Page 4 - Transport studies in high-performance field reversed configuration plasmas

as opposed to the conventional linear force proportional to N. (If N is 106 , the collective force is 106 times greater than its linear counter part).
Lured by this concept, a large body of investigations ensued [21-24]. Norman Rostoker’s program was one of them (some of these efforts are reviewed in this Proceedings of the Norman Rostoker Memorial Symposium [25]). For example, in one of these attempts [26] an electron beam is injected into a plasma to cause a large amplitude plasma wave by the beam-plasma interaction (a collective interaction);, it was suggested that such a large amplitude wave would trap ions and accelerate them to speeds near that of the electron beam. If ions were to be trapped by a
speeding electron cloud or beam with energy εe , the ions would be accelerated to the energy of εi = (M / m)εe ,
where M and m are masses of ions and electrons, respectively, because they would speed with the same velocity. Since the mass ratio M/m of ions to electrons is nearly 2000 for protons and greater for other ions, the collective acceleration of ions would gain a large energy boost. None of the collective acceleration experiments in those days, however, found energy enhancement of the magnitude mentioned above. The primary reason for this was attributed to the sluggishness (inertia) of ions with electrons being pulled back to ions, instead of the other way around, or to too fast ‘reflexing (return flow) of electrons’ as described in [26]. The ion acceleration takes place only over the sheath of electrons (of the beam injected) that are ahead of ions, while the sheath is tied to the beam injection aperture (an immovable metallic boundary in this experiment). Mako and Tajima theoretically found that the ion energy may be enhanced only by a factor of 2α+1 (which is about 6 or 7 for typical experimental situations and α will be defined later) over the electron energy, instead of by a factor of nearly 2000, due to the electron reflexing and no co-propagation of the electron beam and the ions, while the formed sheath is stagnant where it was formed. (For example, Tajima and Mako [27] suggested reducing the culpable electron reflexing by providing a concave geometry. Similar geometrical attempt to facilitate the laser-driven ion acceleration would appear also later in 2000’s-2010’s.) In year 2000 the first experiments [28-30] to collectively accelerate ions by laser irradiation were reported. In these experiments a thin foil of metallic (or other solid materials) was irradiated by an intense laser pulse, which produced a hot stream of electrons from the front surface that faced the laser pulse, propagating through the thin foil emerging from the back surface of the foil. Now this physical situation of what is happening at the rear surface of the foil is nearly equivalent to what the group of Rostoker had done in 1970’s and 80’s in terms of the dynamics of electrons emanating from the metallic boundary and its associated ion response as a result of their injected electron beam. The superheated electrons by the laser caused the acceleration of ions in the sheath which was stuck stationary on the rear surface of the target, but not beyond. Such acceleration was then called the Target Normal Sheath Acceleration (TNSA) [28-31].
The experiments and simulations since then improved the understanding of the importance of increased adiabaticity in the ion acceleration. These studies showed that the proton energy increases as the target thickness decreases for a given laser intensity and that there is an optimal thickness of the target (at several nm) at which the maximum proton energy peaks and below which the proton energy now decreases [32-34]. Figure 3 shows the schematic changes in the original collective accelerator effort as well as the laser-driven acceleration in the TNSA regime in contrast with more adiabatic acceleration (with various improvements such as thinner target, circularly- polarized irradiation, or more intense laser regime of the Radiation Pressure Acceleration [35]). This optimal
thickness for the peak proton energy is consistent with the thickness dictated by the relation a0 ~ σ = n0 d , nc λ
where σ is the (dimensionless) normalized electron areal density, a0 , d are the (dimensionless) normalized amplitude of electric field of laser and target thickness [36-38]. We define here ξ as the ratio of the normalized areal density to the normalized laser amplitude ξ = σ / a0 . The optimal condition ξ ~ 1 is understood as arising from the
condition that the radiation force pushes out electrons from the foil layer if σ ≤ a0 or ξ ≤ 1, while with σ ≥ a0 or ξ ≥ 1 the laser pulse does not have a sufficient power to cause maximal polarization to all electrons. Note that this
optimal thickness for typically available laser intensity is much smaller than for cases with previously attempted target thicknesses (for ion acceleration). Thus we attribute the observed comparatively large value of the maximum proton energy in the experiment [32] to the ability to identify and provide prepared thin targets on the order of nm to reach this optimal condition.
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