Theory
Much of our theoretical
interest is in nonlinear collective laserplasma interactions, e.g. Raman
amplification, electromagnetically induced guiding, electromagnetically
induced transparency, wakefield interactions, and generation of infrared
radiation in plasmafilled undulators. The task is to develop appropriate
theoretical models of the respective interactions, which then guides the
development of numerical hydrodynamic or particle codes for the simulation
of situations relevant to experiments.
The propagation properties of electromagnetic
waves in (unmagnetized) plasma are largely determined by the relation
of their frequency to the (electron) plasma frequency,
,
where e and m are the electron charge
and mass, respectively, n is their number density, and ε_{0}
is the vacuum permittivity. Interactions between two waves are based on
modulations of the electron mass and/or the electron density. Both are
due to the forced oscillation in the electromagnetic fields: while the
former follow from the relativistic mass dependence on the oscillation
velocity, the latter are a consequence of the ponderomotive potential,
which is equal to the oscillation energy.
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Raman scattering occurs when the frequencies
of two waves differ by approximately the plasma frequency, so that longitudinal
oscillations at that frequency are resonantly excited, which then scatter
one wave into the other, and vice versa. Either a scattered wave can grow
spontaneously from noise, or a seed pulse can be amplified at the expense
of a strong pump. It is this latter case that interests us. Under the
right circumstances, the seed pulse is compressed during amplification,
leading to a very short and intense pulse. See here
for more details.
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A different process may take place
when the frequency of the longitudinal modulations is far from the plasma
resonance. Under certain conditions, the scattering of two waves into
each other has a focusing effect counteracting the vacuum diffraction.
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A wave with frequency below the plasma
frequency, cannot propagate through the plasma on its own, but interaction
with a second wave allows propagation. Calculations predict transparency,
when the difference or sum of the laser frequencies is just below the
plasma frequency.
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After an electromagnetic pulse has
passed through plasma, the remaining density inhomogeneities lead to a
wakefield, which oscillates at the plasma frequency. Its phase velocity
coincides with the group velocity of the pulse. There are different possibilities
how a second pulse can interact with this field: If the wake is weak,
i.e. the corresponding density perturbations are small, a wave scattered
at it will undergo a frequency shift of . The more interesting case is
that of a strong wake; a wave propagating in the opposite direction may
then be reflected at it, leadin to a large Doppler shift due to the high
velocity of the wake. On the other hand, a pulse propagating with the
wake and shorter than its wavelength may be compressed in it due to the
longitudinal dependence of the density.
top Wakefields may
also be used to trap and accelerate electrons. Ideally, these should reach
the group velocity of the laser pulse which generated the wake, close
to the vacuum speed of light. See the ALPHAX
Project for more details.
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Also under investigation in the ALPHAX
Project is the topic of radiation generation in the periodic magnetic
field of an undulator filled with plasma. The ponderomotive force due
to a short intense laser pulse sets the plasma electrons in longitudinal
motion. The magnetic field then accelerates them in a transverse direction,
so that they can radiate along the undulator axis. The spatial periodicity
of the magnetic field together with the propagation of the laser pulse
leads to a matching condition for the phases of the radiation generated
at different times, which may be satisfied for frequencies either in the
far infrared or in the Xray spectrum.
Interesting questions related to this scheme concern the
influence of a finite amplitude of the magnetic field on the propagation
of the laser pulse – at high amplitudes, the periodically magnetized
plasma represents an optical lattice, with consequently allowed and forbidden
frequency bands.
