Use is made of the macroscopic cold-fluid Poisson equations to investigate the electrostatic stability properties of nonrelativistic, non-neutral electron flow in a cylindrical diode with applied magnetic field $B_0$e${^}_z$. The cathode is located at r=a and the anode is located at r=b. Space-charge-limited flow with $E_r^0$(r=a)=0 is assumed. Detailed stability properties are investigated analytically and numerically for electrostatic flute perturbations with ∂/∂z=0. Particular emphasis is placed on the influence of the neutral anode plasma on stability behavior assuming uniform cathode electron density (n${^}_b$) extending from the cathode (r=a) to r=$r_b$, and uniform anode plasma density (n${^}_e$=$Z_i$n${^}_i$) extending from r=$r_p$ to the anode (r=b). Depending on the cathode electron density (as measured by $s_b$=ω^ ${}_{\mathrm{pb}}{}^2{}_{}{}^{}$/${\omega }_{\mathrm{ce}}^2$), the anode plasma density (as measured by $s_e$=ω^ ${}_{\mathrm{pe}}{}^2{}_{}{}^{}$/${\omega }_{\mathrm{ce}}^2$), the diode aspect ratio, etc., it is found that there can be a strong coupling of the anode plasma to the cathode electrons, and a concomitant large influence on detailed stability behavior for both the high-frequency (electron-driven) and low-frequency (ion-driven) branches. Detailed stability properties are investigated over a wide range of cathode electron density, anode plasma density, diode aspect ratio, etc.

• Received 15 March 1985

DOI:https://doi.org/10.1103/PhysRevA.32.1044