Particle Phase Space Research Articles

Magnetic mirror end-plugged by field-reversed configurations formed via rotating magnetic fields

A novel magnetic mirror concept with field-reversed configurations (FRCs) formed via rotating magnetic fields (RMFs) serving as end plugs is proposed to improve the mirror's axial confinement. Single-particle orbit calculations suggest that the FRCs in the end plugs can reflect ions back into the central cell if their parallel speeds are not so fast that they can overcome the magnetic field gradient force from the X-point of the FRC to the midplane outside of the FRC. However, this effect is limited and is no different from that of adding a weak mirror cell to the central cell. When the inward Hall electric field generated by the RMFs is considered, an additional Lorentz force emerges that pushes the incoming ions back to the central mirror, thereby dramatically improving the confinement. The Lorentz force is related to the azimuthal drift speed times the radial component of the magnetic field. By surveying the particle phase space of the speeds, we find that this Lorentz force can reflect back or trap >90% of ions escaping from the central mirror given a sufficient Hall electric field in the RMF region. Finally, preliminary experimental results from the Keda Mirror with AXisymmetricity RMF/FRC are reported and show that with the RMFs on, the axial mirror confinement can increase by a factor of ∼1.4 on average.

Superposition Principle and Born’s Rule in the Probability Representation of Quantum States

The basic notion of physical system states is different in classical statistical mechanics and in quantum mechanics. In classical mechanics, the particle system state is determined by its position and momentum; in the case of fluctuations, due to the motion in environment, it is determined by the probability density in the particle phase space. In quantum mechanics, the particle state is determined either by the wave function (state vector in the Hilbert space) or by the density operator. Recently, the tomographic-probability representation of quantum states was proposed, where the quantum system states were identified with fair probability distributions (tomograms). In view of the probability-distribution formalism of quantum mechanics, we formulate the superposition principle of wave functions as interference of qubit states expressed in terms of the nonlinear addition rule for the probabilities identified with the states. Additionally, we formulate the probability given by Born’s rule in terms of symplectic tomographic probability distribution determining the photon states.

Knife-edge based measurement of the 4D transverse phase space of electron beams with picometer-scale emittance

Precise manipulation of high brightness electron beams requires detailed knowledge of the particle phase space shape and evolution. As ultrafast electron pulses become brighter, new operational regimes become accessible with emittance values in the picometer range, with enormous impact on potential scientific applications. Here we present a new characterization method for such beams and demonstrate experimentally its ability to reconstruct the 4D transverse beam matrix of strongly correlated electron beams with sub-nanometer emittance and sub-micrometer spot size, produced with the HiRES beamline at LBNL. Our work extends the reach of ultrafast electron accelerator diagnostics into picometer-range emittance values, opening the way to complex nanometer-scale electron beam manipulation techniques.

Spatial Scales and Plasma Properties of the Distant Magnetopause: Evidence for Selective Ion and Electron Transport

AbstractOne of the most important sources of magnetospheric plasma is particle entry through the distant magnetotail boundary, the nightside magnetopause. This entry mechanism depends on the magnetopause configuration. Off the equator, the strong lobe magnetic field renders the magnetopause a tangential or a rotational discontinuity, and thus the magnetosheath field orientation predominantly controls particle entry through magnetic reconnection. At the equatorial, distant tail magnetopause, however, the magnetic field's control of particle entry is diminished because the plasma beta there is large on both sides of the boundary. Thus, transport there can be significantly different from that at the dayside and off‐equatorial magnetopauses. Using observations from two Acceleration, Reconnection, Turbulence and Electrodynamics of the Moon's Interaction with the Sun probes, we investigate plasma transport mechanisms around the distant equatorial magnetopause. We find that transport occurs as a series of abrupt transitions in density, ion and electron temperatures, and ion kinetic energy of spatial scales as small as a typical plasma sheet ion gyroradius. Analysis of the particle phase space density reveals that an energy‐selection mechanism controls electron transport across the magnetopause, whereas ion transport is likely controlled by spatial diffusion driven by low‐frequency magnetic field fluctuations. We discuss the importance of these fluctuations for the magnetopause structure (e.g., the thickness of the transitions in plasma density, ion and electron temperatures, and ion kinetic energy).

