R ADIO -F REQUENCY Q UADRUPOLES AND M ULTIPOLES : M ASS S ELECTION - - PowerPoint PPT Presentation

RADIO-FREQUENCY QUADRUPOLES AND MULTIPOLES: MASS SELECTION AND PARTICLE TRAPPING

• I. Čermák,

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

• Focusing in 2D or 3D
• Particle trajectories
• Potentials and forces
• Effective potential and adiabaticity

Quadrupole Mass Spectrometry

• Ion motion in linear 4-poles
• Geometry of linear 4-poles

Ion Guides and Traps

• Ion-storage setups, measurement sequences
• Experimental results
• Common geometry
• Technical requirements

Future Developments

FOCUSING OF CHARGED PARTICLES

Electrostatic Field

Electrostatic potential φ = φ(x, y, z) is time independent: ∂φ ∂t = 0 Laplace equation in vacuum: ∆φ = ∂²φ ∂x² + ∂²φ ∂y² + ∂²φ ∂z² = 0 Potential minimum in x and y directions ∂²φ ∂x² > 0, ∂²φ ∂y² > 0 ∂²φ ∂z² < 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(ωt) 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

PARTICLE TRAJECTORIES IN MULTIPOLE TRAPS

Paul Trap 4-pole 8-pole 16-pole

POTENTIALS AND FORCES IN MULTIPOLE DEVICES

Electrostatic potential of a linear multipole: φ(r, θ) = V·

• r

r0

n

cos(nθ) 2n = electrode count (quadrupole: n = 2) ±V = voltages on electrodes r0 electrode inner radius Electrostatic field strength: E(r, θ) = –∇φ(r, θ) Er(r, θ) = dφ dr = n V r0

• r

r0

n–1

cos(nθ) Eθ(r, θ) = 1 r dφ dθ = n V r0

• r

r0

n–1

sin(nθ) E(r, θ) = Er² + Eθ² = n V r0

• r

r0

n–1

Force acting on a charged particle: F(r, θ) = q·E(r, θ) F ~ q·r n–1 quadrupole: F ~ r = harmonic force

4-pole 8-pole 22-pole Ring-Electrode Trap 4-pole 8-pole 22-pole RET

r/r0 _ _ F(r) F(r0) ___ φ(r)

φ(r0)

EFFECTIVE POTENTIAL AND ADIABATICITY

Effective Potential

Electric field strength E = E · sin(ωt) Micro-motion: motion due to the driving frequency, displacement x = q m·ω2 · E · sin(ωt), amplitude xm = q m·ω2 · E Secular motion: displacement X, adiabatic approach: secular motion is slow EOM: m·d2X dt 2 = q·E(X+x)·sin(ωt) ( x = mean value of x) Solution: approximation using Taylor series: E(X+x) = E(X) + x∇·E and considering mean values over one period of the driving frequency m·d2X dt 2 = q 2 4mω2 ·∇|E(X)|2 Effective potential Φ(X) = q 2·|E(X)|2 4mω2 is a measure for the depth of the potential well in a trap, multipole: E = n V r0

• r

r0

n–1

Φ = n2 4 q 2 mω2 V 2 r0

2

• r

r0

2n–2

, quadrupole (n = 2): Φ = q 2 mω2 V 2 r0

2

• r

r0

2

Adiabaticity

Adiabaticity η(X) = 2|xm|·|∇E(X)| |E(X)| = 2q·|∇E(X)| mω2 is a measure for the motion stability, lower values lower field variations over the micro-motion amplitude better motion stability, multipole: η = 2n (n–1) q mω2 V r0

2

• r

r0

n–2

, quadrupole (n = 2): η = 4q mω2 V r0

2 = constant value

Adiabatic motion for η < 0.3 trapped particles do not gain energy from the field

micro-motion secular motion

QUADRUPOLE MASS SPECTROMETRY (QMS)

Electrode System

4 rods supplied by a combination of AC and DC voltages: ±VDC ± VAC sin(ωt) (patented 1956 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: ax,y = ± 8q mω2 VDC r0

2 , qx,y =

4q mω2 VAC r0

2 = ηx,y

ax,y ~ VDC, qx,y ~ VAC, ax,y, qx,y ~ q/m Stability diagram (stable solutions of the Mathieu equation): combination of ax,y, qx,y for stable ion trajectories

