials and forces • Study of ion-neutral reactions • Effective potential and adiabaticity • Comparison of experimental techniques • Technical requirements Quadrupole Mass Spectrometry Future Developments • Ion motion in linear 4-poles • Resolution and transmission • Real devices and technical limitations

F OCUSING OF CHARGED PARTICLES Electrostatic field Electrostatic potential φ = φ ( x , y , z ) is time independent: ∂ φ ∂ t = 0 Laplace equation in vacuum: ∆φ = ∂ ² φ ∂ x ² + ∂ ² φ ∂ y ² + ∂ ² φ ∂ z ² = 0 Potential minimum in x and y directions � ∂ ² φ ∂ x ² > 0, ∂ ² φ ∂ y ² > 0 � ∂ ² φ ∂ z ² < 0 � potential maximum in z � electrostatic potential can only be saddle-shaped � it cannot provide a 3D focussing Electrodynamic field Electrostatic potential is time variable: ∂ φ ∂ t ≠ 0, usually a sinusoidal signal: φ = φ ( x , y , z ) · sin( ω t ) � charged particles can gain/release kinetic energy from/to the electric field (analog to a spacecraft flyby at a planet) Principle used in electrodynamic storage devices: under certain conditions, particle gains and releases kinetic energy � remains trapped Applications: ion guides, mass selectors, ion/particle traps

P ARTICLE T RAJECTORIES IN M ULTIPOLE T RAPS Paul Trap 4-pole 8-pole 16-pole

P OTENTIALS AND F ORCES IN M ULTIPOLE D EVICES 4-pole 8-pole 22-pole Ring-Electrode Trap Electrostatic potential of a linear multipole: n r � � φ ( r , θ ) = V · � cos(n θ ) � � r 0 � 2n = electrode count (quadrupole: n = 2) ± V = voltages on electrodes r 0 electrode inner radius Electrostatic field strength: ___ φ ( r ) E ( r , θ ) = – ∇ φ ( r , θ ) φ ( r 0 ) n– 1 E r ( r , θ ) = d φ d r = n V r � � r 0 � cos(n θ ) _ _ F ( r ) � � r 0 � F ( r 0 ) n– 1 E θ ( r , θ ) = 1 r d φ d θ = n V r 4-pole � � r 0 � sin(n θ ) � � r 0 � n– 1 � E ( r , θ ) = E r ² + E θ ² = n V r � � 8-pole r 0 � RET � � r 0 � Force acting on a charged particle: 22-pole F ( r , θ ) = q · E ( r , θ ) � F ~ q · r n– 1 quadrupole: F ~ r = harmonic force r / r 0

E FFECTIVE P OTENTIAL AND A DIABATICITY Effective Potential Electric field strength E = E · sin( ω t ) Micro-motion: motion due to the driving frequency, secular motion displacement x = q q m · ω 2 · E · sin( ω t ), amplitude x m = m · ω 2 · E Secular motion: displacement X , adiabatic approach: secular motion is slow micro-motion EOM: m ·d 2 X d t 2 = q · E ( X + x )·sin( ω t ) ( x = mean value of x ) Solution: approximation using Taylor series: E ( X + x ) = E ( X ) + x ∇ · E q 2 and considering mean values over one period of the driving frequency � m ·d 2 X d t 2 = 4 m ω 2 · ∇ | E ( X )| 2 q 2 ·| E ( X )| 2 � Effective potential Φ ( X ) = is a measure for the depth of the potential well in a trap, 4 m ω 2 n– 1 q 2 2n–2 q 2 2 � Φ = n 2 m ω 2 V 2 m ω 2 V 2 multipole: E = n V r r r � � � � � � r 0 � 4 2 � , quadrupole (n = 2): Φ = 2 � � � � � � � r 0 r 0 r 0 r 0 r 0 � � � Adiabaticity 2 q ·| ∇ E ( X )| Adiabaticity η ( X ) = 2| x m |·| ∇ E ( X )| = is a measure for the motion stability, m ω 2 | E ( X )| lower values � lower field variations over the micro-motion amplitude � better motion stability, n–2 4 q q m ω 2 V r m ω 2 V � � multipole: η = 2n (n– 1 ) 2 � , quadrupole (n = 2): η = 2 = constant value � � r 0 r 0 r 0 � Adiabatic motion for η < 0.3 � trapped particles do not gain energy from the field

