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**Unformatted text preview: **neering, elementary model of plasma simulation formulated by
Dawson (1962). Rev. Mod. Phys., Vol. 85, No. 2, April–June 2013 FIG. 5. Numerical solution of the electrostatic ‘‘plasma sheet’’
model based on Eq. (10) plus the exchange of initial position for
crossing plasma sheets (see text for details). The trajectories of a
limited number of sheets (1 over 20) in the (x; t) plane are shown.
The driver ﬁeld has the proﬁle of an evanescent wave with peak
amplitude 0:5me !c=e in vacuum and a sin2 ðt=2Þ rising front
with ¼ 5 T where T ¼ 2=!. A density ne =nc ¼ ð!p =!Þ2 ¼ 5
is assumed. 1985). By considering the driver capacitor ﬁeld as a model for
the magnetic force component, the related electron dynamics
may still be described using the above outlined models, but
with two signiﬁcant differences. First, to lowest order the
magnetic force oscillates at 2!, thus leading to the generation
of hot electron bunches twice per laser period. Second, the
oscillating component perpendicular to the surface vanishes
for circular polarization (and normal incidence), so that hot
electron generation might be strongly suppressed under such
conditions. In fact, the vector potential representing a plane,
elliptically polarized ﬁeld may be written as
AðxÞ
^
^
Aðx; tÞ ¼ pﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ ðy cos!t þ z sin!tÞ
1 þ 2 (11) with 0 1. Using B ¼ r Â A and p? ¼ eA=c for the
transverse momentum of electrons, the Àeðv Â B=cÞ force
can be written as
v
e2 @x A2 ðxÞ
1 À 2
^
1þ
cos2!t ; (12)
Àe Â B ¼ Àx
c
4me c2
1 þ 2
showing that the oscillating component vanishes for circular
polarization ( ¼ 1).7
The integral over x of ne fpx , where fpx ¼ hfx i ¼ hÀeðv Â
B=cÞx i is the steady ponderomotive force density on electrons, equals the total radiation pressure on the target surface.
For circular polarization and normal incidence we thus expect
radiation pressure to push the target while electron heating is
quenched. These conditions have been investigated in order
to optimize radiation pressure acceleration of ions versus
other mechanisms driven by hot electrons; see Sec. IV.A.
7
A more detailed analysis shows that electron heating is quenched
when the parameter exceeds some threshold value; see Rykovanov
et al. (2008) and Macchi, Liseikina et al. (2009). Andrea Macchi, Marco Borghesi, and Matteo Passoni: Ion acceleration by superintense laser-plasma . . . 757 2. Simulations, multidimensional effects, and simple estimates A more quantitative description of laser absorption and
hot electron generation requires numerical simulations. To
address electromagnetic effects in his model Brunel (1988)
performed two-dimensional (2D) PIC simulations in a
plane wave, oblique incidence geometry. Several later studies
using 1D simulations with the ‘‘boosted frame’’ technique
(Bourdier, 1983) are summarized and reviewed by Gibbon
et al. (1999). The absorption degree of a P-polarized laser
pulse is quit...

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