Stationarity and the phase space distribution of a laser field

M.P. Reijnders, Nicola Debernardi, S.B. van der Geer +3 more

All applications of high brightness ion beams depend on the possibility to precisely manipulate the trajectories of the ions or, more generally, to control their phase-space distribution. We show that the combination of a laser-cooled ion source and time-dependent acceleration fields gives new possibilities to perform precise phase-space control. We demonstrate reduction of the longitudinal energy spread and realization of a lens with control over its focal length and sign, as well as the sign of the spherical aberrations. This creates new possibilities to correct for the spherical and chromatic aberrations which are presently limiting the spatial resolution.

W. H. Louisell, M. Lax

Richard M. Sillitto

Michael R. Berman

A new Wigner phase-space distribution function is introduced for thermal quasiparticles currently in use in thermo field dynamics. The properties of this phase-space distribution are studied and compared with those of the corresponding zero-temperature distribution. Generalized uncertainty relations are implemented in order to study the explicit spreading in phase space as a function of temperature and quantum number of the thermal excitation, thereby permitting the investigation of quantum and thermal fluctuations.

Н.С. Руденко, V. G. Konareva

Yutaka Kano

In a previous paper a certain new probability distribution function q(z) relating to blackbody radiation was introduced. In the present paper the properties of this function for a general radiation field are studied. Unlike the phase-space distribution function of Sudarshan (1963), this function is nonnegative and is an ordinary function. A series expansion for q(z) is given, and it is shown that the series is absolutely convergent for all eigenvalues z of the destruction operator. It is also shown that the density matrix in the Fock representation can be uniquely determined from this probability distribution function, and vice versa. The relation between q(z) and the Sudarshan's phase-space distribution function is discussed.