Electron-beam cooling by stimulated synchrotron emission and absorption

Abstract

It is shown that stimulated synchrotron emission and absorption can act simultaneously on a relativistic electron beam with a narrow energy spread to reduce the spread significantly. This beam "cooling" mechanism acts most effectively for beam energies belonging to a sequence of discrete values, one for each synchrotron harmonic. The discrete energy values are absolute, and are not influenced by external parameters such as magnetic field strength. Application of this mechanism to cool beams for freeelectron lasers, synchrotron-radiation lasers, and slow-wave cyclotron amplifiers is suggested.PACS numbers: 41.80. Ee, 07.77.+p, 41.70.+t In some applications of electron beams for the generation and amplification of electromagnetic radiation it is desirable to have the smallest possible spread in electron energy or axial velocity. Examples of this include the free-electron laser 1 (FEL) and slow-wave gyrotron amplifiers, 2 where a parallel velocity spread of even a few percent has been shown to be highly detrimental to the achievement of high gain, efficiency, and bandwidth. Another example is in the synchrotron-radiation laser 3 (SRL), where high synchrotron harmonic operation is only possible if the fractional energy spread A 7/7 is less than O -1 , where 0 is the interaction transit angle Inflot/y, with n the synchrotron harmonic number, Sl$ the (rest) electron cyclotron frequency, 7 the relativistic energy factor, and t the interaction time. For a typical mm-wavelength SRL, O is of the order of 500, but for an optical wavelength SRL O could be in the range of 10 6 . A requirement for Ay/y< 10 ~6 may well be beyond the realm of known technology.Therefore, considerable interest could attach to a method of reducing the velocity and energy spread in an electron beam. This Letter outlines a novel method for reducing the energy spread on a gyrating relativistic beam in a strong magnetic field B. The method is based on the fact that the sign of the energy flow from electrons to electromagnetic fields in the cyclotron resonance maser interaction 4 depends upon R^coy/nflo, where co is the (radian) frequency of the electromagnetic radiation field, and il^^eB/m for electrons of charge e and rest mass m. If R is greater than unity, energy flows from the electrons to the fields; and when R is less than unity, energy flows from the fields to the electrons. If electrons with a distribution of energies about some mean value 7 are subjected to the radiation fields, with R set equal to unity for the mean energy, i.e., with co^nClo/y, then one can expect the high-energy electrons to lose energy while the low-energy electronics simultaneously gain energy. This could lead to a decrease in the spread of electron energies, or a "cooling" of the energy distribution function. Under conditions to be described below, it will be shown that the time rate of change of electron energy can be given approximately by the following differential equation: d\n(y-y)/dT=-KT 3(1)where T is the normalized time variable, and K is a constant. The solut...

Synchrotron-radiation laser

“…The former value can be achieved with either linacs or electrostatic accelerators, but the latter value can probably only be achieved with electrostatic accelerators. It is possible that beam cooling, as recently described [10], could be used to produce the required narrow energy spread at across the beam diameter D would occur, depending upon the bounce angle and the intermirror spacing.…”

Cyclotron radiation cooling of a short electron bunch kicked in an undulator with guiding magnetic field

“…Methods providing a decrease in the energy spread (cooling) are actual from the point of view of various applications of such electron bunches, including freeelectron lasers (FELs) [4][5][6]. However, cooling methods are developed now basically for electron beams of very high energies [7][8][9][10][11][12]. As for moderately relativistic (several or tens MeV) high-dense short electron bunches, the strong Coulomb interaction of the particles results in a requirement for a short length of a cooling system.…”

Cyclotron-undulator cooling of a free-electron-laser beam

“…Methods for decrease of the energy spread (cooling) are actual from the point of view of various applications of such beams, including free-electron lasers (FELs). However, cooling methods are developed now basically for electron beams of significantly higher energies [4,5]. As for a moderately-relativistic high-dense short ebunches, the strong Coulomb interaction of the particles results in a requirement for a short (~ 1 m and even less) length of a cooling system.…”