摘要:

The short time behavior of the quasi‐stationary solution of an earlier paper is investigated by linearizing the Boltzmann equation in the perturbations. By the use of a suitable boundary condition on the distribution function in phase space, four one‐dimensional coupled inhomogeneous Fredholm equations of the second kind are obtained for Fourier components of the Laplace transforms with respect to time of the perturbation charge‐current density components. The asymptotic time behavior of the perturbations is determined by that root of the Fredholm determinant (considered as a function ofs, the Laplace transform variable) whose real part is algebraically greatest, provided that this real part is nonnegative. If the real part is negative, then the asymptotic time behavior is sometimes determined by this root of the determinant and sometimes by branch points of the kernel on the imaginary axis. If the determinant has no roots for Res> 0 and no multiple roots for Res= 0, the quasi‐stationary solution is stable. For the azimuthally symmetric Fourier components, the equation for &rgr;v&thgr;is not coupled to the others and is studied in more detail. In the approximate betatron regime, the Landau damping rate for this mode is estimated without use of the Fredholm determinant. In the extreme betatron regime, the undamped vibration frequencies are obtained.

ISSN:0031-9171    

DOI:10.1063/1.1706030

出版商:AIP    

年代:1960

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1706031

出版商:AIP    

年代:1960

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1706032

出版商:AIP    

年代:1960

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1706033

出版商:AIP    

年代:1960

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1706034

出版商:AIP    

年代:1960

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1706035

出版商:AIP    

年代:1960

数据来源: AIP

ISSN:0031-9171    

DOI:10.1063/1.1706036

出版商:AIP    

年代:1960

数据来源: AIP