Autoresonant Excitation of Antiproton Plasmas

We demonstrate controllable excitation of the center-of-mass longitudinal motion of a thermal antiproton plasma using a swept-frequency autoresonant drive. When the plasma is cold, dense, and highly collective in nature, we observe that the entire system behaves as a single-particle nonlinear oscillator, as predicted by a recent theory. In contrast, only a fraction of the antiprotons in a warm plasma can be similarly excited. Antihydrogen was produced and trapped by using this technique to drive antiprotons into a positron plasma, thereby initiating atomic recombination.

Figure 1

On-axis ($r=0$) potentials used in this experiment.Solid blue line, vacuum potential. Dotted line, typical drive potential ($\overline{ϵ}/2\pi \sim 1.8\times {10}^9{\mathrm{s}}^{-2}\mathrm{\text{scaled}}\times 100$). Inset: Total potential for the plasma ($T_{\parallel }=150\mathrm{K}$) with 15 000 (green dashed line) $[n(0,0)\sim 6\times {10}^{12}{\mathrm{m}}^{-3}]$ and 50 000 (red dotted-dashed line) antiprotons $[n(0,0)\sim 1\times {10}^{13}{\mathrm{m}}^{-3}]$.

Figure 2

Energy versus frequency measurements and calculations (frequencies normalized to ${\omega }_0/2\pi =410\mathrm{kHz}$). (a) Distributions of $\sim 15000$ antiprotons driven to different final frequencies. (b) $U({\omega }_b)$ calculated from Eq. (3) for the vacuum potential (solid blue line); total potential with 15 000 (green dashed line) and 50 000 (red dotted-dashed line) antiprotons (see Fig. 1). The open squares denote the mean $U$ of each distribution plotted against its final drive frequency.

Figure 3

Plot of the time evolution of the longitudinal distribution $f(U)dU$ for plasmas with $\sim 50000$ antiprotons excited with an autoresonant drive. Inset: Their mean longitudinal energy as a function of the time between the autoresonant drive and the energy measurement dump.

Figure 4

Chirp and drive amplitude threshold measurements on 15 000 antiprotons. (a) Amplitude threshold measurement for fixed drive parameters ($\alpha /2\pi =200\mathrm{MHz}/\mathrm{s}$, ${\omega }_i/2\pi =420\mathrm{kHz}$, ${\omega }_f/2\pi =360\mathrm{kHz}$), with longitudinal energy $U$ normalized to $U_f\sim 2.9\mathrm{eV}$. Plus signs denote mean energy of final distributions plotted against their drive amplitude and normalized to scale the threshold to 1. The solid blue line denotes the single oscillator final energy calculated as a function of drive amplitude, similarly scaled. (b) The open squares denote measured ${\overline{ϵ}}_c$ for a given chirp rate $\alpha$. Scaling law (solid blue line) ${\alpha }^{3/4}$ [Eq. (4)] fit to the data.

Figure 5

Plot of the fraction of plasma that follows the autoresonant drive ($\alpha /2\pi =60\mathrm{MHz}{\mathrm{s}}^{-1}$, ${\omega }_i/2\pi =420\mathrm{kHz}$, ${\omega }_f/2\pi =360\mathrm{kHz}$). Cold plasma (open squares) and hot plasma (open circles) of 15 000 antiprotons. Solid green line denotes the expected fraction for a single oscillator ($T_{\parallel }=0\mathrm{K}$). Blue plus signs denote calculations for an ensemble of cold oscillators ($T_{\parallel }=150\mathrm{K}$). Red crosses denote calculations for an ensemble of hot oscillators ($T_{\parallel }=1,800\mathrm{K}$). Inset: Distribution functions of a heated (pink [light gray]) and an unheated (blue [dark gray]) plasma after the drive ($\overline{ϵ}/{\overline{ϵ}}_c\sim 1.05$).