Publications and student projects

All the publications are refereed and all are from the Manchester group in the UK.

The publication that users should cite is number 66 below.

Before the widespread use of computers the 'standard' book on electrostatic lenses was:

Electrostatic lenses, by E Harting and F H Read, Elsevier Publishing Company, Amsterdam (1976) -copies of the text (non-data) pages of this book are available in the ‘document’ folder of the CPO package.

The papers are listed in reverse time order.

Below this list are the abstracts of some of the more recent papers.

Below that is a list of student projects used at Manchester.

68. Optimization of the shapes of electrodes of electrostatic lenses, by F H Read, Microscopy and Microanalysis 21 Suppl S4, 276-279 (2015)

67. Achieving the highest accuracy with the BEM, by F H Read, Microscopy and Microanalysis 21 Suppl S4, 182-187 (2015).

66. The CPO programs and the BEM for charged particle optics, by F. H. Read and N. J. Bowring, Nucl. Instr. Meth. A645, 273-277 (2011).

65. Computer simulations of hexapole aberration correctors, by L. A. Baranova, F. H. Read and D. Cubric, Technical Physics 54, 1011-1017 (2009).

64. Stability criteria for a passive electrostatic non-relativistic charge particle storage device, by P Hammond, T J Reddish, AJ Alderman, D R Tessier and F H Read, New Journal of Physics 11, 043033 (2009).

63. Computer simulations of hexapole aberration correctors, by L. A. Baranova, F. H. Read and D. Cubric, Physics Procedia 1, 185-191 (2008).

62. Possibilities for grapheme for field emission: modelling studies using the BEM, by S. Watcharotone, R. S. Ruoff and F. H. Read, Physics Procedia 1, 71-75 (2008).

61. A passive electrostatic recycling spectrometer of desk-top size for charged particles of low kinetic energy, by D R Tessier, Y Niu, D P Secombe, T J Reddish, A J Alderman, B G Birdsey, F H Read and P Hammond, Phys Rev Lett 99, 253201 (2007).

60. Simulation of Thermionic Cathodes, by F. H. Read and N. J.Bowring, Nucl. Instrum. Meth. A531, 407-415 (2004).

59. Field enhancement factors of one-dimensional and two-dimensional arrays of nanotubes, by F H Read and N J Bowring, Microelectronic Engineering 73-74, 679-685 (2004).

58. The contributions of stochastic coulomb interactions and collective space-charge field aberrations to spatial spreading in charged particle projection systems, by F H Read and N J Bowring, Microelectronic Engineering 73-74, 97-105 (2004).

57. Capacitances and singularities of the unit triangle, square, tetrahedron and cube, by F. H. Read, COMPEL 23, 572-578 (2004).

# 56. The Parallel Cylindrical Mirror Analyzer: Axis-to-Axis configuration, by F H Read, D Cubric, S Kumashiro and A Walker, Nucl. Instrum. Meth. A519, 338-344 (2004).

# 55. Field enhancement factors of arrays of carbon nanotubes, by F H. Read and N J.Bowring, Nucl. Instrum. Meth. A519, 305-314 (2004).

# 54. Monte-Carlo Calculation Of Boersch Energy Spreading, by F.H. Read and N.J.Bowring, Nucl. Instrum. Meth. A519, 196-204 (2004).

# 53. Computational simulation of an electrostatic aberration corrector for a low-voltage scanning electron microscope, by L.A.Baranova, F.H.Read and D Cubric, Nucl. Instrum. Meth. A519, 42-48 (2004).

52. Accurate Monte-Carlo calculation of Boersch energy and angle spreading, by F.H. Read and N.J.Bowring, Rev. Sci. Instrum. 74 2280-2287 (2003).

51. The parallel cylindrical mirror electron energy analyzer, by F H Read, Rev. Sci. Instrum. 73 1129-1139 (2002).

50. Aberrations caused by mechanical misalignments in electrostatic quadrupole lens systems, by L A Baranova and F H Read, Optik 112, 1331-138 (2001).

49. An iron-cored coil system for the measurement of angular distributions of charged particles, by D Cubric, R Ward, G C King and F H Read, Rev. Sci. Instrum. 71 3323-3325 (2000).

48. Extrapolating the number of segments to infinity in the Boundary Element Method, by F H Read, International Series on Advances in Boundary Elements, vol 8 (Boundary Elements XXII, Eds. C A Brebbia and H Power, WIT Press, Southampton, UK), pp 139-144 (2000).

47. A fast parallel acquisition electron energy analyzer, by C G H Walker, A Walker, R Badheka, S Kumashiro, M Jacka, M El Gomati, M Prutton and F H Read, SPIE Vol 3777, 252-257 (1999).

