Plasma and trap-based techniques for science with positrons

In recent years, there has been a wealth of new science involving low-energy antimatter (i.e., positrons and antiprotons) at energies ranging from ${10}^2$ to less than ${10}^{-3}\mathrm{eV}$. Much of this progress has been driven by the development of new plasma-based techniques to accumulate, manipulate, and deliver antiparticles for specific applications. This article focuses on the advances made in this area using positrons. However, many of the resulting techniques are relevant to antiprotons as well. An overview is presented of relevant theory of single-component plasmas in electromagnetic traps. Methods are described to produce intense sources of positrons and to efficiently slow the typically energetic particles thus produced. Techniques are described to trap positrons efficiently and to cool and compress the resulting positron gases and plasmas. Finally, the procedures developed to deliver tailored pulses and beams (e.g., in intense, short bursts, or as quasimonoenergetic continuous beams) for specific applications are reviewed. The status of development in specific application areas is also reviewed. One example is the formation of antihydrogen atoms for fundamental physics [e.g., tests of invariance under charge conjugation, parity inversion, and time reversal (the CPT theorem), and studies of the interaction of gravity with antimatter]. Other applications discussed include atomic and materials physics studies and the study of the electron-positron many-body system, including both classical electron-positron plasmas and the complementary quantum system in the form of Bose-condensed gases of positronium atoms. Areas of future promise are also discussed. The review concludes with a brief summary and a list of outstanding challenges.

Figure 1

Early positron trapping experiment using a magnetic mirror trap. Shown is the flux as a function of time of relativistic (megaelectron volt) positrons exiting the trap when increasing pressures [(a)–(c)] of neon gas are used to induce deconfinement. Confinement times of 10 s were observed. Adapted from [163]; see this reference for details.

Figure 2

A first glimpse of stable, neutral antimatter at low energies. Image of antihydrogen atoms annihilating at the inner surface of electrodes used to confine and merge cold antiproton and positron plasmas. See Sec. 8a for details. Adapted from [8].

Figure 3

Schematic of a cylindrical Penning-Malmberg trap for positive charges.

Figure 4

Schematic picture of $\delta n(r,\theta )$ for several $k_z=0$ diocotron modes. The magnetic field $B$ is oriented into the page. The direction of rotation assumes the charge $q>0$ and corresponds to $\theta <0$.

Figure 5

Dispersion relation for $m_{\theta }=0$ modes in spheroidal plasmas [Eq. (55)]. Only the lowest-order azimuthally symmetric modes are shown; the dashed line is the plasma frequency. For the $l=3$ and $l=4$ modes, there are two branches. The sketches indicate the fluid motion for each mode. From [390].

Figure 6

Cross section of the NEPOMUC converter showing the cadmium shell, platinum production, and moderation foils and magnetic beam transport elements. From [212].

Figure 7

Geometries for Penning traps: (a) cylindrical trap with closed end caps, (b) trap with hyperboloidal electrodes (“harmonic trap”), (c) orthogonalized cylindrical trap, (d) open end cap cylindrical trap (i.e., the Penning-Malmberg trap), (e) orthogonalized open end cap design, and (f) multiring trap. For online readers, the color code is as follows: (blue) ring electrode, (green) end caps, (yellow) compensation electrode, (red) confined charge cloud, and (brown) multiring electrodes.

Figure 8

Typical layout for a PM trap for RW compression. Phased sine waves applied to azimuthal segments create the rotating electric field. The RW field is applied along only part of the length of the plasma. For the online readers, the color code is the same as in Fig. 7.

Figure 9

Buffer-gas trap for positron trapping. Top: electrode structure showing the three stages. Bottom: electrostatic potential profile.

Figure 10

Cyclotron cooling of an electron plasma in a magnetic field of 4.8 T, following heating with rf noise. Equation (67) yields ${\mathrm{\Gamma }}_c=6.5{\mathrm{s}}^{-1}$, as compared with a predicted value of $5.9{\mathrm{s}}^{-1}$. From T. R. Weber, unpublished.

Figure 11

Radial confinement time of a pure electron plasma vs pressure of the helium gas for magnetic fields of (□) 0.067, (⋄) 0.017, and (○) 0.0042 T. Adapted from [272].

Figure 12

Outward asymmetry-induced transport vs plasma density for two different plasma lengths, 24 and 10 cm. Vertical arrows correspond to the densities at which ${\nu }_c=3f_b$, where ${\nu }_c$ is the Coulomb collision frequency and $f_b$ is the axial bounce frequency. From [95].

