CPO -- Advanced electrostatics for space-charge, cathodes, and high accuracy
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CPO Examples and Benchmark Tests

CPO includes a large number of examples and tests to verify the accuracy and to provide a starting point in your own experiments. These examples are listed below.

The 'benchmark test' files.

The 'benchmark test' files deal with simulations that have known analytical solutions, to demonstrate the speed, accuracy and capabilities of CPO-2D and CPO-3D.

CPO-2D:

test2d01 Idealised hemispherical deflection analyzer (HDA)
test2d02 Idealised cylindrical deflection analyzer
test2d03 Parabolic motion in uniform field (cylindrical symmetry)
test2d04 Parabolic motion in uniform field (planar symmetry)
test2d05 Relativistic motion in a uniform electric field
test2d06 Capacitance of a sphere
test2d07 Capacitance of coaxial cylinders
test2d08 Time-dependent potentials
test2d09 Coefficients of hemispherical deflection analyser (HDA)
test2d10 Space-charge limited current of a spherical diode (concave cathode)
test2d11 Space-charge limited current of a spherical diode (small convex cathode)
test2d12 Planar Pierce gun
test2d13 Spherical cold field emission diode
test2d14 Cylindrical diode, small inner cathode
test2d15 Field at a circular hole in an infinite sheet
test2d16 Ideal cylindrical mirror analyzer (CMA)
test2d17 Penetration of field and potential through a cylindrical mesh
test2d18 Field penetration through a flat mesh of flat strips
test2d19 Field at the tip of a cone
test2d20 Cylindrical Pierce gun
test2d21 Field at centre of a double cylinder lens
test2d22 Non-meridional rays, cylindrical symmetry
test2d23 Non-xz-plane rays, planar symmetry
test2d24 Motion in a User-supplied oscillating electric field.
test2d25 The 743 test.

CPO-3D:

test3d01 Idealised hemispherical deflection analyzer (HDA)
test3d02 Idealised cylindrical deflection analyzer
test3d03 Parabolic motion in uniform field
test3d04 Relativistic cyclotron motion
test3d05 Relativistic motion in a uniform electric field
test3d06 Capacitance of a cube
test3d07 Capacitance of a sphere
test3d08 Time-dependent oscillating potentials
test3d09 Coefficients of hemispherical deflection analyser (HDA)
test3d10 Space-charge limited current of a spherical diode (concave cathode)
test3d11 Space-charge limited current of a spherical diode (convex cathode)
test3d12 Spherical cold field emission diode
test3d13 Field at a circular hole in an infinite sheet
test3d14 Ideal cylindrical mirror analyzer (CMA)
test3d15 Capacitance of circular disc
test3d16 Motion in a User-supplied oscillating electric field.
test3d17 Capacitance and singularities of a tetrahedron.
test3d18 Capacitance of a unit square.
test3d19 Capacitance of a unit triangle, and summary of capacitance tests.
test3d20 Ideal quadrupole ion trap.

The 'example' data files.

The 'example' data files represent simulations that are of general
interest but that do not have known analytical solutions.

CPO-2D:

