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. Plas mas 5, 3028 (1998)] is used in the smooth-focusing approximation to investi gate detailed electrostatic stability properties of an intense charged part icle beam with pressure anisotropy. The macroscopic fluid-Maxwell equations are linearized for small-amplitude perturbations, and an eigenvalue equati on is derived for the perturbed electrostatic potential delta phi(x,t), all owing for arbitrary anisotropy in the perpendicular and parallel pressures, P-perpendicular to(0)(r) and P-parallel to(0)(r). Detailed stability prope rties are calculated numerically for the case of extreme anisotropy with P- parallel to(0)(r)=0 and P-perpendicular to(0)(r)not equal 0, assuming axisy mmetric wave perturbations (partial derivative/partial derivative theta=0) of the form delta phi(x,t)=delta<(phi)over cap>(r)exp(ik(z)z-i omega t), wh ere k(z) is the axial wavenumber, and Im omega > 0 corresponds to instabili ty (temporal growth). For k(z)=0, the analysis of the eigenvalue equation l eads to a discrete spectrum {omega(n)} of stable oscillations with Im omega (n)=0, where n is the radial mode number. On the other hand, for sufficient ly large values of k(z)r(b), where r(b) is the beam radius, the analysis le ads to an anisotropy-driven instability (Im omega > 0) provided the normali zed Debye length (Gamma(D)=lambda(D perpendicular to)/r(b)) is sufficiently large and the normalized beam intensity (s(b)=<(omega)over cap>(2)(pb)/2 g amma(b)(2)omega(beta perpendicular to)(2)) is sufficiently below the space- charge limit. Depending on system parameters, the growth rate can be a subs tantial fraction of the focusing frequency omega(beta perpendicular to) of the applied field. (C) 2000 American Institute of Physics. [S1070-664X(00)0 2506-4].