Field‐Aligned Structures of the Poloidal‐Mode ULF Wave Electric Field: Phase Relationship Implications

AbstractSpacecraft observations within recent decades have demonstrated that ultralow frequency (ULF) waves play an important role in the dynamics of Earth's magnetosphere through drift and/or drift‐bounce resonance with different particle species. The phase relationship between resonant particles and waves can help us understand the wave‐particle interacting processes. It has been revealed that the phase relationship between the drift resonant particles and the fundamental poloidal‐mode electric field is a signature to judge the energy transfer direction between particles and waves, and the local phase space density gradient. Here we explore whether there are other physical meanings of the phase relationship for drift‐bounce resonant particles in addition to the similar ones as drift resonant particles. In this study, we find that (1) under different field‐aligned structures, the poloidal‐mode electric fields will show different phase relationship with drift‐bounce resonant particles at the magnetic equator. It indicates that the phase relationship can be used to diagnose the parallel morphologies of ULF wave electric field. (2) If particle's phase space density variations caused by resonance effect become more dominant while compared with the nonresonant effect, the phase difference becomes much closer to inphase or antiphase. (3) When wave's parallel morphology is given, the phase relationship can be used to judge the energy transfer direction between waves and particles. These findings can provide new sights into exploring ULF waves' propagation and distribution along magnetic field lines and studying their interaction with charged particles in the magnetosphere.

Modelling of beam-driven Alfvén modes in TJ-II plasmas

The properties of hydrogen neutral beam injection driven Alfvén eigenmodes (AEs) in the TJ-II flexible heliac are investigated using a reduced magnetohydrodynamic (MHD) model coupled to a realistic MHD equilibrium. The simulation results of AE frequency and radial localization are found to be broadly consistent with experimental observations. The simulation results show that an AE with the same poloidal and toroidal harmonics persists under small variations in on-axis iota values, which is consistent with the experimental observations. The corresponding wave-particle resonance maps suggest, for low bounce harmonics, the possibility of describing nonlinear evolution of the AEs in TJ-II by a sum of two ion populations with different weighting factors, one of which is dominated by drag and the other by diffusion. As the bounce harmonic increases, the resonance region starts to expand and can cover a significant area of the particle phase space until this resonance region vanishes at high bounce harmonics.

Optimal observables forZ′models in annihilation leptonic processes

The optimal observables with the best ratio of signal to statistical uncertainty are proposed for a bunch of popular models of the $Z'$ boson. They are the cross sections integrated over the phase space of the final particles with proper weight functions. It is shown that the proposed observables are completely equivalent to the $\chi^2$ fit of the differential cross section, so they could be used as an alternative of aggregating events into bins with further minimization of the $\chi^2$ function, especially in preliminary analysis of experimental data. Application of the observables to the maximum likelihood estimate of the $Z'$ mass and the $Z$--$Z'$ mixing angle as well as to the exclusion reach and statistical efficiency of the signal is investigated in details.

QED Phenomena in an Ultrastrong Magnetic Field. I. Electron–Photon Scattering, Pair Creation, and Annihilation

We evaluate several basic electrodynamic processes as modified by the presence of a very strong magnetic field, exceeding $B_{\rm Q} \equiv m^2/e = 4.4\times 10^{13}$ G. These results are needed to build models of dissipative phenomena outside magnetars and some other neutron stars. Differential and total cross sections and rates are presented for electron-photon scattering, the annihilation of an electron-positron pair into two photons, the inverse process of two-photon pair creation, and single-photon pair creation into the lowest Landau state. The relative importance of these interactions changes as the background magnetic field grows in strength. The particle phase space relevant for a given process may be restricted by single-photon pair creation, which also opens up efficient channels for pair multiplication, e.g. in combination with scattering. Our results are presented in the form of compact formulae that allow for relativistic electron (positron) motion, in the regime where Landau excitations can be neglected (corresponding to $10^3B_{\rm Q} \gg B \gg B_{\rm Q}$ for moderately relativistic motion along the magnetic field). Where a direct comparison is possible, our results are tested against earlier calculations, and a brief astrophysical context is provided. A companion paper considers electron-positron scattering, scattering of electrons and positrons by ions, and relativistic electron-ion bremsstrahlung.