Q UADRUPOLE M ASS S PECTROMETRY (QMS) Electrode System 4 rods supplied by a combination of AC and DC voltages: ± V DC ± V AC sin( ω t ) (patented 1 956 by Wolfgang Paul and Helmut Steinwedel) DC voltage influences the adiabaticity and the effective potential in radial directions x and y Ion motion Stability parameters: a x,y = ± 8 q 4 q m ω 2 V DC m ω 2 V AC Paul Patent 2939952, Fig. 5 2 , q x,y = 2 = η x,y r 0 r 0 � a x,y ~ V DC , q x,y ~ V AC , a x,y , q x,y ~ q / m Stability diagram (stable solutions of the Mathieu equation): combination of a x,y , q x,y for stable ion trajectories stable ion trajectory unstable ion trajectory unstable q / m unstable V DC = 0. 1 68· V AC β x = 1 β y = 0 V DC = 0 a x,y stable q / m β x = 0 V DC + V AC sin( ω t ) – V DC – V AC sin( ω t ) β y = 1 Ion motion in the QMS unstable unstable q x,y

Q UADRUPOLE M ASS S PECTROMETRY (QMS) Resolution Depends on the ratio V DC / V AC = a x,y /2 q x,y : unstable unstable 0. 1 68 ( a – 1 ) q 2 (5 a + 7) q 4 a 2 ( a – 1 ) 2 – q 2 32 ( a – 1 ) 3 ( a – 4) q / m min β = ... 0. 1 66 β x = 1 a x,y q / m 0. 1 64 V DC / V AC β y = 0 stable q / m max q x,y Values m / ∆ m ≈ 1 000 can be reached, requirement: ions have to perform several oscillation periods in the system Transmission Parameter β determines the secular frequency of the harmonic oscillations in the QMS: Ω = ½ βω β is given by the chosen resolution m / ∆ m (borders of the stability diagram: β x,y = 0 and β x,y = 1 ) Harmonic oscillation with Ω � force field F = K · r , K = m Ω 2 = β 2 2 r 2 = β 2 4 m ω 2 � effective potential Φ = K 2 m ω 2 · r 2 � effective potential is deep in one direction but flat in the second one � for proper ion guiding, the driving frequency ω must be high enough: Φ (0.8 r 0 ) > E k = transversal ion energy

Q UADRUPOLE M ASS S PECTROMETRY (QMS) Real QMS Devices Detector Ion Source Tri-Filter QMS, Extrel Pre- and Post-Filter: 4-pole w/o DC � deep effective potential in all radial directions � high ion transmission Entrance and Exit Lens: ion focussing from the ion source to the QMS and from the QMS to the detector Technical Limitations Operation pressure: collisions with residual gas modify ions � mass spectrum distortion, collisions � lower transmission � mass discrimination, high pressure � gas discharge Requirement: deep effective potential � high operating frequency ω � high operating voltage technical limits: several kV, several MHz

I ON G UIDES AND T RAPS Ion-Storage Setups Detector Trap Entry Trap Exit QMS Ion Source RET Entrance Exit Optics Optics Detector Optics continuous gas inlet (reaction gas) l-N 2 (cooling) pulsed gas inlet (buffer gas = He) Ion-storage setup w/ a ring-electrode trap (RET) S ta r t Typical Measurement Sequence G a s P u ls e 1 ) Ion preparation, trap filling, ion cooling 2) Ion storage = time for ion-neutral reactions C a th o d e S to r a g e tim e 3) Ion extraction, mass analysis T ra p E x it 4) Emptying trap � ensure reproducible start conditions for the next run C o u n te r G a te 1 run = measurement for T ra p R F one reaction time and one product mass R u n � many repetitions required for a complete picture E x tr a c tio n E m p ty in g F illin g

I ON G UIDES AND T RAPS Resulting Spectra + + N 2 → N 2 D + + D 2 Example: deuteron transfer D 3 + , D + + D 2 → D 3 + + + N 2 → N 2 D + + D 2 Ion production: e – + D 2 → D + , D 2 Ion reaction: D 3 10 5 + Σ D 3 10 4 N 2 D + 10 3 + , H 2 D + 10 3 D 2 + D 3 Ion Counts per Filling Ion Counts per Cycle + HD 2 10 2 10 2 H 2 D + 10 1 1 5 NND + 10 1 10 0 + N 2 H + D 2 HD + 10 -1 10 0 D + , H 2 + + HD 2 10 -2 D 2 gas pulse 10 -3 10 -1 0 20 40 60 80 100 120 140 160 180 200 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Storage Time /ms Delay / ms Total ion number ( Σ ): important quantity indicating that 1 ) the trap is working well and does not loose ions over the storage time 2) the mass spectrometer and detector scan all product ions 3) there is no mass discrimination in the detection system Evaluation: rate coefficient k + ] d[N 2 D + ] = d[D 3 + ] · [N 2 ] � k d t = k · [D 3 [X] = number density (concentration) of X d t knowledge of [N 2 ] required, evaluation by 1 ) test reaction or 2) precise pressure measurement (e.g. viscovac)