Bubble core field modification by residual electrons inside the bubble

Abstract

Bubble core field modification due to the nondepleted electrons present inside the bubble is investigated theoretically. These residual electrons induce charge and current densities that can induce the bubble core field modification as well as the bubble shape change. It is found that the electrons entering into the bubble move backward at almost light speed and would weaken the transverse bubble fields. This reduces the ratio of longitudinal to transverse radius of the bubble. For the longitudinal bubble field, two effects compensate with each other because of their competition between the enhancement by the shortening of bubble shape and the reduction by the residual electrons. Therefore the longitudinal field is hardly changeable. As a comparison we perform particle-in-cell simulations and it is found that the results from theoretical consideration are consistent with simulation results. Implication of the modification of fields on bubble electron acceleration is also discussed briefly.

Electrons trajectories around a bubble regime in intense laser plasma interaction

“…In our previous work, 18 we have got the elliptic bubble shape and the modified fields, by considering the effects of the bubble residual electron charge and current. Using a convenience gauge A x ¼ Àu and defining a term U ¼ A x À u, in three-dimensional framework of cylindrical coordinates with x as the laser propagation direction and ðr; hÞ as the transverse polar frame, the components of vector potential A and scalar potential U are…”

“…Other parameters n 1 % 1, n 2 % 1 À 2n a with n a ¼ 0:145 are used, which come from PIC simulation results of Ref. 18.…”

“…In particular, the nonlinear dynamics of electrons plays a key role on the electron acceleration to produce a quasi-monoenergetic electron bunch in the bubble regime, where the ponderomotive force of laser pulse pushes away the plasma electrons, so that a nonlinear soliton-like structure of electron density, i.e., plasma cavity or bubble is formed. [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] There is a very large space-charge separation electrostatic field in the bubble regime, which can efficiently trap and accelerate the electrons at the bottom of the bubble. For example, in Ref.…”

“…Recently, some authors 18,19 have considered the elliptic bubble shape and also derived the modified fields. In our previous study, 18 these modifications are due to the effects of the bubble residual electron charge and current, which are consistent with particle-in-cell (PIC) results.…”

“…18. We are intending to study theoretically the electron motion with or without the ponderomotive force of laser pulse resided in the bubble front.…”