  The neutral fermionic edge mode is essential to the non-Abelian topological
property and its experimental detection in $Z_k$ fractional quantum Hall (FQH)
state for $k > 1$. Usually, the identification of the edge modes in a finite
size system is difficult, especially near the region of the edge
reconstruction, due to mixing with the bosonic edge mode and the bulk states as
well. We study the edge-mode excitations of the Moore-Read (MR) and Read-Rezayi
(RR) states by using Jack polynomials in the truncated subspace. It is found
that the electron density, as a detector, has marked different behaviors
between the bosonic and fermionic edge modes. As an application, it helps us to
identify them near the edge reconstruction and in the RR edge spectrum. On the
other hand, we systematically study the edge excitations for the RR state,
extrapolate the edge velocities and their related coherence length and
temperature in the interferometer experiments.
