Electron cyclotron resonance

Electron cyclotron resonance (ECR) is a phenomenon observed in plasma physics, condensed matter physics, and accelerator physics. It happens when the frequency of incident radiation coincides with the natural frequency of rotation of electrons in magnetic fields. A free 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 (ω = 2πf ) of this cyclotron motion for a given magnetic field strength B is given (in SI units)^[1] by

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

where $e$ is the elementary charge and $m$ 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 = 0.0875 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 to:

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

where

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

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How a Microwave Oven Works EngineerGuy Series #4 This microwave oven is a truly remarkable feat of engineering. The rapid heating that makes microwaves popular is made possible by power provided from this vacuum tube Now, if you picture a vacuum tube at all it’s likely in a radio like this. Inevitably, tiny transistors and microchips replaced clunky vacuum tubes, but it's too soon to relegate them to the museum. Microchips can’t easily replace tubes for producing power. For example, in heating food. Now, a microwave contains three main components A vacuum tube called a magnetron it generates the energy that heats food. A waveguide hidden in the wall to direct that energy to the food and a chamber to hold the food and safely contain the microwave radiation. In principle, a microwave oven heats no differently than any other type of heat transfer. At a molecular level heat is a transfer of energy that results in increased motion of the molecules in a substance. Since we aren't quantum-sized, we observe this increase in motion as a rise in temperature. In a traditional oven or stove we heat food by placing a pan on a burner or in the oven where the walls radiate heat, which cooks the outside of the food. The insides cook when heat transfers from the surface of the food to its interior. In contrast, energy from the magnetron penetrates into the food, which means the whole mass of the food can be cooked simultaneously. How does it do this? Well, our food is filled with water, which is positively charged at one end, and negative at the other. To give these molecules more energy, we expose it to electromagnetic waves that emanate from the tube. By definition, the waves have electrical and magnetic fields that change direction rapidly. For this oven, the direction of the fields change two point four five billion times per second. Water will try to align with the radiation’s electric field. The changing field rocks the water molecules back and forth rapidly and molecular friction from this creates heat as the motion disrupts the hydrogen bonds between neighboring water molecules. Now, you can get an idea of the wavelength of the energy emitted from the magnetron using cheese. Now, you can see on here sections where the cheese has completely melted, and other sections where it’s completely unheated. The oven’s metal walls only reflect waves of a length that fits inside the oven. This standing wave causes hot and cold spots inside the oven. The three-dimensional pattern of waves is difficult to predict, but the principle can be seen by looking at the waves in a single dimension. The peaks and valleys in the wave represent the greatest energy of the wave, while the nodes here correspond to the "cold" spots inside the chamber. If I measure the distance between melted cheese spots I find about 2 1/2 inches. That would be half the wavelength the distance between nodes and is pretty close to the actual wavelength of microwave radiation used. Using that wavelength I can estimate the microwave radiation's frequency. The frequency is related to the wavelength by the speed of light. I get an answer that only has a 4 or 5 percent error. Not bad for this primitive measurement. Now, the real engineering in the microwave oven lies in creating the magnetron that generates high powered radio waves. It's truly an amazing and revolutionary device. The vacuum tube is inside here. These are cooling fins thin pieces of metal that dissipate the heat as the magnetron operates. The key parts are these two magnets and the vacuum tube. Now I have another one so you can see the inside. You apply a large voltage across both the inner filament and the circular cooper outside. This voltage “boils” electrons off the center filament and they fly toward the circular copper section. The filament is made from tungsten and thorium. Tungsten because it can withstand high temperatures and thorium because it’s a good source of electrons. The magnets bend these electrons so they swing back toward the center filament. We adjust the magnetic strength so that the now orbiting electrons just brush past the opening of these cavities. Like blowing over a half filled pop bottle to make it whistle, this creates an oscillating wave - the microwave radiation that heats food. It’s simply astonishing that these cavities can be made with high precision, low cost, and incredibly high reliability. I’m Bill Hammack, the EngineerGuy. This video is based on a chapter in the book Eight Amazing Engineering Stories. The chapter features more information about this subject. Learn more about the book at the address below.

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.

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

advanced cancer treatment, where ECR ion sources are crucial for proton therapy,
advanced semiconductor manufacturing, especially for high density DRAM memories, through plasma etching or other plasma processing technologies,
electric propulsion devices for spacecraft propulsion, where a broad range of devices (HiPEP, some ion thrusters, or electrodeless plasma thrusters),
for particle accelerators, on-line mass separation and radioactive ion charge breeding,^[4]
and, as a more mundane example, painting of plastic bumpers for cars.

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 Bi²⁹⁺.^[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 $m^{*}$ . 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

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

where $\tau$ is the carrier scattering lifetime, $k_{B}$ is Boltzmann's 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.

References

^ In SI units, the elementary charge e has the value 1.602×10⁻¹⁹ coulombs, the mass of the electron m_e 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.
^ R. Geller, Peroc. 1st Int. Con. Ion Source, Saclay, p. 537, 1969
^ 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.
^ Handbook of Ion Source, B. Wolf, ISBN 0-8493-2502-1, pp. 136–146
^ R. Gobin et al., Saclay High Intensity Light Ion Source Status The Euro. Particle Accelerator Conf. 2002, Paris, France, June 2002, p. 1712
^ VENUS reveals the future of heavy-ion sources CERN Courier, 6 May 2005

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