Contrib. Plasma Phys. 48, No. 8, 555 – 560 (2008) / DOI 10.1002/ctpp.200810088 Using the Steepened Plasma Profile and Wave Breaking Threshold in Laser-Plasma Interaction P. Zobdeh 1 , R. Sadighi-Bonabi ∗2 , H. Afarideh 1 , E. Yazdani 1 , and R. Rezaei Nasirabad 2 1 Department of Physics, Amirkabir University of Technology, Tehran, Iran 2 Department of Physics, Sharif University of Technology, 11365-9567, Tehran, Iran Received 19 March 2008, accepted 15 June 2008 Published online 10 October 2008 Key words Electron, high intense, plasma accelerator, laser wake field, bubble regime, wave break. PACS 41.75.Jv, 42.62.-b, 52.38.-r, 41.75.Lx In this work we evaluate the interaction of high intense laser beam with a steepened density profile. During laser interaction with underdense plasma by freely expanding plasma regime, modification of density profile is possible. In this paper we have investigated the ultra short laser pulse interaction with nonisothermal and collisionless plasma. We consider self–focusing as an effective nonlinear phenomenon that tends to increase when the laser power is more than critical rate. By leading the expanded plasma to a preferred location near to critical density, laser reflection is obtained, so the density profile will be locally steepened. The electromagnetic fields are evaluated in this new profile. We show the amplitude and period of electrical field oscillation are increased by reducing the steepened scale length. Also our numerical results identify that by reducing the steepened scale length, the electrical field is increased to wave breaking threshold limit. This high gradient electrical field causes the effective beam loading during the wave breaking phenomenon. The wave breaking can be the initial point for other acceleration regime as cavity or channel guiding regime. c  2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim 1 Introduction During the recent 20 years, ultrashort (10 -12 - 10 -16 s) and high intense laser pulses are generated by CPA laser technique. With this progress, concentration of extremely high energy flux into a small volume is pos- sible. With intensities much higher than atom ionization threshold, other phenomena are observable during laser-plasma interaction. Free electron oscillates at nearly the speed of light in the high gradient generated field. In this field several novel relativistic effects occur. These effects include the generation of wake field-plasma- waves, self-focusing, electron cavitations, bubble regime, nonlinear Thomson scattering, electron-positron pair production, ultrarelativistic interactions, and gigagauss magnetic fields [1-3]. Plasma-based accelerators are interested because of their ability to generate the large acceleration gradient in the small length of plasma. These high power lasers have various applications including transmutation of cheap and hazardous materials with long-lived radioactive wastes to the valuable radioisotopes [4]. In the standard scheme of the laser wake field accelerator (LWFA), an ultrashort, intense laser pulse propagates through the underdense plasma. It can generate large amplitude plasma waves by the effect of ponderomotive force. This ponderomotive force is given by: F p ≈ -∇a 2 , where F p is ponderomotive force and a is the laser pulse envelope. Electron plasma wave is limited by wave breaking, which occurs when the wake reaches amplitude sufficient to trap background plasma electrons from rest. In the one dimensional non-relativistic limit, this condition is E 0 = cm e ω p /e, or E 0 (V/cm) ≈ 0.96  n 0 (cm -3 ), where ω p = (4πne 2 ) 1/2 is the electron plasma frequency, n 0 is the ambient electron number density, m e and e are the electron rest mass and charge, respectively, and c is the speed of light in vacuum. For example, a plasma density of n 0 = 10 18 (cm -3 ), yields E 0 ≃ 100 GV/m. The length of the ac- celerating wave in a plasma-based accelerator is approximately the plasma wavelength λ p =2πc/ω p =2π/k p , or λ p (μm) ≃ 3.3 × 10 10  n 0 (cm -3 ) [5-9]. ∗ Corresponding author: e-mail: sadighi@sharif.edu c  2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim