Cyclotron radiation is electromagnetic radiation emitted by accelerating charged particles deflected by a magnetic field.[1] The Lorentz force on the particles acts perpendicular to both the magnetic field lines and the particles' motion through them, creating an acceleration of charged particles that causes them to emit radiation as a result of the acceleration they undergo as they spiral around the lines of the magnetic field.

The name of this radiation derives from the cyclotron, a type of particle accelerator used since the 1930s to create highly energetic particles for study. The cyclotron makes use of the circular orbits that charged particles exhibit in a uniform magnetic field. Furthermore, the period of the orbit is independent of the energy of the particles, allowing the cyclotron to operate at a set frequency. Cyclotron radiation is emitted by all charged particles travelling through magnetic fields, not just those in cyclotrons. Cyclotron radiation from plasma in the interstellar medium or around black holes and other astronomical phenomena is an important source of information about distant magnetic fields.[2][3]

## Properties

The power (energy per unit time) of the emission of each electron can be calculated:[4]

${\displaystyle {-dE \over dt}={\sigma _{t}B^{2}v^{2} \over c\mu _{o}}}$

where E is energy, t is time, ${\displaystyle \sigma _{t}}$ is the Thomson cross section (total, not differential), B is the magnetic field strength, v is the velocity perpendicular to the magnetic field, c is the speed of light and ${\displaystyle \mu _{o}}$ is the permeability of free space.

Cyclotron radiation has a spectrum with its main spike at the same fundamental frequency as the particle's orbit, and harmonics at higher integral factors. Harmonics are the result of imperfections in the actual emission environment, which also create a broadening of the spectral lines.[5] The most obvious source of line broadening is non-uniformities in the magnetic field;[6] as an electron passes from one area of the field to another, its emission frequency will change with the strength of the field. Other sources of broadening include collisional broadening[7] as the electron will invariably fail to follow a perfect orbit, distortions of the emission caused by interactions with the surrounding plasma, and relativistic effects if the charged particles are sufficiently energetic. When the electrons are moving at relativistic speeds, cyclotron radiation is known as synchrotron radiation.

The recoil experienced by a particle emitting cyclotron radiation is called radiation reaction. Radiation reaction acts as a resistance to motion in a cyclotron; and the work necessary to overcome it is the main energetic cost of accelerating a particle in a cyclotron. Cyclotrons are prime examples of systems which experience radiation reaction.

## Examples

In the context of magnetic fusion energy, cyclotron radiation losses translate into a requirement for a minimum plasma energy density in relation to the magnetic field energy density.

Cyclotron radiation would likely be produced in a high altitude nuclear explosion. Gamma rays produced by the explosion would ionize atoms in the upper atmosphere and those free electrons would interact with the Earth's magnetic field to produce cyclotron radiation in the form of an electromagnetic pulse (EMP). This phenomenon is of concern to the military as the EMP may damage solid state electronic equipment.

## References

1. ^ Monreal, Benjamin (Jan 2016). "Single-electron cyclotron radiation". Physics Today. 69 (1): 70. Bibcode:2016PhT....69a..70M. doi:10.1063/pt.3.3060.
2. ^ Dogiel, V. A. (March 1992). "Gamma-ray astronomy". Contemporary Physics. 33 (2): 91–109. Bibcode:1992ConPh..33...91D. doi:10.1080/00107519208219534.
3. ^ Zheleznyakov, V. V. (January 1997). "Space plasma under extreme conditions". Radiophysics and Quantum Electronics. 40 (1–2): 3–15. Bibcode:1997R&QE...40....3Z. doi:10.1007/BF02677820.
4. ^ Longair, Malcolm S. (1994). High Energy Astrophysics: Volume 2, Stars, the Galaxy and the Interstellar Medium. Cambridge University Press. p. 232. ISBN 9780521435840.
5. ^ Hilditch, R. W. (2001). An Introduction to Close Binary Stars. Cambridge University Press. p. 327. ISBN 9780521798006.
6. ^ Cairns, R. A. (2012). Plasma Physics. Springer. p. SA7–PA8. ISBN 9789401096553.
7. ^ Hayakawa, S; Hokkyō, N; Terashima, Y; Tsuneto, T. (1958). Cyclotron Radiation from a Magnetized Plasma (PDF). 2nd Geneva Conference on Peaceful Uses of Atomic Energy.
Abraham–Lorentz force

In the physics of electromagnetism, the Abraham–Lorentz force (also Lorentz–Abraham force) is the recoil force on an accelerating charged particle caused by the particle emitting electromagnetic radiation. It is also called the radiation reaction force or the self force.

