Initial Phase Space Distribution Research Articles

Assessment of the runaway electron load distribution in ITER during 3D MHD induced beam termination

In ITER, disruption-born runaway electrons (REs), unless mitigated, are expected to form a several Mega-Ampere beam that ultimately intercepts the first wall leading to melting of the plasma facing components. Developing a successful mitigation strategy therefore requires modeling that takes into account the coupling between REs and the MHD during the formation and termination of the beam, along with estimates for the wall loads that can be compared to design values. Using the JOREK code, this work aims to provide the latter by presenting a novel model for collisions between REs and the wall and applying it to a beam termination scenario in ITER. To this end, the transport of REs is modeled by tracing particles in the fields calculated by preceding simulations of the disruption event where REs were treated in the fluid picture and self-consistently coupled to the MHD. The resulting heat loads are found to be highly localized in both the poloidal and toroidal directions, with 3D features also playing an important role in the appearance of hot spots. Peak loads were on the order of 107−108Jm2 . The load distribution was found to only be weakly sensitive to the initial phase space distribution of the REs when decoupled from the fields, while modifying properties of the underlying MHD yielded notable differences in wetted area and peak loads, in particular for cases with higher resistivity.

Decay mechanisms of ensemble averages of nonlinear oscillators

The ensemble average of noninteracting particles in a nonlinear oscillator system is investigated. Depending on the initial phase-space distribution, the nonlinearity-induced dephasing mechanism can lead to temporal decays of the average particle position that can be quite different from the standard exponential decay. In fact, the approach to the equilibrium can be Gaussian or even nonmonotonic in time. In the long-time limit, it is possible to construct a single differential equation for the time evolution of the average position. Unlike the infinite set of coupled nonlinear differential equations derived from the standard approach based on the Liouville equation, this equation can be even linear. We also show that the predicted dephasing mechanisms have their direct counterpart in the corresponding dynamics of quantum mechanical wave packets.

Holographic Kolmogorov-Sinai entropy and the quantum Lyapunov spectrum

In classical chaotic systems the entropy, averaged over initial phase space distributions, follows a universal behavior. While approaching thermal equilibrium it passes through a stage where it grows linearly, while the growth rate, the Kolmogorov-Sinai entropy (rate), is given by the sum over all positive Lyapunov exponents. A natural question is whether a similar relation is valid for quantum systems. We argue that the Maldacena-Shenker-Stanford bound on quantum Lyapunov exponents implies that the upper bound on the growth rate of the entropy, averaged over states in Hilbert space that evolve towards a thermal state with temperature T, should be given by πT times the thermal state’s von Neumann entropy. Strongly coupled, large N theories with black hole duals should saturate the bound. To test this we study a large number of isotropization processes of random, spatially homogeneous, far from equilibrium initial states in large N, mathcal{N} = 4 Super Yang Mills theory at strong coupling and compute the ensemble averaged growth rate of the dual black hole’s apparent horizon area. We find both an analogous behavior as in classical chaotic systems and numerical evidence that the conjectured bound on averaged entropy growth is saturated granted that the Lyapunov exponents are degenerate and given by λi = ±2πT. This fits to the behavior of classical systems with plus/minus symmetric Lyapunov spectra, a symmetry which implies the validity of Liouville’s theorem.

Detection and manipulation of the transverse motion of neutral molecules in a Stark decelerator

By enabling precise control over longitudinal velocity of neutral molecules, Stark deceleration has become an important tool for studying cold molecular collisions. However, the information about transverse motion is often hard to extract and to some extent beyond control. Here we demonstrate a new experimental approach that allows us to observe the transverse phase-space distribution of molecules within a Stark decelerator. The transverse dynamics can be tracked along the decelerator, which can be used to measure the initial transverse phase-space distribution of the molecules. The observed frequency of the transverse oscillations agrees well with the one determined from electric field distribution. Thermalization of the molecules at the decelerator entrance must be accounted for in our Monte Carlo simulations of the molecules dynamics to reach agreement with experimental data. We introduce two approaches of manipulating transverse modes. In the first method, a free-flight pulse is introduced to achieve a short phase-space stretching, an equivalent technique to delta kick cooling [Phys. Rev. Lett. 78, 2088 (1997)]. In the second mode we enforce phase-space rotation by varying the applied voltage. Both modes allow us to manipulate the transverse phase-space distribution and, in particular, allow us to tune (in a well-controlled way) the anisotropy of the phase-space distribution.

