1. Department of Chemistry, University of Utah
Octopole Technology
---Sha Joshua Ye 
Department of Chemistry, University of Utah
Nov 6th, 2002

2. 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,
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,

3. 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;

4. If E0 is inhomogeneous, using the 1st order approxation:
Few steps later:
= q2·E02/4m2
Also Es= Φs
If we define an effective potential:

5. 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

6. Under adiabaticity approximations, we obtain the so-call adiabaticity parameter :
=2q| E0|/m2
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?

7. 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

8. 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?

9. 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.

10. Cross views of the effective potential:
Ideal hyperbolic electrodes
Some deformation of electrodes
Total E

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

12. The average kinetic energy distribution
The most probable average Ekin
The fluctuations of the mean Ekin

13. 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.

14. Guided-ion-beam apparatus
26cm
14cm
Crossed-beam arrangement
46cm

15. Agilent 7500c octopole reaction system in Inductively Coupled Plasma MS
The octopole is mounted off-axis to prevent photons reaching the detector

16. New concept of ion traps having field of octopole or hexopole components.
200cm
3.5cm
14cm
FT-ICR
The coulombic interactin of ions in the octople ion trap casue
a strong non-linearity trapping efficiency in the octopole

17. The Trick About Life is Too Make It Look Easy

19. 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 = qE0/m2