46. The charge-tube method for space-charge in beams, by F H Read, A Chalupka and N J Bowring, SPIE Vol 3777, 184-191 (1999).

45. The charge-tube method for space-charge simulations, by F H Read, A Chalupka and N J Bowring, COMPEL (Int. J. for Computation and Mathematics in Electrical and Electronic Engineering), 18, 548-555 (1999).

44. Short and long range penetration of fields and potentials through meshes, grids or gauzes, by F H Read, N J Bowring, P D Bullivant and R R A Ward Nucl. Instr. Meth. A427, 363-367 (1999).

43. Minimisation of the aberrations of electrostatic lens systems composed of quadrupole and octopole lenses, by L A Baranova and F H Read, Int. J. Mass Spect. 189, 19-26 (1999).

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

41. Comparison of FDM, FEM and BEM for electrostatic charged particle optics, by D Cubric, B Lencova, F H Read and J Zlamal, Nucl. Instr. Meth. A427, 357-362 (1999).

40. Reduction of the chromatic and aperture aberrations of the stigmatic quadrupole lens triplet, by L A Baranova and F H Read, Optik 109, 15-21 (1998).

39. Penetration of electrostatic fields and potentials through meshes, grids or gauzes, by F H Read, N J Bowring, P D Bullivant and R R A Ward, Rev. Sci. Instrum. 69, 2000-2006 (1998).

38. A study of photoelectron angular distributions in xenon using a new magnetic angle changing technique, by D Cubric, D B Thompson, D R Cooper, G C King and F H Read, J Phys B 30, L857-864 (1997).

37. Aberrations due to localized potential defects on apertures, by F H Read, L A Baranova, N J Bowring, J Lambourne and T C Ward, Electron Microscopy and Analysis 1997, Institute of Physics Conference Series 153, 101-104 (1997)

36. Comparison of Finite Difference, Finite Element and Boundary Element Methods for electrostatic charges particle optics, by D Cubric, B Lencova and F H Read, Electron Microscopy and Analysis 1997, Institute of Physics Conference Series 153, 91-94 (1997)

35. Aberrations due to localized potential defects on apertures, by F H Read, L A Baranova, N J Bowring, J Lambourne and T C Ward, Rev. Sci. Instr. 69, 84-90 (1998).

34. Improved Extrapolation Technique in the Boundary Element Method to find the Capacitances of the Unit Square and Cube, by F H Read, J. Computational Physics, 133, 1-5 (1997)

33. The production and optical properties of an unscreened but localised magnetic field, by F H Read and J M Channing, Rev. Sci. Instrum. 67, 2372-2377 (1996).

32. Ultimate numerical accuracy of the Surface Charge Method for electrostatics, by F H Read and N J Bowring, Computation in Electromagnetics (Institution of Electrical Engineers, Conference Publication 420, 1996), p57-61.

31. Crossed aperture lenses for the correction of chromatic and aperture aberrations, by L A Baranova, S Ya Yavor and F H Read, Rev. Sci. Instrum. 67, 756-760 (1996).

30. Reduction of energy non-linearity of hemispherical deflection analyzers when used with multidetectors, by S C Page and F H Read, Nucl. Instrum. Methods A363, 249-253 (1995).

29. Defocussing of charged particle beams transmitted through meshes, by D L Williams, F H Read and N J Bowring, Nucl. Instrum. Methods A363, 120-123 (1995).

28. Aberrations of an electrostatic three-cylinder system used to simultaneously focus and deflect charged particles, by I C Dowker, F H Read, N J Bowring and P Hammond, Nucl. Instrum. Methods A363, 54-58 (1995).

27. Electrostatic electron-optical crossed lens with controlled astigmatism, by L A Baranova and F H Read, Rev. Sci. Instrum. 65, 1993-1997 (1994).

26. A linear magnetic field spectrometer for electron energy-loss measurements, by S C Page, L Mei, D Palfreyman and F H Read, Rev.Sci.Inst. 64, 2574-8 (1993).

25. Real-time computer-optimized electron coincidence spectrometer, by A J Murray, B C H Turton and F H Read, Rev.Sci.Inst. 63, 3346-51 (1992).

24. Lens first-order transfer matrices incorporating third-order aberrations, by S C Page and F H Read, Nuclear Instruments and Methods A 309, 594-5 (1991).

23. A new type of crossed-field energy analyser for charged particles: the magnetic-field-immersed Wien filter, by S C Page and F H Read, J.Phys.E (Sci.Instrum.) 22, 93-103 (1989).

22. A high resolution threshold photoelectron spectrometer for use in photoionisation studies, by G C King, M Zubek, P M Rutter and F H Read, J.Phys.E (Sci.Instrum.) 20, 440-443) (1987).

