The propagation of a high-current finite-length ion charge
bunch through a background plasma is of interest for many
applications, including heavy ion fusion, plasma lenses, cosmic
ray propagation, and so forth. Charge neutralization has been
studied both analytically and numerically during ion beam entry,
propagation, and exit from the plasma. A suite of codes has
been developed for calculating the degree of charge and current
neutralization of the ion beam pulse by the background plasma.
The code suite consists of two different codes: a fully
electromagnetic, relativistic particle-in-cell code, and a
relativistic Darwin model for long beams. As a result of a number
of simplifications, the second code is hundreds of times faster
than the first one and can be used for most cases of practical
interest, while the first code provides important benchmarking
for the second. An analytical theory has been developed using
the assumption of long charge bunches and conservation of
generalized vorticity. The model predicts nearly complete charge
neutralization during quasi-steady-state propagation provided
the beam pulse duration τb is much longer
than the inverse electron plasma frequency
ωp−1, where
ωp = (4πnp e2/me)1/2
and np is the background plasma density.
In the opposite limit, the beam head excites large-amplitude
plasma waves. Similarly, the beam current is well neutralized
provided ωpτb >> 1
and the beam radius is much larger than plasma skin depth
δp = c/ωp.
Equivalently, the condition for current neutralization can be expressed
in terms of the beam current as Ib >>
4.25Zb βb(nb
/np)kA, where
nb is the beam density,
Zb is the ion charge, and
Vb = βb c
is the beam velocity; and the condition for charge neutralization
can be expressed as Ib >>
4.25βb3(nb
/np)(rb
/lb)2kA,
where lb and rb
are the beam length and radius, respectively. For long charge bunches, the
analytical results agree well with the results of numerical simulations. The
visualization of the data obtained in the numerical simulations
shows complex collective phenomena during beam entry into and
exit from the plasma.