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.
Plasma sheath material induced dependence due to secondary electron emission