The formula predates the theory of special relativity and is not valid at velocities of the order of the speed of light. Its relativistic generalization is called the "Abraham–Lorentz–Dirac force". Both of these are in the domain of classical physics, not quantum physics, and therefore may not be valid at distances of roughly the Compton wavelength or below. There is, however, an analogue of the formula that is both fully quantum and relativistic, called the "Abraham–Lorentz–Dirac–Langevin equation".The force is proportional to the square of the object's charge, times the jerk (rate of change of acceleration) that it is experiencing. The force points in the direction of the jerk. For example, in a cyclotron, where the jerk points opposite to the velocity, the radiation reaction is directed opposite to the velocity of the particle, providing a braking action.

It was thought that the solution of the Abraham–Lorentz force problem predicts that signals from the future affect the present, thus challenging intuition of cause and effect ( retrocausality ). For example, there are pathological solutions using the Abraham–Lorentz–Dirac equation in which a particle accelerates in advance of the application of a force, so-called pre-acceleration solutions. One resolution of this problem was discussed by Yaghjian and is further discussed by Rohrlich and Medina.

Aneutronic fusion

Aneutronic fusion is any form of fusion power in which neutrons carry no more than 1% of the total released energy. The most-studied fusion reactions release up to 80% of their energy in neutrons. Successful aneutronic fusion would greatly reduce problems associated with neutron radiation such as ionizing damage, neutron activation and requirements for biological shielding, remote handling and safety.

Some proponents see a potential for dramatic cost reductions by converting energy directly to electricity. However, the conditions required to harness aneutronic fusion are much more extreme than those required for the conventional deuterium–tritium (D-T) nuclear fuel cycle.

Auroral kilometric radiation (AKR) is the intense radio radiation emitted in the acceleration zone (at a height of three times the radius of the Earth) of the polar lights. The radiation mainly comes from cyclotron radiation from electrons orbiting around the magnetic field lines of the Earth. The radiation has a frequency of between 50 and 500 kHz and a total power of between about 1 million and 10 million watts. The radiation is absorbed by the ionosphere and therefore can only be measured by satellites positioned at vast heights, such as the Fast Auroral Snapshot Explorer (FAST). According to the data of the Cluster mission, it is beamed out in the cosmos in a narrow plane tangent to the magnetic field at the source. The sound produced by playing AKR over an audio device has been described as "whistles", "chirps", and even "screams".

As some other planets emit cyclotron radiation too, AKR could be used to learn more about Jupiter, Saturn, Uranus and Neptune, and to detect extrasolar planets.

Bremsstrahlung

Bremsstrahlung (German pronunciation: [ˈbʁɛmsˌʃtʁaːlʊŋ] (listen)), from bremsen "to brake" and Strahlung "radiation"; i.e., "braking radiation" or "deceleration radiation", is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., a photon), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases.

Broadly speaking, bremsstrahlung or braking radiation is any radiation produced due to the deceleration (negative acceleration) of a charged particle, which includes synchrotron radiation (i.e. photon emission by a relativistic particle), cyclotron radiation (i.e. photon emission by a non-relativistic particle), and the emission of electrons and positrons during beta decay. However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter.

Bremsstrahlung emitted from plasma is sometimes referred to as free/free radiation. This refers to the fact that the radiation in this case is created by charged particles that are free; i.e., not part of an ion, atom or molecule, both before and after the deflection (acceleration) that caused the emission.

