Electron cyclotron resonance - AbsoluteAstronomy.com

Electron cyclotron resonance is a phenomenon observed both in plasma physics and condensed matter physics

Condensed matter physics

Condensed matter physics deals with the physical properties of condensed phases of matter. These properties appear when a number of atoms at the supramolecular and macromolecular scale interact strongly and adhere to each other or are otherwise highly concentrated in a system. The most familiar...

. An electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

in a static and uniform magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

will move in a circle due to the Lorentz force

Lorentz force

In physics, the Lorentz force is the force on a point charge due to electromagnetic fields. It is given by the following equation in terms of the electric and magnetic fields:...

. The circular motion may be superimposed with a uniform axial motion, resulting in a helix

Helix

A helix is a type of smooth space curve, i.e. a curve in three-dimensional space. It has the property that the tangent line at any point makes a constant angle with a fixed line called the axis. Examples of helixes are coil springs and the handrails of spiral staircases. A "filled-in" helix – for...

, or with a uniform motion perpendicular to the field, e.g., in the presence of an electrical or gravitational field, resulting in a cycloid

Cycloid

A cycloid is the curve traced by a point on the rim of a circular wheel as the wheel rolls along a straight line.It is an example of a roulette, a curve generated by a curve rolling on another curve....

. The angular frequency

Angular frequency

In physics, angular frequency ω is a scalar measure of rotation rate. Angular frequency is the magnitude of the vector quantity angular velocity...

(ω = 2πf

Frequency

Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the frequency...

) of this cyclotron motion for a given magnetic field strength B is given (in SI

Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units) by

.

where

is the elementary charge

Elementary charge

The elementary charge, usually denoted as e, is the electric charge carried by a single proton, or equivalently, the absolute value of the electric charge carried by a single electron. This elementary charge is a fundamental physical constant. To avoid confusion over its sign, e is sometimes called...

and

is the mass of the electron. For the commonly used microwave

Microwave

Microwaves, a subset of radio waves, have wavelengths ranging from as long as one meter to as short as one millimeter, or equivalently, with frequencies between 300 MHz and 300 GHz. This broad definition includes both UHF and EHF , and various sources use different boundaries...

frequency 2.45 GHz and the bare electron charge and mass, the resonance condition is met when B = 875 G

Gauss (unit)

The gauss, abbreviated as G, is the cgs unit of measurement of a magnetic field B , named after the German mathematician and physicist Carl Friedrich Gauss. One gauss is defined as one maxwell per square centimeter; it equals 1 tesla...

= 0.0875 T

Tesla (unit)

The tesla is the SI derived unit of magnetic field B . One tesla is equal to one weber per square meter, and it was defined in 1960 in honour of the inventor, physicist, and electrical engineer Nikola Tesla...

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

where

In plasma physics

An ionized plasma

Plasma (physics)

In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

may be efficiently produced or heated by superimposing a static magnetic field

Magnetic field

and a high-frequency electromagnetic field

Electromagnetic field

An electromagnetic field is a physical field produced by moving 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...

at the electron cyclotron resonance

Resonance

In physics, resonance is the tendency of a system to oscillate at a greater amplitude at some frequencies than at others. These are known as the system's resonant frequencies...

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

Cyclotron radiation

Cyclotron radiation is electromagnetic radiation emitted by moving charged particles deflected by a magnetic field. 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...

can be used as a diagnostic

Plasma diagnostics

Plasma diagnostics are experimental techniques used to measure properties of a plasma such as temperature and density.-Langmuir probe:Measurements with electric probes, called Langmuir probes, are the oldest and most often used procedures for low-temperature plasmas...

of the radial electron temperature profile.

ECR ion sources

Since the early 1980s, following the award-winning

Tom W. Bonner Prize

The Tom W. Bonner Prize in Nuclear Physics is an annual prize awarded by the American Physical Society's Division of Nuclear Physics. Established in 1964, and currently consisting of $7,500 and a certificate, the Bonner Prize was founded in memory of physicist Tom W. Bonner...

pioneering work done by Dr. Richard Geller, Dr. Claude Lyneis, and Dr. H. Postma; respectively from French Atomic Energy Commission

Commissariat à l'Énergie Atomique

The Commissariat à l'énergie atomique et aux énergies alternatives or CEA, is a French “public establishment related to industrial and commercial activities” whose mission is to develop all applications of nuclear power, both civilian and military...

, Lawrence Berkeley National Laboratory

Lawrence Berkeley National Laboratory

The Lawrence Berkeley National Laboratory , is a U.S. Department of Energy national laboratory conducting unclassified scientific research. It is located on the grounds of the University of California, Berkeley, in the Berkeley Hills above the central campus...

and the Oak Ridge National Laboratory

Oak Ridge National Laboratory

Oak Ridge National Laboratory is a multiprogram science and technology national laboratory managed for the United States Department of Energy by UT-Battelle. ORNL is the DOE's largest science and energy laboratory. ORNL is located in Oak Ridge, Tennessee, near Knoxville...

