Dynamically harmonized FT-ICR cell with specially shaped electrodes for compensation of inhomogeneity of the magnetic field
A method and apparatus of compensating a magnetic field inhomogeneity in a dynamically harmonized FT-ICR cell is presented, based on adding of extra electrodes into the cell, the extra electrodes being shaped in such a way that the averaged electric field created by these electrodes produces a counter force to the forces caused by the inhomogeneous magnetic field on the cycling ions.
1. A method of magnetic field inhomogeneity compensation in a FT-ICR cell, with housing electrodes alternately increasing and decreasing in width from ends to a center of the cell, thus creating a dynamically harmonized electric field, the improvement comprising an adding of extra electrodes into the cell, wherein the extra electrodes are shaped on one side by curves of fourth or higher order in the axial direction z such that an average electric field created by a voltage at these extra electrodes produces a counter force to forces caused by second order or, respectively, higher than second order magnetic field inhomogeneities in the axial direction z on ions cycling within the cell.
2. The method of claim 1 , wherein the extra electrodes are inserted between the housing electrodes with decreasing width and those with increasing width on a cylinder surface surrounding the FT-ICR cell.
3. The method of claim 1 , wherein the housing electrodes with widths increasing to the center have boundaries with curves of second order in the axial direction z.
4. The method of claim 1 , wherein the housing electrodes with widths decreasing to the center have boundaries with curves of fourth order in the axial direction z.
5. The method of claim 1 , wherein the housing electrodes with width increasing to the center are grounded.
6. The method of claim 1 , wherein housing electrodes of the dynamically harmonized FT-ICR cell form a cylinder which is segmented into electrodes of different types by curves along the axial direction z, which coincides with the direction of the magnetic field, the curves fulfilling the requirement
α
=
2
π
N
n
±
b
(
1
-
(
z
a
)
2
)
;
n
=
0
,
1
,
…
,
N
-
1
;
b
=
π
/
N
-
π
/
60
;
where a is half the length of the cell, α an angle coordinate of a point on the curve, and N a number of electrodes of each type.
7. The method of claim 1 , wherein trapping electrodes at the ends of the FT-ICR cell are radially segmented, and the extra electrodes are inserted between these segments.
8. The method of claim 1 , further comprising varying the voltage on the extra electrodes in order to make disturbances of a cyclotron frequency caused by the magnetic field inhomogeneity independent of a z-oscillation amplitude.
9. A method of compensating a magnetic field inhomogeneity inside an FT ICR cell with dynamic harmonization by introducing a specific electric field correction, comprising: incorporating into a housing electrode assembly electrodes the borders of which on one side are shaped by a curve of fourth order in an axial direction of the cell, which coincides with a direction of the magnetic field; and compensating an inhomogeneous component of the magnetic field of the second order by an electric field created by voltages applied to the special electrodes.
10. An improved dynamically harmonized FT ICR cell having a shape of a cylinder being made up of electrodes of different types which are folioed by curves along an axial direction z of the cylinder, the axial direction coinciding with a direction of the magnetic field and the curves fulfilling the requirement
α
=
2
π
N
n
±
b
(
1
-
(
z
a
)
2
)
;
n
=
0
,
1
,
…
,
N
-
1
;
b
=
π
/
N
-
π
/
60
;
where a is half the length of the cell, α an angle coordinate of a point on the curve, and N a number of electrodes of each type, the cell further comprising extra electrodes being located between the electrodes of different types and the borders of which being shaped on one side by curves of an order four or higher in z, and further being supplied with an electric potential in order to compensate for magnetic field inhomogeneities of order two or higher, respectively, in the direction z of the magnetic field.
11. The cell of claim 10 , wherein the cylinder is closed by two trapping electrodes with a surface geometry close to spherical.
12. The cell of claim 10 , wherein different electric potentials are set on left and right extra electrodes, the different potentials fulfilling the requirement V l +V r =2·V trap , where V l,r are the voltages on left and right sets of the extra electrodes and V trap is the voltage on cylinder electrodes of different types.