Fig.1 Partition diagrams of potential-distance between two charged nuclei with relative kinetic energy ε (U0 is the depth of potential well. rn and rmin are the nuclear contact radius and the classical turning point, respectively. As the distance between the two nuclei gets closer and closer, they will go through three processes (a) wave packet contact process, (b) tunneling process and (c) fusion process in turn, and finally fuse with a certain probability.)

Fig.2 Cross sections of several important fusion reactions versus relative kinetic energy of reaction nuclei[38]

Fig.3 (a) Potential energy surfaces of a ddμ- molecular ion in a range of static electric fields plotted as an intensity of a laser pulse with same electric field amplitude (Eμ=5.472 3 keV, aμ=0.263×10-12 m); (b) ddμ- dissociation rate versus the field strength of the sample[52]

Fig.4 Phase diagram of laser parameters of currently achievable lasers (The vertical dashed black line represents a laser frequency of 1 keV. The solid blue lines denote η =10-2, 10-3 and 10-4. The solid pink lines denote nd= 0.1, 1, and 10. The black points are three typical laser parameters. Corresponding dimensionless parameters are nd= 3, 6, 9.[8])

Fig.5 The effective potential is rotational symmetry with respect to z axis. (a)-(c) Contour plots on x-z section of the effective potential at nd=3, 6, 9, respectively; (The blue areas represent the section of inner region Din.)(d)-(f) Veff at different angles (θ=0, π/4, π/2) with respect to nd[8]

Fig.6 At nd=0, 3, 6, 9, (a) angle-dependent penetrability for collision energy of ε=64 keV; (b) angle-averaged penetrability versus collision energy[8]

Fig.7 Fusion cross sections versus collision energy at nd=0, 3, 6, 9[8]

Fig.8 Probability distributions of particles that incident at different angles (θ = 0°, 45°, 90°) under different wavelengths (800 nm, 400 nm, 100 nm) of lasers with intensity 1020 W·cm-2 and corresponding fusion cross sections[53] (red curves)

Fig.9 Angle-averaged fusion cross sections at different laser intensities and wavelengths (The horizontal dot lines represent fusion cross sections without laser field[53].)

Fig.10 (a) The process of DT fusion is divided into three regions, Region Ⅰ: classical motion; Region Ⅱ: quantum tunneling; Region Ⅲ: nuclear fusion; (b) A schematic of classical simulations with an initial Gaussian distribution[54]

Fig.11 (a) Typical classical trajectories of a DT collision driven by laser field at ε=5 keV with different initial laser phases; (b) Zoom-in of the trajectory in (a) (Laser parameters are I=1024 W·cm-2, $\hbar \omega$ =10 eV.)

Fig.12 Penetrability P versus initial energy ε for η=0.01 (blue) and η = 0.002 (red) at different frequencies[54]

Fig.13 13 (a)-(b) Total fusion cross section with various laser intensities and frequencies obtained with the SC method (red circles). Others are presented for comparison: the KH results (olive lines) and the VSA results (blue dotted lines). The initial incident energy ε=1 keV. (c)-(d) Phase diagram of the effective region of laser-field-enhanced DT fusion cross sections at different initial energies