Acoustic Funnel and Buncher for Nanoparticle Injection

Acoustics-based techniques are investigated to focus and bunch nanoparticle beams. This process allows us to overcome the prominent problem of the longitudinal and transverse mismatch of particle-stream and x-ray-beam size in single-particle and single-molecule imaging at x-ray free-electron lasers (XFELs). It also enables synchronized injection of particle streams at kilohertz repetition rates. Transverse focusing concentrates the particle flux to the size of the (sub)micrometer X-ray focus. In the longitudinal direction, focused acoustic waves can be used to bunch the particle to the same repetition rate as the x-ray pulses. The acoustic manipulation is based on simple mechanical recoil effects and could be advantageous over light-pressure-based methods, which rely on absorption. The acoustic equipment is easy to implement and can be conveniently inserted into current XFEL endstations. With the proposed method, data collection times could be reduced by a factor of ${10}^4$. This work does not just provide an efficient method for acoustic manipulation of streams of arbitrary gas-phase particles, but also opens up wide avenues for acoustics-based particle optics.

Figure 1

Front view (a), with three-dimensional perspective, of a sketch of the setup, including the configuration of the acoustic funnel and buncher as well as the detection window (DW), which is equipped with white light (WL) illumination and camera. The acoustic funnel is formed by two orthogonal standing wave resonators in the $x,y$ directions, each consisting of a transducer (T) and a reflector (R), and the particle flow is along the $z$ direction. A top view of the created acoustic potential is shown in (b). The coordinates refer to the center of the mechanical setup of transducers and reflectors. Potential minima are characterized by an oval shape and the center of one is marked by a red dot at $-(\lambda /4,\lambda /4)$, corresponding to the position where the focusing experiment is performed. Below the funnel, the acoustic buncher is formed by two tilted transducers that emit synchronized acoustic waves. The acoustic wave is transversely focused by a conical cavity with a pinhole [11]. The upper chamber is filled with helium gas, at a pressure of ${10}^{-3}\mathrm{mbar}$, as the acoustic coupling medium. The particle stream enters from the top and moves downward.

Figure 2

Stability diagram according to Eq. (5) with $\beta =0$. The region with a purely imaginary characteristic exponent of $\mathrm{Im}[\mu (a,q)]>0$ permits stable trajectories according to the Mathieu equation (see color map) and the unstable region is left white. The parameters for our case correspond to the solid lines $a=(\mathrm{\Omega }/\omega {)}^2=(2G/H)q$.

Figure 3

(a) Temporal evolution of a particle distribution with an initial width (waist) $w_0=100\mu \mathrm{m}$ in an acoustic wave with frequency $\nu =26\mathrm{kHz}$ and an intensity of $I=1{\mathrm{W/cm}}^2$. The final width is consistent with the minimal width $w_{\min }=7.5\mu \mathrm{m}$, determined from Eq. (10). Particle number density distributions are plotted at (b) $0\mu \mathrm{s}$ and (c) $70\mu \mathrm{s}$ from numerically simulated dynamics using the 2D potential with explicit time dependence in Eq. (1). The root-mean-square deviation from the center $(-\lambda /4,-\lambda /4)$ is $100$ and $6\mu \mathrm{m}$ at $0$ and $70\mu \mathrm{s}$, respectively.

Figure 4

The calculated longitudinal phase-space distribution of the particles is given at the entrance of the buncher, $t=0.0\mathrm{ms}$, and that in the detection region at $t=5.0\mathrm{ms}$, as well as an intermediate time $t=2.5\mathrm{ms}$ demonstrating the phase-space rotation. All distributions are relative to the phase-space position of the synchronous particle.