, 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

advanced cancer treatment, where ECR ion sources are crucial for proton therapy
Proton therapy
Proton therapy is a type of particle therapy which uses a beam of protons to irradiate diseased tissue, most often in the treatment of cancer. The chief advantage of proton therapy is the ability to more precisely localize the radiation dosage when compared with other types of external beam...

,
advanced semiconductor manufacturing
Semiconductor fabrication
Semiconductor device fabrication is the process used to create the integrated circuits that are present in everyday electrical and electronic devices. It is a multiple-step sequence of photolithographic and chemical processing steps during which electronic circuits are gradually created on a wafer...

, especially for high density DRAM
Dram
Dram or DRAM may refer to:As a unit of measure:* Dram , an imperial unit of mass and volume* Armenian dram, a monetary unit* Dirham, a unit of currency in several Arab nationsOther uses:...

memories, through plasma etching
Plasma etching
Plasma etching is a form of plasma processing used to fabricate integrated circuits. It involves a high-speed stream of glow discharge of an appropriate gas mixture being shot at a sample. The plasma source, known as etch species, can be either charged or neutral...

or other plasma processing
Plasma processing
Plasma processing is a plasma-based material processing technology that aims at modifying the chemical and physical properties of a surface.Plasma processing techniques include:*Plasma activation*Plasma etching*Plasma modification*Plasma functionalization...

technologies,
electric propulsion devices for spacecraft propulsion
Spacecraft propulsion
Spacecraft propulsion is any method used to accelerate spacecraft and artificial satellites. There are many different methods. Each method has drawbacks and advantages, and spacecraft propulsion is an active area of research. However, most spacecraft today are propelled by forcing a gas from the...

, where a broad range of devices (HiPEP, some ion thruster
Electrostatic ion thruster
An electrostatic ion thruster is a design for ion thrusters . These designs use high voltage electrodes in order to accelerate ions with electrostatic forces.-History:...

s, or electrodeless plasma thruster
Electrodeless plasma thruster
The electrodeless plasma thruster is a spacecraft propulsion engine. It was created by Mr. Gregory Emsellem based on technology developed by French Atomic Energy Commission scientist Dr Richard Geller and Dr...

s),
for particle accelerator
Particle accelerator
A particle accelerator is a device that uses electromagnetic fields to propel charged particles to high speeds and to contain them in well-defined beams. An ordinary CRT television set is a simple form of accelerator. There are two basic types: electrostatic and oscillating field accelerators.In...

s, on-line mass separation and radioactive ion charge breeding,
and, as a more mundane example, painting of plastic bumpers for cars.

The ECR ion source makes use of the electron cyclotron resonance to heat a plasma. Microwaves are injected into a volume, at the frequency corresponding to the electron cyclotron resonance defined by a magnetic field applied to a region inside the volume. The volume contains a low pressure gas. The microwaves heat free electrons in the gas which in turn collide with the atoms or molecules of the gas in the volume and cause ionization.
The ions produced correspond to the gas type used. The gas may be pure, a compound gas, or can be a vapour of a solid or liquid material.

ECR ion sources are able to produce singly charged ions with high intensities (e.g. H

Hydrogen

Hydrogen is the chemical element with atomic number 1. It is represented by the symbol H. With an average atomic weight of , hydrogen is the lightest and most abundant chemical element, constituting roughly 75% of the Universe's chemical elemental mass. Stars in the main sequence are mainly...

⁺ and D

Deuterium

Deuterium, also called heavy hydrogen, is one of two stable isotopes of hydrogen. It has a natural abundance in Earth's oceans of about one atom in of hydrogen . Deuterium accounts for approximately 0.0156% of all naturally occurring hydrogen in Earth's oceans, while the most common isotope ...

⁺ ions of more than 100 mA (electrical) in DC mode using a 2.45 GHz ECR ion source).

For multiply charged ions, the ECR ion source has the advantage that it is able to confine the ions for long enough for multiple collisions to take place (leading to multiple ionization) and that the low gas pressure in the source avoids recombination. The VENUS ECR ion source at Lawrence Berkeley National Laboratory

Lawrence Berkeley National Laboratory

has produced in intensity of 0.25 mA (electrical) of Bi

Bismuth

Bismuth is a chemical element with symbol Bi and atomic number 83. Bismuth, a trivalent poor metal, chemically resembles arsenic and antimony. Elemental bismuth may occur naturally uncombined, although its sulfide and oxide form important commercial ores. The free element is 86% as dense as lead...

²⁹⁺.

Some of these industrial fields would not even 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

. Cyclotron resonance is therefore a useful technique to measure effective mass and Fermi surface

Fermi surface

In condensed matter physics, the Fermi surface is an abstract boundary useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals, and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline...

cross-section in solids. In a sufficiently high magnetic field at low temperature in a relatively pure material

where

is the carrier scattering lifetime,

is Boltzmann's constant and

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.

In plasma physics

ECR ion sources

In condensed matter physics

See also