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CPO |
The 'Example' Data Files.The 'Example' data files represent problems that are of general interest but that do not have known analytical solutions. The 'comments' at the ends of the files contain detailed information (including key formulas) on a wide variety of problems in charged particle optics. . See the links below for more information. Further information on the Example files xmpl3d01:
A practical hemispherical deflection analyzer.
xmpl3d47 Simple magnetic lens. xmpl3d48 Photomultiplier. xmpl3d49 Reflection at an electrode. 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: Simple quadrupole ion trap. xmpl3d72: Boersch effect for liquid metal ion sources. 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. '3D Shape' files:
'2D Example' files:
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-2D : xmpl2d01 A double cylinder lens One cylinder extends from z=-5.0 to z=-0.05, the other from z=0.05 to z=5.0, both with a radius of 0.5, and both capped at their far ends. Only one value value of the voltage ratio v2/v1 is chosen in this example, namely 10. The focal and mid-focal lengths and all the third order spatial and chromatic aberration coefficients are obtained, and are extrapolated to an infinite number of segments. To check the computed aberration coefficients, some specific rays are also traced through the lens. xmpl2d02 A double aperture lens The two apertures have a radius of 0.5 and are situated at z=+/-0.25. The lens is enclosed by cylinders of radius 2.5, which are themselves capped by discs at their far ends. The cylinder between the 2 apertures has the appropriate voltage gradient. Only one value value of the voltage ratio v2/v1 is chosen in this example, namely 10. The focal and mid-focal lengths and all the third order spatial and chromatic aberration coefficients are obtained, and are extrapolated to an infinite number of segments. To check the computed aberration coefficients, some specific rays are also traced through the lens. xmpl2d03 A double rectangular tube lens This example is the analogue in planar symmetry of the double cylinder lens dealt with in file xmpl2d01. One pair of plates extends from z=-5.0 to z=-0.05, the other from z=0.05 to z=5.0, both with a spacing of 0.5, and both capped at their far ends. Only one value value of the voltage ratio v2/v1 is chosen in this example, namely 4. The focal and mid-focal lengths and the third order spherical aberration coefficients are obtained, and are checked by tracing some specific rays through the lens. xmpl2d04 A double rectangular tube lens This example is the analogue in planar symmetry of the double aperture lens dealt with in file xmpl2d02. Each slit is composed of 2 plates separated by a distance of 1, and the slits are situated at z=+/-0.25. The lens is enclosed by plates at x=+/-1, capped at their far ends. The plates between the 2 slits have the appropriate voltage gradient. Only one value value of the voltage ratio v2/v1 is chosen in this example, namely 6. The focal and mid-focal lengths and the third order spherical aberration coefficients are obtained, and are checked by tracing some specific rays through the lens. xmpl2d05 A 'beam' of rays focussed by a double-cylinder lens. This file is identical to the 1st example file, xmpl2d01, except that a 'beam' of rays is specified. There are 4 rays in the beam, all starting from a point object at z=-4 and directed towards a 'pupil' of radius 0.2 at z=-2. xmpl2d06 An example of automatic subdivision, for a double-cylinder lens. The geometry is identical to that in the first example file xmpl2d01. 