Fig. 1. The fluid flow velocities and as seen in the shock wave singularity frame of reference and the shock wave velocity and the particle flow velocities and as seen in the laboratory frame of reference.

Fig. 2. (a) The capacitor model for laser irradiances where the ponderomotive force dominates the interaction. (b) The parameters that define our capacitor model: and are the electron and ion densities accordingly, is the electric field, is the distance between the positive and negative DL charges. The DL is geometrically followed by a neutral plasma where the electric field decays within a skin depth and a shock wave is created. (c) The shock wave description in the piston model.

Fig. 3. The compression as a function of the shock wave dimensionless pressure . The numerical values are obtained for .

Fig. 4. The dimensionless shock wave pressure versus the dimensionless laser irradiance in the range 10. For a better understanding of this graph the inserted table shows numerical values in the range .

Fig. 5. The dimensionless shock wave velocity and the particle velocity in the laboratory frame of reference versus the dimensionless laser irradiance in the range . For a better understanding of this graph the inserted tables show numerical values in the range .

Fig. 6. The speed of sound is given in units of the speed of light in (a) and the ratio of the shock velocity to the rarefaction velocity, is shown in (b) as function of the dimensionless laser irradiance in the range . The inserted tables show numerical values in the range .

Fig. 7. The FI scheme suggested in this paper. As a numerical example an initial pellet with radius and DT fuel of density with thickness (i.e., an aspect ratio of 10) is compressed to a density of by nanosecond lasers with a radius of . The picosecond fast igniter laser with a beam diameter creates a shock wave pulse with a thickness of and can be considered a 1D shock wave to a reasonable approximation.

Table 1. The laser is defined by its irradiance , pulse duration , energy W and power P. This laser creates a shock wave with a compression in a pre-compressed target with an initial density . The shock wave thickness , where and are the shock wave velocity and the particle velocity respectively) and its cross section are and , respectively, satisfying in order to have a 1D shock wave.