Undulator

Last updated
Working of the undulator. 1: magnets, 2: electron beam entering from the upper left, 3: synchrotron radiation exiting to the lower right Undulator.png
Working of the undulator. 1: magnets, 2: electron beam entering from the upper left, 3: synchrotron radiation exiting to the lower right

An undulator is an insertion device from high-energy physics and usually part of a larger installation, a synchrotron storage ring, or it may be a component of a free electron laser. It consists of a periodic structure of dipole magnets. These can be permanent magnets or superconducting magnets. The static magnetic field alternates along the length of the undulator with a wavelength . Electrons traversing the periodic magnet structure are forced to undergo oscillations and thus to radiate energy. The radiation produced in an undulator is very intense and concentrated in narrow energy bands in the spectrum. It is also collimated on the orbit plane of the electrons. This radiation is guided through beamlines for experiments in various scientific areas.

Contents

The undulator strength parameter is:

,

where e is the electron charge, B is the magnetic field, is the spatial period of the undulator magnets, is the electron rest mass, and c is the speed of light.

This parameter characterizes the nature of the electron motion. For the oscillation amplitude of the motion is small and the radiation displays interference patterns which lead to narrow energy bands. If the oscillation amplitude is bigger and the radiation contributions from each field period sum up independently, leading to a broad energy spectrum. In this regime of fields the device is no longer called an undulator; it is called a wiggler.

The key difference between undulator and wiggler is coherence. In the case of an undulator, the emitted radiation is coherent with a wavelength determined by the period length and the beam energy, [1] while in wiggler the electrons are not coherent.

The usual description of the undulator is relativistic but classical.[ citation needed ] This means that although a precise calculation is tedious, the undulator can be seen as a black box, where only functions inside the device affect how an input is converted to an output; an electron enters the box and an electromagnetic pulse exits through a small exit slit. The slit should be small enough such that only the main cone passes, and the side lobes of the wavelength spectra can be ignored.

Undulators can provide several orders of magnitude higher flux than a simple bending magnet and as such are in high demand at synchrotron radiation facilities. For an undulator with N periods, the brightness can be up to more than a bending magnet. The first factor of N occurs because the intensity is enhanced up to a factor of N at harmonic wavelengths due to the constructive interference of the fields emitted during the N radiation periods. The usual pulse is a sine with some envelope. The second factor of N comes from the reduction of the emission angle associated with these harmonics, which is reduced as 1/N. When the electrons come with half the period, they interfere destructively, the undulator stays dark. The same is true, if they come as a bead chain.

The polarization of the emitted radiation can be controlled by using permanent magnets to induce different periodic electron trajectories through the undulator. If the oscillations are confined to a plane the radiation will be linearly polarized. If the oscillation trajectory is helical, the radiation will be circularly polarized, with the handedness determined by the helix.

If the electrons follow the Poisson distribution a partial interference leads to a linear increase in intensity. In the free electron laser [2] the intensity increases exponentially with the number of electrons.

An undulator's figure of merit is spectral radiance.

History

The Russian physicist Vitaly Ginzburg showed theoretically that undulators could be built in a 1947 paper. [3] Julian Schwinger published a useful paper in 1949 [4] that reduced the necessary calculations to Bessel functions, for which there were tables. This was significant for solving the design equations as digital computers were not available to most academics at that time.

Hans Motz and his coworkers at Stanford University demonstrated the first undulator in 1952. [5] [6] It produced the first manmade coherent infrared radiation. The design could produce a total frequency range from visible light down to millimeter waves.

Related Research Articles

<span class="mw-page-title-main">Diffraction</span> Phenomenon of the motion of waves

Diffraction is the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a secondary source of the propagating wave. Italian scientist Francesco Maria Grimaldi coined the word diffraction and was the first to record accurate observations of the phenomenon in 1660.

<span class="mw-page-title-main">Wave interference</span> Phenomenon resulting from the superposition of two waves

In physics, interference is a phenomenon in which two coherent waves are combined by adding their intensities or displacements with due consideration for their phase difference. The resultant wave may have greater intensity or lower amplitude if the two waves are in phase or out of phase, respectively. Interference effects can be observed with all types of waves, for example, light, radio, acoustic, surface water waves, gravity waves, or matter waves as well as in loudspeakers as electrical waves.

<span class="mw-page-title-main">Wavelength</span> Distance over which a waves shape repeats

In physics and mathematics, wavelength or spatial period of a wave or periodic function is the distance over which the wave's shape repeats. In other words, it is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, troughs, or zero crossings. Wavelength is a characteristic of both traveling waves and standing waves, as well as other spatial wave patterns. The inverse of the wavelength is called the spatial frequency. Wavelength is commonly designated by the Greek letter lambda (λ). The term "wavelength" is also sometimes applied to modulated waves, and to the sinusoidal envelopes of modulated waves or waves formed by interference of several sinusoids.

