The problem of large-amplitude spherical oscillations of an ion cloud
in an Inertial Electrostatic Confinement (IEC) device is examined. It
is shown that ion fluctuations of a Gaussian profile in a spherical, h
armonic well are stable to all hydrodynamic modes, and stable oscillat
ions about the oscillating equilibrium state may be damped by continuu
m damping. It is also shown that the ion state forms a thermal equilib
rium, in spite of the orders of magnitude, density, and temperature ch
anges during the oscillation cycle. Finally, a brief discussion of how
to experimentally realize the required electron distributions for the
se oscillations is presented. [S1070-664X(98)012307-2]