Laser and plasma interaction leads to several fascinating nonlinear phenomena, out of which bubble wakefield excitation is one of the recent interests. This field is used for the particle acceleration, which is very useful for high energy physics, betatron radiation emission, cancer therapy, etc. In the present work, an electromagnetic field is evaluated in bubble wakefield regime and the shape of the bubble is shown to be controlled by d’Alembert differential equations and different Gauge conditions. Wakefield potential is calculated in different bubble regimes such as spherical, longitudinal ellipsoid, transverse ellipsoid bubble regimes. A geometrical parameter is found to decide the size of the bubble. A detailed study of the same is conducted under the effect of different electron residual density. A comparative study of different Gauge conditions shows that the accelerator gradient is maximum in transverse ellipsoid bubble case. Also, energy gain in dephasing length is evaluated that shows maximum energy when bubble assumes transverse ellipsoid shape. Manuscript profile

Electron-self-injection in bubble wakefield acceleration is the new concept for acceleration of electrons inside bubble. In this technique, self-injected plasma electrons have been used for acceleration whose advantage is that there is no need of external source of electrons. In our case, we have carried out numerical investigations of self-injected plasma electrons in different shaped bubbles such as spherical, longitudinal ellipsoid and transverse ellipsoid bubble. For these numerical investigations, by carrying out relativistic Hamiltonian analysis of plasma electrons, we have used 4th order Runge-Kutta (RK) method by employing MATLAB ode45, a nonstiff differential equations solver. We have discussed different parameters such as impact parameter, radius of bubble, bubble velocity for their effect on the formation of bubbles with different shapes and self-injection of the electrons. Manuscript profile