بررسي مدولاسيون دامنۀ امواج غيرخطي در برهمكنش ليزر-پلاسما با تابع توزيع تساليس براي الكترون ها

Investigation of the amplitude modulation of the nonlinear waves in laser-plasma interaction with Tsallis distribution function for electrons

در اﯾﻦ ﻣﻘﺎﻟﻪ، ﺑﺎ اﺳﺘﻔﺎده از ﻣﺠﻤﻮﻋﮥ ﻣﻌﺎدﻻت ﻣﺪل ﺳﯿﺎﻟﯽ و ﻣﻌﺎدﻻت ﻣﺎﮐﺴﻮل، ﻣﻌﺎدﻟﮥ ﻏﯿﺮﺧﻄﯽ ﺑﺎ ﺟﻮاب ﺳﺎﻟﯿﺘﻮﻧﯽ اﻟﮑﺘﺮوﻣﻐﻨﺎﻃﯿﺴﯽ ﻧﺎﺷﯽ از ﺑﺮﻫﻤﮑﻨﺶ ﺑﯿﻦ ﭘﺎﻟﺲ ﻟﯿﺰر ﺑﺎ ﺷﺪت ﺑﺎﻻ در ﻣﺤﯿﻂ ﭘﻼﺳﻤﺎ ﺑﻪ دﺳﺖ آﻣﺪه اﺳﺖ. ﺗﺎﺑﻊ ﺗﻮزﯾﻊ ﺑﺮاي اﻟﮑﺘﺮونﻫﺎي ﻏﯿﺮﺣﺮارﺗﯽ، ﺗﺎﺑﻊ ﻏﯿﺮﺗﻌﺎدﻟﯽ ﺗﺴﺎﻟﯿﺲ1 در ﻧﻈﺮ ﮔﺮﻓﺘﻪ ﺷﺪه و ﺑﺎ اﺳﺘﻔﺎده از روش ﻣﻘﯿﺎس ﭼﻨﺪﮔﺎﻧﻪ، ﻣﻌﺎدﻟﮥ ﺷﺮودﯾﻨﮕﺮ ﻏﯿﺮﺧﻄﯽ ﺣﺎﮐﻢ ﺑﺮ داﻣﻨﮥ ﭘﺘﺎﻧﺴﻞ ﺑﺮداري ﺑﻪ دﺳﺖ آﻣﺪه اﺳﺖ. ﺑﺎ اﺳﺘﻔﺎده از ﻓﺮﻣﻮلﻫﺎي ﺑﻪ دﺳﺖ آﻣﺪه ﺑﺮاي ﺳﺮﻋﺖ ﻓﺎز و ﮔﺮوه درﻣﯽﯾﺎﺑﯿﻢ ﮐﻪ اﯾﻦ ﺳﺮﻋﺖﻫﺎ ﻣﺴﺘﻘﻞ از ﭘﺎراﻣﺘﺮﻫﺎي ﭘﻼﺳﻤﺎ )ﻧﺴﺒﺖ اﻟﮑﺘﺮونﻫﺎي ﻏﯿﺮﺣﺮارﺗﯽ و ﭘﺎراﻣﺘﺮ ﻧﺎﻓﺰوﻧﻮر( ﻫﺴﺘﻨﺪ. در اداﻣﻪ، اﯾﻦ ﺳﺮﻋﺖﻫﺎ ﺑﺮ ﺣﺴﺐ ﻋﺪد ﻣﻮج رﺳﻢ ﺷﺪﻧﺪ. ﺑﻪ ﻃﻮر ﺗﺤﻠﯿﻠﯽ، ﺷﺮاﯾﻂ ﻧﺎﭘﺎﯾﺪاري ﻣﺪوﻻﺳﯿﻮﻧﯽ و ﻫﻤﭽﻨﯿﻦ وﺟﻮد اﻧﻮاع ﮔﻮﻧﺎﮔﻮن ﻣﺪﻫﺎي ﭘﻮش ﺟﺎﯾﮕﺰﯾﺪه )روﺷﻦ و ﺗﺎرﯾﮏ( ﺑﺮﺣﺴﺐ ﭘﺎراﻣﺘﺮﻫﺎي ﭘﻼﺳﻤﺎ ﺑﺮرﺳﯽ ﺷﺪه اﺳﺖ. در ﻧﻬﺎﯾﺖ ﺑﺎ ترﺳﯿﻢ ﻧﻤﻮدار، ﺑﻪ ﻃﻮر ﻋﺪدي ﻣﻨﺎﻃﻖ ﭘﺎﯾﺪاري و ﻧﺎﭘﺎﯾﺪاري ﻣﺪوﻻﺳﯿﻮﻧﯽ ﺑﺮرﺳﯽ ﺷﺪﻧﺪ.

In this paper, the electromagnetic solitary wave due to the interaction of laser pulse and plasma media was studied by using a system of the nonlinear electron hydrodynamics and Maxwell’s equations. The Tsallis distribution function is assumed for the electron particles. By implementing the multiple scales technique, the nonlinear Schrodinger equation govern on the vector potential was derived. Analytically, the effects of nonextensive and nonthermal parameters on the condition of the modulation instability and existence of the types of envelope modes (bright and dark), were discussed in detail. Finally, the regions of the modulation stability and instability were studied numerically by plotting some figures