Limitation on the accelerating gradient of a wakefield excited by an ultrarelativistic electron beam in rubidium plasma

We have investigated the viability of using plasmas formed by ionization of high Z, low ionization potential element rubidium (Rb) for beam-driven plasma wakefield acceleration. The Rb vapor column confined by argon (Ar) buffer gas was used to reduce the expected limitation on the beam propagation length due to head erosion that was observed previously when a lower Z but higher ionization potential lithium vapor was used. However, injection of electrons into the wakefield due to ionization of Ar buffer gas and nonuniform ionization of ${\mathrm{Rb}}^{1+}$ to ${\mathrm{Rb}}^{2+}$ was a possible concern. In this paper we describe experimental results and the supporting simulations which indicate that such ionization of Ar and ${\mathrm{Rb}}^{1+}$ in the presence of combined fields of the beam and the wakefield inside the wake does indeed occur. Some of this charge accumulates in the accelerating region of the wake leading to the reduction of the electric field—an effect known as beam loading. The beam-loading effect is quantified by determining the average transformer ratio $⟨R⟩$ which is the maximum energy gained divided by the maximum energy lost by the electrons in the bunch used to produce the wake. $⟨R⟩$ is shown to depend on the propagation length and the quantity of the accumulated charge, indicating that the distributed injection of secondary Rb electrons is the main cause of beam loading in this experiment. The average transformer ratio is reduced from 1.5 to less than 1 as the excess charge from secondary ionization increased from 100 to 700 pC. The simulations show that while the decelerating field remains constant, the accelerating field is reduced from its unloaded value of 82 to $46\mathrm{GeV}/\mathrm{m}$ due to this distributed injection of dark current into the wake.

Figure 1

Figure originally appeared in [16]. Beam loading in a drive/trailing electron-driven plasma wakefield accelerator. (a) The longitudinal density profile of drive and trailing electron beams in three different beam loading scenarios. The drive beam density is the same ($n_b\sim 5n_p$) in all three cases. The three cases of trailing beam are: no trailing beam, i.e. unloaded wake (blue), trailing beam with peak density 40% that of the drive bunch (red), and trailing beam with peak density 80% that of the drive bunch (green). (b) The on-axis longitudinal electric field for each of the three cases in (a). One can see progressively stronger beam loading that leads to flattening of the wake and reduction in the transformer ratio as described in the text.

Figure 2

Experimental setup. The electron beam enters from the left. The energy spectrum of the beam before plasma is shown as the inset (E) on the top left. The transition radiation generated as the beam traverses the $1\mu \mathrm{m}$ Ti foil (T) is observed simultaneously by a pyroelectric detector (Pyro) and a THz Michelson interferometer (M). Correlation between the pyro and the inverse of the bunch length deduced from the Michelson interferometer is shown beneath the setup. Foils with progressively higher scattering strength (F1-F3) can be inserted in the path of the beam before it enters the plasma oven, leading to progressively increased beam emittance (see Table 2 for details). The density profiles of neutral Rb and Ar are plotted underneath the schematic of the oven in blue circles and red diamonds, respectively. Absolutely calibrated toroids upstream and downstream of the plasma record the amount of charge entering and exiting the plasma. The quadrupole magnets Q1 and Q2 along with the dipole magnet D form the imaging energy spectrometer. The Cherenkov radiation emitted by the dispersed electrons between silicon wafers (1) and (2) is detected by camera C to give the electron spectrum after the plasma. An example of the energy spectrum charge is shown below the camera C, with the white curve showing the integrated charge. The charge near 20.4 GeV observed not to lose any energy has been attenuated by a factor of 10. The Lanex screen, shielded by a 1 mm copper foil, detects the betatron x rays.

Figure 3

(a) Ionization rates for neutral Rb, neutral Ar, ${\mathrm{Rb}}^{+}$, and ${\mathrm{Ar}}^{+}$ ions as a function of electric field. (b) The ionization fraction for neutral Rb using an electron beam with ${\sigma }_z=40\mu \mathrm{m}$ and ${\sigma }_r=35\mu \mathrm{m}$. The rates are obtained from ADK model. The longitudinal profile of the initial beam is shown in blue lineout and the longitudinal profile of the participating charge is shown in red lineout. (c) Envelope evolution of a beam slice with normalized emittance of ${\epsilon }_n=250\mathrm{mm}\text{−}\mathrm{mrad}$ in an ion column with ion density $n_i$ having the same profile in z as the rubidium plasma. The plot of density is shown in green. The propagation of the electron beam in vacuum and in the presence of blowout regime is shown in blue and orange, respectively. Regions with significant presence of Ar are shown in blue shade. The beam size below ${\sigma }_r<7.9\mu \mathrm{m}$ ionizes neutral Ar and ${\sigma }_r<4.5\mu \mathrm{m}$ ionizes ${\mathrm{Ar}}^{1+}$ and ${\mathrm{Rb}}^{1+}$.

Figure 4

(a) X-ray yield for a set of 77 consecutive shots sorted as a function of ${\sigma }_z$. In this data set, foil F1 is inserted and the variation of ${\sigma }_z$ is due to the shot-to-shot jitter of the phase of the linac. (b) $\mathrm{\Delta }Q$ and x-ray yield are plotted against each other for each shot. (c) $\mathrm{\Delta }{W}^{-}$ sorted as a function of ${\sigma }_z$ for the same data. (d) $\mathrm{\Delta }Q$ correlation with $\mathrm{\Delta }{W}^{-}$ for the same data.