Cyclotron

A cyclotron is a type of particle accelerator invented by Ernest O. Lawrence in 1929-1930 at the University of California, Berkeley, and patented in 1932. A cyclotron accelerates charged particles outwards from the center along a spiral path. The particles are held to a spiral trajectory by a static magnetic field and accelerated by a rapidly varying (radio frequency) electric field. Lawrence was awarded the 1939 Nobel prize in physics for this invention.Cyclotrons were the most powerful particle accelerator technology until the 1950s when they were superseded by the synchrotron, and are still used to produce particle beams in physics and nuclear medicine. The largest single-magnet cyclotron was the 4.67 m (184 in) synchrocyclotron built between 1940 and 1946 by Lawrence at the University of California at Berkeley, which could accelerate protons to 730 million electron volts (MeV). The largest cyclotron is the 17.1 m (56 ft) multimagnet TRIUMF accelerator at the University of British Columbia in Vancouver, British Columbia which can produce 500 MeV protons.

Over 1200 cyclotrons are used in nuclear medicine worldwide for the production of radionuclides.

Cyclotron turnover

Cyclotron turnover is one of two phenomena due to which the power spectrum of synchrotron radiation decreases at very low frequencies. The other is synchrotron self-absorption. While the synchrotron self-absorption is determined from detailed balance, cyclotron turnover occurs when the assumptions of synchrotron radiation are violated. We recall that when a charged particle moves in a magnetic field its orbit is a helix, and its velocities can be divided into two independent components: uniform velocity parallel to the axis of the helix, and rotation about the axis. Synchrotron radiation requires that both velocities be ultra-relativistic, but if the velocity parallel to the axis is relativistic and the rotation is not, then the spectrum would simply be that of a Doppler shifted cyclotron radiation, and this behavior is called cyclotron turnover. In real systems there would be a competition between these two phenomena, so the only one that sets in at higher frequencies will be observed. An interesting feature about the cyclotron turnover is that it allows emission at frequencies lower that the cyclotron frequency, if the particle is moving away from the observer.

Electron rest mass

The electron rest mass (symbol: me) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about 9.109×10−31 kilograms or about 5.486×10−4 atomic mass units, equivalent to an energy of about 8.187×10−14 joules or about 0.5110 MeV.

Galactic Emission Mapping

The Galactic Emission Mapping survey (GEM) is an international project with the goal of making a precise map of the electromagnetic spectrum of our galaxy at low frequencies (radio and microwaves).

High-energy X-rays

High-energy X-rays or HEX-rays are very hard X-rays, with typical energies of 80–1000 keV (1 MeV), about one order of magnitude higher than conventional X-rays (and well into gamma-ray energies over 120 keV). They are produced at modern synchrotron radiation sources such as the beamline ID15 at the European Synchrotron Radiation Facility (ESRF). The main benefit is the deep penetration into matter which makes them a probe for thick samples in physics and materials science and permits an in-air sample environment and operation. Scattering angles are small and diffraction directed forward allows for simple detector setups.

Larmor formula

The Larmor formula is used to calculate the total power radiated by a non relativistic point charge as it accelerates or decelerates. This is used in the branch of physics known as electrodynamics and is not to be confused with the Larmor precession from classical nuclear magnetic resonance. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light.

When any charged particle (such as an electron, a proton, or an ion) accelerates, it radiates away energy in the form of electromagnetic waves. For velocities that are small relative to the speed of light, the total power radiated is given by the Larmor formula:

${\displaystyle P={2 \over 3}{\frac {q^{2}a^{2}}{4\pi \varepsilon _{0}c^{3}}}={\frac {q^{2}a^{2}}{6\pi \varepsilon _{0}c^{3}}}{\mbox{ (SI units)}}}$
${\displaystyle P={2 \over 3}{\frac {q^{2}a^{2}}{c^{3}}}{\mbox{ (cgs units)}}}$

where ${\displaystyle a}$ is the proper acceleration, ${\displaystyle q}$ is the charge, and ${\displaystyle c}$ is the speed of light. A relativistic generalization is given by the Liénard–Wiechert potentials.