Figure 13

Schematic diagram of the design of a 21-cell multicell PM trap for ${10}^{12}$ positrons. It consists of a set of feed electrodes and three banks of seven storage cells in a hexagonally closed packed (HCP) arrangement. A RW electrode is incorporated in each cell. Autoresonant excitation of the diocotron mode (Sec. 6b2) will be used to move plasmas across $B$ for off-axis storage.

Figure 14

(Top) Magnetic mirror arrangement for the experiments to study electron-plasma confinement, and (bottom) the on-axis magnetic field strength as a function of position. Two inner coils provide a magnetic mirror confinement field with a mirror ratio of 5, while an outer pair of coils guide the filling beam from an electron gun and extracted beams to a Faraday cup (F.C. in the upper panel). From [201].

Figure 15

The Columbia non-neutral torus (CNT) showing a cutaway of the vacuum vessel, the four circular magnetic field coils used to produce the stellerator field, and the calculated magnetic surfaces (faint deformed donut). From T. S. Pedersen.

Figure 16

Measured $m_{\theta }=1$ diocotron-mode frequency as a function of $r_w/L_p$ compared with (solid line) the predictions of Eq. (69). Adapted from [143].

Figure 17

Measured dispersion relation of Trivelpiece-Gould modes in a pure electron plasma. Adapted from [89].

Figure 18

Measured quadrupole ($l=2$) mode frequency vs plasma temperature for plasmas with three different aspect ratios (profiles shown in the inset). Solid lines are the results of numerical simulations, and the dashed lines are the predictions of cold-fluid theory. From [390].

Figure 19

Digital camera images of positron plasmas at (a) $t=0$ and (b) $t=4\mathrm{s}$, and (bottom) radial profiles of a positron plasma with $N_{\text{tot}}=5\times {10}^7$ positrons, during rotating-wall compression with $f_{\mathrm{RW}}=2.5\mathrm{MHz}$. From [179].

Figure 20

Electron-plasma compression rate (•, ${\dot{n}}_0/n_0$) and heating rate (∘, $\dot{T}$), using driven Trivelpiece-Gould modes as a coupling mechanism and cyclotron cooling: (top panels) $m_{\theta }=1$, and (bottom panels) $m_{\theta }=2$. From [11].

Figure 21

(a) Plasma density and temperature vs time during strong-drive excitation of an electron plasma cooled by cyclotron radiation. (b) Radial profile before compression ($t=0$) and after reaching steady state ($t=10\mathrm{s}$). Adapted from [95].

Figure 22

Strong-drive compression: plasma density vs time at fixed ${\omega }_{\mathrm{RW}}$. As the drive amplitude is increased, there is a transition from a low-density state to a high-density steady state that is approximately independent of the drive amplitude. The shaded area indicates the transition region between the two states. Adapted from [93].

Figure 23

Steady-state density after strong-drive compression for a broad range of frequencies showing that the steady-state plasma rotation frequency is close to the drive frequency (the solid line is ${\omega }_{\mathrm{RW}}={\omega }_r$). The gap between 1 and 3 MHz is due to a zero-frequency mode; see the text for details. Adapted from [93], [95].

Figure 24

Plasma density vs time for strong-drive compression showing rapid adjustment to new steady-state density when the drive frequency is changed abruptly. Adapted from [95].

Figure 25

Positron density vs drive frequency in the First Point Scientific, Inc. RW experiment ($B=0.04\mathrm{T}$) using buffer-gas cooling (${\mathrm{CF}}_4$, $p\sim 3\times {10}^{-7}\mathrm{torr}$). The solid line is the no-slip condition (${\omega }_{\mathrm{RW}}={\omega }_r$). The maximum positron density reached was a record for leptons, $\sim 17\%$ of the Brillouin limit. The sharp dips at specific frequencies are due to ZFM’s. From R. G. Greaves, unpublished.

Figure 26

Rotating-wall frequency for maximum compression (or expansion) as a function of the parabolic well voltage for radial compression in the single-particle regime. The solid line indicates the single-particle bounce frequency. From [177].

Figure 27

(a) Plasma images for different values of the diocotron-mode drive frequency thus producing different radial displacements $d$ for the phase $\theta =0°$. Note that the plasma extent and shape remains approximately the same, independent of $d$. (b) Plasma images for different angles $\theta$, for $d=0.26\mathrm{cm}$. From [97].

Figure 28

Schematic diagram of a trap-based positron beam used in atomic and molecular physics experiments: (top) experimental arrangement, and (bottom) the electrical potential profile along the magnetic axis. After trapping and cooling, the bottom of the potential well is raised to force particles over the end gate at potential $V$ and through the scattering cell at potential $V_c$, which sets the beam energy $\epsilon =e(V-V_c)$ in the scattering cell.

