The continued demand for higher beam energies, luminosities, and brightness, induces increasing number of beam phenomena that invlove quantum effects. In this paper we review the various quantum aspects of beam physics, with emphasis on their recent advances. These include quantum effects in beam dynamics, electron-photon interaction, beam phenomena under strong fields, fundamental physics under violent acceleration, and quantum methodology in beam physics. We conclude with a future outlook of this very exciting new field by the name quantum beam physics.
WHERE IS ऌ h IN BEAM PHYSICS?It is common knowledge that quantum effects are pronounced in physical systems where the particles involved exihibit the wave nature, or the (radiation) waves involved exhibit the particle nature. In accelerators the de Broglie wavelength of a high energy beam particle iss ae ae ae n ;where ae and ae n are the ae-function and the normalized emittance, respectively. This value is generally much smaller than the typical apertures of the cavities and magnets in the accelerator. In addition, the synchrotron radiation induced by the magnets is typically low-energy and long wavelength, and the number of photons per volume of the wavelength is much larger than unity. Therefore the conventional beam dynamics is essentially classical physics to the leading order. The ever-increasing demand for higher beam energy, luminosity and brightness in accelerators pushes for ever higher acceleration gradients, smaller apertures, and tighter beam phase space, and quantum effects in beam physics become increasingly important.
QUANTUM EFFECTS IN BEAM DYNAMICS
Ultimate Limit of Phase SpaceThe basic assumptions in the standard treatment of synchrotron radiation reaction were that the photon emission occurs instantly and the recoil of the particle is equal and opposite to the momentum of the emitted photon. photon emission is random, its reaction causes random excitations in the beam phase space. It was found[1], however, that these assumptions are violated in a continuous focusing channel. The radiation formation length can in principle be comparable to the betatron oscillation length, and the focusing channel serves as a third party participating in the overall energy-momentum conservation. As a result, the radiation reaction does not cause any excitation of the transverse momentum, but an absolute damping of the emittance. This points to a theoretical minimum action, limited only by the zero-point fluctuations due to the uncertainty principle, i.e., J min = ऌ h=2, or ae n;min = J min =mc = ऌ ऋ c =2 ऎ 10 ,11 cm:The above result can be genralized to combined focusing-bending systems where the radiation formation length (ç=ae) is comparable to the average betatron wavelength (due to a very strong focusing) [2]. Pure bending and pure focusing are the two limiting regimes of the general formalism.
Classical vs. Quantum TrackingIn conventional treatments in particle tracking each point in phase space is assumed to have a perfect resolution. But due to ...
