  Context: Many current and future surveys aim to detect the highest redshift
(z >~ 7) sources through their Lyman-alpha (Ly-alpha) emission, using the
narrow-band imaging method. However, to date the surveys have only yielded
non-detections and upper limits as no survey has reached the necessary
combination of depth and area to detect these very young star forming galaxies.
  Aims: We aim to calculate model luminosity functions and mock surveys of
Ly-alpha emitters at z >~ 7 based on a variety of approaches.
  Methods: We calculate model luminosity functions at different redshifts based
on three different approaches: a semi-analytical model based on CDM, a simple
phenomenological model, and an extrapolation of observed Schechter functions at
lower redshifts. The results of the first two models are compared with
observations made at redshifts z ~ 5.7 and z ~ 6.5, and they are then
extrapolated to higher redshift.
  Results: We present model luminosity functions for redshifts between z = 7 -
12.5 and give specific number predictions for future planned or possible
narrow-band surveys for Ly-alpha emitters. We also investigate what constraints
future observations will be able to place on the Ly-alpha luminosity function
at very high redshift.
  Conclusion: It should be possible to observe z = 7 - 10 Ly-alpha emitters
with present or near-future instruments if enough observing time is allocated.
In particular, large area surveys such as ELVIS (Emission Line galaxies with
VISTA Survey) will be useful in collecting a large sample. However, to get a
large enough sample to constrain well the z >= 10 Ly-alpha luminosity function,
instruments further in the future, such as an ELT, will be necessary.
