Emittance preservation of an electron beam in a loaded quasilinear plasma wakefield

We investigate beam loading and emittance preservation for a high-charge electron beam being accelerated in quasilinear plasma wakefields driven by a short proton beam. The structure of the studied wakefields are similar to those of a long, modulated proton beam, such as the AWAKE proton driver. We show that by properly choosing the electron beam parameters and exploiting two well known effects, beam loading of the wakefield and full blow out of plasma electrons by the accelerated beam, the electron beam can gain large amounts of energy with a narrow final energy spread (%-level) and without significant emittance growth.

Figure 1

A simplified illustration of the experimental setup for AWAKE Run 2. The SPS proton beam undergoes self-modulation in the first plasma section. The electron witness beam is injected into the accelerating structure, and undergoes acceleration in the second plasma section [9, 17].

Figure 2

QuickPIC simulation results showing the initial time step for the single proton drive beam and witness beam setup. Plasma electron density is shown in grey with the drive beam (blue) and the witness beam (red) superimposed. The line plot indicates the transverse wakefield gradient $\mathrm{d}{W}_x/\mathrm{d}x$ where $W_x=E_x-v_b{B}_y$, evaluated along the beam axis. Beams move to the left.

Figure 3

Top plot: Unloaded longitudinal electric field with no witness beam (dashed blue line) and loaded field (whole blue line) along the beam axis. The beam density along the axis for both beams are shown in red. Bottom plot: Plasma densities along the beam axis for a drive beam with no witness beam (dashed green line), witness beam with no drive beam (dash-dotted green line), and both beams present (continuous green line). The position in the simulation box $\xi =z-tc$, moving toward the left. The plots show the initial time step.

Figure 4

Longitudinal phase space charge distribution of a 100 pC, $60\mu \mathrm{m}$ long witness beam after 4 m of plasma. The mean momentum is $1.67\mathrm{GeV}/\mathrm{c}$ with an RMS energy spread of $87\mathrm{MeV}/\mathrm{c}$ (5.2%) for the full beam.

Figure 5

Beam density in blue along the beam axis for an on-axis beam with respect to the drive beam axis (left), and an offset beam (right) with an offset of one ${\sigma }_{x,eb}=5.24\mu \mathrm{m}$ in the x-plane—at four different positions $z$ in the plasma stage. The red lines show a moving window calculation of transverse normalised emittance. The moving window calculation uses longitudinal slices of $l=4·\mathrm{\Delta }\xi =9.38\mu \mathrm{m}$ with a step of $\mathrm{\Delta }\xi$. Only slices with more than 100 macro particles have been included. The plasma density profile is included in green, and scaled up by a factor of 100 to be visible. These simulations were run with an LHC energy drive beam of 7 TeV.

Figure 6

Plots $\mathbf{a}$ to $\mathbf{f}$ show the transverse phase space of the offset electron beam at different plasma positions. Plot $\mathbf{g}$ shows the macro particle mean position, and plot $\mathbf{h}$ their RMS spread. Plots $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{c}$, as well as the blue lines in plots $\mathbf{g}$ and $\mathbf{h}$ represent particles not in the ion column (see Fig. 5), with position $1.40\mu \mathrm{m}<\xi <1.42\mu \mathrm{m}$. Plots $\mathbf{d}$, $\mathbf{e}$, and $\mathbf{f}$, and the red lines in plots $\mathbf{g}$ and $\mathbf{h}$ represent particles in the ion column with position $1.55\mu \mathrm{m}<\xi <1.57\mu \mathrm{m}$.

Figure 7

Ratio of witness beam charge with emittance preserved, $\tilde{Q}/Q$ (blue symbols, lines), as a function of initial beam charge, and relative energy spread of the accepted charge (red symbols, dashed lines), after 4 m of plasma and with an initial emittance ${\epsilon }_{\mathrm{N},0}=2\mu \mathrm{m}$. These are shown for four different ${\sigma }_z$ from $40\mu \mathrm{m}$ to $100\mu \mathrm{m}$. The detailed studies presented in beam loading section correspond to the square marked lines at 100 pC.

Figure 8

Witness beam charge with emittance preserved, $\tilde{Q}$ (blue symbols, lines), as a function of initial beam charge, and final energy (red symbols, dashed lines), after 4 m of plasma and with an initial emittance ${\epsilon }_{\mathrm{N},0}=2\mu \mathrm{m}$.

Figure 9

Ratio of witness beam charge with emittance preserved, $\tilde{Q}/Q$ (blue symbols, line), as a function of beam initial emittance (right), with relative energy spread of the accepted charge (red symbols, dashed line), after 4 m of plasma.

Figure 10

Ratio of witness beam charge with emittance preserved, $\tilde{Q}/Q$ (blue symbols, line), as a function of beam offset, with relative energy spread of the accepted charge (red symbols, dashed line), after 4 m of plasma.