Space-Charge Aberrations in Single-Shot Time-Resolved Transmission Electron Microscopy

In this paper, we discuss effects of space charge fields on imaging performance in a single shot time-resolved electron microscope (TEM). Using a Green's function perturbation method, we derive analytical estimates for the effects of space charge nonlinearity on the image formation process and the associated aberration coefficients. The dependence of these coefficients on the initial beam phase space distribution is elucidated. The results are validated by particle tracking simulations and provide fundamental scaling laws for the trade-off between temporal and spatial resolution in single-shot time-resolved TEM.

Thermalization of Local Observables in the $$\alpha $$-FPUT Chain

Most studies on the problem of equilibration of the Fermi-Pasta-Ulam-Tsingou (FPUT) system have focused on equipartition of energy being attained amongst the normal modes of the corresponding harmonic system. In the present work, we instead discuss the equilibration problem in terms of local variables, and consider initial conditions corresponding to spatially localized energy. We estimate the time-scales for equipartition of space localized degrees of freedom and find significant differences with the times scales observed for normal modes. Measuring thermalization in classical systems necessarily requires some averaging, and this could involve one over initial conditions or over time or spatial averaging. Here we consider averaging over initial conditions chosen from a narrow distribution in phase space. We examine in detail the effect of the width of the initial phase space distribution, and of integrability and chaos, on the time scales for thermalization. We show how thermalization properties of the system, quantified by its equilibration time, defined in this work, can be related to chaos, given by the maximal Lyapunov exponent. Somewhat surprisingly we also find that the ensemble averaging can lead to thermalization of the integrable Toda chain, though on much longer time scales.

Charge asymmetry dependence of the elliptic flow splitting in relativistic heavy-ion collisions

The elliptic flow splitting $\Delta v_2$ between $\bar{u}$ and $u$ quarks as well as between $\pi^-$ and $\pi^+$ in midcentral Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV has been studied, based on the framework of an extended multiphase transport model with the partonic evolution described by the chiral kinetic equations of motion. Within the available statistics, the slope of $\Delta v_2$ between $\bar{u}$ and $u$ quarks with respect to the electric charge asymmetry $A_{ch}$ from the linear fit is found to be negative, due to the correlation between the velocity and the coordinate in the initial parton phase-space distribution. Simulations with the magnetic field in QGP overestimate the splitting of the spin polarization between $\Lambda$ and $\bar{\Lambda}$ observed experimentally, with the latter more consistent with results under the magnetic field in vacuum. Considering the uncertainties from the magnetic field, the quark-antiquark vector interaction, and the hadronization, as well as the hadronic evolution, our study shows that the experimentally observed positive slope of $\Delta v_2$ with respect to $A_{ch}$ is not likely due to the chiral magnetic wave.

New Model of Density Distribution for Fermionic Dark Matter Halos

We formulate a new model of density distribution for halos made of warm dark matter (WDM) particles. The model is described by a single microphysical parameter – the mass (or, equivalently, the maximal value of the initial phase-space density distribution) of dark matter particles. Given the WDM particle mass and the parameters of a dark matter density profile at the halo periphery, this model predicts the inner density profile. In the case of initial Fermi–Dirac distribution, we successfully reproduce cored dark matter profiles from N-body simulations. We calculate also the core radii of warm dark matter halos of dwarf spheroidal galaxies for particle masses mFD = 100, 200, 300, and 400 eV.

A new method for analyzing and visualizing plasma simulations using a phase-space tessellation

We apply a novel phase-space interpolation technique referred to as the simplex-in-cell (SIC) method to analyze two- and three-dimensional particle-in-cell (PIC) simulations of electromagnetic plasmas. SIC relies on a discretization of the initial phase-space distribution function into simplices, which allows an approximation to the full, continuously defined distribution function to be constructed at any later time in the simulation. This allows densities, currents, and even full momentum distribution functions to be measured at any point in the simulation domain without averaging over control volumes. The SIC approach applies to any PIC simulation for which a tessellation of the initial particle distribution can be constructed. In this study, we use outputs from standard PIC simulations of the Weibel instability and compare physical quantities such as charge and current densities calculated in postprocessing using SIC and standard particle deposits. Using 2D simulations with 1–65 536 particles-per-cell, we find that SIC eliminates discrete particle noise and in some cases can reach a given noise level using ∼1000 times fewer simulation particles than with standard particle deposition schemes. In regions of low density, such as between current filaments, SIC is able to capture small amplitude features even with fewer particles than gridpoints due to the deformable nature of the SIC volume elements. By calculating momentum distributions, we show how SIC can capture low density tails in the spectrum using far fewer particles than are necessary for standard particle deposits. We calculate the charge density on spatial grids of increasing resolution to demonstrate the ability of SIC to reveal fine-scale details that are not accessible with standard particle deposits. Finally, we show how SIC can be extended to 3D and give an example of its use to calculate the charge density from 3D PIC simulations of the Weibel instability. These results motivate the future implementation of SIC directly in the simulation force calculation for a novel low-noise electromagnetic plasma simulation method.

Correlations between the final momenta of electrons and their initial phase-space distribution during photoionization

We present both full quantum mechanical and semiclassical calculations for the photoionization of a hydrogen atom induced by a few-cycle linearly polarized infrared laser pulse. As a quantum treatment, we applied the direct integration of the time-dependent Schrödinger equation. In the three-dimensional semiclassical trajectory Monte Carlo approximation, it is assumed that the wavepacket propagation in the post-tunneling process can be well described within the classical framework. By comparing the results of two methods, we found good agreement in the final momentum distributions of the emitted electrons for longer exciting pulses. This allowed us to use the semiclassical approximation and clearly identify and separate the initial conditions that correspond to various regions in the final momentum distributions of the emitted electrons. We also illustrate the corresponding regions with typical electron trajectories.

Core-halo quasi-stationary states in the Hamiltonian mean-field model

A characteristic feature of long-range interacting systems is that they become trapped in a non-equilibrium and long-lived quasi-stationary state (QSS) during the early stages of their development. We present a comprehensive review of recent studies of the core-halo structure of QSSs, in the Hamiltonian mean-field model (HMF), which is a mean-field model of mutually coupled ferromagnetic XY spins located at a point, obtained by starting from various unsteady rectangular water-bag type initial phase-space distributions. The main result exposed in this review is that the core-halo structure can be described by the superposition of two independent Lynden–Bell distributions. We discuss the completeness of collisionless relaxation of this double Lynden–Bell distribution by using both of Lynden–Bell entropy and double Lynden–Bell entropy for the systems at low energies per particle.

Suppression of the emittance growth induced by coherent synchrotron radiation in triple-bend achromats**Supported by National Natural Science Foundation of China (11475202, 11405187) and Youth Innovation Promotion Association of Chinese Academy of Sciences (2015009)

The coherent synchrotron radiation (CSR) effect in a bending path plays an important role in transverse emittance dilution in high-brightness light sources and linear colliders, where the electron beams are of short bunch length and high peak current. Suppression of the emittance growth induced by CSR is critical to preserve the beam quality and help improve the machine performance. It has been shown that the CSR effect in a double-bend achromat (DBA) can be analyzed with the two-dimensional point-kick analysis method. In this paper, this method is applied to analyze the CSR effect in a triple-bend achromat (TBA) with symmetric layout, which is commonly used in the optics designs of energy recovery linacs (ERLs). A condition of cancelling the CSR linear effect in such a TBA is obtained, and is verified through numerical simulations. It is demonstrated that emittance preservation can be achieved with this condition, and to a large extent, has a high tolerance to the fluctuation of the initial transverse phase space distribution of the beam.

Toolkit for semiclassical computations for strongly driven molecules: Frustrated ionization ofH2driven by elliptical laser fields

We study the formation of highly excited neutral atoms during the breakup of strongly driven molecules. Past work on this significant phenomenon has shown that during the formation of highly excited neutral atoms (${\mathrm{H}}^{*}$) during the breakup of ${\mathrm{H}}_{2}$ in a linear laser field the electron that escapes does so either very quickly or after remaining bound for a few periods of the laser field. Here, we address the electron-nuclear dynamics in ${\mathrm{H}}^{*}$ formation in elliptical laser fields, through Coulomb explosion. We show that with increasing ellipticity two-electron effects are effectively ``switched off.'' We perform these studies using a toolkit we have developed for semiclassical computations for strongly driven multicenter molecules. This toolkit includes the formulation of the probabilities of strong-field phenomena in a transparent way. This allows us to identify the shortcomings of currently used initial phase-space distributions for the electronic degrees of freedom. In addition, it includes a three-dimensional method for time propagation that fully accounts for the Coulomb singularity. This technique has been previously developed in the context of celestial mechanics and we currently adopt it to strongly driven systems. Moreover, we allow for tunneling during the time propagation. We find that this is necessary in order to accurately describe the fragmentation of strongly driven molecules.

Thermal emittance from ionization-induced trapping in plasma accelerators

The minimum obtainable transverse emittance (thermal emittance) of electron beams generated and trapped in plasma-based accelerators using laser ionization injection is examined. The initial transverse phase space distribution following ionization and passage through the laser is derived, and expressions for the normalized transverse beam emittance, both along and orthogonal to the laser polarization, are presented. Results are compared to particle-in-cell simulations. Ultralow emittance beams can be generated using laser ionization injection into plasma accelerators, and examples are presented showing normalized emittances on the order of tens of nm.

Microscopic Reversibility for Nonequilibrium Classical Open Systems

We rigorously show that the probability to have a specific trajectory of an externally perturbed classical open system satisfies a universal symmetry for Hamiltonian dynamics. It connects the ratio between the probabilities of time forward and reversed trajectories to a degree of the time reversal asymmetry of the final phase space distribution in a model-independent framework. Especially, it amounts to a nonequilibrium generalization of the detailed balance between the probabilities of the forward and reversed trajectories under the condition that the initial phase space distribution is described by an equilibrium ensemble. An expression of the microscopic reversibility for the subsystem is also derived based on this relation.

SU-E-T-474: Monte Carlo Phase Space Production to Model Magnetically Scanned Proton Beams for IMPT.

Accurate dose predictions in proton beam therapy using magnetically scanned beams are highly dependent on the accurate modeling of the lateral dose profiles. This study was performed to provide proton phase spaces for Monte Carlo simulations, used to accurately simulate doses at distances up to 12 cm from the central axis of the beam. Measured lateral dose profiles at various depths in water were compared to Monte Carlo simulations of doses for 90 discreet initial proton energies. Phase spaces were produced using a one dimensional energy distribution, and a combination of several two dimensional spatial and directional distributions. Simulations were performed iteratively using variations in the initial phase space distributions to achieve acceptable agreement between measured and simulated lateral dose profiles, i.e. differences in FWHM < 0.5 mm and dose differences less that 0.1% at distances up to 12.5 cm. 90 phase spaces of proton sources for different initial beam energies were created for use in Monte Carlo simulations of scanned proton beam therapy patient plans. At a depth of 2 cm in water, the simulated and measured FWHM of the lateral dose profiles differed in in-plane direction by an average of 0.05 mm, in cross-plane direction by 0.13 mm. All simulated profiles were within 0.1% of the measured doses at distances between 2cm and 12.5 cm from the central beam axis. A library of 90 phase space files has been created to accurately simulate magnetically scanned proton beams for IMPT, providing accurate dose distributions up to 12 cm distance from the central beam axis. This project is supported in part by P01CA021239 from the National Cancer Institute. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Cancer Institute or the National Institutes of Health.

