Electrostatic lens

Last updated

An electrostatic lens is a device that assists in the transport of charged particles. [1] [2] [3] For instance, it can guide electrons emitted from a sample to an electron analyzer, analogous to the way an optical lens 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 an ion beam, for example to make a microbeam for irradiating individual cells.

Contents

Cylinder lens

Cylinder lenses in a cathode ray tube electron gun Kathodestraalbuis2.jpg
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.

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

Path of ions in an einzel lens. Einzel lens ions.png
Path of ions in an einzel lens.

An einzel lens 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 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. [4]

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.

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 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

Related Research Articles

<span class="mw-page-title-main">Lens</span> Optical device which transmits and refracts light

A lens is a transmissive optical device that 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), usually arranged along a common axis. Lenses are made from materials such as glass or plastic and are ground, polished, or molded to the required shape. A lens can focus light to form an image, unlike a prism, which refracts light without focusing. Devices that similarly focus or disperse waves and radiation other than visible light are also called "lenses", such as microwave lenses, electron lenses, acoustic lenses, or explosive lenses.

<span class="mw-page-title-main">Transmission electron microscopy</span> Technique in microscopy

Transmission electron microscopy (TEM) is a microscopy technique in which a beam of electrons is transmitted through a specimen to form an image. The specimen is most often an ultrathin section less than 100 nm thick or a suspension on a grid. An image is formed from the interaction of the electrons with the sample as the beam is transmitted through the specimen. The image is then magnified and focused onto an imaging device, such as a fluorescent screen, a layer of photographic film, or a sensor such as a scintillator attached to a charge-coupled device.

<span class="mw-page-title-main">Linear particle accelerator</span> Type of particle accelerator

A linear particle accelerator is a type of particle accelerator that accelerates charged subatomic particles or ions to a high speed by subjecting them to a series of oscillating electric potentials along a linear beamline. The principles for such machines were proposed by Gustav Ising in 1924, while the first machine that worked was constructed by Rolf Widerøe in 1928 at the RWTH Aachen University. Linacs have many applications: they generate X-rays and high energy electrons for medicinal purposes in radiation therapy, serve as particle injectors for higher-energy accelerators, and are used directly to achieve the highest kinetic energy for light particles for particle physics.

<span class="mw-page-title-main">Time of flight</span> Timing of substance within a medium

Time of flight (ToF) is the measurement of the time taken by an object, particle or wave to travel a distance through a medium. This information can then be used to measure velocity or path length, or as a way to learn about the particle or medium's properties. The traveling object may be detected directly or indirectly.

Accelerator physics is a branch of applied physics, concerned with designing, building and operating particle accelerators. As such, it can be described as the study of motion, manipulation and observation of relativistic charged particle beams and their interaction with accelerator structures by electromagnetic fields.

<span class="mw-page-title-main">Electron gun</span> Electrical component producing a narrow electron beam

An electron gun is an electrical component in some vacuum tubes that produces a narrow, collimated electron beam that has a precise kinetic energy. The largest use is in cathode-ray tubes (CRTs), used in nearly all television sets, computer displays and oscilloscopes that are not flat-panel displays. They are also used in field-emission displays (FEDs), which are essentially flat-panel displays made out of rows of extremely small cathode-ray tubes. They are also used in microwave linear beam vacuum tubes such as klystrons, inductive output tubes, travelling wave tubes, and gyrotrons, as well as in scientific instruments such as electron microscopes and particle accelerators. Electron guns may be classified by the type of electric field generation, by emission mechanism, by focusing, or by the number of electrodes.

<span class="mw-page-title-main">Quadrupole magnet</span> Group of four magnets

Quadrupole magnets, abbreviated as Q-magnets, consist of groups of four magnets laid out so that in the planar multipole expansion of the field, the dipole terms cancel and where the lowest significant terms in the field equations are quadrupole. Quadrupole magnets are useful as they create a magnetic field whose magnitude grows rapidly with the radial distance from its longitudinal axis. This is used in particle beam focusing.

<span class="mw-page-title-main">Electrostatic deflection</span>

Electrostatic deflection refers to a way for modifying the path of a beam of charged particles by the use of an electric field applied transverse to the path of the particles. The technique is called electrostatic because the strength and direction of the applied field changes slowly relative to the time it takes for the particles to transit the field, and thus can be considered not to change for any single particle.

