Ion Acceleration in a Solitary Wave by Laser Pulse with Ramping-up Amplitude

Recent work by Jung \textit{et al}. demonstrated experimentally the acceleration of mono-energetic ion beam by solitary waves generated and maintained by laser light with ramping-up amplitude.\footnote{D. Jung, L. Yin, B.J. Albright, D.C. Gautier, R. H\"orlein, D. Kiefer, A. Henig, R. Johnson, S. Letzring, S. Palaniyappan, R. Shah, T. Shimada, X.Q. Yan, K.J. Bowers, T. Tajima, J.C. Fern\'andez, D. Habs, and B.M. Hegelich, Phys. Rev. Lett. 107,115002(2011).} Theoretical model is developed in this work to study the formation of the solitary wave and effects of the radiation pressure force on a soliton in the accelerating plasma. 2D Particle-In-Cell (PIC) simulations are performed to compare and validate the theory. Differences in generating and maintaining solitary wave for laser with and without ramping-up amplitude are also investigated. We will also investigate effects of radiation pressure acceleration of plasma with near critical density.