Penning-Malmberg Trap Research Articles

Shot-noise-induced lower temperature limit of the nonneutral plasma parallel temperature diagnostic

We develop a new algorithm to estimate the temperature of a nonneutral plasma in a Penning-Malmberg trap. The algorithm analyzes data obtained by slowly lowering a voltage that confines one end of the plasma and collecting escaping charges, and is a maximum likelihood estimator based on a physically-motivated model of the escape protocol presented in (Beck in Measurement of the magnetic and temperature dependence of the electron-electron anisotropic temperature relaxation rate. PhD thesis, 1990). Significantly, our algorithm may be used on single-count data, allowing for improved fits with low numbers of escaping electrons. This is important for low-temperature plasmas such as those used in antihydrogen trapping. We perform a Monte Carlo simulation of our algorithm, and assess its robustness to intrinsic shot noise and external noise. The assumptions in this paper allow for a lower bound for measurable plasma temperatures of approximately 3K for plasmas of length 1cm, with approximately 100 particle counts needed for an accuracy of ±10%.

Controlling the initial separation distance between two electron plasma vortices in a Malmberg–Penning trap

This paper presents a novel method to continuously control the initial separation distance d between two plasma vortices of electrons. In this method, the two electron columns are initially confined individually in two coaxial Malmberg–Penning traps with different axial lengths. They rotate around the trap axis at different rotation frequencies due to the \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varvec{E}\ imes \\varvec{B}$$\\end{document} drift. Their different rotation rates cause periodic changes in their relative azimuthal positions. The initial conditions are established when the two columns are stretched along magnetic field lines of a unified Malmberg–Penning trap. This method precisely provides a simple and continuous adjustment of the initial d and facilitates efficient investigation of the interaction of the two plasma electron vortices.

Injection and capture of antiprotons in a Penning–Malmberg trap using a drift tube accelerator and degrader foil

The Antiproton Decelerator (AD) at CERN provides antiproton bunches with a kinetic energy of 5.3 MeV. The Extra-Low ENergy Antiproton ring at CERN, commissioned at the AD in 2018, now supplies a bunch of electron-cooled antiprotons at a fixed energy of 100 keV. The MUSASHI antiproton trap was upgraded by replacing the radio-frequency quadrupole decelerator with a pulsed drift tube to re-accelerate antiprotons and optimize the injection energy into the degrader foils. By increasing the beam energy to 119 keV, a cooled antiproton accumulation efficiency of (26±6)% was achieved.

Vortex splitting in two-dimensional fluids and non-neutral electron plasmas with smooth vorticity profiles

Initially, elliptical, quasi-two-dimensional (2D) fluid vortices can split into multiple pieces if the aspect ratio is sufficiently large due to the growth and saturation of perturbations known as Love modes on the vortex edge. Presented here are experiments and numerical simulations, showing that the aspect ratio threshold for vortex splitting is significantly higher for vortices with realistic, smooth edges than that predicted by a simple “vortex patch” model, where the vorticity is treated as piecewise constant inside a deformable boundary. The experiments are conducted by exploiting the E × B drift dynamics of collisionless, pure electron plasmas in a Penning–Malmberg trap, which closely model 2D vortex dynamics due to an isomorphism between the Drift–Poisson equations describing the plasmas and the Euler equations describing ideal fluids. The simulations use a particle-in-cell method to model the evolution of a set of point vortices. The aspect ratio splitting threshold ranges up to about twice as large as the vortex patch prediction and depends on the edge vorticity gradient. This is thought to be due to spatial Landau damping, which decreases the vortex aspect ratio over time and, thus, stabilizes the Love modes. Near the threshold, asymmetric splitting events are observed in which one of the split products contains much less circulation than the other. These results are relevant to a wide range of quasi-2D fluid systems, including geophysical fluids, astrophysical disks, and drift-wave eddies in tokamak plasmas.

Measurements of Penning-Malmberg trap patch potentials and associated performance degradation

Antiprotons created by laser ionization of antihydrogen are observed to rapidly escape the ALPHA trap. Further, positron plasmas heat more quickly after the trap is illuminated by laser light for several hours. These phenomena can be caused by patch potentials—variations in the electrical potential along metal surfaces. A simple model of the effects of patch potentials explains the particle loss, and an experimental technique using trapped electrons is developed for measuring the electric field produced by the patch potentials. The model is validated by controlled experiments and simulations. Published by the American Physical Society 2024

Multi-cell trap developments towards the accumulation and confinement of large quantities of positrons

