Comparison of different types of deflector.

These form a set of 12 data files on electrostatic deflectors:

(and please note that the description 'edgeways' could also be 'transverse flat' or 'edge-on')

xmpl3d33: 2-fold deflector, flared plates.

xmpl3d34: 2-fold deflector, split-cylinder plates.

xmpl3d35: 2-fold deflector, curved edgeways plates.

xmpl3d36: 4-fold deflector, conventional flat plates.

xmpl3d37: 4-fold deflector, flared plates.

xmpl3d38: 4-fold deflector, sloping plates.

xmpl3d39: 4-fold deflector, split-cylinder plates.

xmpl3d40: 4-fold deflector, split-cylinder plates, staggered.

xmpl3d41: 4-fold deflector, edgeways plates.

xmpl3d42: 4-fold deflector, curved edgeways plates, staggered.

xmpl3d43: 8-fold deflector, split-cylinder plates.

xmpl3d44: 8-fold deflector, edgeways plates.

The purpose of these files was to develop the â€˜edgeways deflectorâ€™, see xmpl3d42, which was the subject of the publication number 42:

Edgeways electrostatic deflectors with reduced aberrations, by F H Read, Nucl. Instr. Meth. A427, 177-181 (1999).

The (unexpected) conclusion was that the 4-fold 'edgeways' (or 'transverse flat plate' or 'edge-on') deflector is much better than the conventional deflectors in current use (in 1999).

It should be said that the new edgeways deflectors have not yet been fully explored, nor fully optimised. Also, their geometries can now be more accurately modelled using the users equations option.

For standardisation, the minimum transverse separation s of the deflector plates is always 1.

The beam initially converges from a radius of 1 at z = -8 to the axis at z = 8. The deflection voltages are such that the deflection at z = 8 is always 0.5.

The parameters given in the tables are the spreads dx and dy at the gaussian plane and the aberration coeffient (arbitrarily) defined here by the equation

dr = Cs*alpha3

where dr is the greater of dx and dy and alpha is the half-angle in image space.

Results for the 2-fold deflectors studied here:

(although these deflect in only the x direction they also cause spreading in the y direction)

type |
file |
dx |
dy |
Cs |

flared |
xmpl3d33 |
0.0142 |
0.0019 |
58 |

split_cyl |
xmpl3d34 |
0.0199 |
0.0161 |
81 |

edgways |
xmpl3d35 |
0.0159 |
0.0020 |
65 |

planar |
- |
0.0097 |
- |
40 |

Here 'planar' signifies edgeways plates that have a straight edge. The data for 'planar' have been deduced by extrapolating data obtained with xmpl3d35 for a range of values of the curvature of the edge, and the deduced Cs is consistent with that obtained from the truly 2D planar. deflector given in xmpl2d22.

The unit of length is the minimum transverse separation s of the deflector plates

Results for the 4-fold deflectors studied here:

type |
file |
dx |
dy |
Cs |

flat |
xmpl3d36 |
0.2922 |
0.2922 |
1200 |

flared |
xmpl3d37 |
0.0758 |
0.0848 |
310 |

sloping |
xmpl3d38 |
0.0594 |
0.0682 |
279 |

split-cylinder |
xmpl3d39 |
0.1670 |
0.2004 |
680 |

split-cyl, staggered |
xmpl3d40 |
0.0478 |
0.0550 |
225 |

edgeways |
xmpl3d41 |
0.0918 |
0.1085 |
440 |

edgeways, staggered |
xmpl3d42 |
0.0159 |
0.0063 |
65 |

Here 'staggered' means that the x and y deflections occur at separated axial positions.

Results for the 8-fold deflectors:

type |
file |
dx |
dy |
Cs |

edgeways |
xmpl3d43 |
0.01741 |
0.00492 |
71 |

split cylinder |
xmpl3d44 |
0.01814 |
0.01621 |
74 |

4-fold deflectors are used more often than the 2-fold and 8-fold types, and for the 4-fold we see that the staggered edgways deflector is significantly better than the conventional configurations that are in widespread use.

More complete information can be found in the footnotes of the data files.

To help in understanding the advantages of the staggered edgeways deflector, it is said in the publication cited above that there are 3 significant objectives that should be aimed at to minimise aberrations.

The first is that the entrance and exit fringing fields should be brought close together so that the trajectories before and after have approximately the same radial positions and directions in the two fringing fields. This has the effect of approximately cancelling the aberrations, as can be seen from an inspection of the integral expressions for the aberration coefficients, as given by P. W. Hawkes and E. Kasper, Principles of Electron Optics, Academic Press, New York, 1989.

The second is that it is better in principle to physically separate the processes of deflection in the x and y directions, since it is known that the aberrations of 2-fold (dipole) systems can be very much smaller than those of 4-fold systems (as evidenced in the tables above).

The third objective is to position the two 2-fold systems as near as possible to each other, in order to minimise the sideways displacement of the beam at the second 2-fold deflector, and hence to minimise the aberrations produced by the second deflector. But at the same time the two sets should be sufficiently far apart so that there is a minimum disturbance between their fringing fields.

The three objectives are of course conflicting. Edgeways deflectors certainly help very much with the first objective. They also help with the third, since their thinness in the axial direction means that the separation of the active deflecting fields is the physical separation of the plates rather than the physical separation of the mean axial positions of traditional designs. And of course for the second objective they must be 'staggered'. So we are led to the conclusion that the best way of reducing the conflicts between the objectives is to use staggered edgeways deflectors, as we have found.