Figure 5

(a) Excess charge as a function of the x-ray yield in four cases obtained with the insertion of various foils that change the beam emittance. The data is filtered by selecting pyro values between 5000 and 5300, (${\sigma }_z\sim 40\mu \mathrm{m}$) so that the current profiles are nearly identical as judged by the similarity of the electron beam spectra before the plasma. The data shown in red triangles is a subset of data in Fig. 4. (b) Reproduced from [38]; energy loss is shown as a function of excess charge for the same data as in (a). (c) The electron beam energy spectra for the data shown in (a) and (b). The spectra related to each foil is averaged.

Figure 6

Data from a 71 shot data set where no foils F1-F3 were inserted. (a) Peak energy loss $\mathrm{\Delta }{W}^{-}$ as a function of ${\sigma }_z$, grouped by a range of 300 in pyro corresponding to $\sim 3\mu \mathrm{m}$ change in ${\sigma }_z$. (b) $\mathrm{\Delta }Q$ plotted as a function of $\mathrm{\Delta }{W}^{-}$, where each point corresponds to one of the six groups in (a). The corresponding groups in (a) and (b) are indicted by numbers above or below data points. The value of $\mathrm{\Delta }{W}^{-}$ for each data point in (b) corresponds to the mean value of $\mathrm{\Delta }{W}^{-}$ for a group in (a) and the mean of $\mathrm{\Delta }Q$ for each group is plotted with the error bars representing the standard deviation of $\mathrm{\Delta }Q$ in a group. (c) Correlation of x-ray yield and $\mathrm{\Delta }Q$ data shown in (a). (d) Peak energy gain $\mathrm{\Delta }{W}^{+}$ as a function of $\mathrm{\Delta }Q$ for the same data. 1 GeV is added to the raw $\mathrm{\Delta }{W}^{+}$ value to compensate for the head-to-tail energy chirp of the incoming electron beam. (e) Waterfall plot for data shown in (a). Each vertical slice represents the energy spectra for a shot, which is obtained by integrating the spectra along the nondispersive direction. The shot number is shown on the horizontal axis, and the data is sorted by increasing values of $\mathrm{\Delta }Q$ along this axis.The counts near the initial beam energy ($\sim 20.35\mathrm{GeV}$) and the counts below the initial energy (energy loss area) are divided by 10 and 2, respectively, and as indicated on the images. (f) Average transformer ratio, $⟨R⟩=\mathrm{\Delta }{W}^{+}/\mathrm{\Delta }{W}^{-}$ plotted for the same data set shown in (e).

Figure 7

Originally appeared in [38]. (a) Measured energy spectra for the same shots as displayed in Fig. 5. The white line shows $\mathrm{\Delta }{W}^{-}$ and $\mathrm{\Delta }{W}^{+}$, where each point represents moving average of five shots. (b) The measured average transformer ratio $⟨R⟩=\mathrm{\Delta }{W}^{+}/\mathrm{\Delta }{W}^{-}$ as a function of $\mathrm{\Delta }Q$.

Figure 8

A density plot of a snapshot in the simulation. All densities are normalized to $2.7\times 10^{17}{\mathrm{cm}}^{-3}$. Rb II electrons in the area to the left of the red dashed line are made transparent, so that the deflection of the sheath due to the beam loading of excess charge is visible. Since the simulation is cylindrically symmetric, only $r>0$ is shown in this image. Rb I electrons form the wake and are shown in gray scale while Rb II electrons, shown in green, are tracked separately from Rb I electrons. The color plots are restricted for better visibility of lower density features.

Figure 9

Comparison of simulations with and without Ar and secondary Rb ionization. (a) On-axis electric field for the two simulations with the beam having propagated 12 cm in the plasma in each simulation. The red curve represents the value of the field where only ionization of Rb I is present. For the blue curve both ionization levels of Ar and Rb are included. (b) Same parameters plotted as (a), except that the frame represents a time at 30 cm of beam propagation. (c) The energy space of the beam at the end of the simulation for the beam loaded case. Peak energy loss of 8 GeV and energy gain of 12 are clearly observed. Part (d) is the same for the simulation without beam loading—i.e. secondary ionization injection.

Figure 10

(a) $\overline{\mathrm{\Psi }}$ for the simulation frame shown in Fig. 9 for the case where no secondary ionization is present. The black curve shows the outline of radial location, where Rb I electron density corresponds to 50% neutral density, i.e. the bubble sheath for $\xi <160\mu \mathrm{m}$. The spike in the region $165<\xi <170\mu \mathrm{m}$ indicates the region over which the neutral Rb is ionized. (b) The outline of on-axis plasma density (blue) and $\overline{\mathrm{\Psi }}$ (shown in orange) corresponding to the $r=0$ line in (a). On-axis density reaches 1 (indicating full ionization on axis) at $\xi =165\mu \mathrm{m}$. In the region $73.0\mu \mathrm{m}<\xi <144.8\mu \mathrm{m}$, $\overline{\mathrm{\Psi }}>0.7$. Electrons born in this region that reach the back of the wake where $\overline{\mathrm{\Psi }}\sim -0.3$ satisfy the trapping condition $\mathrm{\Delta }\overline{\mathrm{\Psi }}<-1$.