Stability of different plasma sheaths near a dielectric wall with secondary electron emission

Abstract

The linear theory stability of different collisionless plasma sheath structures, including the classic sheath, inverse sheath and space-charge limited (SCL) sheath, is investigated as a typical eigenvalue problem. The three background plasma sheaths formed between a Maxwellian plasma source and a dielectric wall with a fully self-consistent secondary electron emission condition are solved by recent developed 1D3V (one-dimensional space and three-dimensional velocities), steady-state, collisionless kinetic sheath model, within a wide range of Maxwellian plasma electron temperature $T_{e}$ . Then, the eigenvalue equations of sheath plasma fluctuations through the three sheaths are numerically solved, and the corresponding damping and growth rates $\unicode[STIX]{x1D6FE}$ are found: (i) under the classic sheath structure (i.e. $T_{e}<T_{ec}$ (the first threshold)), there are three damping solutions (i.e. $\unicode[STIX]{x1D6FE}_{1}$ , $\unicode[STIX]{x1D6FE}_{2}$ and $\unicode[STIX]{x1D6FE}_{3}$ , $0>\unicode[STIX]{x1D6FE}_{1}>\unicode[STIX]{x1D6FE}_{2}>\unicode[STIX]{x1D6FE}_{3}$ ) for most cases, but there is only one growth-rate solution $\unicode[STIX]{x1D6FE}$ when $T_{e}\rightarrow T_{ec}$ due to the inhomogeneity of sheath being very weak; (ii) under the inverse sheath structure, which arises when $T_{e}>T_{ec}$ , there are no background ions in the sheath so that the fluctuations are stable; (iii) under the SCL sheath conditions (i.e. $T_{e}\geqslant T_{e\text{SCL}}$ , the second threshold), the obvious ion streaming through the sheath region again emerges and the three damping solutions are again found.