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Input files
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EllipticalEinzelIn.DST, EllipticalEinzel1515.MIN, EllipticalEinzel1515.HIN, EllipticalEinzel1515.OIN, EllipticalEinzel1520.MIN, EllipticalEinzel1520.HIN, EllipticalEinzel1520.OIN
Download EllipticalEinzelLens.zip
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Description
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This example illustrates the transformation of a circular beam to a sharp line focusing using an einzel lens with an elliptical aperture. Among other techniques, the example shows the use of the EllipCyl model of MetaMesh and a method to local the best beam focus using the Intersection mode in OmniView plots. An einzel lens consists of a central high voltage electrode between two grounded transport tubes, defining accelerating and decelerating gaps. The top figure (with expanded radial scale) shows equipotential lines and particle trajectories in a lens with cylindrical symmetry. The radial electric field in the initial gap is defocusing at the entrance and focusing at the exit. Because the beam radius is larger at the exit, the net effect is focusing. The fields in the second gap are reversed, focusing then defocusing. Again, the change in beam radius gives a net focusing effect.
The file EllipticalEinzelIn.DST creates an input PRT file representing a parallel, uniform current proton beam of kinetic energy 10.0 KeV and radius 1.0 cm at position z = -9.99 cm. A large number of particles (1304) is used for good statistics. In the initial solution (EllipticalEinzel1515), entrance tube, electrode and exit tube all have radii of 1.5 cm (a cylndrical einzel lens). In the second solution (EllipticalEinzel1520), the EllipCyl model of MetaMesh is used to create an elliptical aperture in the central electrode with minor and major radii Rx = 1.5 cm, Ry = 2.0.
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Results
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For the cylindrical lens, an applied central potential of +5500.0 V gives the trajectories used in the top figure. Using OmniView slice plots normal to z in the Intersection mode, the focal point can be accurately located at z = 17.1 cm. The transverse spatial distribution at this point is a circle with radius 0.04 cm (compression ratio of 25.0). The spot size is limited by spherical aberration in the lens.
For the elliptical lens, a reduced voltage of +4500.0 V gives a line focus in x at z = 14.9 cm. (The stronger focusing in x is expected -- for the same voltage, a slot einzel lens has a focal length half that of a cylindrical one.) The central figure illustrates trajectories projected to the x plane (top) and y plane (bottom). The lower figure (left) shows that a the line focus point the beam has a half width of only 0.025 cm in the x-direction (a 50:1 compression). The lens has almost no effect on beam dynamics in the y-plane. The right-hand plot of the lower figure shows that the beam density is fairly uniform in the y-direction, close to an ideal line focus.
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