SU-E-T-488: Dose Calculation Model Using the Simplified Monte Carlo Method with an Initial Beam Model Adapted to a Beam-Wobbling System

We have developed an accurate dose calculation model based on a simplified Monte Carlo (SMC) method adapted to a beam-wobbling delivery system at National Cancer Center Hospital East (NCCHE). We used an initial beam model specific to the beam-wobbling system to reproduce accurately different dose distributions in two lateral directions (x- and y-directions) perpendicular to each other. The SMC calculates a dose distribution by tracking individual protons. The SMC starts tracking protons at an entrance of a range compensator. Protons are generated in an initial phase space adapted to the wobbler system. Since two wobbling-magnets are located at separate places with different distances from the iso-center, different dose distributions are formed in x- and y-directions. We derived an initial phase space distribution for the beam-wobbling system using an analytical method. We used the SMC method with the initial beam model to calculate dose distributions accurately. To verify accuracy of the calculation method, we measured the dose distribution in a homogeneous phantom formed by 235 MeV protons passing through a L-shaped range compensator. We used a 2D-array of parallel-plate ionization chambers (2D Array seven29®) to measure dose distributions with a sampling period of 5 mm. The measured dose distribution in the x-direction was different from that in the y-direction. Our calculation model reproduces the measurement results well in both lateral directions. In addition, the calculation reproduced the dose increments in edge regions contributed by edge-scattered protons in collimator. It indicates the advantage of the SMC. A dose calculation model has been developed based on the simplified Monte Carlo method applied to a beam-wobbling system. By adapting the initial beam model to the wobbling system, the SMC method is found to reproduce observed different dose distributions in x- and y-directions well.

Chromatic energy filter and characterization of laser-accelerated proton beams for particle therapy

The application of laser accelerated protons or ions for particle therapy has to cope with relatively large energy and angular spreads as well as possibly significant random fluctuations. We suggest a method for combined focusing and energy selection, which is an effective alternative to the commonly considered dispersive energy selection by magnetic dipoles. Our method is based on the chromatic effect of a magnetic solenoid (or any other energy dependent focusing device) in combination with an aperture to select a certain energy width defined by the aperture radius. It is applied to an initial 6D phase space distribution of protons following the simulation output from a Radiation Pressure Acceleration model. Analytical formula for the selection aperture and chromatic emittance are confirmed by simulation results using the TRACEWIN code. The energy selection is supported by properly placed scattering targets to remove the imprint of the chromatic effect on the beam and to enable well-controlled and shot-to-shot reproducible energy and transverse density profiles.

Study of ion beam extraction and transport from an electron cyclotron resonance ion source

We have started an experimental and theoretical program to better understand the extraction and transport of intense multiply charged ion beams from an electron cyclotron resonance ion source (ECRIS). In this paper we present the first results of this program concerning a simple, monocomponent He(+) beam extracted from an ECRIS. We have calculated the ion trajectories starting from the ECRIS plasma electrode up to the image plane of the analyzing magnet taking into account space-charge effects and fringe fields. The initial phase-space distribution of the He(+) beam at the extraction aperture has been calculated with a particle-in-cell code. To check the simulations we have measured beam profiles with a viewing screen both before and after the analyzing magnet. In addition also measurements with a pepperpot emittance meter located behind the analyzing magnet have been performed. We find good agreement between these measurements and simulations showing that (i) there is a significant compensation of the space charge and that (ii) our analyzing magnet causes a severe increase in effective beam emittance.

Generation of initial kinetic distributions for simulation of long-pulse charged particle beams with high space-charge intensity

Self-consistent Vlasov-Poisson simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel---both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of kinetic distributions commonly in use as initial Vlasov distributions in simulations of unbunched or weakly bunched beams with intense space-charge fields including the following: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various nonequilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of standard accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial kinetic distributions are constructed using transformations that preserve linear focusing, single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for noncontinuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulations that more precisely probe intrinsic stability properties and machine performance.