'Automatic subdivision' is used to increase the number of subdivisions from 10 to 50, in 4 stages. At each stage the segments that carry the largest charges are subdivided the most, so that eventually all the segments carry approximately the same charge. xmpl2d07 Automatic iteration to focus a beam by a three-cylinder lens. The initial voltages on the three cylinders (all of radius 0.5) are 1, 7 and 4, the middle one of which is varied by the program to produce the best on-axis focus at z=3. Four rays are used, all starting from z=-4, with initial launch angles of .01, .02, .03 and .04 rad. xmpl2d08 Lens coefficients of double-cylinder lens. This file is identical to the 1st example file, xmpl2d01, except that various 'lens coefficients' are asked for, including the linear and angular magnifications and the spherical and chromatic aberrations. xmpl2d09 Space-charge limited planar diode, cylindrical symmetry. An infinite planar diode cannot be simulated and so it is necessary to add boundary electrodes in this problem. These are cylinders that are given the theoretical potentials, proportional to z**(4/3). Childs Law is used in the immediate vicinity of the cathode surface, assuming a zero cathode temperature. CPO-3D). The average current of the innermost rays is given after 3 iterations with an error of 3.7% (in a total computing time of much less than a minute. This error decreases to 1.6% in later iterations. xmpl2d10 Space-charge limited diode in planar symmetry (ie flat, parallel cathode and anode, infinite in one direction). This example is similar to the 9th example, given in file xmpl2d09. xmpl2d11 Simulation of the space-charge repulsion of an isolated beam that initially converges to a point, using the 'ray space-charge tube' method. This cannot be a benchmark test because the beam is not infinite in extent. A beam is directed towards a point on the axis. The size and position of the beam waist are approximately correct. xmpl2d12 Simulation of the space-charge repulsion of a mixed beam of electrons and carbon ions. The set-up is almost the same as in example file xmpl2d11, except that the beam is a mixture of electrons and positively charged carbon ions. xmpl2d13 A relativistic double-cylinder lens. This file is almost identical to the 1st example file xmpl2d01, except that the energies are relativistic xmpl2d14 A double-cylinder lens with a linear voltage bridge across the gap. The geometry of the lens is identical to that in the 'example' file xmpl2d01, except that the gap between the cylinders is filled with an extra cylinder, the voltage of which varies linearly across the gap. xmpl2d15 Automatic iterative variation of the grid voltage of a simple thermionic electron gun. A simple cathode is set up, with a grid and anode. The grid voltage is adjustable, to give the smallest focus on a screen in front of the anode. There are 'inner' and 'outer' iterative loops. The inner loop deals with space-charge iterations, while in the outer loop the grid voltage is varied. xmpl2d16 Multiple focussing of a Hemispherical Deflecton Analyzer. The HDA is set up as in test2d01. There are six rays. The first three start from (r,z) = (0.0,-1.0), with angles of 0, +/-0.1 rad and with an energy of 1 eV, and the next three with an energy of 1.05 eV. The focal points of the 2 sets are specified as as (r,z) = (0.0,1.0) and (0.0,1.1) respectively. The initial voltages on the spheres are 1.6667 and 0.6. After 12 iterations the best voltages are found to be 1.665 and 0.601, and after further iterations they become 1.6661 and 0..6024. xmpl2d17 A mirror that has negative spherical and chromatic aberrations. The equipotential surface at which the electrons are reflected has a curvature that decreases as the distance from the axis increases, which gives rise to a negative third order spherical aberration. The chromatic aberration is also negative. The mirror is therefore useful for correcting the aberrations of electron microscope lenses. xmpl2d18 Practical cylindrical mirror analyzer (CMA). A practical cylindrical mirror analyzer is simulated with apertures for the beam in the inner cylinder. The presence of the apertures profoundly alters the properties of the analyzer. 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. Derived from test2d13.dat. Field emission from a spherical cathode. xmpl2d28 Carbon nano-tube, for field emission source. The nanotube has inner and outer diameters of 6 and 10nm respectively, and has a emi-circular end. To create a field a plate is placed arbitrarily 100nm away, with a potential of 20V. xmpl2d29 Field enhancement factor for a cone. The tip of the cone is spherical and the half-angle of the cone is arctan(0.5). xmpl2d30 Field enhancement factor for a ‘hemisphere on post’. The 'post' has a height of 1 micron and a radius of 1nm. 