<span class="mw-page-title-main">Electron-beam welding</span>

Electron-beam welding (EBW) is a fusion welding process in which a beam of high-velocity electrons is applied to two materials to be joined. The workpieces melt and flow together as the kinetic energy of the electrons is transformed into heat upon impact. EBW is often performed under vacuum conditions to prevent dissipation of the electron beam.

<span class="mw-page-title-main">Teltron tube</span>

A teltron tube (named for Teltron Inc., which is now owned by 3B Scientific Ltd.) is a type of cathode ray tube used to demonstrate the properties of electrons. There were several different types made by Teltron including a diode, a triode, a Maltese Cross tube, a simple deflection tube with a fluorescent screen, and one which could be used to measure the charge-to-mass ratio of an electron. The latter two contained an electron gun with deflecting plates. The beams can be bent by applying voltages to various electrodes in the tube or by holding a magnet close by. The electron beams are visible as fine bluish lines. This is accomplished by filling the tube with low pressure helium (He) or Hydrogen (H2) gas. A few of the electrons in the beam collide with the helium atoms, causing them to fluoresce and emit light.

<span class="mw-page-title-main">Electron optics</span>

Electron optics is a mathematical framework for the calculation of electron trajectories along electromagnetic fields. The term optics is used because magnetic and electrostatic lenses act upon a charged particle beam similarly to optical lenses upon a light beam.

An electron spectrometer is a device used to perform different forms of electron spectroscopy and electron microscopy. This requires analyzing the energy of an incoming beam of electrons. Most electron spectrometers use a hemispherical electron energy analyzer in which the beam of electrons is bent with electric or magnetic fields. Higher energy electrons will be bent less by the beam, this produces a spatially distributed range of energies.

An einzel 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 apertures or tubes in series along an axis. It is used in ion optics to focus ions in flight, which is accomplished through manipulation of the electric field in the path of the ions.

<span class="mw-page-title-main">Strong focusing</span> Converging particle beams using alternating field gradients

In accelerator physics strong focusing or alternating-gradient focusing is the principle that, using sets of multiple electromagnets, it is possible to make a particle beam simultaneously converge in both directions perpendicular to the direction of travel. By contrast, weak focusing is the principle that nearby circles, described by charged particles moving in a uniform magnetic field, only intersect once per revolution.

<span class="mw-page-title-main">Magnetic lens</span>

A magnetic lens is a device for the focusing or deflection of moving charged particles, such as electrons or ions, by use of the magnetic Lorentz force. Its strength can often be varied by usage of electromagnets.

<span class="mw-page-title-main">Sextupole magnet</span>

A sextupole magnet consist of six magnetic poles set out in an arrangement of alternating north and south poles arranged around an axis. They are used in particle accelerators for the control of chromatic aberrations and for damping the head tail instability. Two sets of sextupole magnets are used in transmission electron microscopes to correct for spherical aberration.

<span class="mw-page-title-main">Explorer 54</span> NASA satellite of the Explorer program

Explorer 54, also called as AE-D, was a NASA scientific satellite belonging to series Atmosphere Explorer, being launched on 6 October 1975 from Vandenberg Air Force Base board a Thor-Delta 2910 launch vehicle.

This glossary of physics is a list of definitions of terms and concepts relevant to physics, its sub-disciplines, and related fields, including mechanics, materials science, nuclear physics, particle physics, and thermodynamics. For more inclusive glossaries concerning related fields of science and technology, see Glossary of chemistry terms, Glossary of astronomy, Glossary of areas of mathematics, and Glossary of engineering.

Direct energy conversion (DEC) or simply direct conversion converts a charged particle's kinetic energy into a voltage. It is a scheme for power extraction from nuclear fusion.

A stigmator is a component of electron microscopes that reduces astigmatism of the beam by imposing a weak electric or magnetic quadrupole field on the electron beam.

References

  1. D.W.O. Heddle (13 December 2000). Electrostatic Lens Systems, 2nd edition. CRC Press. ISBN   978-1-4200-3439-4.
  2. Jon Orloff (24 October 2008). Handbook of Charged Particle Optics, Second Edition. CRC Press. ISBN   978-1-4200-4555-0.
  3. A El-Kareh (2 December 2012). Electron Beams, Lenses, and Optics. Elsevier Science. pp. 54–. ISBN   978-0-323-15077-4.
  4. Joshi (2010). Engineering Physics. Tata McGraw-Hill Education. ISBN   9780070704770.

Further reading