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Tham khảo tài liệu 'acoustic waves from microdevices to helioseismology part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 348 Acoustic Waves - From Microdevices to Helioseismology irradiated spot and outward from the spot along the surface. Temperature evolution at any moment t T and for any position z 0 proceeds according to the following equation Prokhorov Konov et al. 1990 T z. t t1 2ierfc t t 1 2 ierfc --- ----- 11 1 2 t - K t ierfc 2Y 1 2 t T 2 pt - 2 11 where Y is the thermal diffusivity of the metal which can be expressed as Y K cp . The function ierfc x is given by ierfc x - n 1 2 exp -x2 - x 1 - erf x 12 2 x where erf x - -Á 1 exp - 2 dệ in 0 Eqs. 10 and 11 are the solutions of the one-dimensional heat diffusion equation and are valid only if the laser beam size r0 is significantly greater than both the foil thickness h and the thermal diffusion length lth calculated as lth Y t 1 2. The strong rise of the surface temperature given by Eq. 10 results in the surface melting and evaporation as well as in plasma plume formation ablation regime Miller and Haglund 1998 . Despite the fact that laser plasma generation and evolution have been the focus of numerous studies no general mechanisms exist that describe the plasma recoil pressure on the surface for a broad range of laser intensities Phipps Turner et al. 1988 due to the complexity of the phenomenon. For GW cm2 peak laser powers hot and dense plasma is formed in the vicinity of the surface which can screen the surface and prevent laser radiation from reaching it. In this case the ablative pressure very weakly depends on the target material parameters Phipps Turner et al. 1988 and has a sub-linear dependence on laser intensity. In a semi-regulating one-dimensional plasma model which can be applied to our case as a simplified first-order approximation this equation is written as follows Gospodyn Sardarli et al. 2002 P mx 7.26 108 13 4 xT 4 13 where I is expressed in GW cm2 Ằ in microns T in nanoseconds and Pa max in Pa. While Eq. 13 was derived for an aluminum target in vacuum and for a supercritical plasma density it exhibits .