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.

This paper examines analytically and numerically the effects of self-consistent collective oscillations excited in a high-intensity charged particle beam on the motion of a test particle in the beam core. Even under ideal conditions, assuming a constant transverse focusing force (smooth focusing approximation), and perturbations about a uniform-density, constant radius beam, it is found that collective mode excitations, in combination with the applied focusing force and the equilibrium test fields, can eject particles from the beam core to large radii. Test particle orbits are calculated for collective oscillations with n = 1 and 2 radial mode structure, and an estimate is obtained for the range of initial conditions for which particles will be expelled from the beam interior. Resonances for meridional particles are found to be unimportant, while a class of particles with nonzero angular momentum are found to participate in resonant behavior. Once expelled from the beam, numerical solutions of the orbit equations indicate that Kolmogorov-Arnold-Moser curves, phase space spanning integrals of motion, confine particles within 1.5 times the beam radius for moderately low mode amplitudes, but are successively destabilized for higher amplitudes.

The plasma-filled rod-pinch diode is a new technique to concentrate an intense electron beam to high power and energy density. Current from a pulsed power generator (typically ∼MV, MA, 100 ns pulse duration) flows through the injected plasma, which short-circuits the diode for 10–70 ns, then the impedance increases and a large fraction of the ∼MeV electron-beam energy is deposited at the tip of a 1 mm diameter, tapered rod anode, producing a small (sub-mm diameter), intense x-ray source. The current and voltage parameters imply 20–150 μm effective anode-cathode gaps at the time of maximum radiation, much smaller gaps than can be used between metal electrodes without premature shorting. Interferometric diagnostics indicate that the current initially sweeps up plasma in a snowplow-like manner, convecting current toward the rod tip. The density distribution is more diffuse at the time of beam formation with a low-density region near the rod surface where gap formation could occur. Particle simulations of the beam formation phase are dominated by rapid field penetration along the anode and radial J×B forces leading to gap formation and high-energy beam propagation to the rod tip. Beam deposition at the rod tip produces a high thermal energy-density (∼0.75 MJ/cm3), highly ionized (Z∼10, T∼25 eV) expanding tungsten plasma. Potential applications of this technique include improved radiography sources, high-energy-density plasma generation, and intense 10–100 keV x-ray production for nuclear-weapon-effects testing.