# Electron cyclotron resonance

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Electron cyclotron resonance is a phenomenon observed in plasma physics, condensed matter physics, and accelerator physics. An electron in a static and uniform magnetic field will move in a circle due to the Lorentz force. The circular motion may be superimposed with a uniform axial motion, resulting in a helix, or with a uniform motion perpendicular to the field (e.g., in the presence of an electrical or gravitational field) resulting in a cycloid. The angular frequency = 2πf ) of this cyclotron motion for a given magnetic field strength B is given (in SI units) [1] by

Condensed matter physics is the field of physics that deals with the macroscopic and microscopic physical properties of matter. In particular it is concerned with the "condensed" phases that appear whenever the number of constituents in a system is extremely large and the interactions between the constituents are strong. The most familiar examples of condensed phases are solids and liquids, which arise from the electromagnetic forces between atoms. Condensed matter physicists seek to understand the behavior of these phases by using physical laws. In particular, they include the laws of quantum mechanics, electromagnetism and statistical mechanics.

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.

The electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. As it is a fermion, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

## Contents

${\displaystyle \omega _{\text{ce}}={\frac {eB}{m_{\text{e}}}}}$.

where ${\displaystyle e}$ is the elementary charge and ${\displaystyle m}$ is the mass of the electron. For the commonly used microwave frequency 2.45 GHz and the bare electron charge and mass, the resonance condition is met when B = 875  G = 0.0875234740965  T.

The elementary charge, usually denoted by e or sometimes qe, is the electric charge carried by a single proton, or equivalently, the magnitude of the electric charge carried by a single electron, which has charge e. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called the elementary positive charge. This charge has a measured value of approximately 1.6021766208(98)×10−19 C (coulombs). When the 2019 redefinition of SI base units takes effect on 20 May 2019, its value will be exactly1.602176634×10−19 C by definition of the coulomb. In the centimetre–gram–second system of units (CGS), it is 4.80320425(10)×10−10 statcoulombs.

Microwaves are a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter; with frequencies between 300 MHz (1 m) and 300 GHz (1 mm). Different sources define different frequency ranges as microwaves; the above broad definition includes both UHF and EHF bands. A more common definition in radio engineering is the range between 1 and 100 GHz. In all cases, microwaves include the entire SHF band at minimum. Frequencies in the microwave range are often referred to by their IEEE radar band designations: S, C, X, Ku, K, or Ka band, or by similar NATO or EU designations.

The industrial, scientific and medical (ISM) radio bands are radio bands reserved internationally for the use of radio frequency (RF) energy for industrial, scientific and medical purposes other than telecommunications. Examples of applications in these bands include radio-frequency process heating, microwave ovens, and medical diathermy machines. The powerful emissions of these devices can create electromagnetic interference and disrupt radio communication using the same frequency, so these devices were limited to certain bands of frequencies. In general, communications equipment operating in these bands must tolerate any interference generated by ISM applications, and users have no regulatory protection from ISM device operation.

For particles of charge q, electron rest mass m0,e moving at relativistic speeds v, the formula needs to be adjusted according to the special theory of relativity to:

${\displaystyle \omega _{\text{ce}}={\frac {eB}{\gamma m_{0,{\text{e}}}}}}$

where

${\displaystyle \gamma ={\frac {1}{\sqrt {1-\left({\frac {v}{c}}\right)^{2}}}}}$.

## In plasma physics

An ionized plasma may be efficiently produced or heated by superimposing a static magnetic field and a high-frequency electromagnetic field at the electron cyclotron resonance frequency. In the toroidal magnetic fields used in magnetic fusion energy research, the magnetic field decreases with the major radius, so the location of the power deposition can be controlled within about a centimeter. Furthermore, the heating power can be rapidly modulated and is deposited directly into the electrons. These properties make electron cyclotron heating a very valuable research tool for energy transport studies. In addition to heating, electron cyclotron waves can be used to drive current. The inverse process of electron cyclotron emission can be used as a diagnostic of the radial electron temperature profile.

Plasma is one of the four fundamental states of matter, and was first described by chemist Irving Langmuir in the 1920s. Plasma can be artificially generated by heating or subjecting a neutral gas to a strong electromagnetic field to the point where an ionized gaseous substance becomes increasingly electrically conductive, and long-range electromagnetic fields dominate the behaviour of the matter.

