Analytical approach for the use of different gauges in bubble wakefield acceleration

Laser and plasma interaction leads to several fascinating nonlinear phenomena, out of which bubble wakefieldexcitation is one of the recent interests. this field is used for the particle acceleration, which is very useful forhigh energy physics, betatron radiation emission, cancer therapy, etc. in the present work, an electromagneticfield is evaluated in bubble wakefield regime and the shape of the bubble is shown to be controlled by d’alembertdifferential equations and different gauge conditions. wakefield potential is calculated in different bubble regimessuch as spherical, longitudinal ellipsoid, transverse ellipsoid bubble regimes. a geometrical parameter is foundto decide the size of the bubble. a detailed study of the same is conducted under the effect of different electronresidual density. a comparative study of different gauge conditions shows that the accelerator gradient ismaximum in transverse ellipsoid bubble case. also, energy gain in dephasing length is evaluated that showsmaximum energy when bubble assumes transverse ellipsoid shape.