The multi-cell Penning–Malmberg trap concept has been proposed as a way to accumulate and confine unprecedented numbers of antiparticles, an attractive but challenging goal. We report on the commissioning and first results (using electron plasmas) of the World's second prototype of such a trap, which builds and improves on the findings of its predecessor. Reliable alignment of both ‘master’ and ‘storage’ cells with the axial magnetic field has enabled confinement of plasmas, without use of the ‘rotating wall’ (RW) compression technique, for over an hour in the master cell and tens of seconds in the storage cells. In the master cell, attachment to background neutrals is found to be the main source of charge loss, with an overall charge-confinement time of 8.6 h. Transfer to on-axis and off-axis storage cells has been demonstrated, with an off-axis transfer rate of$50\,\%$of the initial particles, and confinement times in the storage cells in the tens of seconds (again, without RW compression). This, in turn, has enabled the first simultaneous plasma confinement in two off-axis cells, a milestone for the multi-cell trap concept.

Magnetic field considerations for a multi-cell Penning–Malmberg trap for positrons

Multi-cell positron traps have been proposed to accumulate and store large numbers of positrons (e.g. ${\ge }10^{10}$ ). This design arranges lines of Penning–Malmberg traps (‘cells’) on and off the magnetic axis in a vacuum chamber in a common, uniform magnetic field. Confinement considerations impose additional constraints on the magnetic field beyond the usual on-axis homogeneity requirements. These requirements are discussed. A prototype magnetic field and associated coil geometry is suggested to achieve good single-component plasma confinement in all cells. Experimental confinement data as a function of electrode alignment with respect to a nominally uniform magnetic field are also presented. These results are related to the field-alignment considerations of the magnet design study.

Thermal equilibrium of collisional non-neutral plasma in a magnetic dipole trap

This paper discusses thermal equilibrium states of single-species plasmas, such as pure electron plasmas and pure positron plasmas, that are confined in a dipole trap. Thermal equilibrium states for such plasmas are routinely realized in the homogeneous magnetic field of Penning–Malmberg traps. We generalize the theory of these states to include inhomogeneous magnetic dipole fields. The approach to thermal equilibrium takes place in two stages with well separated time scales. On the collision time scale, thermal equilibrium is established along each magnetic field line. On the much longer transport time scale, heat conduction and viscosity bring the plasmas on different flux contours into thermal equilibrium, we call this a state of global thermal equilibrium. We present numerical results for local and global thermal equilibria. These results agree with the analytic predictions for charge collections that are large compared with the Debye length. There is, in principle, no limit to the confinement time of a single-species plasma in a global thermal equilibrium state. Experiments with hot electron–ion plasmas performed in the LDX and RT1 devices give us confidence that, in contrast to a Penning–Malmberg trap, a magnetic dipole field can also confine cold quasi-neutral electron–positron pair plasmas on the time scale of the phenomena of interest. Such pair plasmas are assumed to form in the magnetosphere of neutron stars but have so far not been realized in a laboratory. The creation of an electron–positron pair plasma is the main goal of the APEX collaboration.

Eulerian simulations of electrostatic waves in plasmas with a single sign of charge

An Eulerian, numerical simulation is used to model the launching of plasma waves in a non-neutral plasma that is confined in a Penning–Malmberg trap. The waves are launched by applying an oscillating potential to an electrically isolated sector at one end of the conducting cylinder that bounds the confinement region and are received by another electrically isolated sector at the other end of the cylinder. The launching of both Trivelpiece–Gould waves and electron acoustic waves is investigated. Adopting a stratagem, the simulation captures essential features of the finite length plasma, while retaining the numerical advantages of a simulation employing periodic spatial boundary conditions. As a benchmark test of the simulation, the results for launched Trivelpiece–Gould waves of small amplitude are successfully compared to a linearized analytic solution for these fluctuations.

Design study of an antiproton trap for the GBAR experiment

The GBAR (Gravitational Behaviour of Antihydrogen at Rest) experiment at CERN has been proposed to measure the gravitational acceleration of the ultracold antihydrogen atoms. This experiment produces antihydrogen ions through interactions between antiprotons and positronium atoms. Then, antihydrogen atoms are produced for the free-fall experiment after the photo-detachment of an excess positron from the cold antihydrogen ions. The energy of the antiproton beam before the positronium target chamber will be in the range of 1–10 keV. The cross-section for the reaction between the antiprotons and positroniums depends mainly on the energy of the antiprotons. Hence, to maximize the productivity of antihydrogen ions, a sufficient number of antiprotons should be provided with well-controlled energy. In this regard, an antiproton trap is considered to accumulate and slow down antiproton beams, and cool them utilizing the electron cooling technique. This trap is designed based on the Penning-Malmberg trap, which consists of a superconducting solenoid magnet and a series of ring electrodes including high-voltage electrodes to trap antiprotons. In addition, a set of extraction electrodes and optics for beam transport are used. Each electrode has been designed and optimized using the WARP PIC simulations. In this study, the design and simulation results of each trap component are presented.

