In this work, we introduce a new ellipsoid model to describe bubble acceleration of electrons and discuss the required conditions of forming it. We have found that the electron trajectory is strongly related to background electron energy and cavity potential ratio. In the ellipsoid cavity regime, the quality of the electron beam is improved in contrast to other methods, such as that using periodic plasma wakefield, spherical cavity regime, and plasma channel guided acceleration. The trajectory of the electron motion can be described as hyperbola, parabola, or ellipsoid path. It is influenced by the position and energy of the electrons and the electrostatic potential of the cavity. In the experimental part of this work, a 20 TW power and 30 fs laser pulse was focused on a pulsed He gas jet. We have focused the laser pulse in the best matched point above the nozzle gas to obtain a stable ellipsoid bubble. The finding of the optimum points will be described in analytical details.

Key words Electron, high intense, plasma accelerator, laser wake field, bubble regime, wave break. PACS 41.75.Jv, 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.

In this work we present an ellipsoid cavity regime for the production of a bunch of quasi-monoenergetic electrons. The electron output beam is more effective than the periodic plasma wave method or the plasma-channel-guided method. A hyperbola, parabola or ellipsoid path is described for the electron trajectory motion in this model. A dense bunch of relativistic electrons with a quasi-monoenergetic spectrum is self-generated here. The obtained results show a smaller width for the electron energy spectrum in comparison with the previous results. We found that there are optimum conditions to form the ellipsoid cavity. Laser beam properties (such as the spot size, power and pulse duration) and plasma features can control the ellipsoid cavity formation. The optimum conditions for effective electron beam production can be determined from these results.

Electron cavity acceleration is one of the relativistic regimes to describe the monoenergetic electron acceleration. In this work, we introduce a new ellipsoid model that could improve the quality of the electron beam in contrast to other methods such as that using periodic plasma wakeˇeld, spherical cavity regime and plasma channel-guided acceleration. The trajectory of the electron motion can be described as hyperbola, parabola or ellipsoid path. It is in uenced by the position and energy of the electrons and the electrostatic potential of the cavity. We have noticed that the electron output energy is not affected by the elongation of the transverse cavity radius in the ellipsoid regime. "¸±μ•¥´¨¥¸ ¶μ³μÐÓÕ Ô²¥±É•μ´´μ£μ •¥ §μ´ Éμ• Ö¢²Ö¥É¸Ö μ¤´¨³¨ § •¥²Öɨ¢¨¸É¸±¨Ì •¥¦¨³μ¢ μ ¶¨¸ ´¨Ö ³μ´μÔ´¥•£¥É¨Î¥¸±μ£μ ¶Êα Ô²¥±É•μ´μ¢. ‚ ¶•¥¤¸É ¢²¥´´μ°• ¡μÉ¥ • ¸¸³ É•¨¢ ¥É¸Ö ³μ-¤¥²Ó Ô²²¨ ¶¸μ¨¤ , ¢ ±μÉμ•μ°³μ¦´μ ʲÊÎϨÉÓ ± Î¥¸É¢μ Ô²¥±É•μ´´μ£μ ¶Êα ¶μ¸• ¢´¥´¨Õ¸¤•Ê£¨³3 ¥Éμ¤ ³¨, É ±¨³¨± ±¨¸ ¶μ²Ó §μ¢ ´¨¥ ¶¥•¨μ¤¨Î¥¸±μ£μ ¢μ §¡Ê¦¤¥´¨Ö ¶² §³Ò, •¥¦¨³¸Ë¥•¨Î¥¸±μ£μ •¥ §μ´ Éμ• ¨± ´ ²Ó´μ¥ ʸ±μ•¥´¨¥ ¶² §³Ò. '• ¥±Éμ•¨Õ ¤¢¨¦¥´¨Ö Ô²¥±É•μ´ ³μ¦´μ μ ¶¨¸ ÉÓ £¨ ¶¥•-¡μ²μ°, ¶ • ¡μ²μ°¨²¨Ô²²¨ ¶¸μ¨¤μ³. Éμ § ¢¨¸¨É μÉ ¶μ²μ¦¥´¨Ö¨Ô´¥•£¨¨Ô²¥±É•μ´μ¢¨Ô²¥±É•μ-É É¨Î¥¸±μ£μ ¶μÉ¥´Í¨ ² •¥ §μ´ Éμ•. ‚ • ¡μÉ¥ μɳ¥Î ¥É¸Ö, ÎÉμ ¢ Ô²²¨ ¶¸μ¨¤ ²Ó´μ³ •¥¦¨³¥ Ô´¥•£¨Ö Ô²¥±É•μ´ ´ ¢ÒÌ줥´¥ § ¢¨¸¨É μÉ ¢¥²¨Î¨´Ò ¶μ ¶¥•¥Î´μ£μ • ¤¨Ê¸ •¥ §μ´ Éμ• .

The electron acceleration in the bubble regime is considered during the laser-plasma interaction. The PIC and experimental results show that the obtained ellipsoid cavity model is more consistent than the spherical model. We prove the fields inside the cavity depend linearly on the coordinates and the spherical cavity is a special case of the ellipsoid model. The quasi mono-energetic electrons output beam tracing the laser plasma can be more appropriately described with this model.