21. A 'movable' electrostatic lens, by F H Read, J.Phys.E (Sci.Instrum.) 16, 636-42 (1983).

20. Four-cylinder electrostatic lens II: energy scanning at constant image position and magnification, by G Martinez, M Sancho and F H Read, J.Phys.E (Sci.Instrum.) 16, 631-635 (1983).

19. Magnetic field paralleliser for 2 electron spectrometer and electron image magnifier, by P Kruit and F H Read, J.Phys.E (Sci.Instrum.) 16, 313-24 (1983).

18. The charge-density method of solving electrostatic problems with and without the inclusion of space-charge, by A Renau, F H Read and J N H Brunt, J.Phys.E (Sci.Instrum.) 15, 347-54 (1982).

17. Electrostatic Lenses, by F H Read, Radiation Effects 44, 129-36. (1979).

16. The realisation of high energy-resolution using the hemispherical electrostatic energy selector in electron impact spectrometry, by J N H Brunt F H Read and G C King, J.Phys.E (Sci.Instrum.) 10, 134-9 (1977).

15. Electrostatic Lenses, by F H Read, Conference Series of the Institute of Physics, no 38, 249-56 (1978).

14. Electrostatic lenses, by E Harting and F H Read, Elsevier Publishing Company, Amsterdam (1976) (Copies of the text (non-data) pages of this book are available in the ‘document’ folder of the CPO package.)

13. Aberrations in electrostatic lenses, by J N H Brunt and F H Read, J.Phys.E (Sci.Instrum.) 8, 1015-20 (1975).

12. The optimization of electrostatic energy selection systems for low energy electrons, by F H Read, J Comer, R E Imhof, J N H Brunt and E Harting, J.Electron.Spect. 4, 293-312 (1974).

11. Theoretical limitations of electron beams of rectangular cross section, F H Read, J.Phys.D (Appl.Phys.) 7, 1604-11 (1974).

10. Electrostatic cylinder lenses III: Three element asymmetric voltage lenses, by A Adams and F H Read, J.Phys.E (Sci.Instrum.) 5, 156-60 (1972).

9. Electrostatic cylinder lenses II: Three element einzel lenses, by A Adams and F H Read, J.Phys.E (Sci.Instrum.) 5, 150-5 (1972).

8. Electrostatic cylinder lenses I: Two element lenses, by F H Read, A Adams and J R Soto-Montiel, J.Phys.E (Sci.Instrum.) 4, 625-32 (1971).

7. "Zero gap" electrostatic aperture lenses, by F H Read, J.Phys.E (Sci.Instrum.) 4, 562-6 (1971).

6. A collocation method for solving Laplace's equation, by F H Read, J.Computational Physics 6, 527-32 (1970).

5. Asymmetric electrostatic lenses of three apertures, by F H Read, J.Phys.E (Sci.Instrum.) 3, 127-131 (1970).

4. Calculated properties of electrostatic einzel lenses of three apertures, by F H Read, J.Phys.E (Sci.Instrum.) 2, 679-84 (1969).

3. Accurate calculations of double-aperture electrostatic immersion lenses, by F H Read, J.Phys.E (Sci.Instrum.) 2, 165-9 (1969).

2. A three-aperture electron optical lens for producing an image of variable energy but fixed positions, by R E Imhof and F H Read, J.Phys.E (Sci.Instrum.) 1, 859-60 (1968).

1. Electron optical systems with fixed image positions for beams of variable energy, by J D Cross, F H Read and E A Riddle, J.Sci.Inst. 44, 993-6 (1967).

Some comments on the above papers:

No. 1 represents the invention of the electron optical 'zoom lens'.

No. 8 is the first use of the BEM in electron optics.

No. 19 has been cited well over 500 times.

No. 42 is the invention of a deflector system that has unsurpassed aberrations.

No. 51 is the invention of a powerful new energy analyzer.

No. 68 shows the considerable gains to be made in optimising the shapes of lens electrodes.

Abstracts of some of the more recent publications from the Manchester group, using the CPO programs, in reverse time order:

68. Optimization of the shapes of electrodes of electrostatic lenses, by F H Read, Microscopy and Microanalysis 21 Suppl S4, 276-279 (2015)

Following the success achieved by Cubric et al in considerably decreasing the aberrations of electrostatic energy analysers by using novel electrode configurations, we explore here the benefits of using novel electrode shapes in electrostatic lenses. The study is facilitated by the ability of the CPO programs to define curved shapes by user-supplied equations. Two representative types of lenses are considered and significant improvements are obtained in their spherical aberrations.