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.

An electromagnetic field is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature.

 Example of cyclotron resonance between a charged particle and linearly polarized electric field (shown in green). The position vs. time (top panel) is shown as a red trace and the velocity vs. time (bottom panel) is shown as a blue trace. The background magnetic field is directed out towards the observer. Note that the circularly polarized example below assumes there is no Lorentz force due to the wave magnetic field acting on the charged particle. This is equivalent to saying that the charged particle's velocity orthogonal to the wave magnetic field is zero. Example of cyclotron resonance between a charged particle and circularly polarized electric field (shown in green). The position vs. time (top panel) is shown as a red trace and the velocity vs. time (bottom panel) is shown as a blue trace. The background magnetic field is directed out towards the observer. Note that the circularly polarized example below assumes there is no Lorentz force due to the wave magnetic field acting on the charged particle. This is equivalent to saying that the charged particle's velocity orthogonal to the wave magnetic field is zero.

## ECR ion sources

Since the early 1980s, following the award-winning pioneering work done by Dr. Richard Geller, [2] Dr. Claude Lyneis, and Dr. H. Postma; [3] respectively from French Atomic Energy Commission, Lawrence Berkeley National Laboratory and the Oak Ridge National Laboratory, the use of electron cyclotron resonance for efficient plasma generation, especially to obtain large numbers of multiply charged ions, has acquired a unique importance in various technological fields. Many diverse activities depend on electron cyclotron resonance technology, including

Richard Geller was an experimental nuclear and plasma physicist. He was born in Vienna and died in Grenoble.

Lawrence Berkeley National Laboratory (LBNL), commonly referred to as Berkeley Lab, is a United States national laboratory that conducts scientific research on behalf of the United States Department of Energy (DOE). It is located in the Berkeley Hills near Berkeley, California, overlooking the main campus of the University of California, Berkeley. It is managed and operated by the University of California.

Oak Ridge National Laboratory (ORNL) is an American multiprogram science and technology national laboratory sponsored by the U.S. Department of Energy (DOE) and administered, managed, and operated by UT–Battelle as a federally funded research and development center (FFRDC) under a contract with the DOE. ORNL is the largest science and energy national laboratory in the Department of Energy system by size and by annual budget. ORNL is located in Oak Ridge, Tennessee, near Knoxville. ORNL's scientific programs focus on materials, neutron science, energy, high-performance computing, systems biology and national security.

In the field of medical procedures, proton therapy, or proton radiotherapy, is a type of particle therapy that uses a beam of protons to irradiate diseased tissue, most often in the treatment of cancer. The chief advantage of proton therapy over other types of external beam radiotherapy is that as a charged particle the dose is deposited over a narrow range of depth, and there is minimal entry, exit, or scattered radiation dose.

Plasma etching is a form of plasma processing used to fabricate integrated circuits. It involves a high-speed stream of glow discharge (plasma) of an appropriate gas mixture being shot at a sample. The plasma source, known as etch species, can be either charged (ions) or neutral. During the process, the plasma generates volatile etch products at room temperature from the chemical reactions between the elements of the material etched and the reactive species generated by the plasma. Eventually the atoms of the shot element embed themselves at or just below the surface of the target, thus modifying the physical properties of the target.

Plasma processing is a plasma-based material processing technology that aims at modifying the chemical and physical properties of a surface.

The ECR ion source makes use of the electron cyclotron resonance to ionize a plasma. Microwaves are injected into a volume at the frequency corresponding to the electron cyclotron resonance, defined by the magnetic field applied to a region inside the volume. The volume contains a low pressure gas. The alternating electric field of the microwaves is set to be synchronous with the gyration period of the free electrons of the gas, and increases their perpendicular kinetic energy. Subsequently, when the energized free electrons collide with the gas in the volume they can cause ionization if their kinetic energy is larger than the ionization energy of the atoms or molecules. The ions produced correspond to the gas type used, which may be pure, a compound, or vapor of a solid or liquid material.

ECR ion sources are able to produce singly charged ions with high intensities (e.g. H + and D + ions of more than 100 mA (electrical) in DC mode [5] using a 2.45 GHz ECR ion source).

