Fusion Programme - ENEA - Fusione

5. Inertial Fusion2007 Progress Reportthe order of the laser pulse duration or the target expansion time or any time ofinterest in the interaction process. Under these conditions, the time topropagate any information in a round trip, between the target and the massivesupport, is longer than t. The additional condition that the total mass in thespokes has to be smaller than that in the disk gives an upper limit for w. Noreturn current can affect the fast-electron confinement in the time of interest.The additional spoke mass potentially involved in the interaction process issmaller than the mass of the disk. Thus the amount of mass involved in theinteraction process can be predetermined, as well as the laser energy to betransferred by the electrons to the ions to get an assigned ionic energy.0rR 0ZSuitable interaction regimes can be found to limit the number of energeticelectrons escaping from the target before supplying the absorbed laser energyto the ions [5.6]. Thus the fast electrons trapped in the target transfer theabsorbed laser energy (fraction η) to the ions via a quasi-neutrality electrostaticfield that couples electrons to ions and drives the target expansion (at therequired ion velocity = ν ion ).Δ 0 /2Fig. 5.1- Target geometryLow-aspect-ratio disks having initial values of thickness Δ=Δ 0 and radius R=R 0 chosen to make Δ 0 /2R 0 ∂z ∂r(5.1)(p(o) is the pressure in the target centre).During target expansion the pressure gradients get comparable values along the r and z directions(Δ→2R 0 ). Thus the ion collimation effect becomes relaxed at this time t c ≈ R 0 /(ν ion /2). So as not to affectthe attained collimation degree, the allowed laser pulse duration has to be t las ≤t c . Due to massconservation during the quasi-1D target expansion (until t=t c ) it follows thatπR 2 0 Δ 0 ρ 0 ≈R2 0 2R 0 ρ c →Δ 0 /2R 0 =ρ c /ρ 0 where ρ 0 is the initial target density and ρ c is the density at the time t c .Assuming ρ c equal to the critical density then represents the condition for allowing the maximum laserpulse duration before the plasma becomes transparent.Adding the energy conservation to these assumptions on the previous condition on the target aspect ratioit follows that [5.4]Δ 0 = 2 ( ηE 1112lasρ c ) 3 ηE; Rρ 20 = ( las ) 3 ηE; t2 c = 2( las ) 3 ; Φ5 las = v 3ion ρco πv ionπv ionρcπv ionρc2η(5.2)[5.4] C. Strangio, et al., Laser Part. Beams 25, 1–7 (2007)[5.5] C. Strangio, et al., A study for target modificationinduced by the pre-pulse in Petawatt-class lightmatterinteraction experiments, Proc. of the 28 thEuropean Conference on Laser Interaction with Matter- ECLIM (Rome 2004), p. 271-276 (2004)[5.6] C. Strangio and A. Caruso, Laser Part. Beams 23, 33-41 (2005)(Φ las is the laser power density and E las the laserenergy).Under the selected interaction regime (fig. 5.2), thequasi-neutrality condition λ D 2 /Δ 0 2