Bremsstrahlung

Bremsstrahlung (German pronunciation: (listen)), from bremsen 'to brake' and Strahlung 'radiation'; i.e., 'braking radiation' or 'deceleration radiation', is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., a photon), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases. Bremsstrahlung (German pronunciation: (listen)), from bremsen 'to brake' and Strahlung 'radiation'; i.e., 'braking radiation' or 'deceleration radiation', is electromagnetic radiation produced by the deceleration of a charged particle when deflected by another charged particle, typically an electron by an atomic nucleus. The moving particle loses kinetic energy, which is converted into radiation (i.e., a photon), thus satisfying the law of conservation of energy. The term is also used to refer to the process of producing the radiation. Bremsstrahlung has a continuous spectrum, which becomes more intense and whose peak intensity shifts toward higher frequencies as the change of the energy of the decelerated particles increases. Broadly speaking, bremsstrahlung or braking radiation is any radiation produced due to the deceleration (negative acceleration) of a charged particle, which includes synchrotron radiation (i.e. photon emission by a relativistic particle), cyclotron radiation (i.e. photon emission by a non-relativistic particle), and the emission of electrons and positrons during beta decay. However, the term is frequently used in the more narrow sense of radiation from electrons (from whatever source) slowing in matter. Bremsstrahlung emitted from plasma is sometimes referred to as free/free radiation. This refers to the fact that the radiation in this case is created by charged particles that are free; i.e., not part of an ion, atom or molecule, both before and after the deflection (acceleration) that caused the emission. This section is written from a purely classical perspective, with quantum mechanics neglected. A charged particle accelerating in a vacuum radiates power, as described by the Larmor formula and its relativistic generalizations. Although the term, bremsstrahlung, is usually reserved for charged particles accelerating in matter, not vacuum, the formulas are similar. (In this respect, bremsstrahlung differs from Cherenkov radiation, another kind of braking radiation which occurs only in matter, and not in a vacuum.) The most established relativistic formula for total radiated power is given by where β → = v → c {displaystyle {vec {eta }}={frac {vec {v}}{c}}} (the velocity of the particle divided by the speed of light), γ = 1 1 − β 2 {displaystyle gamma ={frac {1}{sqrt {1-eta ^{2}}}}} is the Lorentz factor, β → ˙ {displaystyle {dot {vec {eta }}}} signifies a time derivative of β → {displaystyle {vec {eta }}} , and q is the charge of the particle. This is commonly written in the mathematically equivalent form using ( β → ⋅ β → ˙ ) 2 = β ˙ 2 β 2 − ( β → × β → ˙ ) 2 {displaystyle left({vec {eta }}cdot {dot {vec {eta }}} ight)^{2}={dot {eta }}^{2}eta ^{2}-left({vec {eta }} imes {dot {vec {eta }}} ight)^{2}} : In the case where velocity is parallel to acceleration (for example, linear motion), the formula simplifies to where a ≡ v ˙ = β ˙ c {displaystyle aequiv {dot {v}}={dot {eta }}c} is the acceleration. For the case of acceleration perpendicular to the velocity ( β → ⋅ β → ˙ = 0 ) {displaystyle left({vec {eta }}cdot {dot {vec {eta }}}=0 ight)} (a case that arises in circular particle accelerators known as synchrotrons), the total power radiated reduces to Power radiated in the two limiting cases is proportional to γ 4 {displaystyle gamma ^{4}} ( a ⊥ v ) {displaystyle left(aperp v ight)} or γ 6 {displaystyle gamma ^{6}} ( a ∥ v ) {displaystyle left(aparallel v ight)} . Since E = γ m c 2 {displaystyle E=gamma mc^{2}} , we see that the total radiated power goes as m − 4 {displaystyle m^{-4}} or m − 6 {displaystyle m^{-6}} , which accounts for why electrons lose energy to bremsstrahlung radiation much more rapidly than heavier charged particles (e.g., muons, protons, alpha particles). This is the reason a TeV energy electron-positron collider (such as the proposed International Linear Collider) cannot use a circular tunnel (requiring constant acceleration), while a proton-proton collider (such as the Large Hadron Collider) can utilize a circular tunnel. The electrons lose energy due to bremsstrahlung at a rate ( m p / m e ) 4 ≈ 10 13 {displaystyle (m_{p}/m_{e})^{4}approx 10^{13}} times higher than protons do.