67. Achieving the highest accuracy with the BEM, by F H Read, Microscopy and Microanalysis 21 Suppl S4, 182-187 (2015).

The high accuracy that can be achieved by the Boundary Element Method when it is used to solve the Laplace and Poisson equations for electrostatic systems is discussed. Applications to charged particle optics are described, with the emphasis on the commercial CPO programs[1]. The BEM is a charge-based method and so is ideally suitable for systems that include space-charge and/or cathodes. It can deal easily with electrodes of very different sizes. These and other properties of the BEM are illustrated by a range of benchmark tests. A recently added option that allows users to easily define electrode shapes by user-supplied equations is described. The use of this option to optimize the shapes of the electrodes of electrostatic lenses is illustrated.

66. The CPO programs and the BEM for charged particle optics, by F. H. Read and N. J. Bowring, Nucl. Instr. Meth. A645, 273-277 (2011).

The Boundary Element Method for solving the Laplace and Poisson equations will be outlined, with the emphasis on 3D systems and the commercial CPO programs. Some applications to charged particle optics will be described. Since the BEM is a charge-based method it is ideally suited for systems that include space-charge and/or cathodes. Several ‘benchmark tests’ will be presented, in which systems that have known analytic solutions are used to test the accuracy of the results of simulations

63. Computer simulations of hexapole aberration correctors, by L. A. Baranova, F. H. Read and D. Cubric, Physics Procedia 1, 185-191 (2008).

The use of hexapole systems to correct the spherical aberration of the objective lenses of low-voltage scanning electron microscopes has been investigated. These systems are simpler than the more conventional quadrupole-octupole correctors, are easier to tune and are less sensitive to mechanical and electrical imperfections. We have considered two designs of telescopic corrector having the lens arrangements RHRHR and HRRH, where R and H represent round lenses and hexapole components respectively. Both designs give a significant correction of the objective lens spherical aberration but do not correct chromatic aberrations. The second design possesses some important advantages over the first: it is mechanically and electrically simpler and the tuning procedure is simpler. In the present investigation we have found the further advantages that the hexapole voltages are smaller for the second design, the aberration correction is better and the corrector is less sensitive to mechanical defects. On the other hand the chromatic aberration is larger for the second design.

62. Possibilities for grapheme for field emission: modelling studies using the BEM, by S. Watcharotone, R. S. Ruoff and F. H. Read, Physics Procedia 1, 71-75 (2008).

The Boundary Element Method has been used to model the field enhancement factors of free-standing sub-nanometre graphite sheets, which are thought to be suitable for use as field emission sources. The variation of the enhancement factor over the surfaces of the edges and corners of the sheets of rectangular shape has been explored. The dependence of the enhancement factor on the thickness, height and width of the sheets has been found and the results have been parameterized where possible by simple empirical functions.

61. A passive electrostatic recycling spectrometer of desk-top size for charged particles of low kinetic energy, by D R Tessier, Y Niu, D P Secombe, T J Reddish, A J Alderman, B G Birdsey, F H Read and P Hammond, Phys Rev Lett 99, 253201 (2007).

A new system for achieving passive electrostatic storage of monochromatic low energy (~5 to 50 eV) charged particles in a desktop sized apparatus has been constructed

60. Simulation of Thermionic Cathodes, by F. H. Read and N. J.Bowring, Nucl. Instrum. Meth. A531, 407-415 (2004).

A technique is described of simulating thermionic cathodes in the Boundary Element Method by replacing the space⌀charges in the cathode region by a set of thin sheets of charge. These sheets are subdivided into segments in the same way that the cathode itself is subdivided. This technique has been applied to cathodes that have zero and non⌀zero temperature T. It is shown that for T > 0 the potential and position of the virtual cathode is well reproduced. Planar and non⌀planar cathodes are considered as well as unsaturated cathodes.

59. Field enhancement factors of one-dimensional and two-dimensional arrays of nanotubes, by F H Read and N J Bowring, Microelectronic Engineering 73-74, 679-685 (2004).

The field enhancement factors of flat arrays of randomly⌀spaced, aligned, closed-end nanotubes have been determined by computational modeling. Arrays that contain a large number of nanotubes have been considered as well as isolated clusters that contain a limited number of nanotubes. The standard deviation of the enhancement factors in large arrays has been found to be approximately proportional to the mean enhancement factor but not to be strongly correlated with the radius, length or spacing of the nanotubes. A simple procedure is given for estimating the density of high⌀emitting nanotubes, that is, ‘hot⌀spots’. For isolated clusters the dependence of the average enhancement factor on the number of nanotubes in the cluster has been investigated.

58. The contributions of stochastic coulomb interactions and collective space-charge field aberrations to spatial spreading in charged particle projection systems, by F H Read and N J Bowring, Microelectronic Engineering 73-74, 97-105 (2004).

