  We propose a theoretical ground for emissive capacitively coupled
radio-frequency plasma sheath under low pressure. The rf sheath is assumed to
be collisionless, and oscillates with external source. A known sinusoidal
voltage instead of current is taken as prerequisite to derive sheath dynamics.
Kinetic studies are performed to determine mean wall potential as a function of
secondary emission coefficient and applied voltage amplitude, with which the
complete mean DC sheath is resolved. Analytical analyses under homogeneous
model and numerical analyses under inhomogeneous model are conducted to deduce
real time sheath properties including space potential, capacitance and
stochastic heating. Obtained results are validated by a continuum kinetic
simulation without ionization. The influences of collisionality and ionization
induced by secondary electrons are elucidated with a particle-in-cell
simulation, which further formalizes proposed theories and inspires future
works.