Beam-Ion Acceleration during Edge Localized Modes in the ASDEX Upgrade Tokamak.

The acceleration of beam ions during edge localized modes (ELMs) in a tokamak is observed for the first time through direct measurements of fast-ion losses in low collisionality plasmas. The accelerated beam-ion population exhibits well-localized velocity-space structures which are revealed by means of tomographic inversion of the measurement, showing energy gains of the order of tens of keV. This suggests that the ion acceleration results from a resonant interaction between the beam ions and parallel electric fields arising during the ELM. Orbit simulations are carried out to identify the mode-particle resonances responsible for the energy gain in the particle phase space. The observation motivates the incorporation of a kinetic description of fast particles in ELM models and may contribute to a better understanding of the mechanisms responsible for particle acceleration, ubiquitous in astrophysical and space plasmas.

Generalized Symplectization of Vlasov Dynamics and Application to the Vlasov–Poisson System

In this paper, we study a Hamiltonian structure of the Vlasov-Poisson system, first mentioned by Fr\"ohlich, Knowles, and Schwarz. To begin with, we give a formal guideline to derive a Hamiltonian on a subspace of complex-valued $L^2$ integrable functions $\alpha$ on the one particle phase space $\mathbb{R}^{2d}$, s.t. $f=\left|\alpha\right|^2$ is a solution of a collisionless Boltzmann equation. The only requirement is a sufficiently regular energy functional on a subspace of distribution functions $f\in L^1$. Secondly, we give a full well-posedness theory for the obtained system corresponding to Vlasov-Poisson in $d\geq3$ dimensions. Finally, we adapt the classical globality results for $d=3$ to the generalized system.

Design considerations for a pulse line ion accelerator (PLIA)-based PET isotope generator.

Positron emission tomography (PET) imaging remains limited due to the cost associated with on-site production of short half-life, positron-emitting isotopes. In this work, we examine the use of a pulse line ion accelerator (PLIA) to accelerate protons for single-dose PET isotope production. Time-domain electromagnetic field and particle-in-cell (PIC) simulations were performed for a 1.5-m PLIA structure modeled in CST Microwave Studio and Particle Studio software. Scaled measurements from a kV ramp-pulse generator were incorporated into the simulations to accelerate a 1 A, 50 ns proton beam injected with initial kinetic energy of 100 keV. A uniform, 3 T, solenoidal magnetic field was used to provide external beam focusing. Electromagnetic fields and particle phase space were recorded with ns resolution for subsequent analysis. Applying a scaled 100 kV, 20 ns ramped voltage pulse to the PLIA input resulted in a travelling electric field wave inside the structure with accelerating gradient of 2.4 MV/m. The observed wave speed was 1.2 × 107 m/s and is in good agreement with theoretical predictions. Phase space monitors showed both acceleration and bunching of the proton beam, with a maximum kinetic energy of 2.5 MeV, observed at the exit of the single PLIA stage. Evaluation of beam position monitors at different locations in the accelerator showed bunch compression and minimal beam divergence, illustrating that the 3 T field is adequate to contain the beam over the length of the PLIA structure. Simulations performed in this work demonstrate the feasibility of using a PLIA structure to accelerate protons with MV/m level gradients. Combining several PLIA stages in series could allow for a low-cost accelerator suitable for dose-on-demand PET isotope production.

A low-frequency variational model for energetic particle effects in the pressure-coupling scheme

Energetic particle effects in magnetic confinement fusion devices are commonly studied by hybrid kinetic-fluid simulation codes whose underlying continuum evolution equations often lack the correct energy balance. While two different kinetic-fluid coupling options are available (current coupling and pressure coupling), this paper applies the Euler–Poincaré variational approach to formulate a new conservative hybrid model in the pressure-coupling scheme. In our case the kinetics of the energetic particles are described by guiding center theory. The interplay between the Lagrangian fluid paths and phase space particle trajectories reflects an intricate variational structure which can be approached by letting the four-dimensional guiding center trajectories evolve in the full six-dimensional phase space. Then, the redundant perpendicular velocity is integrated out to recover a four-dimensional description. A second equivalent variational approach is also reported, which involves the use of phase space Lagrangians. Not only do these variational structures confer on the new model a correct energy balance, but also they produce a cross-helicity invariant which is lost in the other pressure-coupling schemes reported in the literature.

Destabilization of counter-propagating Alfvénic instabilities by tangential, co-current neutral beam injection

Injection of high-energy neutrals is a common tool to heat the plasma and drive current non-inductively in fusion devices. Once neutrals ionize, the resulting energetic particles can drive instabilities that are detrimental for the performance and the predictability of plasma discharges. A broad deposition profile of neutrals from neutral beam injection, e.g. by aiming the beam tangentially on the outboard midplane (i.e. off-axis), is often assumed to limit those undesired effects by reducing the radial gradient of the EP density, thus reducing the drive for instabilities. However, this work presents new evidence that tangential neutral beam injection, including off-axis injection near the plasma mid-radius, can also lead to undesired effects such as the destabilization of Alfvénic instabilities. Time-dependent analysis with the TRANSP code indicates that instabilities are driven by a combination of radial and energy gradients in the distribution function of the energetic particles. The mechanisms for wave-particle interaction revealed by the energetic particle phase space resolved analysis are the basis to identify strategies to mitigate or suppress the observed instabilities.

Visualizing the Phase Space of Heterogeneous Inertial Particles in 2D Flows

AbstractIn many scientific disciplines, the motion of finite‐sized objects in fluid flows plays an important role, such as in brownout engineering, sediment transport, oceanology or meteorology. These finite‐sized objects are called inertial particles and, in contrast to traditional tracer particles, their motion depends on their current position, their own particle velocity, the time and their size. Thus, the visualization of their motion becomes a high‐dimensional problem that entails computational and perceptual challenges. So far, no visualization explored and visualized the particle trajectories under variation of all seeding parameters. In this paper, we propose three coordinated views that visualize the different aspects of the high‐dimensional space in which the particles live. We visualize the evolution of particles over time, showing that particles travel different distances in the same time, depending on their size. The second view provides a clear illustration of the trajectories of different particle sizes and allows the user to easily identify differences due to particle size. Finally, we embed the trajectories in the space‐velocity domain and visualize their distance to an attracting manifold using ribbons. In all views, we support interactive linking and brushing, and provide abstraction through density volumes that are shown by direct volume rendering and isosurface slabs. Using our method, users gain deeper insights into the dynamics of inertial particles in 2D fluids, including size‐dependent separation, preferential clustering and attraction. We demonstrate the effectiveness of our method in multiple steady and unsteady 2D flows.

Radiation of quantum black holes and modified uncertainty relation

In this paper, using a deformed algebra [Formula: see text] which is originated from various theories of gravity, we study thermodynamical properties of quantum black holes (BHs) in canonical ensembles. We exactly calculate the modified internal energy, entropy and heat capacity. Moreover, we investigate a tunneling mechanism of massless particle in phase space. In this regard, the tunneling radiation of BH receives new corrections and the exact radiant spectrum is no longer precisely thermal. In addition, we show that our results are compatible with other quantum gravity (QG) approaches.

Floquet many-body engineering: topology and many-body physics in phase space lattices

Hamiltonians which are inaccessible in static systems can be engineered in periodically driven many-body systems, i.e., Floquet many-body systems. We propose to use interacting particles in a one-dimensional (1D) harmonic potential with periodic kicking to investigate two-dimensional topological and many-body physics. Depending on the driving parameters, the Floquet Hamiltonian of single kicked harmonic oscillator has various lattice structures in phase space. The noncommutative geometry of phase space gives rise to the topology of the system. We investigate the effective interactions of particles in phase space and find that the point-like contact interaction in quasi-1D real space becomes a long-rang Coulomb-like interaction in phase space, while the hardcore interaction in pure-1D real space becomes a confinement quark-like potential in phase space. We also find that the Floquet exchange interaction does not disappear even in the classical limit, and can be viewed as an effective long-range spin–spin interaction induced by collision. Our proposal may provide platforms to explore new physics and exotic phases by Floquet many-body engineering.

