Correction to: Scientific Reports https://doi.org/10.1038/s41598-019-47677-5, published online 02 August 2019


This Article contains errors. In the Introduction,


“Plasma frequency is defined by the formula \({\omega }_{p}=\)(\(4\pi {n}_{0}{e}^{2}\)/\({m}^{0.5}\) with \({n}_{0}\) being plasma density, \(m\) is electron rest mass and \(e\) is the elementary charge.”


should read:


“Plasma frequency is defined by the formula \({\omega }_{p}= \left(4\pi {n}_{0}{e}^{2} / {m}^{0.5}\right)\) with \({n}_{0}\) being plasma density, \(m\) is electron rest mass and \(e\) is the elementary charge.”


Additionally, in the Discussion,


“In the PIC simulations, we applied 3 types of density profiles, shown in Fig. 2a: one trapezoidal profile with peak density 1 × 1019 electrons/cm3 (case i), one trapezoidal profile with peak density 1.4 × 1019 electrons/cm+ (case iii) and one profiles with 3 ramps (case ii).”


should read:


“In the PIC simulations, we applied 3 types of density profiles, shown in Fig. 2a: one trapezoidal profile with peak density 1 × 1019 electrons/cm3 (case i), one trapezoidal profile with peak density 1.4 × 1019 electrons/cm3 (case iii) and one profiles with 3 ramps (case ii).”


Additionally, in the Figure Legend for Figure 2


“Quasi-3D PIC simulation to show the of density ramp on the LWFA: Figure (a) highlights the initial density profiles used to simulate three cases, and (b) compares the electron energy spectrum for the three cases when the maximum energy is obtained at time t = 1452 \({\upomega }_{p}^{-1}\) for case (i) and (ii), and at time t = 1313 \({\upomega }_{p}^{-1}\) for case (iii). Figure (c–e) show the longitudinal phase space and electric field lineout at the axis (blue line) for the three cases at time t = 1194 \({\upomega }_{p}^{-1}\).”


should read:


“Quasi-3D PIC simulation to show the effect of density ramp on the LWFA: Figure (a) highlights the initial density profiles used to simulate three cases, and (b) compares the electron energy spectrum for the three cases when the maximum energy is obtained at time t = 1452 \({\upomega }_{p}^{-1}\) for case (i) and (ii), and at time t = 1313 \({\upomega }_{p}^{-1}\) for case (iii). Figure (c–e) show the longitudinal phase space and electric field lineout at the axis (blue line) for the three cases at time t = 1194 \({\upomega }_{p}^{-1}\).”


Finally, in the Methods,


“Here the results are discussed for three density profiles plotted in Fig. 2(a), where in case (i) The plasma density rises to n0 in plasma scale length 900c\ωp, stay flat for 800c\ωp, and drops down to 0 in next 900c\ωp plasma length. In case (ii) after reaching the density n0 in plasma scale length 900c\ωp, the electron density further grows to 1.4 n0 in next 800c\ωp, and in case (iii) the density profile is similar to the case i, with flat density at 1.4 n0.”


should read:


“Here the results are discussed for three density profiles plotted in Fig. 2(a), where in case (i) The plasma density rises to n0 in plasma scale length 900 c/ωp, stays flat for 800 c/ωp, and drops down to 0 in next 900 c/ωp plasma length. In case (ii) after reaching the density n0 in plasma scale length 900 c/ωp, the electron density further grows to 1.4 n0 in next 800 c/ωp, and in case (iii) the density profile is similar to the case i, with flat density at 1.4 n0.”