摘要:

AbstractThe propagation of thermal and mechanical disturbances in a non‐conducting crystal is studied on the basis of a generalized transport equation for phonons, derived in a previous paper. This equation agrees with the Peierls‐Boltzmann equation for slowly varying inhomogeneities in space and time and is consistent with the perturbation treatment of the phonon self energy for high frequencies and short wave‐lengths. A formal solution of the transport equation is obtained, which allows us to study in detail the transition between the low‐frequency, collision‐dominated regime and the high‐frequency, essentially collision‐less regime. Using a single relaxation time approximation we discuss the propagation of “sound” waves and obtain explicit expressions for the dispersion of the sound velocity and the damping, valid for arbitrary frequencies. In order to elucidate more clearly the technique used we consider in this paper an one‐dimensional crystal, but the essential results can easily be taken over to the threedimensional case. A separate report on this will be

ISSN:0015-8208    

DOI:10.1002/prop.19690170402

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

摘要:

AbstractMethods and results of beam optics with respect to the transport of charged particle beams in experiments on high energy accelerators are reviewed.

ISSN:0015-8208    

DOI:10.1002/prop.19690170403

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY

ISSN:0015-8208    

DOI:10.1002/prop.19690170401

出版商:WILEY‐VCH Verlag    

年代:1969

数据来源: WILEY