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. When the rays hit an electrode at z=1 they produce secondary electrons. The routine that defines the distribution of energies and angles of the secondaries is supplied with the package but can be altered by the User. xmpl2d38 Scattering option, absorption and scattering by background gas. Between z=-0.5 and z=0.5 the particles interact with the molecules of a background gas. The routine that defines the distribution of energies and angles of the scattered particles is supplied with the package but can be altered by the User. xmpl2d39 Scattering option, scattering at a grid. When the rays reach z = 0 they are randomly scattered, as by a grid. The routine that defines the scattering function is supplied with the package but can be altered by the User. When the rays reach z = 0 they are randomly scattered, as by a grid. The routine that defines the scattering function is supplied with the package but can be altered by the User. xmpl2d40 Scattering option, simulation of a thin lens. When the rays reach z = 0 they are focused by a thin lens. The routine that defines the lens action is supplied with the package but can be altered by the User. xmpl2d41 Photocathode. The photocathode is at 0V and the screen is at 10000. A middle electrode is at 500V. xmpl2d42 Defining relationships between voltages. Based on test2d01.dat, ideal hemispherical deflection analyzer, which had inner (outer) voltage = V1 (V2). Here we have created two extra voltages and have defined inner (outer) voltage = V3 + 0.5*V4 (V3 - 0.5*V4). Now V3 and V4 can be varied. xmpl2d43 X-ray tube with thermal energies. The simulation is of an x-ray tube that has a flat thermionic cathode and a target (anode) voltage 100kV. xmpl2d44 Converting an electric field to a magnetic field. The magnetic field of an x-ray tube is simulated by using the analogy between magnetostatic and electrostatic fileds.. xmpl2d45: Rectangular waveform for oscillating voltages. xmpl2d46: Space-charge expansion of an electron beam. CPO-3D: xmpl3d01 A practical hemispherical deflection analyzer. The analyzer consists of two hemispheres of radii 0.75 and 1.25, with 4 hoops being used to correct for the end effects. xmpl3d02 A practical cylindrical deflection analyzer, 127 degrees. The two cylindrical sectors have radii of 0.75cm and 1.25cm, and are of depth 2cm. Six strips are used at the entrance and exit to correct for the end effects xmpl3d03 Orbit of a proton outside a charged sphere. The proton starts with a kinetic energy of 0.25 eV, at a distance of 2 (the unit of distance is arbitrary for this problem) from the centre of a sphere of radius 1 and at a voltage of -1. The orbits are ellipses. xmpl3d04 A demonstration of automatic subdivision. The geometry is same as that of the 3rd benchmark test (see file test3d03), but the segments are progressively subdivided in 4 stages with a 'weight charge' factor of 1.0, to give automatic subdivision (ie adaptive segmentation)aimed at making all the segments carry approximately the same charge. xmpl3d05 Quadrupole filter with oscillating field. The exact electrode shapes for the ideal quadrupole field are simulated in this example by a mixture of 'cylindrical' rectangles (ie rectangles that are part of a cylindrical surface) and flat rectangles. The particles are singly charged nitrogen molecular ions. xmpl3d06 Automatic iteration to optimise the focus of a 4-cylinder lens. A simple 4-cylinder lens is used in this example. The 1st and 4th cylinders are at fixed voltages (1 and 2 respectively), while the 2nd and 3rd have voltages that are adjusted by the program. They are given the initial values of 15 each, and initial excursions of 5. These two voltages are also constrained (or more accurately, inhibited), to stop them from going far above 50 volts, and the final angles have also been constrained. xmpl3d07 Space-charge repulsion of an isolated beam that initially converges to a point. This cannot be a benchmark test because the beam is not infinite in extent. A beam is directed towards a point on the axis. The size and position of the beam waist are approximately correct. xmpl3d08 Space-charge repulsion in a mixed beam of electrons and positively charged carbon ions. Simulation of the space-charge repulsion of a mixed beam of electrons and positively