For multiply charged ions, the ECR ion source has the advantages that it is able to confine the ions for long enough for multiple collisions and multiple ionization to take place, and the low gas pressure in the source avoids recombination. The VENUS ECR ion source at Lawrence Berkeley National Laboratory has produced in intensity of 0.25 mA (electrical) of Bi 29+. [6]

Some important industrial fields would not exist without the use of this fundamental technology, which makes electron cyclotron resonance ion and plasma sources one of the enabling technologies of today's world.

## In condensed matter physics

Within a solid the mass in the cyclotron frequency equation above is replaced with the effective mass tensor ${\displaystyle m^{*}}$. Cyclotron resonance is therefore a useful technique to measure effective mass and Fermi surface cross-section in solids. In a sufficiently high magnetic field at low temperature in a relatively pure material

{\displaystyle {\begin{aligned}\omega _{\text{ce}}&>{\frac {1}{\tau }}\\\hbar {\omega }_{\text{ce}}&>k_{B}T\\\end{aligned}}}

where ${\displaystyle \tau }$ is the carrier scattering lifetime, ${\displaystyle k_{B}}$ is Boltzmann's constant and ${\displaystyle T}$ is temperature. When these conditions are satisfied, an electron will complete its cyclotron orbit without engaging in a collision, at which point it is said to be in a well-defined Landau level.

## Related Research Articles

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 electric field. Lawrence was awarded the 1939 Nobel prize in physics for this invention.

Ionization or ionisation, is the process by which an atom or a molecule acquires a negative or positive charge by gaining or losing electrons, often in conjunction with other chemical changes. The resulting electrically charged atom or molecule is called an ion. Ionization can result from the loss of an electron after collisions with subatomic particles, collisions with other atoms, molecules and ions, or through the interaction with electromagnetic radiation. Heterolytic bond cleavage and heterolytic substitution reactions can result in the formation of ion pairs. Ionization can occur through radioactive decay by the internal conversion process, in which an excited nucleus transfers its energy to one of the inner-shell electrons causing it to be ejected.

An ion source is a device that creates atomic and molecular ions. Ion sources are used to form ions for mass spectrometers, optical emission spectrometers, particle accelerators, ion implanters and ion engines.

The multipactor effect is a phenomenon in radio-frequency (RF) amplifier vacuum tubes and waveguides, where, under certain conditions, secondary electron emission in resonance with an alternating electric field leads to exponential electron multiplication, possibly damaging and even destroying the RF device.

A Penning trap is a device for the storage of charged particles using a homogeneous axial magnetic field and an inhomogeneous quadrupole electric field. This kind of trap is particularly well suited to precision measurements of properties of ions and stable subatomic particles. Geonium atoms have been created and studied this way, to measure the electron magnetic moment. Recently these traps have been used in the physical realization of quantum computation and quantum information processing by trapping qubits. Penning traps are used in many laboratories worldwide, including CERN, to store antimatter like antiprotons.

A synchrocyclotron is a special type of cyclotron, patented by Edwin McMillan, in which the frequency of the driving RF electric field is varied to compensate for relativistic effects as the particles' velocity begins to approach the speed of light. This is in contrast to the classical cyclotron, where this frequency is constant.

A polaron is a quasiparticle used in condensed matter physics to understand the interactions between electrons and atoms in a solid material. The polaron concept was first proposed by Lev Landau in 1933 to describe an electron moving in a dielectric crystal where the atoms move from their equilibrium positions to effectively screen the charge of an electron, known as a phonon cloud. This lowers the electron mobility and increases the electron's effective mass.

An inductively coupled plasma (ICP) or transformer coupled plasma (TCP) is a type of plasma source in which the energy is supplied by electric currents which are produced by electromagnetic induction, that is, by time-varying magnetic fields.

Plasma oscillations, also known as Langmuir waves, are rapid oscillations of the electron density in conducting media such as plasmas or metals in the ultraviolet region. The oscillations can be described as an instability in the dielectric function of a free electron gas. The frequency only depends weakly on the wavelength of the oscillation. The quasiparticle resulting from the quantization of these oscillations is the plasmon.

In plasma physics, waves in plasmas are an interconnected set of particles and fields which propagate in a periodically repeating fashion. A plasma is a quasineutral, electrically conductive fluid. In the simplest case, it is composed of electrons and a single species of positive ions, but it may also contain multiple ion species including negative ions as well as neutral particles. Due to its electrical conductivity, a plasma couples to electric and magnetic fields. This complex of particles and fields supports a wide variety of wave phenomena.

