Effect of magnetic field inhomogeneity on ion cyclotron motion coherence at high magnetic field.

A three-dimensional code based on the particle-in-cell algorithm modified to account for the inhomogeneity of the magnetic field was applied to determine the effect of Z(1), Z(2), Z(3), Z(4), X, Y, ZX, ZY, XZ(2) YZ(2), XY and X(2)-Y(2) components of an orthogonal magnetic field expansion on ion motion during detection in an FT-ICR cell. Simulations were performed for magnetic field strengths of 4.7, 7, 14.5 and 21 Tesla, including experimentally determined magnetic field spatial distributions for existing 4.7 T and 14.5 T magnets. The effect of magnetic field inhomogeneity on ion cloud stabilization ("ion condensation") at high numbers of ions was investigated by direct simulations of individual ion trajectories. Z(1), Z(2), Z(3) and Z(4) components have the largest effect (especially Z(1)) on ion cloud stability. Higher magnetic field strength and lower m/z demand higher relative magnetic field homogeneity to maintain cloud coherence for a fixed time period. The dependence of mass resolving power upper limit on Z(1) inhomogeneity is evaluated for different magnetic fields and m/z. The results serve to set the homogeneity requirements for various orthogonal magnetic field components (shims) for future FT-ICR magnet design.