  Theoretical analysis of e-cloud instability in the Fermilab Recycler is
represented in the paper. The e-cloud in strong magnetic field is treated as a
set of immovable snakes each being initiated by some proton bunch. It is shown
that the instability arises because of injection errors of the bunches which
increase in time and from bunch to bunch along the batch being amplified by the
e-cloud electric field. The particular attention is given to nonlinear
additions to the cloud field. It is shown that the nonlinearity is the main
factor which restricts growth of the bunch amplitude. Possible role of the
field free parts of the Recycler id discussed as well. Results of calculations
are compared with experimental data demonstrating good correlation.
