A condition for sheath instability due to secondary electron emission (SEE) is derived for low collisionality plasmas. When the SEE coefficient of the electrons bordering the depleted loss cone in energy space exceeds unity, the sheath potential is unstable to a negative perturbation. This result explains three different instability phenomena observed in Hall thruster simulations including a newly found state with spontaneous $\sim 20\mathrm{MHz}$ oscillations. When instabilities occur, the SEE propagating between the walls becomes the dominant contribution to the particle flux, energy loss and axial transport.

• Received 11 October 2011

DOI:https://doi.org/10.1103/PhysRevLett.108.235001