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The instability of a monoenergetic electron beam in a collisionalone-dimensional plasma bounded between grounded walls is considered bothanalytically and numerically. Collisions between electrons and neutrals areaccounted for the plasma electrons only. Solution of a dispersion equationshows that the temporal growth rate of the instability is a decreasing linearfunction of the collision frequency which becomes zero when the collisionfrequency is two times the collisionless growth rate. This result is confirmedby fluid simulations. Practical formulas are given for the estimate of thethreshold beam current which is required for the two-stream instability todevelop for a given system length, neutral gas pressure, plasma density, andbeam energy. Particle-in-cell simulations carried out with different neutraldensities and beam currents demonstrate good agreement with the fluid theorypredictions for both the growth rate and the threshold beam current.

Effect of collisions on the two-stream instability in a finite length plasm