Observation and analysis of a large banana orbit in the diocotron mode of a coaxial Malmberg–Penning trap

The diocotron mode of an off-axis electron column is studied in a coaxial version of the Malmberg–Penning trap. Measurements of the diocotron frequency as a function of the bias on the central conductor agree well with a derived theory including finite-length corrections and confinement potential contributions. When the experimental parameters are adjusted to give a very low diocotron frequency, the column motion abruptly changes from an axis-encircling orbit to a large banana-shaped orbit in the r−θ plane with extent Δθ≈270° and Δr/R≈0.25, where R is the wall radius. This banana motion is apparently in response to a previously unknown background construction asymmetry. The size of the asymmetric potential is deduced from orbit data and found to be 45–100 mV. Theoretical modeling shows this to be consistent with a small radial offset δ in the center wire position of δ/R=0.034. Implications and applications of these findings are discussed and a note on obtaining the line density of an electron column in a coaxial trap is given.

Reducing the background temperature for cyclotron cooling in a cryogenic Penning–Malmberg trap

Magnetized nonneutral plasma composed of electrons or positrons couples to the local microwave environment via cyclotron radiation. The equilibrium plasma temperature depends on the microwave energy density near the cyclotron frequency. Fine copper meshes and cryogenic microwave absorbing material were used to lower the effective temperature of the radiation environment in ASACUSA's Cusp trap, resulting in significantly reduced plasma temperature.

Precision antihydrogen annihilation reconstructions using the ALPHA-g detector

The ALPHA (Antihydrogen Laser PHysics Apparatus) collaboration aims to test fundamental symmetries with matter and antimatter by testing CPT (charge conjugation, parity reversal, time reversal) theory and observing whether antimatter follows Einstein’s Weak Equivalence Principle (WEP), where the acceleration due to gravity that a body experiences is independent of its structure or composition. A measurement of the gravitational mass of antimatter has never been done before, as previous experiments used charged particles, which meant the experiments were dominated by electromagnetic forces. The ALPHA-g apparatus will use electrically neutral antihydrogen atoms produced in a vertical Penning-Malmberg trap and hold the antihydrogen in a magnetic well. Once the antihydrogen is released, the position of the resulting annihilations can be reconstructed with a radial time projection chamber (rTPC) surrounding the trapping volume. Tracing the annihilation position within the rTPC is imperative to measuring the gravitational mass of antihydrogen. These proceedings will highlight simulations of antihydrogen annihilations, and how to calibrate the detector for z-positions. This data will be used to measure the gravitational mass of antihydrogen; an important measurement in testing the fundamental symmetry of matter and antimatter. The ALPHA-g apparatus is currently being commissioned at CERN, and the first gravitational measurements of antihydrogen are underway.

Inviscid damping of an elliptical vortex subject to an external strain flow

Inviscid spatial Landau damping is studied experimentally for the case of oscillatory motion of a two-dimensional vortex about its elliptical equilibrium in the presence of an applied strain flow. The experiments are performed using electron plasmas in a Penning–Malmberg trap. They exploit the isomorphism between the two-dimensional Euler equations for an ideal fluid and the drift-Poisson equations for the plasma, where plasma density is the analog of vorticity. Perturbed elliptical vortex states are created using E×B strain flows, which are generated by applying voltages to electrodes surrounding the plasma. Measurements of spatial Landau damping (also called critical-layer damping) are in agreement with previous studies in the absence of an applied strain, where the damping is due to a resonance between the local fluid motion and the vortex oscillations. Interestingly, the damping rate does not change significantly over a wide range of applied strain rates. This can be accurately predicted from the initial vorticity profile, even though the resonant frequency is reduced substantially due to the applied strain. For higher amplitude perturbations, nonlinear trapping oscillations also exhibit behavior similar to the strain-free case. In principle, higher-order effects of the applied strain, such as separatrix crossing of peripheral vorticity and interactions with harmonics of the fundamental resonance, are expected to change the damping rate. However, this occurs only for conditions that are not realized in the experiments described here. Vortex-in-cell simulations are used to investigate the possible roles of these effects.

Non-neutral plasma manipulation techniques in development of a high-capacity positron trap.

