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Date maintenance tags and general fixes

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[[Image:Einzel lens.png|thumb|300px|Implementation of an Einzel lens showing the ion path. Six plates are parallel to the ion flight path with the middle plate at a particular potential.]]
An '''einzel lens''' is a charged particle lens that focuses without changing the energy of the beam. It consists of three or more sets of cylindrical or rectangular tubes in series along an axis. It is used in [[ion optics]] to focus [[ion]]s in flight which is accomplished through manipulation of the [[electric field]] in the path of the ions.

The lens elements are symmetric so the ions will regain their initial [[energy]] on exiting the lens although the [[velocity]] of the outer particles will be altered such that they converge on to the axis. This causes the outer particles to arrive at the [[focus (optics)|focus]] intersection slightly later than the ones that travel along a straight path as they have to travel an extra distance.

==Theory==
[[Image:Einzel lens 3d.png|thumb|right|250 px|A perspective view of an einzel lens.]]
The equation for the change in radial velocity for a particle as it passes between any pair of cylinders in the lens is:

<math>\Delta v_r = \int \frac{qE_r(r,z)}{m_0v_z} dz</math>

z is the axis passing through the middle of the lens. r is the direction normal to z. If the lens is constructed with cylindrical plates, the field is symmetrical around z. <math>E_r(r,z)</math> is the magnitude of the electric field in the radial direction for a particle at a particular radial distance and distance across the gap, <math>m_o</math> the rest mass of the particle passing through the field, <math>v_z</math> is the velocity of the particle and q is the charge of the particle. The integral occurs over the gap between the plates. This is also the interval where the lensing occurs.

The pair of plates is also called an electrostatic immersion lens, thus an einzel lens can be described as two or more electrostatic immersion lenses. Solving the equation above twice to find the change in radial velocity for each pair of plates can be used to calculate the focal length of the lens.

==Application to television tubes==
[[Image:Einzel lens ions.png|thumb|right|300px|Path of ions as they travel through an einzel lens. The ion mass is 200 kDa accelerated to 40 kV, the middle plate potential is at 200 V and the plate size is 1m (note that these values are atypical for illustrative purposes).]]
The einzel lens principle in a simplified form was also used as a focusing mechanism in modern display and television cathode ray tubes,<ref>"Radio and Television" by C. A. Quarrington, 1952-1963.</ref><ref>"Television Receiver Servicing" by E. A. W. Spreadbury, 1953</ref> and has the advantage of providing a good sharply focused spot throughout the useful life of the tube's electron gun, with minimal or no readjustment needed (many mono TVs did not have or need focus controls), although in high-resolution mono displays and all colour CRT displays an (engineer-adjustable) focus potentiometer control is provided.

==See also==
* [[Time of flight]]
* [[Mass spectrometry]]
* [[Cathode ray tube]]

==References==
{{Reflist}}
*{{Citation | doi = 10.1063/1.1686484 | title = Construction of an einzel lens capable of high voltage operation | year = 1974 | author = Aberth, William H. | journal = Review of Scientific Instruments | volume = 45 | pages = 1289|bibcode = 1974RScI...45.1289A | issue = 10 }}

[[Category:Electrostatics]]
[[Category:Mass spectrometry]]

Paranormal subgroup - Revision history

en>SmackBot: Date maintenance tags and general fixes