Beam Loading by Distributed Injection of Electrons in a Plasma Wakefield Accelerator

We show through experiments and supporting simulations that propagation of a highly relativistic and dense electron bunch through a plasma can lead to distributed injection of electrons, which depletes the accelerating field, i.e., beam loads the wake. The source of the injected electrons is ionization of the second electron of rubidium (Rb II) within the wake. This injection of excess charge is large enough to severely beam load the wake, and thereby reduce the transformer ratio $T$. The reduction of the average $T$ with increasing beam loading is quantified for the first time by measuring the ratio of peak energy gain and loss of electrons while changing the beam emittance. Simulations show that beam loading by Rb II electrons contributes to the reduction of the peak accelerating field from its weakly loaded value of $43\mathrm{GV}/\mathrm{m}$ to a strongly loaded value of $26\mathrm{GV}/\mathrm{m}$.

Figure 1

(a) The experimental setup. The dipole (D) and quadrapole magnets (Q1 and Q2) form the imaging spectrometer used as the energy diagnostic, Cherenkov radiation produced in air between Si wafers (1) and (2) is recorded using a 12 bit camera (C). Foils can be inserted in the beam (arrow) as it enters the plasma to change ${\epsilon }_N$ by factors of 1.2 ($F1$), 1.3 ($F2$), and 1.4 ($F3$), respectively, from the nominal value of ${\epsilon }_{N0}=250\times 50\mu \mathrm{m}$ without any foils. The Lanex screen, placed behind a 1 mm copper sheet, is the betatron x-ray diagnostic; (b) an example of the energy spectrum with the white curve showing the percentage of the total beam charge. The charge near 21 GeV, observed not to lose any energy, has been attenuated by a factor of 10 on the image. The electron bunch has a head-to-tail correlated energy spread of 0.5 GeV.

Figure 2

(a) Excess charge $\mathrm{\Delta }Q$ as a function of energy loss $\mathrm{\Delta }{W}^{-}$ for four different beam propagation lengths in the plasma determined by changing ${\epsilon }_n$ by inserting foils in the path of the beam (${\sigma }_z=40\mu \mathrm{m}$); (b) $\mathrm{\Delta }Q$ as a function of $\mathrm{\Delta }{W}^{-}$ as the peak current of the beam is changed by changing ${\sigma }_z$. Estimated bunch length is given on the scale at the top [23] (${\epsilon }_n=1.3{\epsilon }_{N0}$, Foil 2). The variation in ${\sigma }_z$ is either from shot to shot variation or from a change in bunch compression setting (shorter bunch setting as blue circles, longer bunch setting as black triangles). Linear fit to the observed correlation between $\mathrm{\Delta }{W}^{-}$ and ${\sigma }_z$ is used to obtain the ${\sigma }_z$ scale in this figure.

Figure 3

(a) Measured energy spectra of the same shots as displayed in Fig. 2. The values of energy loss $\mathrm{\Delta }{W}^{-}$ and gain $\mathrm{\Delta }{W}^{+}$ are shown as white lines and are displayed as a moving average of five shots. The numbers on the left hand side indicate the factors used on the data in the three primary energy ranges for better visibility, (b) the measured average transformer ratio $⟨T⟩=\mathrm{\Delta }{W}^{+}/\mathrm{\Delta }{W}^{-}$ as a function of excess charge $\mathrm{\Delta }Q$ leaving the plasma.

Figure 4

2D cylindrical OSIRIS simulation of the experiment. (a) on axis electric field ($E_z$) as a function of the beam propagation distance in the plasma. The dashed white rectangle indicates where the wake gets severely beam loaded by $\mathrm{\Delta }Q$. The arrow marked HE shows the receding of the wake in the speed of light frame due to beam head erosion, (b) lineouts at two different locations [indicated by two horizontal arrows in (a)], the first one just at the end of the up ramp, and the second one after 30 cm of propagation in plasma at the end of the flat density region. The location used to measure $E^{+}$ is shown by the red dashed line and is the location of a 2% beam charge at the end of the simulation. The effect of beam loading is evident in the bottom frame of (b) as a strong damping of the $E^{+}$ field (circle).