An electrostatic lens is a device that assists in the transport of charged particles. For instance, it can guide

electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have n ...

s emitted from a sample to an

electron analyzer An electrostatic analyzer or ESA is an instrument used in ion optics that employs an electric field to allow the passage of only those ions or electrons that have a given specific energy. It usually also focuses these particles (concentrates them) ...

, analogous to the way an

optical lens A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements ...

assists in the transport of light in an optical instrument. Systems of electrostatic lenses can be designed in the same way as optical lenses, so electrostatic lenses easily magnify or converge the electron trajectories. An electrostatic lens can also be used to

focus Focus, or its plural form foci may refer to: Arts * Focus or Focus Festival, former name of the Adelaide Fringe arts festival in South Australia Film *''Focus'', a 1962 TV film starring James Whitmore * ''Focus'' (2001 film), a 2001 film based ...

an ion beam, for example to make a

microbeam A microbeam is a narrow beam of radiation, of micrometer or sub-micrometer dimensions. Together with integrated imaging techniques, microbeams allow precisely defined quantities of damage to be introduced at precisely defined locations. Thus, the mi ...

for irradiating individual

cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...

Cylinder lens

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 Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in si ...

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 In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acce ...

, the voltage ratio is kept constant when the optical parameters are not changed. While a charged particle is in an electric field force acts upon it. The faster the particle the smaller the accumulated impulse. For a collimated beam the focal length is given as the initial impulse divided by the accumulated (perpendicular) impulse by the lens. This makes the focal length of a single lens a function of the second order of the speed of the charged particle. Single lenses as known from photonics are not easily available for electrons. The cylinder lens consists of defocusing lens, a focusing lens and a second defocusing lens, with the sum of their refractive powers being zero. But because there is some distance between the lenses, the electron makes three turns and hits the focusing lens at a position farther away from the axis and so travels through a field with greater strength. This indirectness leads to the fact that the resulting refractive power is the square of the refractive power of a single lens.

Einzel lens

einzel lens An einzel lens (from german: Einzellinse – single lens), or unipotential lens, is a charged particle electrostatic lens that focuses without changing the energy of the beam. It consists of three or more sets of cylindrical or rectangular apertur ...

is an electrostatic 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.

Quadrupole lens

The

quadrupole lens A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...

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. A

magnetic quadrupole A quadrupole or quadrapole is one of a sequence of configurations of things like electric charge or current, or gravitational mass that can exist in ideal form, but it is usually just part of a multipole expansion of a more complex structure refl ...

works very similar to an electric quadrupole, however the

Lorentz force In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...

increases with the velocity of the charged particle. In spirit of a

Wien filter A Wien filter also known as velocity selector is a device consisting of perpendicular electric and magnetic fields that can be used as a velocity filter for charged particles, for example in electron microscopes and spectrometers. It is used in ...

, a combined magnetic, electric quadrupole is achromatic around a given velocity.

Bohr Niels Henrik David Bohr (; 7 October 1885 – 18 November 1962) was a Danish physicist who made foundational contributions to understanding atomic structure and quantum theory, for which he received the Nobel Prize in Physics in 1922. B ...

and

Pauli Pauli is a surname and also a Finnish male given name (variant of Paul) and may refer to: * Arthur Pauli (born 1989), Austrian ski jumper * Barbara Pauli (1752 or 1753 - fl. 1781), Swedish fashion trader *Gabriele Pauli (born 1957), German politi ...

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 The Stern–Gerlach experiment demonstrated that the spatial orientation of angular momentum is quantized. Thus an atomic-scale system was shown to have intrinsically quantum properties. In the original experiment, silver atoms were sent throug ...

Magnetic lens

A magnetic field can also be used to focus charged particles. The Lorentz force acting on the electron is perpendicular to both the direction of motion and to the direction of the magnetic field (vxB). A homogeneous field deflects charged particles, but does not focus them. The simplest magnetic lens is a donut-shaped coil through which the beam passes, preferably along the axis of the coil. To generate the magnetic field, an electric current is passed through the coil. The magnetic field is strongest in the plane of the coil and gets weaker moving away from it. In the plane of the coil, the field gets stronger as we move away from the axis. Thus, a charged particle further from the axis experiences a stronger Lorentz force than a particle closer to the axis (assuming that they have the same velocity). This gives rise to the focusing action. Unlike the paths in an electrostatic lens, the paths in a magnetic lens contain a spiraling component, i.e. the charged particles spiral around the optical axis. As a consequence, the image formed by a magnetic lens is rotated relative to the object. This rotation is absent for an electrostatic lens. The spatial extent of the magnetic field can be controlled by using an iron (or other magnetically soft material) magnetic circuit. This makes it possible to design and build more compact magnetic lenses with well defined optical properties. The vast majority of electron microscopes in use today use magnetic lenses due to their superior imaging properties and the absence of the high voltages that are required for electrostatic lenses.

Multipole lenses

Multipoles beyond the quadrupole can correct for spherical aberration and in

particle accelerators A particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle ...

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 An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a hi ...

Electron spectroscopy

The recent development of

electron spectroscopy Electron spectroscopy refers to a group formed by techniques based on the analysis of the energies of emitted electrons such as photoelectrons and Auger electrons. This group includes X-ray photoelectron spectroscopy (XPS), which also known as Ele ...

makes it possible to reveal the electronic structures of

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...

s. 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.

References

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