Warm-fluid stability properties of intense non-neutral charged particle beams with pressure anisotropy

The macroscopic warm-fluid model developed by Lund and Davidson [Phys. Plasmas 5, 3028 (1998)] is used in the smooth-focusing approximation to investigate detailed electrostatic stability properties of an intense charged particle beam with pressure anisotropy. The macroscopic fluid-Maxwell equations are linearized for small-amplitude perturbations, and an eigenvalue equation is derived for the perturbed electrostatic potential δφ(x,t), allowing for arbitrary anisotropy in the perpendicular and parallel pressures, P⊥0(r) and P‖0(r). Detailed stability properties are calculated numerically for the case of extreme anisotropy with P‖0(r)=0 and P⊥0(r)≠0, assuming axisymmetric wave perturbations (∂/∂θ=0) of the form δφ(x,t)=δφ̂(r)exp(ikzz−iωt), where kz is the axial wavenumber, and Imω>0 corresponds to instability (temporal growth). For kz=0, the analysis of the eigenvalue equation leads to a discrete spectrum {ωn} of stable oscillations with Imωn=0, where n is the radial mode number. On the other hand, for sufficiently large values of kzrb, where rb is the beam radius, the analysis leads to an anisotropy-driven instability (Imω>0) provided the normalized Debye length (ΓD=λD⊥/rb) is sufficiently large and the normalized beam intensity (sb=ω̂pb2/2γb2ωβ⊥2) is sufficiently below the space-charge limit. Depending on system parameters, the growth rate can be a substantial fraction of the focusing frequency ωβ⊥ of the applied field.