In plasma physics, an upper hybrid oscillation is a mode of oscillation of a magnetized plasma. It consists of a longitudinal motion of the electrons perpendicular to the magnetic field with the dispersion relation

In plasma physics, an electrostatic ion cyclotron wave is a longitudinal oscillation of the ions in a magnetized plasma, propagating nearly perpendicular to the magnetic field. The angle between the direction of propagation and the direction perpendicular to the magnetic field must be greater than about the square root of the mass ratio,

Fourier-transform ion cyclotron resonance mass spectrometry is a type of mass analyzer for determining the mass-to-charge ratio (m/z) of ions based on the cyclotron frequency of the ions in a fixed magnetic field. The ions are trapped in a Penning trap, where they are excited to a larger cyclotron radius by an oscillating electric field orthogonal to the magnetic field. After the excitation field is removed, the ions are rotating at their cyclotron frequency in phase. These ions induce a charge on a pair of electrodes as the packets of ions pass close to them. The resulting signal is called a free induction decay (FID), transient or interferogram that consists of a superposition of sine waves. The useful signal is extracted from this data by performing a Fourier transform to give a mass spectrum.

In plasma physics, an electromagnetic electron wave is a wave in a plasma which has a magnetic field component and in which primarily the electrons oscillate.

Plasma parameters define various characteristics of a plasma, an electrically conductive collection of charged particles that responds collectively to electromagnetic forces. Plasma typically takes the form of neutral gas-like clouds or charged ion beams, but may also include dust and grains. The behaviour of such particle systems can be studied statistically.

The gyroradius is the radius of the circular motion of a charged particle in the presence of a uniform magnetic field. In SI units, the gyroradius is given by

Cyclotron resonance describes the interaction of external forces with charged particles experiencing a magnetic field, thus already moving on a circular path. It is named after the cyclotron, a cyclic particle accelerator that utilizes an oscillating electric field tuned to this resonance to add kinetic energy to charged particles.

In plasma physics, the Hasegawa–Mima equation, named after Akira Hasegawa and Kunioki Mima, is an equation that describes a certain regime of plasma, where the time scales are very fast, and the distance scale in the direction of the magnetic field is long. In particular the equation is useful for describing turbulence in some tokamaks. The equation was introduced in Hasegawa and Mima's paper submitted in 1977 to Physics of Fluids, where they compared it to the results of the ATC tokamak.

Ion cyclotron resonance is a phenomenon related to the movement of ions in a magnetic field. It is used for accelerating ions in a cyclotron, and for measuring the masses of an ionized analyte in mass spectrometry, particularly with Fourier transform ion cyclotron resonance mass spectrometers. It can also be used to follow the kinetics of chemical reactions in a dilute gas mixture, provided these involve charged species.

A non-neutral plasma is a plasma for which the total charge is sufficiently different from zero, so that the electric field created by the un-neutralized charge plays an important or even dominant role in the plasma dynamics. The simplest non-neutral plasmas are plasmas consisting of a single charge species. Examples of single species non-neutral plasmas that have been created in laboratory experiments are plasmas consisting entirely of electrons, pure ion plasmas, positron plasmas, and antiproton plasmas.

## References

1. In SI units, the elementary charge e has the value 1.602×10−19 coulombs, the mass of the electron me has the value 9.109×10−31 kilograms, the magnetic field B is measured in teslas, and the angular frequency ω is measured in radians per second.
2. R. Geller, Peroc. 1st Int. Con. Ion Source, Saclay, p. 537, 1969
3. H. Postma (1970). "Multiply charged heavy ions produced by energetic plasmas". Physics Letters A. 31 (4): 196. Bibcode:1970PhLA...31..196P. doi:10.1016/0375-9601(70)90921-7.
4. Handbook of Ion Source, B. Wolf, ISBN   0-8493-2502-1, p136-146
5. R. Gobin et al., Saclay High Intensity Light Ion Source Status The Euro. Particle Accelerator Conf. 2002, Paris, France, June 2002, p1712
6. VENUS reveals the future of heavy-ion sources CERN Courier, 6 May 2005