Cosmological neutrino simulations at extreme scale

Constraining neutrino mass remains an elusive challenge in modern physics. Precision measurements are expected from several upcoming cosmological probes of large-scale structure. Achieving this goal relies on an equal level of precision from theoretical predictions of neutrino clustering. Numerical simulations of the non-linear evolution of cold dark matter and neutrinos play a pivotal role in this process. We incorporate neutrinos into the cosmological N-body code CUBEP3M and discuss the challenges associated with pushing to the extreme scales demanded by the neutrino problem. We highlight code optimizations made to exploit modern high performance computing architectures and present a novel method of data compression that reduces the phase-space particle footprint from 24 bytes in single precision to roughly 9 bytes. We scale the neutrino problem to the Tianhe-2 supercomputer and provide details of our production run, named TianNu, which uses 86% of the machine (13 824 compute nodes). With a total of 2.97 trillion particles, TianNu is currently the world’s largest cosmological N-body simulation and improves upon previous neutrino simulations by two orders of magnitude in scale. We finish with a discussion of the unanticipated computational challenges that were encountered during the TianNu runtime.

Bilocal model for the relativistic spinning particle

In this work we show that a relativistic spinning particle can be described at the classical and the quantum level as being composed of two physical constituents which are entangled and separated by a fixed distance. This bilocal model for spinning particles allows for a natural description of particle interactions as a local interaction at each of the constituents. This form of the interaction vertex provides a resolution to a long standing issue on the nature of relativistic interactions for spinning objects in the context of the worldline formalism. It also potentially brings a dynamical explanation for why massive fundamental objects are naturally of lowest spin. We analyze first a non-relativistic system where spin is modeled as an entangled state of two particles with the entanglement encoded into a set of constraints. It is shown that these constraints can be made relativistic and that the resulting description is isomorphic to the usual description of the phase space of massive relativistic particles with the restriction that the quantum spin has to be an integer.

Energetic particle modes of q = 1 high-order harmonics in tokamak plasmas with monotonic weak magnetic shear

Linear and nonlinear simulations of high-order harmonics q=1 energetic particle modes excited by trapped energetic particles in tokamaks are carried out using kinetic/magnetohydrodynamic hybrid code M3D-K. It is found that with a flat safety factor profile in the core region, the linear growth rate of high-order harmonics (m=n>1) driven by energetic trapped particles can be higher than the m/n=1/1 component. The high m=n>1 modes become more unstable when the pressure of energetic particles becomes higher. Moreover, it is shown that there exist multiple resonant locations satisfying different resonant conditions in the phase space of energetic particles for the high-order harmonics modes, whereas there is only one precessional resonance for the m/n=1/1 harmonics. The fluid nonlinearity reduces the saturation level of the n=1 component, while it hardly affects those of the high n components, especially the modes with m=n=3,4. The frequency of these modes does not chirp significantly, which is different with the typical fishbone driven by trapped particles. In addition, the flattening region of energetic particle distribution due to high-order harmonics excitation is wider than that due to m/n=1/1 component, although the m/n=1/1 component has a higher saturation amplitude.

Slow electrostatic fluctuations generated by beam-plasma interaction

Eulerian simulations of the Vlasov-Poisson equations have been employed to analyze the excitation of slow electrostatic fluctuations (with phase speed close to the electron thermal speed), due to a beam-plasma interaction, and their propagation in linear and nonlinear regimes. In 1968, O'Neil and Malmberg [Phys. Fluids 11, 1754 (1968)] dubbed these waves “beam modes.” In the present paper, previous analytical results on the beam modes in both linear and nonlinear regimes have been revisited numerically, pointing out that, when an electron beam is launched in a plasma of Maxwellian electrons and motionless protons and this initial equilibrium is perturbed by a monochromatic density disturbance, the electric field amplitude grows exponentially in time and then undergoes nonlinear saturation, associated with the kinetic effects of particle trapping and phase space vortex generation. Moreover, new numerical results give evidence that, when the initial density perturbation is setup in the form of a low amplitude random phase noise, the whole Fourier spectrum of wavenumbers is excited. As a result, the electric field profile appears as a train of isolated pulses, each of them being associated with a phase space vortex in the electron distribution function. At later times, these vortical structures tend to merge and, correspondingly, the electric pulses collapse, showing the tendency towards a time asymptotic configuration characterized by the appearance of electric soliton-like pulses. This dynamical evolution is driven by purely kinetic processes, possibly at work in many space and laboratory plasma environments.