Brightness temperature or radiance temperature is a measure of the intensity of electromagnetic energy coming from a source. In particular, it is the temperature at which a black body would have to be in order to duplicate the observed intensity of a grey body object at a frequency . This concept is used in radio astronomy, planetary science, materials science and climatology.

<span class="mw-page-title-main">X-ray photoelectron spectroscopy</span> Spectroscopic technique

X-ray photoelectron spectroscopy (XPS) is a surface-sensitive quantitative spectroscopic technique that measures the very topmost 200 atoms, 0.01 um, 10 nm of any surface. It belongs to the family of photoemission spectroscopies in which electron population spectra are obtained by irradiating a material with a beam of X-rays. XPS is based on the photoelectric effect that can identify the elements that exist within a material or are covering its surface, as well as their chemical state, and the overall electronic structure and density of the electronic states in the material. XPS is a powerful measurement technique because it not only shows what elements are present, but also what other elements they are bonded to. The technique can be used in line profiling of the elemental composition across the surface, or in depth profiling when paired with ion-beam etching. It is often applied to study chemical processes in the materials in their as-received state or after cleavage, scraping, exposure to heat, reactive gasses or solutions, ultraviolet light, or during ion implantation.

<span class="mw-page-title-main">Thermal radiation</span> Electromagnetic radiation generated by the thermal motion of particles

Thermal radiation is electromagnetic radiation emitted by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. The emission of energy arises from a combination of electronic, molecular, and lattice oscillations in a material. Kinetic energy is converted to electromagnetism due to charge-acceleration or dipole oscillation. At room temperature, most of the emission is in the infrared (IR) spectrum, though above around 525 °C (977 °F) enough of it becomes visible for the matter to visibly glow. This visible glow is called incandescence. Thermal radiation is one of the fundamental mechanisms of heat transfer, along with conduction and convection.

<span class="mw-page-title-main">Synchrotron light source</span> Particle accelerator designed to produce intense x-ray beams

A synchrotron light source is a source of electromagnetic radiation (EM) usually produced by a storage ring, for scientific and technical purposes. First observed in synchrotrons, synchrotron light is now produced by storage rings and other specialized particle accelerators, typically accelerating electrons. Once the high-energy electron beam has been generated, it is directed into auxiliary components such as bending magnets and insertion devices in storage rings and free electron lasers. These supply the strong magnetic fields perpendicular to the beam that are needed to stimulate the high energy electrons to emit photons.

In many areas of science, Bragg's law, Wulff–Bragg's condition, or Laue–Bragg interference are a special case of Laue diffraction, giving the angles for coherent scattering of waves from a large crystal lattice. It describes how the superposition of wave fronts scattered by lattice planes leads to a strict relation between the wavelength and scattering angle. This law was initially formulated for X-rays, but it also applies to all types of matter waves including neutron and electron waves if there are a large number of atoms, as well as visible light with artificial periodic microscale lattices.

<span class="mw-page-title-main">Insertion device</span> Component of synchrotron light sources

An insertion device (ID) is a component in modern synchrotron light sources, so called because they are "inserted" into accelerator tracks. They are periodic magnetic structures that stimulate highly brilliant, forward-directed synchrotron radiation emission by forcing a stored charged particle beam to perform wiggles, or undulations, as they pass through the device. This motion is caused by the Lorentz force, and it is from this oscillatory motion that we get the names for the two classes of device, which are known as wigglers and undulators. As well as creating a brighter light, some insertion devices enable tuning of the light so that different frequencies can be generated for different applications.

<span class="mw-page-title-main">Free-electron laser</span> Laser using electron beam in vacuum as gain medium

A free-electron laser (FEL) is a fourth generation light source producing extremely brilliant and short pulses of radiation. An FEL functions much as a laser but employs relativistic electrons as a gain medium instead of using stimulated emission from atomic or molecular excitations. In an FEL, a bunch of electrons passes through a magnetic structure called an undulator or wiggler to generate radiation, which re-interacts with the electrons to make them emit coherently, exponentially increasing its intensity.

The Smith–Purcell effect was the precursor of the free-electron laser (FEL). It was studied by Steve Smith, a graduate student under the guidance of Edward Purcell. In their experiment, they sent an energetic beam of electrons very closely parallel to the surface of a ruled optical diffraction grating, and thereby generated visible light. Smith showed there was negligible effect on the trajectory of the inducing electrons. Essentially, this is a form of Cherenkov radiation where the phase velocity of the light has been altered by the periodic grating. However, unlike Cherenkov radiation, there is no minimum or threshold particle velocity.

