In accelerator physics, the mean transverse energy (MTE) is a quantity that describes the variance of the transverse momentum of a beam. While the quantity has a defined value for any particle beam, it is generally used in the context of photoinjectors for electron beams. [1]
For a beam consisting of particles with momenta and mass traveling prominently in the direction the mean transverse energy is given by
Where is the component of the momentum perpendicular to the beam axis . For a continuous, normalized distribution of particles the MTE is
Emittance is a common quantity in beam physics which describes the volume of a beam in phase space, and is normally conserved through typical linear beam transformations; for example, one may transition from a beam with a large spatial size and a small momentum spread to one with a small spatial size and a large momentum spread, both cases retaining the same emittance. Due to its conservation, the emittance at the species source (e.g., photocathode for electrons) is the lower limit on attainable emittance.
For a beam born with a spatial size and a 1-D MTE the minimum 2-D ( and ) emittance is [2]
The emittance of each dimension may be multiplied together to get the higher dimensional emittance. For a photocathode the spatial size of the beam is typically equal to the spatial size of the ionizing laser beam and the MTE may depend on several factors involving the cathode, the laser, and the extraction field. Due to the linear independence of the laser spot size and the MTE, the beam size is often factored out, formulating the 1-D thermal emittance [3]
Likewise, the maximum brightness, or phase space density, is given by
In physics, the cross section is a measure of the probability that a specific process will take place when some kind of radiant excitation intersects a localized phenomenon. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross section is typically denoted σ (sigma) and is expressed in units of area, more specifically in barns. In a way, it can be thought of as the size of the object that the excitation must hit in order for the process to occur, but more exactly, it is a parameter of a stochastic process.
Diffraction is defined as 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.
Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.
In quantum mechanics, the particle in a box model describes a particle free to move in a small space surrounded by impenetrable barriers. The model is mainly used as a hypothetical example to illustrate the differences between classical and quantum systems. In classical systems, for example, a particle trapped inside a large box can move at any speed within the box and it is no more likely to be found at one position than another. However, when the well becomes very narrow, quantum effects become important. The particle may only occupy certain positive energy levels. Likewise, it can never have zero energy, meaning that the particle can never "sit still". Additionally, it is more likely to be found at certain positions than at others, depending on its energy level. The particle may never be detected at certain positions, known as spatial nodes.
Optical tweezers are scientific instruments that use a highly focused laser beam to hold and move microscopic and sub-microscopic objects like atoms, nanoparticles and droplets, in a manner similar to tweezers. If the object is held in air or vacuum without additional support, it can be called optical levitation.
In condensed matter physics, Bloch's theorem states that solutions to the Schrödinger equation in a periodic potential take the form of a plane wave modulated by a periodic function. The theorem is named after the physicist Felix Bloch, who discovered the theorem in 1929. Mathematically, they are written
A photocathode is a surface engineered to convert light (photons) into electrons using the photoelectric effect. Photocathodes are important in accelerator physics where they are utilised in a photoinjector to generate high brightness electron beams. Electron beams generated with photocathodes are commonly used for free electron lasers and for ultrafast electron diffraction. Photocathodes are also commonly used as the negatively charged electrode in a light detection device such as a photomultiplier or phototube.
The Drude model of electrical conduction was proposed in 1900 by Paul Drude to explain the transport properties of electrons in materials. Basically, Ohm's law was well established and stated that the current J and voltage V driving the current are related to the resistance R of the material. The inverse of the resistance is known as the conductance. When we consider a metal of unit length and unit cross sectional area, the conductance is known as the conductivity, which is the inverse of resistivity. The Drude model attempts to explain the resistivity of a conductor in terms of the scattering of electrons by the relatively immobile ions in the metal that act like obstructions to the flow of electrons.
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 crystalline lattice and from the occupation of electronic energy bands. The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle, which allows a maximum of one electron per quantum state. The study of the Fermi surfaces of materials is called fermiology.
In accelerator physics, emittance is a property of a charged particle beam. It refers to the area occupied by the beam in a position-and-momentum phase space.
Electron scattering occurs when electrons are displaced from their original trajectory. This is due to the electrostatic forces within matter interaction or, if an external magnetic field is present, the electron may be deflected by the Lorentz force. This scattering typically happens with solids such as metals, semiconductors and insulators; and is a limiting factor in integrated circuits and transistors.
