R ADIO -F REQUENCY Q UADRUPOLES AND M ULTIPOLES : M ASS S ELECTION AND P ARTICLE T RAPPING I. Č ermák, CGC Instruments, Chemnitz, Germany, www.cgc-instruments.com CGC Instruments Research and development company founded in 2003 • Expertise in • electronics, software, particle and ion trapping technique, vacuum technology, optical and mass spectrometry Design and construction of customer-specific precise electronic measurement devices • Presentation Outline Physics of Electrodynamic Multipoles Ion Guides and Traps Focusing in 2D or 3D Ion-storage setups, measurement sequences • • Particle trajectories Experimental results • • Potentials and forces Common geometry • • Effective potential and adiabaticity Technical requirements • • Quadrupole Mass Spectrometry Future Developments Ion motion in linear 4-poles • Geometry of linear 4-poles •
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 q q displacement x = 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 q 2 q 2 n– 1 2n–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 q 4 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
L INEAR Q UADRUPOLES - C OMMON G EOMETRY Ideal hyperbolic geometry Wire quadrupole Semicircle rods Circular rods Optimum geometry: x 2 + y 2 = r 0 2 (hyperbolic electrode) Multipole Terms of a Linear Quadrupole Rod System resulting field: pure quadrupole term 4 complicated manufacturing � rarely used C6/C2 C10/C2 x10 Relative Multipole Coefficient / % 3 Approximations: C14/C2 x10 C18/C2 x100 wire quadrupol: 2 excellent field approximation easy to evacuate 1 accessible for light sensors or lasers 0 complicated manufacturing semicircle rods -1 good field approximation around system axis compact construction -2 circular rods -3 good field approximation around system axis (the 1 2-pole contribution can be suppressed) -4 16 18 20 22 24 26 28 30 32 34 easiest manufacturing Relative Electrode Radius / %
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 l-N 2 continuous gas inlet (reaction gas) (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 Experimental Results + + N 2 → N 2 D + + D 2 Example: deuteron transfer D 3 Evaluation: rate coefficient k : Σ + ] d[N 2 D + ] = d[D 3 + ] · [N 2 ] � k d t = k · [D 3 N 2 D + d t 10 3 + D 3 Ion Counts per Filling [X] = number density (concentration) of X 10 2 1 5 NND + 10 1 N 2 H + Knowledge of [N 2 ] required, evaluation by 1 ) test reaction with a known rate 10 0 2) precise pressure measurement (e.g. viscovac) + HD 2 10 -1 0 200 400 600 800 1000 1200 1400 1600 1800 2000 Storage Time /ms Total ion number ( Σ ): important quantity, its constant value indicates that: 1 ) the trap is working well and does not loose ions over the storage time 2) the mass spectrometer and the detector scan all product ions 3) there is no mass discrimination in the detection and the trapping system
I ON G UIDES AND T RAPS - C OMMON G EOMETRY Linear Systems Ideal hyperbolic geometry Circular rods (22-pole, D. Gerlich) Ring electrode system Ion funnel Ideal 2D multipole geometry: r n ·cos(n θ ) = ± r 0 n (n = multipole order, n = 2 for a quadrupole) Multipole field: higher order � better approximation of a box potential, but complicated manufacturing Typical approximations: circular rods or ring electrodes Ion funnels for high-pressure focussing 3D Systems Ideal hyperbolic geometry (3D Paul trap) Split-Ring Trap Linear system w/ 3D focusing Ideal hyperbolic geometry ( r 2 – 2 z 2 = ± r 0 2 ): closed design and complicated manufacturing � various approximations with worse field but larger openings
I ON G UIDES AND T RAPS Technical Requirements Ion temperature (transversal kinetic temperature) and mass range � operating parameters of the trap: effective potential: Φ (0.8 r 0 ) > E k = transversal ion energy adiabaticity: η < 0.3 q 2 2n–2 n–2 Multipole: Φ = n 2 m ω 2 V 2 q r m ω 2 V r � � � � 4 2 � > E k , η = 2n (n– 1 ) 2 � < 0.3 r 0 � r 0 � r 0 � r 0 � � � � requirements on operating frequency and voltage Example: 1 6-pole, electrode inner radius r 0 = 1 0 mm 300V, 1 .5MHz 500V, 1 MHz limit: 0.3 effective potential / eV 300V, 1 .5MHz adiabaticity 500V, 1 MHz 500V, 3MHz 750V, 1 0MHz 500V, 3MHz limit: 1 00meV (~300K) 750V, 1 0MHz ion mass / amu ion mass / amu
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