<span class="mw-page-title-main">Wiggler (synchrotron)</span> Insertion device for a synchrotron

A wiggler is an insertion device in a synchrotron. It is a series of magnets designed to periodically laterally deflect ('wiggle') a beam of charged particles inside a storage ring of a synchrotron. These deflections create a change in acceleration which in turn produces emission of broad synchrotron radiation tangent to the curve, much like that of a bending magnet, but the intensity is higher due to the contribution of many magnetic dipoles in the wiggler. Furthermore, as the wavelength (λ) is decreased this means the frequency (ƒ) has increased. This increase of frequency is directly proportional to energy, hence, the wiggler creates a wavelength of light with a larger energy.

Radiation damping in accelerator physics is a phenomenum where betatron oscillations and longitudinal oscilations of the particle are damped due to energy loss by synchrotron radiation. It can be used to reduce the beam emittance of a high-velocity charged particle beam.

Interference lithography is a technique for patterning regular arrays of fine features, without the use of complex optical systems or photomasks.

<span class="mw-page-title-main">Mainz Microtron</span> Particle physics facility

The Mainz Microtron, abbreviated MAMI, is a microtron which provides a continuous wave, high intensity, polarized electron beam with an energy up to 1.6 GeV. MAMI is the core of an experimental facility for particle, nuclear and X-ray radiation physics at the Johannes Gutenberg University in Mainz (Germany). It is one of the largest campus-based accelerator facilities for basic research in Europe. The experiments at MAMI are performed by about 200 physicists of many countries organized in international collaborations.

Self-amplified spontaneous emission (SASE) is a process within a free-electron laser (FEL) by which a laser beam is created from a high-energy electron beam.

High-harmonic generation (HHG) is a non-linear process during which a target is illuminated by an intense laser pulse. Under such conditions, the sample will emit the high harmonics of the generation beam. Due to the coherent nature of the process, high-harmonics generation is a prerequisite of attosecond physics.

<span class="mw-page-title-main">European XFEL</span>

The European X-Ray Free-Electron Laser Facility is an X-ray research laser facility commissioned during 2017. The first laser pulses were produced in May 2017 and the facility started user operation in September 2017. The international project with twelve participating countries; nine shareholders at the time of commissioning, later joined by three other partners, is located in the German federal states of Hamburg and Schleswig-Holstein. A free-electron laser generates high-intensity electromagnetic radiation by accelerating electrons to relativistic speeds and directing them through special magnetic structures. The European XFEL is constructed such that the electrons produce X-ray light in synchronisation, resulting in high-intensity X-ray pulses with the properties of laser light and at intensities much brighter than those produced by conventional synchrotron light sources.

The Kapitza–Dirac effect is a quantum mechanical effect consisting of the diffraction of matter by a standing wave of light, in complete analogy to the diffraction of light by a periodic grating, but with the role of matter and light reversed. The effect was first predicted as the diffraction of electrons from a standing wave of light by Paul Dirac and Pyotr Kapitsa in 1933. The effect relies on the wave–particle duality of matter as stated by the de Broglie hypothesis in 1924. The matter-wave diffraction by a standing wave of light was first observed using a beam of neutral atoms. Later, the Kapitza-Dirac effect as originally proposed was observed in 2001.

<span class="mw-page-title-main">X-ray emission spectroscopy</span>

X-ray emission spectroscopy (XES) is a form of X-ray spectroscopy in which a core electron is excited by an incident x-ray photon and then this excited state decays by emitting an x-ray photon to fill the core hole. The energy of the emitted photon is the energy difference between the involved electronic levels. The analysis of the energy dependence of the emitted photons is the aim of the X-ray emission spectroscopy.

References

  1. Klaus Wille, Introduction to insertion devices, Part of Synchrotron radiation and free electron lasers. Proceedings, CERN Accelerator School, CAS, Grenoble, France, April 22-27, 1996 (pp. 61-75)
  2. Paolo Luchini, Hans Motz, Undulators and Free-electron Lasers, Oxford University Press, 1990.
  3. Ginsburg, Vitaly Lazarevich (1947). "ОБ ИЗЛУЧЕНИИ МИКРОРАДИОВОЛН И ИХ ПОГЛОЩЕНИИ В ВОЗДУХЕ" [On the emission of microradiowaves and their absorption in the air]. Izv. AN USSR ser. phys. (in Russian). T. XI No.2. USSR Academy of Sciences: (pp. 165-182). ISSN   0367-6765 . Retrieved 22 September 2024.
  4. Schwinger, Julian (1949). "On the Classical Radiation of Accelerated Electrons". Physical Review. 75 (12): 1912. Bibcode:1949PhRv...75.1912S. doi:10.1103/PhysRev.75.1912.
  5. Motz, Hans (1951). "Applications of the Radiation from Fast Electron Beams". Journal of Applied Physics. 22 (5): 527. Bibcode:1951JAP....22..527M. doi:10.1063/1.1700002.
  6. Motz, H.; Thon, W.; Whitehurst, R. N. (1953). "Experiments on Radiation by Fast Electron Beams". Journal of Applied Physics. 24 (7): 826. Bibcode:1953JAP....24..826M. doi:10.1063/1.1721389.