Now, it is assumed that for a given element the motion is ballistic after an initial kick by the laser pulse delivering a transverse momentum p ⊥ = m i ϖ 0 r ⊥ ( 0 ), i.e. r ⊥ ( t ) = Λ ( t ) r ⊥ ( 0 ), and D is the dimensionality of the system D = 1 corresponds to planar geometry (constant σ), D = 2 to two-dimensional Cartesian geometry, and D = 3 to three-dimensional geometry with cylindrical symmetry. Where Λ ( t ) describes the dilatation of the transverse position of a fluid element of the sail, i.e. These data suggest that tight focusing of the laser pulse and, possibly, imperfect conversion to CP may prevent efficient LS operation, at least in the intensity regime investigated so far, i.e. Experiments performed so far, however, have shown a limited impact of the use of CP and non-LS effects such as species separation in the spectrum (in the ideal LS regime, all species move at the same velocity, thus the energy per nucleon is independent on the mass number). Detailed 3D simulations in the relativistic regime also showed that for CP pulses higher energies and better collimation of the ion beam are obtained with respect to LP pulses. The use of CP pulses has then been proposed by several authors to obtain an efficient LS regime at “any” intensity. Heating of electrons occurs via oscillations across the laser-plasma interface driven by the oscillating term, which vanishes for circular polarization (CP). At normal incidence, electrons are driven in the direction perpendicular to the target surface by the v × B force which for linear polarization (LP) has an oscillating term at 2 ω (where ω is the laser frequency) in addition to the secular ponderomotive force. To find the conditions in which the radiation pressure P \tiny rad will dominate the acceleration let us briefly recall the heating dynamics of electrons. Ions initially in the x d < x < x s layer are accelerated by the charge separation field E x up to the velocity υ i at the time t = t c. ![]() The densities of ions ( n i) and electrons ( n e) are approximated by step-like functions. Figure 2: Cartoon sketching the first stage of ion acceleration driven by radiation pressure. The situation is more complex for finite width pulses in multidimensional geometry because the transverse expansion of the foil leads to a decrease of the surface density σ in time. Actually Eq.( 4) may be considered as slightly pessimistic because as the foil moves the reflectivity increases due to the decrease of the pulse frequency in the moving frame. ![]() Despite the very simplified underlying model, Eq.( 4) describes fairly well the onset of transparency and the breakdown of LS acceleration observed in 1D simulations. Where a 0 = ( I / m e n c c 3 ) 1 / 2, ζ = π σ 0 / ( Z m i n c λ ), n c = π m e c 2 / ( e 2 λ 2 ) = π / ( r c λ 2 ) is the cut-off density and λ is the laser wavelength. Notice that the equation of motion for the sail ( 1) and the expression for the mechanical efficiency may be simply obtained by considering the Doppler shift of the reflected radiation and the conservation of the “number of photons”, see e.g. The sail is pushed by a plane wave of intensity I and frequency ω. The sail is modeled as a perfect mirror of surface density σ = ρ ℓ with ρ the mass density and ℓ the thickness. the use of collective effects to accelerate large amounts of particles to high energies. The fundamental point of Veksler’s proposal was that the radiation force on the cluster scaled as N 2, providing an example of his new principle of coherent acceleration, i.e. In 1957, V. I. Veksler suggested that Thomson scattering by a small cluster containing N electrons may accelerate the cluster to high velocities. The scattering of an EM wave by a particle also leads to momentum absorption and acceleration.
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