The magnetic field must be oriented in three mutually perpendicular directions with respect to the trap electrodes, which are the source of the external quadrupole field
, but with the same magnitude of the magnetic field.
The more complicated quadrupole field would be created by two bar magnets laid end to end with their respective north or south poles touching.
These variations, as well as measurements of light polarization -- the orientation of a light wave's electric and magnetic fields -- signaled to Bohlender and Landstreet that HD 3776 has a dipole field of 3,500 gauss and a whopping quadrupole field of 53,000 gauss.
This design requires that a large transverse quadrupole field be realized in a rod whose diameter decreases in direct proportion to an increase in frequency; 20 GHz would seem to be the upper frequency limit for this device.
The ferrite half-wave plate uses a quadrupole field geometry  that must be rotated to effect phase shift.
Simulations using the OPERA-2d software package confirmed that, by itself, the quadrupole field
quality was excellent, but close proximity of the gradient magnet invalidated the fundamental assumptions of the matrix model upon which the design was based.
"You can get that by displacing the dipole or by adding a quadrupole field
. One of the guys who's big on diffusion theory says if you add a quadrupole, you get one pole fatter.'
The quadrupole fields
are of higher quality in the center, and the performance of the mass spectrometer is dramatically improved.