Electrostatic lens

Short description: Device for focusing charged particles

An electrostatic lens is a device that assists in the transport of charged particles.[1][2][3] Electrostatic lenses can focus, and also accelerate or decelerate charged particles by creating an electric field that exterts a force on the charged particles. For instance, they are widely used in the extraction and acceleration of electron or ion beams [4] Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or converge the charged particle trajectories. As the focusing properties are independent of the charge-to-mass ratio of the particles at non-relativistic speeds, this means the same system can be used with different ions[5]

## Contents

* 1 Cylinder lens
* 2 Einzel lens
* 3 Quadrupole lens
* 4 Multipole lenses
* 5 Electron spectroscopy
* 6 See also
* 7 References
* 8 Further reading

## Cylinder lens

Cylinder lenses in a cathode-ray tube electron gun

A cylinder lens consists of several cylinders whose sides are thin walls. Each cylinder lines up parallel to the optical axis into which electrons enter. There are small gaps put between the cylinders. When each cylinder has a different voltage, the gap between the cylinders works as a lens. The magnification is able to be changed by choosing different voltage combinations. Although the magnification of two cylinder lenses can be changed, the focal point is also changed by this operation. Three cylinder lenses achieve the change of the magnification while holding the object and image positions because there are two gaps that work as lenses. Although the voltages have to change depending on the electron kinetic energy, the voltage ratio is kept constant when the optical parameters are not changed.

## Einzel lens

Path of ions in an einzel lens.

An einzel lens is an electrostatic lens that can focus without changing the energy of the beam. It consists of three or more sets of cylindrical or rectangular tubes in series along an axis.[6]

## Quadrupole lens

The quadrupole lens consists of two single quadrupoles turned 90° with respect to each other. Let z be the optical axis then one can deduce separately for the x and the y axis that the refractive power is again the square of the refractive power of a single lens.[7]

A magnetic quadrupole works very similar to an electric quadrupole, however the Lorentz force increases with the velocity of the charged particle. In spirit of a Wien filter, a combined magnetic, electric quadrupole is achromatic around a given velocity. Bohr and Pauli claim that this lens leads to aberration when applied to ions with spin (in the sense of chromatic aberration), but not when applied to electrons which also have a spin. See Stern–Gerlach experiment.

## Multipole lenses

Multipoles beyond the quadrupole can correct for spherical aberration and in particle accelerators the dipole bending magnets are really composed of a large number of elements with different superpositions of multipoles.

Usually the dependency is given for the kinetic energy itself depending on the power of the velocity. So for an electrostatic lens the focal length varies with the second power of the kinetic energy, while for a magnetostatic lens the focal length varies proportional to the kinetic energy. And a combined quadrupole can be achromatic around a given energy.

If a distribution of particles with different kinetic energies is accelerated by a longitudinal electric field, the relative energy spread is reduced leading to less chromatic error. An example of this is in the electron microscope.

## Electron spectroscopy

The recent development of electron spectroscopy makes it possible to reveal the electronic structures of molecules. Although this is mainly accomplished by electron analysers, electrostatic lenses also play a significant role in the development of electron spectroscopy.

Since electron spectroscopy detects several physical phenomena from the electrons emitted from samples, it is necessary to transport the electrons to the electron analyser. Electrostatic lenses satisfy the general properties of lenses.

## See also

* Ion funnel
* Magnetic lens
* SIMION

## References

1. ↑ D.W.O. Heddle (13 December 2000). Electrostatic Lens Systems, 2nd edition. CRC Press. ISBN 978-1-4200-3439-4. https://books.google.com/books?id=ixmUMS47QfwC.
2. ↑ Jon Orloff (24 October 2008). Handbook of Charged Particle Optics, Second Edition. CRC Press. ISBN 978-1-4200-4555-0. https://books.google.com/books?id=y0FF19lud5YC&pg=PA204.
3. ↑ A El-Kareh (2 December 2012). Electron Beams, Lenses, and Optics. Elsevier Science. pp. 54–. ISBN 978-0-323-15077-4. https://books.google.com/books?id=AlypM0iJ8EwC&pg=PA410.
4. ↑ "Ion optics with electrostatic lenses". CERN. https://cds.cern.ch/record/1005034/files/p27.pdf.
5. ↑ Electrostatic Lenses. In: Electron and Ion Optics. Microdevices. Springer, Boston, MA. ISBN 978-1-4613-0923-9. https://doi.org/10.1007/978-1-4613-0923-9_7.
6. ↑ "Scanning Electron Microscopy | Principles of Scanning Electron Microscopy | Thermo Fisher Scientific - UK". ThermoFisher. https://www.thermofisher.com/uk/en/home/materials-science/learning-center/applications/scanning-electron-microscope-sem-electron-column.html.
7. ↑ Joshi (2010) (in en). Engineering Physics. Tata McGraw-Hill Education. ISBN 9780070704770. https://books.google.com/books?id=mgA5JgiT8ZkC&q=quadrupole+lens+90.

## Further reading

* E. Harting, F.H. Read, Electrostatic Lenses, Elsevier, Amsterdam, 1976.

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