A new computational technique based on the ‘nearest⌀neighbor’ method has been used to study the effects of stochastic electron⌀electron coulomb interactions on the blurring of the focus spots in a lithographic electron projection system. It has been found that the collective (that is, global) space⌀charge introduces two other distinct forms of spatial spreading: these are collective space⌀charge field aberrations and pattern⌀dependent aberrations. We have been able to separately simulate the first two of these three forms of blurring and to study them in isolation from lens aberrations. It has been found that the blurring is dominated by stochastic coulomb interactions when the beam pencil angle is small but conversely is dominated by collective space⌀charge field aberrations when the pencil angle is large. The blurring due to pattern⌀dependent aberrations has been found to be relatively less important. Results are presented for a range of currents and pencil angles for a representative projection system.

57. Capacitances and singularities of the unit triangle, square, tetrahedron and cube, by F. H. Read, COMPEL 23, 572-578 (2004).

The boundary element method has been used to obtain the electrical capacitances and singularity exponents of the unit triangle, square, tetrode and cube.

# 56. The Parallel Cylindrical Mirror Analyzer: Axis-to-Axis configuration, by F H Read, D Cubric, S Kumashiro and A Walker, Nucl. Instrum. Meth. A519, 338-344 (2004).

The operation of the parallel cylindrical mirror analyzer (PCMA) in the axis-to-axis configuration is described. A wide range of energies can be covered in the parallel acquisition mode. A second⌀order focusing mode also exists for which a region of limited energy range can be viewed with higher energy resolution. The PCMA can easily be switched between the parallel acquisition and second⌀order modes. The acceptance full width in the transverse direction can be as large as 90. The effects of the meshes at the entrance and exit regions are considered. The PCMA is compared with the hyperbolic field analyzer (HFA).

# 55. Field enhancement factors of arrays of carbon nanotubes, by F H. Read and N J.Bowring, Nucl. Instrum. Meth. A519, 305-314 (2004).

The field enhancement factors of flat arrays of aligned, closed-end nanotubes have been determined by accurate computational modelling. Square and random arrays have been considered. The dependence of the enhancement factor on the radius, length and density of the nanotubes has been found for square arrays and the results have been parametrized by a simple empirical function. The density fluctuations of random arrays have been simulated to determine the distribution of enhancement factors. A simple procedure is given for estimating the number of ‘high⌀emitting’ nanotubes that have enhancement factors much higher than the mean value for the array.

# 54. Monte-Carlo Calculation Of Boersch Energy Spreading, by F.H. Read and N.J.Bowring, Nucl. Instrum. Meth. A519, 196-204 (2004).

The effects of electron-electron coulomb interactions have been simulated by a general computational technique that can be applied to almost any system, independently of the shape of the beam or the regimes that might be present, provided that the ‘closest⌀encounter’ approximation is valid for the system. The technique has been applied to the ‘benchmark test’ of the energy spreading in a converging round beam. The results are compared with previous analytical results.

# 53. Computational simulation of an electrostatic aberration corrector for a low-voltage scanning electron microscope, by L.A.Baranova, F.H.Read and D Cubric, Nucl. Instrum. Meth. A519, 42-48 (2004).

Two aspects of the design of electrostatic aberration correctors for low voltage scanning electron microscopes are considered. The first is that of optimizing the geometry and scale size so that the fields at the surfaces of the electrodes do not exceed the breakdown value. The second aspect is that of providing an accurate computational simulation of the paraxial fields of the lens system.

52. Accurate Monte-Carlo calculation of Boersch energy and angle spreading, by F.H. Read and N.J.Bowring, Rev. Sci. Instrum. 74 2280-2287 (2003).

The effects of stochastic electron-electron interactions have been studied by a computational technique that attempts to avoid all systematic errors, leaving only the random errors that are inherent in a Monte-Carlo calculation. The technique has been applied to the energy spreading in a converging round beam. The results are compared with previous analytical results.

The effects of stochastic electron-electron interactions have been studied by a computational technique that attempts to avoid all systematic errors, leaving only the random errors that are inherent in a Monte-Carlo calculation. The technique has been applied to the energy spreading in a converging round beam. The results are compared with previous analytical results.

51. The parallel cylindrical mirror electron energy analyzer, by F H Read, Rev. Sci. Instrum. 73 1129-1139 (2002).

50. Aberrations caused by mechanical misalignments in electrostatic quadrupole lens systems, by L A Baranova and F H Read, Optik 112, 1331-138 (2001).

49. An iron-cored coil system for the measurement of angular distributions of charged particles, by D Cubric, R Ward, G C King and F H Read, Rev. Sci. Instrum. 71 3323-3325 (2000).