charged carbon ions. The electron and ion beam currents have been made equal and opposite, and the electrons and ions have been given the same velocity. The combined space charge should therefore be zero, and both types of particle should travel in straight lines. This behaviour is accurately reproduced. xmpl3d09 Space-charge limitation of current in a strong magnetic field. Electrons of energy 1 eV in a beam of radius 1 mm are in a field of 0.1 Tesla. Theoretically, the maximum current is 0.0324 mA and the potential depression at the centre of the beam is then such that the electrons there have a kinetic energy of 0.174 eV. Since it is impossible to simulate the idealised system, for which the beam has an infinite length and the potential at the outer surface of the beam is a constant, the beam is enclosed between 2 discs and a cylinder, all of potential zero. The current is put at 95% of the theoretical maximum value, and after several iterations the kinetic energy at the centre of the beam converges to 0.306 eV. If the full current is used the calculation fails to converge. xmpl3d10 Space-charge limited planar diode. An infinite planar diode cannot be simulated and so it is necessary to add boundary electrodes in this problem. The average current of the innermost rays is given after 3 iterations with an error of 0.7% (in a total computing time of less than a minute. The error becomes 0.1% in later iterations. xmpl3d11 Space-charge limited planar diode, with thermal energies. The set-up is as described in file xmpl3d10, except that the thermal energy is non-zero. The effect on the directions of the rays is apparent. The potential minimum in front of the cathode can also be seen in the contour plots. For example when kT = 0.2eV and the emitted current density is put at 100 mA/mm^2 (a factor of 3600 higher than the saturated current) the potential of the virtual cathode is 1.64 volts lower than that of the real cathode and its position is 0.18mm in front of the real cathode. xmpl3d12 Automatic optimisation of an electron gun with a hairpin cathode. A hairpin cathode is set up, with a grid and anode. The cathode is at 0 volts and the anode at 100 volts, while the grid voltage is adjustable, to give the smallest focus on a screen in front of the anode. There are 'inner' and 'outer' iterative loops. The inner loop deals with space-charge iterations, while in the outer loop the grid voltage is varied. Only 3 space-charge iterations are used at each value of the grid voltage, for a quick demonstration. It is interesting to note that the focussing is strongly astigmatic, being weaker in the plane of the hairpin than transverse to the plane, which seems not to have been remarked on before. xmpl3d13 Cathode ray tube. A simple cathode ray tube, with variation of the grid voltage to produce a small spot on the screen. xmpl3d14 Miniature lens for microelectronic switching. A micro-lens, formed by lithography (and hence imperfect), for micoswitching. xmpl3d15 Hairpin cathode with potential drop and current. The set-up is as in xmpl3d12.dat, except that a voltage difference of 2 V is applied across the hiarpin, and a current of 2 A through the hairpin is simulated to provide a local magnetic field. The voltage difference causes a shift in the position of the beam at the anode. xmpl3d16 Extended Schottky emission, spherical cathode. The cathode and anode have radii of 1m m and 1cm respectively, the cathode-anode voltage difference is 1000V, the work function of the cathode is 2.7eV, and the temperature is 1800K. A modification of the Richardson-Dushman equation is used, as given by Hawkes and Kasper. The initial velocity components are randomised. The current that should be given by the program is 0.3130 mA, and in fact is 0.3127 mA. xmpl3d17 Magnetic angle changing technique In the new (in 1996) 'magnetic angle changing' technique, solenoids are used to create a confined magnetic field. The strength of the field in this example is such that an electron of energy 1 eV is deflected through 90 degrees. The solenoids are as defined by Read and Channing. xmpl3d18 Multiple focussing of hemispherical deflection analyzer. The HDA is set up as in test3d01. Six rays move in the xz plane. The first three start from y = -1, with angles