Octopole Technology

---Sha Joshua Ye 

Department of Chemistry, University of Utah

Nov 6th, 2002

Outline

• Theory behind the octopole

• Some experimental applications

• Gerlich, D. Inhomogeneous rf Fields: A Versatile Tool for the Study of Processes with Slow Ions. In State-Selected and Sate-to State Ion-Molecule Reaction Dynamics, Part I: Experiment, Ng, D.-Y.; Baer, M., Eds.; 1992; pp 1-176

• Ervin, K. M.; Armentrout, P. B. Translational Energy Dependence of Ar+ + XY ArX+ + Y (XY = H2, D2, HD) from Thermal to 30 eV cm. J. Chem. Phys. 1985, 83, 166-189.

• Armentrout, P. B. Mass Spectrometry—Not Just a Structural Tool: The Use of Guided Ion Beam Tandem Mass Spectrometry to Determine Thermochemistry. J. Am. Soc. Mass Spectrom. 2002, 13, 419-434.

Development of the theory

• Thomson’s (1903) determination of the X-ray scattering cross section.

• Electron motion eq:

• If include a static field, the above eq can be:

• If E0 is homogeneous, we get the special solution:

where

E is the electronic field; is the angular freq;

m2trd

d

2 q E0 cos t

m2trd

d

2 qE0 r( ) cos t qEs r( )

r t( ) r 0( ) a cos t m

2trd

d

2 qE0 r( ) cos t qEs r( )

r t( ) r 0( ) a cos t a qE0

m 2

• If E0 is inhomogeneous, using the 1st order approxation:

• Few steps later:

= q2·E02/4m2

• Also Es= Φs

• If we define an effective potential:

r t( ) R0 t( ) Rl t( )

m2tR0

d

d

2

V R0 q2 E0 2

4m 2 q s

• We get a simple expression: = -V(R0)

• The first integral of that is:

• Because

• Motion through an inhomogeneous field leads to an exchange between kinetic energies and electrostatic potential energy

m2tR0

d

d

2

1

2m

tR0

d

d

2

q2 E0 2

4m 2 q s Em

1

2m

tRl

d

d

2

q2 E0 2

4m 2

Rt t( ) q E0R0

m 2cos t

• Under adiabaticity approximations, we obtain the so-call adiabaticity parameter :

=2q| E0|/m2 • The empirical safe operation value of is

<0.3, derived from that the (r/r0)max<0.8

• How to obtain the effective potential for the 2D multipole device?

v 8

1

2 n 1( )v

r0

• By solving the Laplace’s Equation Ф(r)=0 assuming the equipotential surfaces of electrodes, we obtain the potential for long cylindrical conductors:

• For the 2D multipole, we adopt the following form for the applied potential:

• So

by setting Ф(r=r0,φ)=Ф0cosnφ, Ф(r=0,φ)=0

q2 E0rm 2

4m 2 q s rm Em

r Ar n Br n C sin n D cos n

0 U0 V0 cos t

r 0r

r0

cos n

• A couple of steps later,

where 2n is the number of poles, r0 is the inner radius to the poles,and

the rf potential applied to alternate rods is V0cos(t)

• The r2n-2 term tells us why octopole is mainly used for confining ion(guiding ion beam).

• How is the trapping field of octopole looks like compared to that of quatrupole?

Vn2

4

q2

m 2

V0 2

r0 2

r

r0

2n 2

q U0r

r0

n

cos n

• Collect more scattered reactant and product ions.• Bring the usable energy region down to

0.04eV(lab).• The relatively flat well renders much less

pertubation in ions’ radial momentum.

• Cross views of the effective potential:

Total E

Ideal hyperbolic electrodes Some deformation of electrodes

The total instaneous kinetic energy of an ion during one reflection from an rf wall.

E t( ) kin1

2m

tr0

d

d trl

d

d

2

1

2m

trl

d

d

2

2 V sin t 2

• The average kinetic energy distribution

The most probable average Ekin The fluctuations of the mean Ekin

Some applications

• The first octopole technique was used to by Gerlich in 1971 to make the first version of the guided-ion-beam apparatus.

• The improved one by Gerlich in 1984 extend the energy range to below 0.01eV(lab).

• Commercially, it has also been widely used.

Guided-ion-beam apparatus

26cm 14cm

46cm

Crossed-beam arrangement

Agilent 7500c octopole reaction system in Inductively Coupled Plasma MS

The octopole is mounted off-axis to prevent photons reaching the detector

The coulombic interactin of ions in the octople ion trap casue a strong non-linearity trapping efficiency in the octopole

200cm

3.5cm 14cm

FT-ICR

• New concept of ion traps having field of octopole or hexopole components.

The Trick About Life is Too Make It Look Easy

q n 2n n 1( )qV0

m2r0 2

2n 1( )

n

qV0

an 4n n 1( )qU0

m2r0 2

2n 1( )

n

qU0

2n n 1( )qV0

m 2 r0 2

r

r0

n 2

• In reality, the inscribed circle radius

r0=(n-1)d/2

• This figure shows the potential disturbtion from the cylinder surrounding an octopole.

where a = qE0/m2