xmpl2d01 A double cylinder lens
xmpl2d02 A double aperture lens
xmpl2d03 A double rectangular tube lens
xmpl2d04 A double rectangular tube lens
xmpl2d05 A 'beam' of rays focussed by a double-cylinder lens.
xmpl2d06 An example of automatic subdivision, for a double-cylinder lens.
xmpl2d07 Automatic iteration to focus a beam by a three-cylinder lens.
xmpl2d08 Lens coefficients of double-cylinder lens.
xmpl2d09 Space-charge limited planar diode, cylindrical symmetry.
xmpl2d10 Space-charge limited diode in planar symmetry (ie flat, parallel cathode and anode, infinite in one direction).
xmpl2d11 Simulation of the space-charge repulsion of an isolated beam that initially converges to a point, using the 'ray space-charge tube' method.
xmpl2d12 Simulation of the space-charge repulsion of a mixed beam of electrons and carbon ions.
xmpl2d13 A relativistic double-cylinder lens.
xmpl2d14 A double-cylinder lens with a linear voltage bridge across the gap.
xmpl2d15 Automatic iterative variation of the grid voltage of a simple thermionic electron gun.
xmpl2d16 Multiple focussing of a Hemispherical Deflection Analyzer.
xmpl2d17 A mirror that has negative spherical and chromatic aberrations.
xmpl2d18 Practical cylindrical mirror analyzer (CMA).
xmpl2d19 Field penetration through a cylindrical mesh of round wires.
xmpl2d20 Field penetration through a flat mesh of round wires.
xmpl2d21 Parallel wire deflector, planar symmetry.
xmpl2d22 Parallel edge deflector, planar symmetry.
xmpl2d23 Conventional plate deflector, planar symmetry.
xmpl2d24 Conventional flared plate deflector, planar symmetry.
xmpl2d25 Creation of secondary rays, Maxwell and Ura energy distributions.
xmpl2d26 Creation of secondary rays, specular reflection.
xmpl2d27 Field emission electron gun.
xmpl2d28 Carbon nano-tube, for field emission source.
xmpl2d29 Enhancement factor for a cone.
xmpl2d30 Enhancement factor for a hemisphere on post.
xmpl2d31 Conical lens with apertures transverse to axis of lens.
xmpl2d32 Conical lens with apertures transverse to axis of cones.
xmpl2d33 PCMA (Parallel CMA) analyzer, axis-to-cylinder mode.
xmpl2d34 PCMA (Parallel CMA) analyzer, axis-to-axis mode.
xmpl2d35 PCMA (Parallel CMA) analyzer, axis-to-disc mode.
xmpl2d36 Triple cylinder einzel lens.
xmpl2d37 Scattering option, production of secondary electrons.
xmpl2d38 Scattering option, absorption and scattering by background gas.
xmpl2d39 Scattering option, scattering at a grid.
xmpl2d40 Scattering option, simulation of a thin lens.
xmpl2d41 Photocathode.
xmpl2d42 Defining relationships between voltages.
xmpl2d43 X-ray tube with thermal energies.
xmpl2d44 Converting an electric field to a magnetic field.
xmpl2d45 Rectangular waveform for oscillating voltages.
xmpl2d46 Space-charge expansion of an electron beam.

CPO-3D:

xmpl3d01 A practical hemispherical deflection analyzer.
xmpl3d02 A practical cylindrical deflection analyzer, 127 degrees.
xmpl3d03 Orbit of a proton outside a charged sphere.
xmpl3d04 A demonstration of automatic subdivision.
xmpl3d05 Quadrupole filter with oscillating field.
xmpl3d06 Automatic iteration to optimise the focus of a 4-cylinder lens.
xmpl3d07 Space-charge repulsion of an isolated beam that initially converges to a point.
xmpl3d08 Space-charge repulsion in a mixed beam of electrons and positively charged carbon ions.
xmpl3d09 Space-charge limitation of current in a strong magnetic field.
xmpl3d10 Space-charge limited planar diode.
xmpl3d11 Space-charge limited planar diode, with thermal energies.
xmpl3d12 Automatic optimisation of an electron gun with a hairpin cathode.
xmpl3d13 Cathode ray tube.
xmpl3d14 Miniature lens for microelectronic switching.
xmpl3d15 Hairpin cathode with potential drop and current.
xmpl3d16 Extended Schottky emission, spherical cathode.
xmpl3d17 Magnetic angle changing technique
xmpl3d18 Multiple focussing of hemispherical deflection analyzer.
xmpl3d19 Split-lens deflector.
xmpl3d20 Magnetic bottle.
xmpl3d21 Space-charged limited cylindrical diode with thermal energies.
xmpl3d22 Practical cylindrical mirror analyzer (CMA).
xmpl3d23 Penetration of field and potential through a mesh.
xmpl3d24 CRT electron gun, cylindrical symmetry.
xmpl3d25 CRT electron gun, rectangular grid.
xmpl3d26 Aberrations due to a localised potential defect on an aperture.
xmpl3d27 Simplest unbalanced deflector.
xmpl3d28 Pierce gun, potassium 39 ions, with thermal energies.
xmpl3d29 Penetration of field and potential through a mesh of flat strips.
xmpl3d30 Magnetic deflector.
xmpl3d31 Penetration of potential through a circular hole in a flat sheet.
xmpl3d32 Double-cylinder lens, parameters and coefficients.
xmpl3d33 2-fold deflector, flared plates.
xmpl3d34 2-fold deflector, split-cylinder plates.
xmpl3d35 2-fold deflector, curved edge-on plates.
xmpl3d36 4-fold deflector, flat plates.
xmpl3d37 4-fold deflector, flared plates.
xmpl3d38 4-fold deflector, angled plates.
xmpl3d39 4-fold deflector, split-cylinder plates.
xmpl3d40 4-fold deflector, staggered split-cylinder plates.
xmpl3d41 4-fold deflector, split-disc edge-on plates.
xmpl3d42 4-fold deflector, staggered curved edge-on plates.
xmpl3d43 8-fold deflector, split-cylinder plates.
xmpl3d44 8-fold deflector, split-disc plates.
xmpl3d45 Photocathode, with photoelectrons of fixed energy and lambertian distribution of directions.
xmpl3d46 Creation of secondary rays, Maxwell and Ura energy distributions.
xmpl3d47 Simple magnetic lens.
xmpl3d48 Photomultiplier.
xmpl3d48 Photomultiplier.
xmpl3d49 Reflected secondaries.
xmpl3d50 Illustration of the scattering option, scattering at a grid.
xmpl3d51 Illustration of the scattering option, simulation of a thin lens.
xmpl3d52 Enhancement factor for a nano-cone.
xmpl3d53 Enhancement factor for a cone in an array of nano-cones.
xmpl3d54 An example of a field emission flat screen display system.
xmpl3d55 Use of a rectangular beam, for space-charge spreading.
xmpl3d56 Defining relationships between voltages.
xmpl3d57 Archards method of correcting chromatic aberration.
xmpl3d58 Scattering option, production of secondary electrons.
xmpl3d59 Scattering option, absorption and scattering by background gas.
xmpl3d60 Stochastic scattering option, Boersch energy spreading.
xmpl3d61 Option for User-supplied near-axis electric field.
xmpl3d62 Enhancement factor for a nanotube, 'hemisphere on post'.
xmpl3d63 Enhancement factor for 2 nearby nanotubes.
xmpl3d64 Enhancement factor for a square array of nanotubes.
xmpl3d65 Enhancement factor for a 'spoilt' array of nanotubes.
xmpl3d66 Enhancement factor for a random array of nanotubes.
xmpl3d67 Enhancement factor for a linear array of nanotubes.
xmpl3d68 Spatial stochastic scattering.
xmpl3d69 Rectangular waveform for oscillating voltages.
xmpl3d70 Stark barrel.
xmpl3d71 Ion trap.
xmpl3d72 Liquid metal ion source.
xmpl3d73 Electron impact ion source.
xmpl3d74 Space-charge spreading in an electron beam.
xmpl3d75 Using CPO to solve for a magnetic field.
xmpl3d76 Simple achromatic quadrupole lens.

The 'shape' data files.

The 'shape' files give examples of the shapes that are possible with CPO-3D.

CPO-2D:

shap2d01 A sphere stretched to make an ellipsoid, using stretching option.
shap2d02 A toroidal energy analyzer.
shap2d03 A hyperbolic surface.

CPO-3D:

shap3d01 An ellipsoid created by stretching a sphere.
shap3d02 A cylinder of elliptical cross section, created by stretching transversely.
shap3d03 An elliptical hole in an elliptical disc.
shap3d04 A cylinder of elliptical cross section, created by segments of elliptical cross section.
shap3d05 A cone.
shap3d06 An 'evenly divided' disc.
shap3d07 A split disc.
shap3d08 A clipped (truncated) hemispherical deflection analyzer.
shap3d09 A split cylinder deflector.
shap3d10 A thick flat plate with a rectangular hole in it.
shap3d11 A cylinder truncated at an angle of 45 degrees to its axis, by using the 'clipping' option.
shap3d12 A cylinder truncated at an angle of 45 degrees to its axis, by using 'cylindrical triangular' segments.
shap3d13 3 circular holes symmetrically positioned in a disc.
shap3d14 A circular hole at the centre of a disc, surrounded by 6 others.
shap3d15 A cylindrical deflection analyzer, using 'cre'.
shap3d16 A toroidal surface.
shap3d17 Program used when final electron energies are much higher than initial energies.
shap3d18 A torus, and the program for generating it.
shap3d19 A grid of 289 holes.
shap3d20 A grid of 9 holes.
shap3d21 A rectangular plate with a rectangular slot.
shap3d22 A rectangular plate with a circular hole, 1st method.
shap3d23 A rectangular plate with a circular hole, 2nd method.
shap3d24 A rectangular slot in a spherical cap.
shap3d25 A cylinder with an end cut at an angle to the axis.