of 0, +/-0.1 rad and with an energy of 1 eV, and the next three with an energy of 1.05 eV. The focal points of the 2 sets are specified as y = 1 and 1.1 respectively. xmpl3d19 Split-lens deflector. An example of a split-lens deflector xmpl3d20 Magnetic bottle. Electrons are confined between two circular loops of current. xmpl3d21 Space-charged limited cylindrical diode with thermal energies. A cathode of radius 1 and length 8 is coaxial with an anode of radius 4 and potential 100V. The thermal energy of emission is kT = 0.1 eV. The space-charge limited current is found to be approximately 4% higher than the theoretical current for kT = 0. xmpl3d22 Practical cylindrical mirror analyzer (CMA). A practical cylindrical mirror analyzer is simulated with apertures for the beam in the inner cylinder. The presence of the apertures profoundly alters the properties of the analyzer. xmpl3d23 Penetration of field and potential through a mesh A flat mesh is composed of thin crossed wires that form an array of square holes, and has a transparency of 90 percent. The mesh is at zero potential and a field is created on one side of it by means of a continuous plate at a different potential. An extrapolation technique is used to simulate a mesh that is infinite in extent. It is found that the external field penetrates only a short distance through the mesh, but that there is a finite change of the potential in the field-free region. xmpl3d24 CRT electron gun, cylindrical symmetry. A simple tetrode design. The 'ray space charge tube' method of assigning space charge is used. The 'phase space' option is also used. xmpl3d25 CRT electron gun, rectangular grid. A tetrode design, as specified by J Hasker, IEEE Transactions on Electron Devices, Vol ED-18 (Number 9), 703-712 (1971). A grid at -145 V with a rectangular hole of 0.1125*0.35 mm is followed by an anode at 1000 V with a circular opening of radius 0.2 mm, which is followed by a plate at 2500 V. xmpl3d26 Aberrations due to a localised potential defect on an aperture. This is one of the data files used for the study: Aberrations due to localised potential defects on defining apertures, by F H Read, L A Baranova, N J Bowring, J Lambourne and T C Whitwell, to appear in Rev. Sci. Instrum. (1998) xmpl3d27 Simplest unbalanced deflector. Simple deflector plates are put at +/- x and +/- y. All have voltage 0, except the plate at +x, which has voltage 1. xmpl3d28 Pierce gun, potassium 39 ions, with thermal energies. The system approximates to a Pierce gun. The cathode emits potassium 39 ions at a temperature of 1500C. 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. 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. Photocathode, illustrating the option of initial ray conditions of fixed energy and lambertian directions. xmpl3d46: Creation of secondary rays, Maxwell and Ura energy distributions. xmpl3d47 Magnetic lens. A simple lens, with an axial magnetic field Bz given by the Glaser formula. The '2D grid' option is used here for the magnetic field. xmpl3d48 Photomultiplier. A primitive photomultiplier, to illustrate how a secondary ray can be created when a ray hits an electrode. The rays start with a fixed energy (0.5eV) and normal to the cathode surface, but a Maxwellian energy distribution and/or a Lambertian direction can easily be activated. xmpl3d49. Reflection at an electrode. Demonstrate of the option to 'create secondary rays' when a ray hits an electrode. Here the secondary rays are specularly reflected, with the same energy, when the primary energy is at least 1eV, and has a current that is multiplied by 2.0 at each impact. xmpl3d50. Illustration of the scattering option, scattering at a grid. This option is available only in the 'special' scattering version of CPO3D or CPO3DS. The geometry is that of the 3rd benchmark test. The rays start at z = -0.5, in a field-free region. When the rays reach z = 0 they are scattered through random angles. The routine that defines the scattering function is in file sct3grid.cpp, which is supplied with the CPO3D package. xmpl3d51. Illustration of the scattering option, simulation of a thin lens. This option is available only in the 'special' scattering version of CPO3D or CPO3DS. When the rays reach z = 1 they are focussed by