In either unit system, the power radiated by a single electron can be expressed in terms of the classical electron radius and electron mass as:

${\displaystyle P={2 \over 3}{\frac {m_{e}r_{e}a^{2}}{c}}}$
Levitated dipole

A levitated dipole is a type of nuclear fusion reactor design using a superconducting torus which is magnetically levitated inside the reactor chamber. The name refers to the magnetic dipole that forms within the reaction chamber, similar to Earth's or Jupiter's magnetospheres. It is believed that such an apparatus could contain plasma more efficiently than other fusion reactor designs.The Levitated Dipole Experiment (LDX) was funded by the US Department of Energy's Office of Fusion Energy. The machine was run in a collaboration between MIT and Columbia University. Funding for the LDX was ended in November 2011 to concentrate resources on tokamak designs.

List of plasma physics articles

This is a list of plasma physics topics.

Magnetic sail

A magnetic sail or magsail is a proposed method of spacecraft propulsion which would use a static magnetic field to deflect charged particles radiated by the Sun as a plasma wind, and thus impart momentum to accelerate the spacecraft. A magnetic sail could also thrust directly against planetary and solar magnetospheres.

Physics World

Physics World is the membership magazine of the Institute of Physics, one of the largest physical societies in the world. It is an international monthly magazine covering all areas of physics, pure and applied, and is aimed at physicists in research, industry, physics outreach, and education worldwide.

Plasma diagnostics

Plasma diagnostics are a pool of methods, instruments, and experimental techniques used to measure properties of a plasma, such as plasma components' density, distribution function over energy (temperature), their spatial profiles and dynamics, which enable to derive plasma parameters.

Polar (star)

A Polar is a highly magnetic type of cataclysmic variable binary star system, originally known as an AM Herculis star after the prototype member AM Herculis. Like other cataclysmic variables (CVs), polars contain two stars: an accreting white dwarf (WD), and a low-mass donor star (usually a red dwarf) which is transferring mass to the WD as a result of the WD's gravitational pull, overflowing its Roche lobe. Polars are distinguished from other CVs by the presence of a very strong magnetic field in the WD. Typical magnetic field strengths of polar systems are 10 million to 80 million gauss (1000–8000 teslas). The WD in the polar AN Ursae Majoris has the strongest known magnetic field among cataclysmic variables, with a field strength of 230 million gauss (23 kT).

Spectral energy distribution

A spectral energy distribution (SED) is a plot of energy versus frequency or wavelength of light (not to be confused with a 'spectrum' of flux density vs frequency or wavelength). It is used in many branches of astronomy to characterize astronomical sources. For example, in radio astronomy they are used to show the emission from synchrotron radiation, free-free emission and other emission mechanisms. In infrared astronomy, SEDs can be used to classify young stellar objects.

Technosignature

Technosignature or technomarker is any measurable property or effect that provides scientific evidence of past or present technology.

Technosignatures are analogous to the biosignatures that signal the presence of life, whether or not intelligent. Some authors prefer to exclude radio transmissions from the definition, but such restrictive usage is not widespread.

Jill Tarter has proposed that the search for extraterrestrial intelligence (SETI) be renamed "the search for technosignatures".

Various types of technosignatures, such as radiation leakage from megascale astroengineering installations such as Dyson spheres, the light from an extraterrestrial ecumenopolis, or Shkadov thrusters with the power to alter the orbits of stars around the Galactic Center, may be detectable with hypertelescopes. Some examples of technosignatures are described in Paul Davies's 2010 book The Eerie Silence, although the terms "technosignature" and "technomarker" do not appear in the book.

X-ray source

X-ray sources abound around us. They include the following:

Natural X-ray sources:

Astrophysical X-ray source, as viewed in X-ray astronomy

X-ray background

Artificial X-ray sources

Brachytherapy

X-ray tube, a vacuum tube that produces X-rays when current flows through it

X-ray laser

X-ray generator, any of various devices using X-ray tubes, lasers, or radioisotopes

Synchrotron, which produces X-rays as synchrotron radiation

Cyclotron, which produces X-rays as cyclotron radiation

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