Electron cyclotron resonance (ECR) is a phenomenon observed in

plasma physics Plasma ()πλάσμα
, Henry George Liddell, R ...

accelerator physics 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 ...

. It happens when the frequency of incident radiation coincides with the natural frequency of rotation of electrons in magnetic fields. A free

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 no ...

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 A helix () is a shape like a corkscrew or spiral staircase. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis. Helices are important in biology, as the DNA molecule is formed as two intertwined helic ...

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

cycloid In geometry, a cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. A cycloid is a specific form of trochoid and is an example of a roulette, a curve generated by a curve rolling on another cu ...

. The

angular frequency In physics, angular frequency "''ω''" (also referred to by the terms angular speed, circular frequency, orbital frequency, radian frequency, and pulsatance) is a scalar measure of rotation rate. It refers to the angular displacement per unit tim ...

(ω = 2π ''f'' ) of this ''cyclotron'' motion for a given magnetic field strength ''B'' is given (in SI units) by :

\omega_\text = \frac

. where

e

is the elementary charge and

m

is the mass of the electron. For the commonly used

microwave Microwave is a form of electromagnetic radiation with wavelengths ranging from about one meter to one millimeter corresponding to frequencies between 300 MHz and 300 GHz respectively. Different sources define different frequency ra ...

frequency 2.45 GHz and the bare electron charge and mass, the resonance condition is met when ''B'' = 875 G = 0.0875 T. For particles of charge ''q'', electron rest mass ''m''_0,e moving at relativistic speeds ''v'', the formula needs to be adjusted according to the

special theory of relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...

to: :

\omega_\text = \frac

where :

\gamma = \frac

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 Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...

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 Diagnosis is the identification of the nature and cause of a certain phenomenon. Diagnosis is used in many different disciplines, with variations in the use of logic, analytics, and experience, to determine " cause and effect". In systems engin ...

of the radial electron temperature profile.

ECR ion sources

Since the early 1980s, following the award-winning pioneering work done by Dr. Richard Geller, Dr.

Claude Lyneis Claude may refer to: __NOTOC__ People and fictional characters * Claude (given name), a list of people and fictional characters * Claude (surname), a list of people * Claude Lorrain (c. 1600–1682), French landscape painter, draughtsman and etch ...

, and Dr. H. Postma; respectively from

French Atomic Energy Commission The French Alternative Energies and Atomic Energy Commission or CEA ( French: Commissariat à l'énergie atomique et aux énergies alternatives), is a French public government-funded research organisation in the areas of energy, defense and securit ...

, Lawrence Berkeley National Laboratory and the

Oak Ridge National Laboratory Oak Ridge National Laboratory (ORNL) is a U.S. 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 an ...

, 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, * advanced

semiconductor manufacturing Semiconductor device fabrication is the process used to manufacture semiconductor devices, typically integrated circuit (IC) chips such as modern computer processors, microcontrollers, and memory chips such as NAND flash and DRAM that are pres ...

, especially for high density DRAM memories, through

plasma etching 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 (in pulses) at a sample. The plasma source, known as etch spe ...

or other

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 ashing *Plasma cleaning *Plasma electr ...

technologies, *

electric propulsion Spacecraft electric propulsion (or just electric propulsion) is a type of spacecraft propulsion technique that uses electrostatic or electromagnetic fields to accelerate mass to high speed and thus generate thrust to modify the velocity of a sp ...

devices for spacecraft propulsion, where a broad range of devices (

HiPEP High Power Electric Propulsion (HiPEP) is a variation of ion thruster for use in nuclear electric propulsion applications.

In condensed matter physics

Within a solid the mass in the cyclotron frequency equation above is replaced with the effective mass tensor

m^*

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

Fermi surface In condensed matter physics, the Fermi surface is the surface in reciprocal space which separates occupied from unoccupied electron states at zero temperature. The shape of the Fermi surface is derived from the periodicity and symmetry of the crys ...

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

\begin
         \omega_\text &> \frac \\
  \hbar_\text &> k_B T \\
\end

where

\tau

is the carrier scattering lifetime,

k_B

Boltzmann's constant The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant ...

and

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.

In plasma physics

ECR ion sources

See also

References

Further reading