xml3d48 - Photomultiplier. Produced from the 48th 3D example file. A series of rays start from a line on the photocathode. When a ray hits a dynode its energy is reduced to that of a secondary electron and its current is multiplied by a factor of 3 (as chosen by the User). The initial energies and directions of the secondaries are also chosen by the User and can be randomised.

xmpl3d05 - Quadrupole mass filter. From the 5th 3D example file. Perspective view. The hyberbolic electrodes are generated by a subsidiary program that is supplied with the CPO package. Several other subsidiary programs are also included (eg to generate a toroidal surface or a torus). Note that in the Boundary Element Method it is not necessary to enclose the system.

xmpl3d27 - Simple deflector system. From the 27th 3D example file.. Here the x and y deflector plates are flat rectangles. Note that the density of segments is highest at the edges, where the charge density is highest. 12 other types of more sophisticated deflector systems are included as examples in the CPO package.

test2d12 - Pierce Gun. From the 12th 2D benchmark test file. The ray tracing is automatically iterated several times until the results converge. A damping factor is provided which is controlled by the User. Some potential contours are also shown. Note that the combined effects of the surface charges on the electrodes and the space charges in the beam give contours that are perpendicular to the beam, as required for the Pierce gun. The test and example files deal with several other types of cathode systems, including thermionic, Schottky and field emission cathodes.

test2d16 - Ideal CMA (cylindrical mirror analyzer). From the 16th 2D benchmark test file. Here the 5 rays simulate a beam of full angle 10 and they are allowed to pass through the inner cylinder. The second order focusing action of the CMA gives a small spot at the focal point. Several other ideal and practical energy analyzers are included in the test and example files.

xmpl2d36 - A 3-cylinder einzel lens. From the 36th 2D example file. The vertical scale has been expanded in this picture and some potential contours are shown. Examples of several other lenses are included in the CPO package. The programs can automatically vary one or more lens voltages to produce the smallest spot at some defined position (or even to produce a series of spots at different positions, for example for different energies). The program also gives accurate thirdorder lens parameters derived from paraxial integrations.

test2d08 - Time-varying fields. From the 8th 2D benchmark test file. Here there is sinusoidal motion in a sinusoidal field. There are also options for tophat and sawtooth time dependencies. Up to three different time dependencies can be applied simultaneously (for example a sine wave plus two harmonics). Or the User can define a time dependence via an external program. Examples of these programs are included, together with detailed instructions on how to link them to the main program.

xmpl2d43 - X-ray tube. Produced from the 43rd 2D example file. A simple tube with a flat thermionic cathode and an anode at 100kV. This view is expanded in the transverse direction. The iterative automatic focusing option is used to find the optimum grid voltage. In each iteration step the spacecharge spreading is automatically established by a separate iterative procedure.

shap3d19 - A grid of 289 holes. Produced from the 19th 3D shape file.

xmpl3d47 - A magetic lens. From the 47th 3D example file. The CPO3D programs can be used to synthesize magnetic fields by superimposing fields from a menu of several different types (eg the fields produced by solenoids, hoops, straight or circular lengths of current, dipoles, etc). Or the User can generate fields externally on a grid of points and read them in as arrays of precalculated values. The User can also define a field via an external program which can be easily linked to the main program.

xmpl3d53 - An array of conical nano-tubes used as field emission sources. Produced from the 53rd 3D example file. Several other examples deal with carbon nanotubes, for example to find the enhancement factors of single tubes or arrays of tubes. The Surface Charge Method is ideal for dealing with very small structures in the presence of electrodes that are much larger.

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