a thin lens that has f = 2, Cs = 0.1, Cc = 0. The routine that defines the scattering function is in file sct3lens.cpp, which is supplied with the CPO3D package. xmpl3d52. Enhancement factor for a nano-cone. The tip of the cone is spherical, with radius of 1mm. The half-angle of the cone is arctan(0.5). The cone has a base radius of 50.9mm and a height of 101.6mm. The dimensions can of course be scaled. xmpl3d53. Enhancement factor for a cone in an array of nano-cones. The geometry is the same as in files xmpl3d52.dat and xmpl2d29.dat, except that an array of 9 cones is used. The spacing between the tips of the cones is 200mm in the x and y directions. xmpl3d54. An example of a field emission flat screen display system. A conical cathode has a tip radius of 10nm and a work function of 2.7eV. xmpl3d55. Use of a rectangular beam, for space-charge spreading. A rectangular beam originates at a rectangle that has a half-width 3 in the x direction and 1.5 in the r direction. xmpl3d56. Defining relationships between voltages. Ideal hemispherical deflection analyzer. Two extra voltages and have defined: inner voltage = V1 = V3 + 0.5*V4, outer voltage = V2 = V3 - 0.5*V4. Now V3 and V4 can be varied instead of V1 and V2. xmpl3d57. Archards method of correcting chromatic aberration. A quick simulation of a simple system based on one component of one of the systems proposed by G. D. Archard to cancel chromatic aberration in one plane. xmpl3d58. Scattering option, production of secondary electrons. This option is available only in the 'special' scattering version of CPO3D or CPO3DS. When the rays hit the electrode at z=1 they produce secondary electrons. The external 'User-supplied' routine that defines the scattering function is supplied with the CPO3D package. xmpl3d59. Scattering option, absorption and scattering by background gas. This option is available only in the 'special' scattering version of CPO3D or CPO3DS. Between z=-0.5 and z=0.5 the rays interact with the molecules of a background gas. The external 'User-supplied' routine that defines the scattering function is supplied with the CPO3D package. xmpl3d60: Stochastic scattering option, Boersch energy spreading. This option is available only in the 'special' scattering version of CPO3D or CPO3DS. The rays are directed towards a pupil of radius 1.0 at z = 0, with a beam half-angle 0.01. The energy of the electrons is 10keV. The external 'User-supplied' routine that defines the stochastic scattering function is supplied with the CPO3D package. xmpl3d61: Option for User-supplied near-axis electric field. A central cylinder is split into 8 parts that can be used as a quadrupole, octupole or monopole (ie round) lens. xmpl3d62: Enhancement factor for a nanotube, 'hemisphere on post'. The 'post' has height 1 micron and radius 1nm. xmpl3d63: Enhancement factor for 2 nearby nanotubes. Both nanotubes have the form 'hemisphere on post'. The 'posts' have height 0.5 micron, radius 1nm, and separation 80nm. xmpl3d64: Enhancement factor for a square array of nanotubes. All the nanotubes have the form of 'hemisphere on post'. The 'posts' have height 0.5 micron, radius 1nm and separation 160nm. xmpl3d65: Enhancement factor for a 'spoilt' array of nanotubes. All the nanotubes have the form of 'hemisphere on post'. The 'posts' have height 0.5 micron, radius 1nm and separation 160nm. xmpl3d66: Enhancement factor for a random array of nanotubes. All the nanotubes have the form of 'hemisphere on post'. The 'posts' have height 500nm, radius 1nm and average separation 160nm. They are placed randomly inside a circle of radius 285.5nm. xmpl3d67: Enhancement factor for a linear array of nanotubes. All the nanotubes have the form of 'hemisphere on post'. The 'posts' have height 0.5 micron, radius 1nm and separation 80nm. xmpl3d68: Spatial stochastic scattering. A doublet lithographic projection system. Mask radius 0.5mm, 2 ideal thin lenses at z = 160 and 360, with f = 160 and 40, overall magnification 1/4. xmpl3d69: Rectangular waveform for oscillating voltages. xmpl3d70: Stark barrel. xmpl3d71: Simple quadrupole ion trap. xmpl3d72: Boersch effect for liquid metal ion sources. 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. |
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