The 'Stark barrel' described by J. L. Hom, D. M. Homan, C. S. Hwang,
W. L. Fuqua III and K. B. MacAdam, Rev. Sci. Istrum. vol 69 (1998) 4086-93.
A cylindrical arrangement of electrodes that provides a nearly uniform electric field over a considerable volume.
Here there are 16 rods of diameter 1.58mm and length 70mm, enclosing an unobstructed volume of diameter 20mm.
The potentials applied to a rod is cos(theta), where theta is the angle between the xz plane and a line from the centre of the rod to the centre of the assembly. The values of theta are j*11.25 degrees, where j= 1, 3, 5 and 7.
3 planes of reflection symmetry (or anti-symmetry) are used to give a total number of segments 8*960. A larger number can easily be used to give higher accuracy.
The output information is given below. We see that the field at the centre of the device is 9.43187E-02 V/mm.
The deviations from this field for a selection of non-central positions are:
Coordinate Fractional deviation
x y z
0 3 0 +3.2E-6
0 4 0 +4.2E-6
0 5 0 -3.1E-5
2 0 0 +1.1E-6
4 0 0 +8.5E-6
0 0 2 -5.3E-6
0 0 4 -1.8E-5
It would not be difficult to improve the uniformity of the field at non-zero values of x and y by empirically adjusting the potentials applied to the rods. It would also not be difficult to improve the field for non-zero values of z by replacing the ends of the rods by separate systems of rods that have higher applied potentials.
Please see the contents of the output file temp70a.dat.