CERN Accelerating science

Example of a self-modulated proton bunch resonantly driving plasma wakefields sustained by the plasma density perturbation (OSIRIS simulations~\cite{osiris}). Beam parameters are optimized for visibility of the effect.

Typical distribution of the beams at (a) the entrance to the plasma, (b) after propagating 4\,m in the plasma, and at (c) the exit from the plasma cell. Electrons first appear at $z=4$,\,m and the laser pulse is the line at $z-ct=0$. The laser pulse quickly creates the plasma and thus seeds the SMI for the proton bunch. The case of side injected electrons is shown.

The maximum wakefield amplitude versus the propagation distance for the stepped-up and uniform plasmas for a simulation with an LHC bunch. The step $\delta n_{e}$ is 1.6\%~\cite{PoP18-103101}. The inset illustrates the change in the plasma density profile at $z=3$\,m.

Calculated energy spectrometer images of the SPS proton beam with and without the plasma \cite{IPAC11-2835}.

First layout of the experimental installation (from \cite{LoI}).

Relative phasing of the accelerated electron bunch and the wave in plasmas of the increased density (a), proper density (b), and reduced density (c).

Positions along the bunch $(z-ct)$ where the wakefields are both accelerating and focusing for witness electrons (shown in grey) as a function of propagation along the plasma. This position varies over the first 4\,m of propagation and remains at the same $z-ct$ after that. The parameters used in the simulation are those of the Design Report baseline design (2nd data column in Table~\protect\ref{t-history}), although here also serve to illustrate the effect in general.

Various designs of electron beam side injection.

Results of the test 1 for kinetic LCODE with the square grid of size (a) $0.01c/\omega_p$, (b) $0.025c/\omega_p$, and (c) $0.05c/\omega_p$; maps of the electric field $E_z$ far behind the driver produced by (d) fluid LCODE (e) and QuickPIC.

Results of the test 2 for several codes in (a) normal and (b) semi-logarithmic scales.

Calculated maximum amplitudes of the accelerating field $E_\text{z,max}$ and of the wakefield potential $\Phi_\text{max}$ excited along the bunch plotted as functions of position along the plasma for proton bunch populations $N_b = 1.15 \times 10^{11}$ (lower curves) and $N_b = 3 \times 10^{11}$ (upper curves). The curves overlap for the low population.

Maps of the wakefield amplitude for (a) low beam population, $N_b = 1.15 \times 10^{11}$, (b) high beam population, $N_b = 3 \times 10^{11}$, and (c) high beam population with immobile ions.

The AWAKE experiment in the CNGS facility (from \cite{NIMA-740-48}).

Final electron energy spectra for the baseline side injection variant and for several variants with slightly detuned injection parameters (indicated near the curves).

Final energy spectra for the optimized on-axis injection into the sharp-boundary plasma (thick line) and for three optimized variants of side injection: DR parameters; $\alpha_0=3$\,mrad, $W_e=20$\,MeV, $\xi_e = 12$\,cm, $z_0=2$\,m; and $\alpha_0=6$\,mrad, $W_e=10$\,MeV, $\xi_e = 10$\,cm, $z_0=1.7$\,m.

Simulation of plasma edge smearing after instantaneous opening the valve with a Direct Simulation Monte Carlo (DSMC) code~\cite{Bird96}.

Schematics of plasma cell with Rb vapor flow through orifices into expansion volumes.

Simulated rubidium pressure in the vicinity of the orifice. The inset shows the gas density distribution along the axis: the thick red (grey) line is DSMC simulations and the thin black line is the approximation~(\ref{e6}).

The radial force exerted on an axially moving relativistic electron in the plasma of the density $4 \times 10^{12}\text{cm}^{-3}$. The laser pulse is at $\xi=0$. The vertical axis is inverted for better visibility of the surface.

The oblique injection scenario.

Wakefield acceptance map. The color shows the accelerated fraction of the electron charge that enters the expansion volume plasma (at $z=-40$\,cm) at certain angle $r'$ and radial offset $r$. The shaded area shows the electron beam at the optimum injection conditions.

Dependence of the maximum electron energy on the steepness of the density gradient. To produce this graph, many test 16\,MeV electrons injected with different delay $\xi_e$, angle $\alpha_i$, and radial offset $r$ were followed up to the end of the plasma section.

(top) Longitudinal motion of test electrons in the case of negative (--10\%, left) and positive (+10\%, right) plasma density gradients (black lines); the color map shows the amplitude of the longitudinal electric field on the axis. (bottom) The energy of these electrons.

Final energy spectra of electrons in cases of side, on-axis, and oblique injection methods. The parameters for the oblique injection case are those given in Table~\ref{t-history} (last column). Beam loading is taken into account.