Figure 29

(a) Cartoon of the experimental arrangement used to extract beams of small spatial extent from an SCP in a PM trap. (b) Normalized profiles for the (▪) beam and plasma (dashed line). The inset in (b) shows the density for both on an absolute density scale (i.e., in the trap). From [98].

Figure 30

(a) Transverse profiles of beams extracted from plasmas with different densities (▪) $1.9\times {10}^{15}{\mathrm{m}}^{-3}$, (▾) $6.5\times {10}^{15}{\mathrm{m}}^{-3}$, and (▴) $1.2\times {10}^{16}{\mathrm{m}}^{-3}$. (b) The transverse width of the extracted beam vs the Debye length of the parent plasma. From [98], and [408].

Figure 31

Energy of antiprotons after an autoresonant chirped drive is applied with different final frequencies: (a) energy distributions of 15 000 antiprotons after reaching the frequencies shown, and (b) mean calculated energy vs chirp frequency, normalized to linear bounce frequency for the trap potential well. From [18].

Figure 32

Arrangement for (a) harmonic potential bunching. The resistor divider chain is configured to produce a harmonic potential within the buncher electrode structure when a high voltage pulse is applied to the left end of the chain. (b) Timed potential bunching: the potential on the buncher is raised according to a $1/t^2$ ($t<0$), as the positron passes through the buncher gap. In both cases the spatial extent of the positron pulse must be shorter than the respective electrode structure.

Figure 33

(Upper panel) Schematic diagram of an experiment to (nonadiabatically) extract an electron beam from a plasma in a PM trap in a 5 T field, then electrostatically focus the particles into a Faraday cup. (Lower panel) The magnetic field profile along the direction of the extracted beam. Saddle coils (not shown) are used to align the field at $z\approx 140\mathrm{cm}$. From [410].

Figure 34

(a) ATHENA mixing trap and antihydrogen detector, with the positron cloud (ellipse); also shown is a typical $\overline{\mathrm{H}}$ annihilation into three charged pions and back-to-back 511-keV photons. (b) (Solid line) The electrical potential during mixing, and (dashed line) immediately before antiproton transfer. From [8].

Figure 35

(a) ATRAP electrode arrangement for nested Penning traps. Shaded regions indicate the magnitude of the electric field (i.e., used to ionize the $\overline{\mathrm{H}}$); (b) potential on axis for positron cooling of antiprotons (solid line) during which $\overline{\mathrm{H}}$ formation takes place; (dashed line) modified potential used to launch $\overline{p}$ into the well. From [154].

Figure 36

Simulation of the probability $P$ for an $\overline{\mathrm{H}}$ atom to have a given binding energy for the assumed positron-plasma temperatures indicated. To survive a $25\mathrm{V}/\mathrm{cm}$ field, an atom needs a binding energy greater than $\sim 40\mathrm{K}$. From [343].

Figure 37

Analysis of ATRAP data for the field-ionization spectrum of $\overline{\mathrm{H}}$ atoms that survive an electric field $F$ compared to Monte Carlo calculations assuming an $\overline{\mathrm{H}}$ temperature of 2 meV; (inset) analysis to verify that charge-exchange effects do not alter the spectrum. From [337].

Figure 38

Illustration of the inner section of the ALPHA experiment showing the PM trap electrodes and the minimum-$B$ neutral trap, with octupole and mirror coils, and the silicon-based annihilation detector. From [7].

Figure 39

(Top) ALPHA data for the number of trapped $\overline{\mathrm{H}}$ per attempt as a function of confinement time. (Bottom) Comparison of the time distributions between the data (circles) with simulations for various initial energy distributions (histograms). The shaded histogram represents the best fit. From [19].

Figure 40

Overview of the AEgIS proposed experiment to measure the deflection of an $\overline{\mathrm{H}}$ beam due to Earth’s gravity. From [113].

Figure 41

Schematic phase diagram of the electron-positron many-body system as a function of density $n$ and temperature $T$. While the quantum $e^{+}\text{−}{e}^{-}$ liquid is beyond current technology, besides the studies (in progress) of ${\mathrm{Ps}}_2$, it is possible to contemplate near-term studies of a Ps BEC and a classical pair plasma. Adapted from [421].

Figure 42

Apparatus for creating a dense Ps gas and the ${\mathrm{Ps}}_2$ molecule. (Top) BGT and accumulator, and (bottom) pulsed magnet and sample location. From [58].