Paul Patent 2939952, Fig. 5 Ion motion in the QMS VDC + VAC sin(ωt) –VDC – VAC sin(ωt) stable ion trajectory unstable ion trajectory βx = 0 βy = 0 βx = 1 βy = 1 VDC = 0 VDC = 0.168·VAC q/m q/m unstable stable unstable unstable unstable

ax,y qx,y

LINEAR QUADRUPOLES - COMMON GEOMETRY

Ideal hyperbolic geometry Wire quadrupole Semicircle rods Circular rods

Optimum geometry: x2 + y2 = r0

2 (hyperbolic electrode)

resulting field: pure quadrupole term complicated manufacturing rarely used Approximations: wire quadrupol: excellent field approximation easy to evacuate accessible for light sensors or lasers complicated manufacturing semicircle rods good field approximation around system axis compact construction circular rods good field approximation around system axis (the 12-pole contribution can be suppressed) easiest manufacturing

Multipole Terms of a Linear Quadrupole Rod System Relative Electrode Radius / %

16 18 20 22 24 26 28 30 32 34

Relative Multipole Coefficient / %

• 4
• 3
• 2
• 1

1 2 3 4

C6/C2 C10/C2 x10 C14/C2 x10 C18/C2 x100

ION GUIDES AND TRAPS

Ion-Storage Setups

Ion-storage setup w/ a ring-electrode trap (RET)

Typical Measurement Sequence

1) Ion preparation, trap filling, ion cooling 2) Ion storage = time for ion-neutral reactions 3) Ion extraction, mass analysis 4) Emptying trap ensure reproducible start conditions for the next run 1 run = measurement for

• ne reaction time and
• ne product mass

many repetitions required for a complete picture

T ra p E x it T ra p R F R u n S to r a g e tim e C o u n te r G a te C a th o d e S ta r t F illin g E x tr a c tio n E m p ty in g G a s P u ls e

Ion Source Detector RET QMS Detector Optics Entrance Optics Exit Optics Trap Exit Trap Entry l-N2 (cooling) continuous gas inlet (reaction gas) pulsed gas inlet (buffer gas = He)

ION GUIDES AND TRAPS

Experimental Results

Evaluation: rate coefficient k: d[N2D+] dt = d[D3

+]

dt = k · [D3

+] · [N2] k

[X] = number density (concentration) of X Knowledge of [N2] required, evaluation by 1) test reaction with a known rate 2) precise pressure measurement (e.g. viscovac) 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 Example: deuteron transfer D3

+ + N2 → N2D+ + D2

Storage Time /ms

200 400 600 800 1000 1200 1400 1600 1800 2000

Ion Counts per Filling

10-1 100 101 102 103

D3

+

HD2

+

N2H+ N2D+

15NND+

Σ

ION GUIDES AND TRAPS - COMMON GEOMETRY

Linear Systems

Ideal hyperbolic geometry Circular rods (22-pole, D. Gerlich) Ring electrode system Ion funnel

Ideal 2D multipole geometry: rn·cos(nθ) = ±r0

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 (r2 – 2z2 = ±r0

2): closed design and complicated manufacturing

various approximations with worse field but larger openings

ION GUIDES AND TRAPS

Technical Requirements

Ion temperature (transversal kinetic temperature) and mass range operating parameters of the trap: effective potential: Φ (0.8r0) > Ek = transversal ion energy adiabaticity: η < 0.3 Multipole: Φ = n2 4 q 2 mω2 V 2 r0

2

• r

r0

2n–2

> Ek, η = 2n (n–1) q mω2 V r0

2

• r

r0

n–2

< 0.3 requirements on operating frequency and voltage Example: 16-pole, electrode inner radius r0 = 10 mm

limit: 100meV (~300K) limit: 0.3 300V, 1.5MHz 500V, 1MHz 750V, 10MHz 500V, 3MHz 300V, 1.5MHz 500V, 1MHz 750V, 10MHz 500V, 3MHz effective potential / eV

ion mass / amu ion mass / amu

adiabaticity

FUTURE DEVELOPMENTS

Mass Analysis

Combination of traps and TOF advantages: analysis of the complete trap content difficulties: usual multipole trap does not provide radial and axial focussing bad TOF resolution Mass analysis via image charge advantages: non-destructive ion detection, analysis of the complete trap content difficulties: image charge obscured by the RF drive

Ion Preparation and Manipulation

Traps with switchable geometry switching between a higher multipole and quadrupole ion focussing - e.g. for TOF detection switching between 2D and 3D multipoles smooth switching between an ion guide and ion trap simpler ion capture and extraction Difficulties: complex electronics for switching the RF drive