  We present 1.5D Vlasov code simulations of the dynamics of electron holes in
non-uniform magnetic and electric fields typical of current sheets and,
particularly, of the Earth's magnetotail current sheet. The simulations show
that spatial width and amplitude of electron holes do not substantially vary in
the course of propagation, but there arises a double layer localized around the
electron hole and manifested as a drop of the electrostatic potential along the
electron hole. We demonstrate that electron holes produced around the neutral
plane of a current sheet slow down in the course of propagation toward the
current sheet boundaries. The leading contribution to electron hole braking is
provided by the non-uniform magnetic field, though electrostatic fields typical
of the current sheets do provide a noticeable contribution. The simulations
also show that electron holes with larger amplitudes are slowed faster. The
simulation results suggest that some of slow electron holes recently reported
in the Earth's plasma sheet boundary layer may appear due to braking of
initially fast electron holes in the course of propagation in the current
sheet.