Figure 43

(∘) Nnormalized quenching parameter $Q$ plotted as a function of the beam areal density $n_{2\mathrm{D}}$ impinging on porous silica, and (solid line) fit to a density-dependent decay function. From [67]. At large $n_{2\mathrm{D}}$, all but spin aligned Ps atoms quench. Assuming spin alignment from the ${}^{22}\mathrm{Na}$ is preserved, the asymptotic high-density value of $Q$ will be the initial degree of spin polarization $p_0$. The expected value in those experiments was $p_0=0.35$ as compared with the measured value of $p_0=0.28$. From [55][56].

Figure 44

Normalized, delayed fraction of annihilations vs the probe laser wavelength for ${\mathrm{Ps}}_2$ in porous silica. A second laser ionizes the ${\mathrm{Ps}}_2$, once excited. The vertical dashed line is the expected position of the ${\mathrm{Ps}}_2$ resonance in vacuum. From [65].

Figure 45

Beam-plasma interaction in the cylindrical trap: (a) positron heating rate (inset: time-resolved positron heating), and (b) the calculated growth rates for waves with wave numbers of 0.4 and $0.2{\mathrm{cm}}^{-1}$. From [178].

Figure 46

Schematic diagram of the RT-1 ring trap which is a superconducting levitated dipole. From [426].

Figure 47

A Penning-Paul trap for pair-plasma confinement. From [182].

Figure 48

Experimental values of the normalized annihilation rate $Z_{\text{eff}}/Z$ plotted against the total electronic charge $Z$ on the molecule, demonstrating the importance of chemical composition on annihilation rates: (•) noble gases, (▽) simple molecules, (∘) alkanes, (△) perfluorinated alkanes, (□) perchlorinated alkanes, (⋄) perbrominated and periodated alkanes, (▪) ring alkanes, alkenes, and alkynes, (▴) oxygen containing compounds, ($⬡$) ring hydrocarbons, (▾) substituted benzenes, and (♦) large organic molecules. From [223].

Figure 49

The Doppler-broadened $\gamma$-ray spectrum resulting from positrons annihilating on Kr atoms. Shown are (∘) experimental data, (dotted line) a static Hartree-Fock calculation, and (dashed line) the best fit to the data which includes a 1.3% contribution from inner-shell electrons. From [225].

Figure 50

Electronic excitation (▽) ([374]) and positronium formation (•) ([278]) cross sections for molecular nitrogen as a function of incident positron energy. The region of energies around 10 eV, where electronic excitation dominates, is optimum for the operation of the BGT.

Figure 51

Positron-impact cross section for excitation of the ${\nu }_3$ vibrational mode of ${\mathrm{CF}}_4$ as a function of incident positron energy in atomic units $a_0^2=2.8\times {10}^{-21}{\mathrm{m}}^2$. This relatively large cross section above the threshold energy ${\epsilon }_i=0.16\mathrm{eV}$ provides a very efficient positron cooling mechanism. From [279].

Figure 52

Comparison between measured $Z_{\text{eff}}$ [•, 26] and theoretical $Z_{\text{eff}}$ (solid curves) for ${\epsilon }_b=0.3\mathrm{meV}$ (${\mathrm{CH}}_3\mathrm{F}$), 25 meV (${\mathrm{CH}}_3\mathrm{Cl}$), and 40 meV (${\mathrm{CH}}_3\mathrm{Br}$). Dashed curves show the nonresonant contribution $Z_{\text{eff}}^{\text{dir}}$. Vertical bars show the energies of molecular fundamentals. The only fitted parameter in each spectrum is ${\epsilon }_b$. From [186].

Figure 53

$Z_{\text{eff}}$ as a function of incident positron energy for the alkanes (${\mathrm{C}}_n{\mathrm{H}}_{2n+2}$). Arrows on the vertical axes indicate $Z_{\text{eff}}$ for a room temperature thermal distribution of positrons. As molecular size increases, so does ${\epsilon }_b$; the $Z_{\text{eff}}$ value increases and the spectrum shifts to lower energy. From [25].

Figure 54

Contour plots of calculated bound (a) positron ([388]) and (b) electron ([362]) wave functions for the positive and negative acetonitrile (${\mathrm{CH}}_3\mathrm{CN}$) molecular ions. The positron does not penetrate the valence shell due to repulsion from the nuclei, and the electron is kept outside due to Pauli exclusion. From [92].

Figure 55

Left: Instrument function and lifetime spectrum for a chitosan biopolymer from a trap-based lifetime system. Right: Extracted lifetime components for three different samples. From [75].

Figure 56

Single shot lifetimes for porous silica samples with higher and lower densities of positrons in each bunch (labeled “compressed” and “expanded,” respectively). The resolution function is also shown. From [60].