Intrabeam scattering (IBS) is an effect in accelerator physics where collisions between particles couple the beam emittance in all three dimensions. This generally causes the beam size to grow. In proton accelerators, intrabeam scattering causes the beam to grow slowly over a period of several hours. This limits the luminosity lifetime. In circular lepton accelerators, intrabeam scattering is counteracted by radiation damping, resulting in a new equilibrium beam emittance with a relaxation time on the order of milliseconds. Intrabeam scattering creates an inverse relationship between the smallness of the beam and the number of particles it contains, therefore limiting luminosity.
Self-focusing is a non-linear optical process induced by the change in refractive index of materials exposed to intense electromagnetic radiation. A medium whose refractive index increases with the electric field intensity acts as a focusing lens for an electromagnetic wave characterized by an initial transverse intensity gradient, as in a laser beam. The peak intensity of the self-focused region keeps increasing as the wave travels through the medium, until defocusing effects or medium damage interrupt this process. Self-focusing of light was discovered by Gurgen Askaryan.
The Weibel instability is a plasma instability present in homogeneous or nearly homogeneous electromagnetic plasmas which possess an anisotropy in momentum (velocity) space. This anisotropy is most generally understood as two temperatures in different directions. Burton Fried showed that this instability can be understood more simply as the superposition of many counter-streaming beams. In this sense, it is like the two-stream instability except that the perturbations are electromagnetic and result in filamentation as opposed to electrostatic perturbations which would result in charge bunching. In the linear limit the instability causes exponential growth of electromagnetic fields in the plasma which help restore momentum space isotropy. In very extreme cases, the Weibel instability is related to one- or two-dimensional stream instabilities.
In physics, slowly varying envelope approximation is the assumption that the envelope of a forward-travelling wave pulse varies slowly in time and space compared to a period or wavelength. This requires the spectrum of the signal to be narrow-banded—hence it is also referred to as the narrow-band approximation.
The angular momentum of light is a vector quantity that expresses the amount of dynamical rotation present in the electromagnetic field of the light. While traveling approximately in a straight line, a beam of light can also be rotating around its own axis. This rotation, while not visible to the naked eye, can be revealed by the interaction of the light beam with matter.
The spin angular momentum of light (SAM) is the component of angular momentum of light that is associated with the quantum spin and the rotation between the polarization degrees of freedom of the photon.
Heat transfer physics describes the kinetics of energy storage, transport, and energy transformation by principal energy carriers: phonons, electrons, fluid particles, and photons. Heat is energy stored in temperature-dependent motion of particles including electrons, atomic nuclei, individual atoms, and molecules. Heat is transferred to and from matter by the principal energy carriers. The state of energy stored within matter, or transported by the carriers, is described by a combination of classical and quantum statistical mechanics. The energy is different made (converted) among various carriers. The heat transfer processes are governed by the rates at which various related physical phenomena occur, such as the rate of particle collisions in classical mechanics. These various states and kinetics determine the heat transfer, i.e., the net rate of energy storage or transport. Governing these process from the atomic level to macroscale are the laws of thermodynamics, including conservation of energy.
Ultrafast electron diffraction (UED), also known as femtosecond electron diffraction (FED), is a pump-probe experimental method based on the combination of optical pump-probe spectroscopy and electron diffraction. UED provides information on the dynamical changes of the structure of materials. It is very similar to time resolved crystallography, but instead of using X-rays as the probe, it uses electrons. In the UED technique, a femtosecond (fs) laser optical pulse excites (pumps) a sample into an excited, usually non-equilibrium, state. The pump pulse may induce chemical, electronic or structural transitions. After a finite time interval, a fs electron pulse is incident upon the sample. The electron pulse undergoes diffraction as a result of interacting with the sample. The diffraction signal is, subsequently, detected by an electron counting instrument such as a CCD camera. Specifically, after the electron pulse diffracts from the sample, the scattered electrons will form a diffraction pattern (image) on a CCD camera. This pattern contains structural information about the sample. By adjusting the time difference between the arrival of the pump and probe beams, one can obtain a series of diffraction patterns as a function of the various time differences. The diffraction data series can be concatenated in order to produce a motion picture of the changes that occurred in the data. UED can provide a wealth of dynamics on charge carriers, atoms, and molecules.
Accelerations in special relativity (SR) follow, as in Newtonian Mechanics, by differentiation of velocity with respect to time. Because of the Lorentz transformation and time dilation, the concepts of time and distance become more complex, which also leads to more complex definitions of "acceleration". SR as the theory of flat Minkowski spacetime remains valid in the presence of accelerations, because general relativity (GR) is only required when there is curvature of spacetime caused by the energy–momentum tensor. However, since the amount of spacetime curvature is not particularly high on Earth or its vicinity, SR remains valid for most practical purposes, such as experiments in particle accelerators.