Preliminary experiments have been performed toward the development of a multi-cell Penning-Malmberg trap for the storage of large numbers of positrons (≥1010 e+). We introduce the master-cell test trap and the diagnostic tools for first experiments with electrons. The usage of a phosphor screen to measure the z-integrated plasma distribution and the number of confined particles is demonstrated, as well as the trap alignment to the magnetic field (B = 3.1 T) using the m = 1 diocotron mode. The plasma parameters and expansion are described along with the autoresonant excitation of the diocotron mode using rotating dipole fields and frequency chirped sinusoidal drive signals. We analyze the reproducibility of the excitation and use these findings to settle on the path for the next generation multi-cell test device.

Rotational pumping revisited

This paper considers a pure electron plasma, with a small admixture of negative ions, confined in a Penning–Malmberg trap. When a diocotron mode is excited on the plasma, the end sheaths of the plasma are azimuthally distorted. During reflection at a distorted end sheath, an ion steps off of the surface characterizing the drift motion in the plasma interior, and this step produces transport. The diocotron mode transfers canonical angular momentum to the ions, and in response damps. These transport mechanism and associated damping are called rotational pumping. It is particularly strong when the axial bounce motion and the rotational drift motion, in the rotating frame of the mode, satisfy a resonance condition. This paper calculates the transport flux of ions and the associated damping rate of the mode in the resonant regime. Previous papers have discussed the theory and the experimental observation of rotational pumping for the special case of a diocotron mode with azimuthal wave number l = 1, and this paper extends the theory to modes with l≠1, which may sound like a trivial extension, but in fact is not.

Flux-driven algebraic damping of m = 2 diocotron mode

Experiments with pure electron plasmas in a Malmberg–Penning trap have observed linear in time, algebraic damping of m = 2 diocotron modes. Transport due to small field asymmetries produces a low-density halo of electrons moving radially outward from the plasma core, and the mode damping begins when the halo reaches the resonant radius of the mode. The damping rate is proportional to the flux of halo particles through the resonant layer. The damping is related to, but distinct from spatial Landau damping in which a linear wave–particle resonance produces exponential damping. This paper reports an analytic theory that captures the main signatures reported for this novel damping, namely, that the damping begins when the halo particles reach the resonant radius and that the damping is algebraic in time with nearly constant damping rate. The model also predicts a nonlinear frequency shift. The model provides two ways to think about the damping. It results from a transfer of canonical angular momentum from the mode to halo particles being swept by the mode field through the nonlinear cat's eye orbits of the resonant region. More mechanistically, the electric field produced by the perturbed charge density of the resonant particles acts back on the plasma core causing E×B drift that gives rise to the damping and nonlinear frequency shift.

Plasma temperature measurement with a silicon photomultiplier (SiPM).

The temperature of a nonneutral plasma confined in a Penning-Malmberg trap can be determined by slowly lowering one side of the trap's electrostatic axial confinement barrier; the temperature is inferred from the rate at which particles escape the trap as a function of the barrier height. In many experiments, the escaping particles are directed toward a microchannel plate, and the resulting amplified charge is collected on a phosphor screen. The screen is used for imaging the plasma but can also be used as a Faraday cup (FC) for a temperature measurement. The sensitivity limit is then set by microphonic noise enhanced by the screen's high-voltage bias. Alternately, a silicon photomultiplier (SiPM) can be employed to measure the charge via the light emitted from the phosphor screen. This decouples the signal from the microphonic noise and allows the temperature of colder and smaller plasmas to be measured than could be measured previously; this paper focuses on the advantages of a SiPM over a FC.

Computational and theoretical analysis of electron plasma cooling by resonant interaction with a microwave cavity

Recent experiments demonstrated that the cyclotron cooling rate of an electron plasma in a Penning–Malmberg trap can be increased by placing the plasma in a cavity and adjusting the magnetic field to make the cyclotron motion resonant with a cavity mode. Here this physics is studied with a coupled oscillator model and analyzed both analytically and numerically. Plasma cooling performance is evaluated over a wide range of system parameters, including the number of electrons, the coupling to the local electric field, the magnetic field gradient, and the detuning between the cavity and cyclotron frequencies. Scaling the equations shows that the system is well-described by a few key dimensionless quantities.

A pulse stretcher for a LINAC-based pulsed slow-positron beam providing a quasi-continuous beam with an energy of 5.2 keV

A pulse stretcher providing a 5.2keV quasi-continuous beam has been developed for use with a pulsed slow-positron beam generated by an electron linear accelerator operated with a repetition frequency of 50Hz. Pulses of positrons, of width 1.2µs, were trapped in a Penning–Malmberg trap and then gradually released downstream, stretching the pulse width to nearly 20ms.