48. Extrapolating the number of segments to infinity in the Boundary Element Method, by F H Read, International Series on Advances in Boundary Elements, vol 8 (Boundary Elements XXII, Eds. C A Brebbia and H Power, WIT Press, Southampton, UK), pp 139-144 (2000).

47. A fast parallel acquisition electron energy analyzer, by C G H Walker, A Walker, R Badheka, S Kumashiro, M Jacka, M El Gomati, M Prutton and F H Read, SPIE Vol 3777, 252-257 (1999).

A new type of electrostatic electron energy analyzer is described that can acquire an electron energy spectrum in ‘one shot’. It uses a hyperbolic field to focus electrons emitted from a solid in the energy range 50 eV to 2500 eV into a dispersive plane of about 50 mm length. An expression for the energy resolution is given and the effect of side and base plates on the behaviour of the device is discussed. The main intended area of application for this type of analyzer is parallel data acquisition in Auger electron spectroscopy (AES) and X-ray photoelectron spectroscopy (XPS). The potential to acquire a spectrum in just a few seconds is possible with this device.

46. The charge-tube method for space-charge in beams, by F H Read, A Chalupka and N J Bowring, SPIE Vol 3777, 184-191 (1999).

The charge-tube method is an accurate and efficient way of assigning the space-charge of a beam in computational simulations of charged particle systems. The method makes use of the trajectory steps that result from the process of trajectory integration. The space-charge associated with each step of each trajectory is assigned to a narrow cylindrical tube that surrounds the step. The total space-charge of a beam is then the sum of the charges in all the resulting the tubes. In systems of 2-dimensional axial symmetry the charge tubes become conical sheets of charge, and for some purposes these need to be given a finite thickness. The charge-tube method is particularly useful for simulating the space-charge of beams that are very narrow compared with their length. The implementation of the method is described and results obtained with it are compared with those obtained by the traditional charge-cell method.

45. The charge-tube method for space-charge simulations, by F H Read, A Chalupka and N J Bowring, COMPEL (Int. J. for Computation and Mathematics in Electrical and Electronic Engineering), 18, 548-555 (1999).

The charge-tube method is an accurate way of assigning the space-charge of a beam in computational simulations of charged particle systems. The method is described and is compared with the traditional charge-cell method.

44. Short and long range penetration of fields and potentials through meshes, grids or gauzes, by F H Read, N J Bowring, P D Bullivant and R R A Ward Nucl. Instr. Meth. A427, 363-367 (1999).

When a conducting partially⌀transparent mesh is used to separate two regions of different electrostatic field strength there are short range changes to the field and potential distributions in the vicinity of the mesh and also long range changes far from the mesh. The forms and magnitudes of these changes are investigated computationally for meshes that consist of parallel or crossed round wires or crossed flat strips.

43. Minimisation of the aberrations of electrostatic lens systems composed of quadrupole and octopole lenses, by L A Baranova and F H Read, Int. J. Mass Spect. 189, 19-26 (1999).

Aberrations are investigated and compared for two types of multiplets based on electrostatic quadrupole and octupole lenses: ‘mid-acceleration’ systems in which an accelerating potential is applied to the middle lenses of a set of quadrupole lenses and systems in which some of the quadrupole lenses are replaced by combined quadrupole-octupole lenses. It is shown that for systems consisting of three lenses the mid-acceleration type has the smaller aberrations. For systems consisting of four or five lenses the third order aperture aberration can be eliminated in the quadrupole-octupole type, while the mid-acceleration type has the advantages of lower levels of chromatic and fifth order aperture aberrations and also relative simplicity of construction and voltage adjustment.

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

Electrostatic deflection systems in which the deflector plates are edgeways to the beam -that is, the plates are flat sheets that lie in a plane perpendicular to the beam- are investigated. A deflection system that can deflect in both transverse directions is considered and the geometry is optimised to minimize the aberrations, which are found to be from 4 to 30 times smaller than the aberrations of conventional deflection systems.

41. Comparison of FDM, FEM and BEM for electrostatic charged particle optics, by D Cubric, B Lencova, F H Read and J Zlamal, Nucl. Instr. Meth. A427, 357-362 (1999).

The accuracy and speed of three programs based on different methods for solving problems in electrostatic charged particle optics are compared, using a set of benchmark tests. The methods are the Finite Difference, Finite Element and Boundary Element Methods (FDM, FEM and BEM respectively).

40. Reduction of the chromatic and aperture aberrations of the stigmatic quadrupole lens triplet, by L A Baranova and F H Read, Optik 109, 15-21 (1998).

