Macroscopic Description of Pressure - anisotropy - driven Collective Instability in Intense Charged Particle Beams

The macroscopic warmuid model developed by Lund and Davidson [Phys. Plasmas 5, 3028 (1998)] is used in the smooth-focusing approximation to investigate detailed stability properties of an intense charged particle beam with pressure anisotropy, assuming small-amplitude electrostatic perturbations about a waterbag equilibrium. Stability properties are calculated numerically for the case of extreme pressure anisotropy with P 0 k (r) = 0 and P 0 ?(r) 6= 0, assuming axisymmetric wave perturbations (@=@ = 0) of the form Æ (x; t) = Æ̂(r) exp(ikzz i!t), where kz is the axial wavenumber, and Im! > 0 corresponds to instability (temporal growth). For suÆciently large values of kzrb, where rb is the beam radius, the analysis leads to an anisotropy-driven instability (Im! > 0) provided the normalized Debye length ( D = D?=rb) is suÆciently large and the normalized beam intensity (sb = !̂ 2 pb=2 2 b! 2 ?) is suÆciently below the space-charge limit.