Influence of ion motion in a resonantly driven wakefield accelerator

Several different schemes for plasma wakefield acceleration using a train of drivers have been pursued, based on the resonant excitation of a plasma wave. Since these schemes rely on the plasma electron wave surviving for many periods, the motion of the plasma ions can have a significant impact on the beam–plasma interaction. In this work, simulations are used to study the impact of this ion motion on the development of the self-modulation of a long beam, directly applicable to recent experiments. It is shown that two related but distinct effects contribute to the suppression of the wakefield excitation: the loss of resonance between the drive beam and the plasma wave it excites, and phase mixing due to transverse wavebreaking. Although only the latter has previously been investigated, we show that the two effects follow the same scaling with ion mass.

💡 Research Summary

Plasma wakefield acceleration (PWFA) promises ultra‑high accelerating gradients, and the AWAKE experiment at CERN demonstrates this concept using a 400 GeV proton driver. Because the driver is much longer than a plasma wavelength, the beam self‑modulates into a train of micro‑bunches that resonantly drive a large‑amplitude wake. This resonant excitation must persist over many plasma periods, making the system sensitive to the slow motion of plasma ions.

The authors employ axisymmetric particle‑in‑cell (PIC) simulations (LCODE) to reproduce the AWAKE discharge‑plasma‑source (DPS) experiments performed with xenon, argon and helium gases. By keeping all beam and plasma parameters identical except for the ion species, they isolate the effect of ion mass on the self‑modulation instability (SMI). Experimental streak‑camera images of the proton beam after the plasma are compared with simulated beam profiles, showing excellent qualitative agreement: in vacuum the beam simply diverges; with xenon the head of the beam is modestly focused; with argon the profile is essentially unchanged; with helium a pronounced tail appears, indicating strong suppression of the SMI.

The simulations reveal two distinct mechanisms by which ion motion damps the wakefield. First, the ponderomotive force of the growing wake exerts a predominantly transverse force on ions, causing them to migrate radially. Light ions (helium) develop a pronounced on‑axis density spike surrounded by a low‑density annulus. This radial density modulation reduces the local plasma frequency, shifting the phase of the on‑axis longitudinal electric field (E_z). The phase shift causes micro‑bunches to fall out of resonance with the wake, effectively detuning the driver from the plasma wave. The effective current (I_{\rm eff}(\zeta)), a proxy for the wake amplitude, drops sharply in the beam tail.

Second, the same ion‑induced density non‑uniformity enhances transverse wavebreaking. As the wake amplitude grows, electron trajectories cross, ejecting electrons transversely and generating a sheath field (E_{\rm sh}) at the plasma edge. The sheath field is markedly larger in the helium case in the beam’s trailing half, confirming that wavebreaking proceeds more vigorously when ions have moved. Wavebreaking leads to phase mixing and irreversible energy transfer from the plasma wave to electrons, further damping the wake.

Both effects—detuning and transverse wavebreaking—exhibit the same scaling with ion mass, roughly proportional to (1/\sqrt{m_i}). This scaling had previously been identified only for wavebreaking; the present work shows that detuning follows the same law, unifying the description of ion‑motion‑induced wake suppression.

Quantitatively, the simulations show that for xenon (heavy ions) the ion density remains essentially uniform, the wake amplitude stays near the cold wave‑breaking limit, and the phase remains locked to the driver, preserving the SMI. For helium, the wake amplitude initially rises (an energy‑transport effect) but then rapidly decays after (\zeta \approx 100/k_p) due to the combined phase shift and wavebreaking. Argon displays intermediate behavior, consistent with its intermediate ion mass.

The authors conclude that ion motion is a critical limitation for long‑distance resonant PWFA using light‑ion plasmas. To maintain efficient self‑modulation and high wake amplitudes, one must either employ heavy‑ion gases (e.g., xenon) or implement strategies to mitigate ion motion, such as pre‑forming a density step or using tailored plasma profiles. The unified scaling law provides a practical guideline for designing future high‑energy plasma accelerators where the driver length far exceeds the plasma wavelength.