39. Penetration of electrostatic fields and potentials through meshes, grids or gauzes, by F H Read, N J Bowring, P D Bullivant and R R A Ward, Rev. Sci. Instrum. 69, 2000-2006 (1998).

A theoretical, computational and experimental study has been carried out of the penetration of electrostatic fields and potentials through meshes. For a mesh that is used to shield an inner region from an external field it is found that there is a finite change in the potential throughout the internal region. Similarly it is found that for a flat mesh used to shield the region on one side of a mesh from a field on the other side, a finite change in potential exists in the field-free region. Meshes consisting of parallel wires and of crossed wires that form square holes are considered. Excellent agreement is obtained between the theoretical and computational results, enabling the theoretical formulae to be used to calculate the potential penetration for meshes of any transparency. It is found that for the calculation of electrostatic fields or potentials the mesh can be replaced by a coincident surface which has an 'equivalent potential' that depends on the field difference at the mesh.

38. A study of photoelectron angular distributions in xenon using a new magnetic angle changing technique, by D Cubric, D B Thompson, D R Cooper, G C King and F H Read, J Phys B 30, L857-864 (1997).

37. Aberrations due to localized potential defects on apertures, by F H Read, L A Baranova, N J Bowring, J Lambourne and T C Ward, Electron Microscopy and Analysis 1997, Institute of Physics Conference Series 153, 101-104 (1997)

36. Comparison of Finite Difference, Finite Element and Boundary Element Methods for electrostatic charges particle optics, by D Cubric, B Lencova and F H Read, Electron Microscopy and Analysis 1997, Institute of Physics Conference Series 153, 91-94 (1997)

35. Aberrations due to localized potential defects on apertures, by F H Read, L A Baranova, N J Bowring, J Lambourne and T C Ward, Rev. Sci. Instr. 69, 84-90 (1998).

The aberrations caused by localised potential defects near the edges of apertures that are used to define charged particle beams are investigated. Such defects arise in practice from the charging-up of insulating layers deposited by the beam. In the weak-field limit of small aberrations it is established that the change in direction of a ray passing through an aperture depends on the position of the ray at the plane of the aperture but not on the slope of the ray. It is found that the resulting changes to the spot size of a converging beam cannot be characterised in terms of aberrations coefficients if the beam fills the aperture. A new characterisation of the aberrations is therefore defined, and a numerical evaluations are carried out for a representative types of potential defect. Examples are given of the increases in spot size caused by such defects.

34. Improved Extrapolation Technique in the Boundary Element Method to find the Capacitances of the Unit Square and Cube, by F H Read, J. Computational Physics, 133, 1-5 (1997).

Extrapolation of the number N of subdivisions to infinity in the Boundary Element Method involves fitting computed results to a power series in 1/N. A technique is described of choosing the sizes of the subdivisions in such a way that the terms of lowest order in 1/N are eliminated, giving a more accurate extrapolation. The technique is used to establish the capacitances of the unit square and cube with relative errors of 3.10-7 and 10-6 respectively.

33. The production and optical properties of an unscreened but localised magnetic field, by F H Read and J M Channing, Rev. Sci. Instrum. 67, 2372-2377 (1996).

A technique is described of using current carrying coils to produce a magnetic field that is well localised, falling off quickly with distance. The basis of the technique is that the first few magnetic multipole moments of the system are arranged to be zero. The electron optical properties of this type of field are then investigated.

32. Ultimate numerical accuracy of the Surface Charge Method for electrostatics, by F H Read and N J Bowring, Computation in Electromagnetics (Institution of Electrical Engineers, Conference Publication 420, 1996), p57-61.

The highest accuracy that can be obtained in practice with the Surface Charge Method is considered for various types of problem, including (1) capacitance calculations, (2) the calculation of potentials and fields, (3) trajectory integrations, and (4) cathode and space-charge problems.

31. Crossed aperture lenses for the correction of chromatic and aperture aberrations, by L A Baranova, S Ya Yavor and F H Read, Rev. Sci. Instrum. 67, 756-760 (1996).

The chromatic and aperture aberrations of crossed five-aperture lenses are analysed by direct ray tracing. The apertures are rectangular and the voltages are applied in such a way that the first-order properties of the crossed lens are similar to those of a quadrupole doublet. It is shown that in astigmatic modes the chromatic and aperture aberrations of one of the linear images can be simultaneously eliminated or made negative. It is also shown that stigmatic modes exist in which the magnification is different in two perpendicular planes and in which the image blurring caused by the chromatic and aperture aberrations in the direction of smaller magnification is ten times smaller than that given by a round lens of the same focal length and the blurring in the other direction is at least two times smaller. The stigmatic crossed lens also gives a larger working distance than the equivalent round lens. The crossed lens will therefore be preferable for many probe forming systems.

