Operating plasma density issues on large-scale laser-plasma accelerators toward high-energy frontier

Consideration of laser-driven plasma-based electron/positron accelerators with a 2 TeV center-of-mass energy is presented, employing a multistaging scheme consisting of successive multi-GeV laser wakefield accelerators operated at the plasma density range of ${10}^{15}–{10}^{18}{\mathrm{cm}}^{-3}$ in the quasilinear regime. A total accelerator length is determined by an operating plasma density and a coupling distance allowed for both laser and beam focusing systems. We investigate beam dynamics and synchrotron radiation due to the betatron oscillation of the beam in laser-plasma acceleration, characterizing the beam qualities such as energy spread and transverse emittance. According to the criteria on the beam qualities for applications and available laser sources, the operating plasma density will be optimized. We note that in the low density operation the required wall-plug power for the laser driver will be much reduced in comparison with the high-density options.

Figure 1

The beam dynamics over one stage for the $n_e={10}^{15}{\mathrm{cm}}^{-3}$ case in Table : (a) mean energy, (b) relative energy spread, and (c) normalized transverse emittance for an initially matched beam with an initial emittance of $2060\mu \mathrm{m}\mathrm{rad}$ injected into a 333 m long, low density LPA stage ($n_e={10}^{15}{\mathrm{cm}}^{-3}$) with initial energy 1 GeV, initial energy spread of 1%, and constant acceleration $E_z=1.5\mathrm{GV}/\mathrm{m}$. The blue curves represent our numerical calculations, while the red dashed curves correspond to the respective analytical expressions, Eqs. (26, 27). The maximum propagation distance $⟨{\omega }_{\beta }{⟩}_0{t}_{\max }$ corresponds to the stage length.

Figure 2

Results of scaled simulation: (a) scaling of the peak accelerating electric field $E_z$ and the transverse electric field $E_r$ for various plasma densities. The normalized laser vector potential initially has a Gaussian form in the transverse direction and a ${sin}^2$ temporal profile with $a_0=\sqrt{2}$, $k_p{r}_L=3$, and ${\omega }_p{\tau }_L=1.7$. The laser pulse propagates in a matched parabolic density channel with the channel depth at $r_L$ are $\Delta n_c/n_e=0.44$. The solid lines show scaling calculated by Eq. (2) for the peak accelerating field $E_z$ and the average transverse electric field $E_r\simeq E_z/3\sqrt{2}$ given by Eq. (15). (b) Evolution of the laser field $a$ in terms of the initial laser field $a_0$ as a function of the propagation distance $k_p^{3}z/k_0^2=k_{p}z(n_e/n_c)$ at various plasma densities. The stage length corresponds to $k_p^3{L}_{\mathrm{stage}}/k_0^2=\pi /2$ and the effective dephasing length corresponds to $k_p^3{L}_{dp}/k_0^2=\pi$.

Figure 3

Laser wakefields in the quasilinear regime: (a) longitudinal electric field $E_z(k_{p}y,k_p\xi )/E_0$, (b) its on-axis distribution $E_z(0,k_p\xi )/E_0$, (c) transverse electric field $E_r(k_{p}y,k_p\xi )/E_0$, and (d) its transverse distribution $E_r(k_{p}y,-2.5)/E_0$ at the plasma density $n_e={10}^{18}{\mathrm{cm}}^{-3}$, where $\xi =z-ct$ is the coordinate moving with the laser pulse from the left to the right.

Figure 4

2D PIC scaled simulation results of an electron bunch acceleration for $a_0=1.4$, $r_L=5\mu \mathrm{m}$, ${\tau }_L=9\mathrm{fs}$, and $N_b=8.8\times {10}^7$ at the plasma density $n_e=7.5\times {10}^{18}{\mathrm{cm}}^{-3}$; (a) the electron energy spectrum and (b) the transverse phase space plot $(x,p_x/p_z)$. The red curve shows the initial energy spectrum and the red dots plot the initial transverse phase space distribution.

Figure 5

Schematic illustrations of multistaged laser-plasma accelerators composed of the LPA stages and the coupling section made of the conventional technologies (a) and the plasma-based technologies (b). For example, the conventional coupling uses an off-axis parabolic mirror for laser focusing and two triplet lenses for beam focusing, while the plasma-based coupling uses a curved plasma channel for the laser off-axis injection and a plasma lens for the beam injection to the next LPA stage.