Fig. 1. Evolution of average fraction of defects, given by xt,Q,β=Q1+Q1−exp(−t(1+Q))+xeq(β) in Eq. (15), as a function of exposure time t. The temperature β = 1/k_BT is expressed in units of 1/E_v, and the power flux Q is expressed in units of Q₀.

Fig. 2. Average fraction of defects for Q^* = 4.76 × 10⁻⁴Q₀ as a function of exposure time t. The filled circle corresponds to the predicted fraction of defects for the case of tungsten exposed to power flux Q^* for t^* = 75 ns.²⁷ This value is consistent with melting, as we observed in our experiment, because a fraction of defects of between 10⁻⁴ and 10⁻³ is required to melt a material.^54,58–60

Fig. 3. Asymptotic values xmax as a function of free parameters Q and β. The contour lines indicate combinations of Q and β that lead to the same value of xmax.

Fig. 4. Average fraction of defects as a function of exposure time for different values of integral damage factor (IDF) F.

Fig. 5. Maximum fraction of defects as a function of IDF F=Qt. The behavior is linear in accordance with Eq. (25).

Fig. 6. Maximum fraction of defects as a function of normalized IDF F/F₀, up to F = 0.6 F₀. The blue curve is the numerical solution of Eqs. (B1) and (B2), and the orange curve is the linear approximation in Eq. (25).

Fig. 7. Maximum effective temperature as a function of IDF, computed by matching x_max(F) to exp(−E_v/k_BT_eff).

Fig. 8. Effective temperature Teff(F)=Ev/kBln(1/xt(F)) as a function of exposure time t along lines of constant IDF F (measured in units of W s^1/2/cm²).