30. Reduction of energy non-linearity of hemispherical deflection analyzers when used with multidetectors, by S C Page and F H Read, Nucl. Instrum. Methods A363, 249-253 (1995).

A '3-dimensional' computational study has been carried out on the energy non-linearity of a hemispherical deflection analyzer (HDA) used in conjunction with a multidetector. It is found that the energy non-linearity can be minimised by keeping the detector and its mounting at a single potential and not attempting to correct the fringing field to reproduce the field for the 'perfect' HDA. The values of the energy aberrations and the position of the focal plane are computed for a range of values of the ratio of the radii of the two hemispheres.

29. Defocusing of charged particle beams transmitted through meshes, by D L Williams, F H Read and N J Bowring, Nucl. Instrum. Methods A363, 120-123 (1995).

A mesh that separates two regions of different electrostatic field strength exerts a 'micro-lensing' effect on charged particles that are transmitted through the mesh, causing the directions of the particles to change. A computational study has been carried out to establish the magnitudes of the directional changes for four types of mesh that are commonly used, square holes in thin and thick plates, welded and woven.

28. Aberrations of an electrostatic three-cylinder system used to simultaneously focus and deflect charged particles, by I C Dowker, F H Read, N J Bowring and P Hammond, Nucl. Instrum. Methods A363, 54-58 (1995).

The properties have been studied of an electrostatic three-cylinder lens-deflector in which the middle cylinder is split longitudinally into four parts, allowing the system to be used to simultaneously focus and deflect a beam of charged particles. The aberrations are found to be of the first order in the deflection.

27. Electrostatic electron-optical crossed lens with controlled astigmatism, by L A Baranova and F H Read, Rev. Sci. Instrum. 65, 1993-1997 (1994).

A crossed lens consisting of square and rectangular apertures in four equally spaced electrodes has been studied. The two inner apertures are rectangular with their longer directions mutually at right angles and the two outer apertures are square.. The strength and astigmatism of the lens can be separately controlled through the voltages applied to the rectangular apertures, enabling line images of variable position and length to be produced from point objects.

An associated note is authors of the CPO programs.

See also textbooks on electron optics.

Student projects

The CPO2D and CPO3D programs, and their forerunner the MAN-2D program, were used for project work in the Physics Department at the University of Manchester in the period 1970-2002. Many publications have resulted (see above). This project work was very much enjoyed by the students (and the supervisors!), and it occasionally lead to published papers.

Projects that last three half-days:

The demo and evaluation versions of CPO2D and CPO3D were used by about 24 students each year, for project work that forms part of a lecture course on 'Charged Particle Dynamics'. Most of these students were in the final-year of a four-year undergraduate degree course, while a few of them were first-year masters students or doctoral students. The choice of topics included:

Behaviour of charged particles in crossed electric and magnetic fields.

Confinement of electrons in a magnetic bottle.

Relativistic motion in a uniform electric or magnetic field.

Investigation of the focussing properties of a two-cylinder electrostatic lens.

Investigation of the energy resolution of a hemispherical deflection analyzer.

Projects that last 20 days:

The full editions of CPO2D and CPO3D were used by 8 final-year undergraduate students each year, for extended project work. The topics that have been studied in the past include:

Penetration of electrostatic fields through wire meshes.

Effects of parasitic 'patch fields'.

Changes to the properties of the cylindrical mirror analyzer due to the apertures in the inner cylinder.

Optimisation of the geometry of simple plate deflectors.

Effect of stray magnetic fields on the performance of energy analyzers.

Effects of mechanical misalignment of a three-cylinder lens.

Effects of mechanical misalignment of a hemispherical deflection analyzer.

Space-charge effects in a field emission source.

Why are the space-charge fields radial for converging beams of finite length?

Accurate evaluation of capacitance of the tetrahedron and other solids of regular shapes.

Elliptical lenses.

Trapping of electrons.

Projects that last 6 months:

The full editions were also used by a small number of students for research projects that formed part of the masters or doctoral courses. Some of the resulting publications are listed below. The topics included:

The astigmatism of hair-pin cathodes.

The effect of thermal velocity spread on the properties of the Pierce gun.

The 'micro-lensing' effects of wire meshes.

Aberrations of split-lens deflectors.

Charge neutralisation of conducting surfaces in the presence of magnetic fields.

Aberrations and optimisation of electrostatic deflectors.

Restoration of second order focussing of the cylindrical mirror analyzer with apertures in the inner cylinder.

Optimisation of space-charge for a system of electron gun and high resolution energy selector.

Use of a localised magnetic field for initial energy selection of an electron gun.

Effect of space charge on the energy resolution of the hemispherical deflection analyser.