Journal of Theoretical and Applied Physics (JTAP) Numerical investigations of electron-self-injection in different shaped bubbles in wakefield acceleration Volume 17 (2023) JTAP Issue 2, May & June 2023 2023 11 17 Numerical investigations of electron-self-injection in different shaped bubbles in wakefield acceleration 10.57647/J.JTAP.2023.1702.21 EN Sonu Kumar Department of Physics, Indian Institute of Technology Delhi, New Delhi - 110016, India Dhananjay K Singh Department of Physics, PKRM College, Dhanbad - 826004, Jharkhand, India Hitendra K. Malik Plasma Science and Technology Laboratory, Department of Physics, Indian Institute of Technology Delhi, New Delhi 110016, India 0000-0002-9432-8140 Journal Article 2023 11 17 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.