**Unformatted text preview: **05) or with ad hoc modeling of Th ðtÞ (Bychenkov
et al., 2004).
Analytical solutions for the plasma expansion can be
found in the quasineutral approximation, also for the kinetic
Vlasov equation (18), using either the self-similar theory
(Dorozhkina and Semenov, 1998) or a renormalized group
theoretical approach (Kovalev, Bychenkov, and Tikhonchuk, FIG. 17 (color online). Velocity spectrum of heavy ions (H) and
light ions (L) at two different times from the numerical simulation of
the expansion of a two-species plasma using a Boltzmann-VlasovPoisson model. Black dashed lines are analytical proﬁles based on
self-similar solutions. The spectrum of light ions shows a peak typical
of a multispecies expansion. From Tikhonchuk et al., 2005. 2001, 2002). Two-temperature electron distributions have
also been considered.13
3. Multispecies expansion We now describe the expansion of a two species plasma, in
which the dynamics of a heavy ion component (labeled with
H in the following) is considered in addition to light ions
(labeled with L). The most peculiar effect of the presence of
two (or more) ion species, for appropriate parameters, is the
appearance of spectral peaks, which are of interest as both a
strong experimental signature and for application purposes.
The problem of two species expansion was studied by
Gurevich, Pariiskaya, and Pitaevskii (1973), Bezzerides,
Forslund, and Lindman (1978), and Srivastava, Sinha, and
Lawande (1988). Here we mostly follow the more recent
work of Tikhonchuk et al. (2005), where a simpliﬁed description is given based on the ordering assumptions ¼ AH =ZH
) 1;
AL =ZL N¼ ZH nH
> :
ZL nL (25) These conditions state that the H species is quite heavier than
the L one, that the concentration of the latter is small, and that
the L ion plasma frequency is higher so that the dynamics of
L ions is faster. These assumptions allow one to assume that,
near the rarefaction front, the effect of L ions is unimportant
and that the dynamics of the H ions can be described as a
single species expansion as in Sec. III.C.2, ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ
q where the relevant
parameter is the H ion sound speed cH ¼ ZH Th =AH mp <cL ,
the L ions sound speed. L ions are treated as test particles in
this region, where they are accelerated by the electric ﬁeld
E / cÀ1 [see Eq. (13)], which is thus stronger than what
H
would be created in the expansion of the L ions alone. The
L ion velocity and density in this region can be obtained using
the 1D ﬂuid, self-similar equations with the above given 12 See, e.g., Widner, Alexeff, and Jones (1971), Crow, Auer, and
Allen (1975), Pearlman and Morse (1978), Denavit (1979), and
Mora (2003) for the case of a single electron population and
Bychenkov et al. (2004), Mora (2005), and Tikhonchuk et al.
(2005) for the case of two electron components.
Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013 13 See, e.g., Bezzerides, Forslund, and Lindm...

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