Macroparticle Simulations Research Articles

Dynamics of longitudinal phase-space modulations in an rf compressor for electron beams

Free-electron lasers operating in the UVor x-ray radiation spectrum require peak beam currents that are generally higher than those obtainable by present electron sources, thus making bunch compression necessary. Compression, however, may heighten the effects of collective forces and degrade the beam quality. In this paper we provide a framework for investigating some of these effects in rf compressors by focusing on the longitudinal dynamics of small-amplitude density perturbations, which have the potential to cause the disruptive appearance of the so-called microbunching instability. We develop a linear theory valid for low-to-moderate compression factors under the assumption of a 1D impedance model of longitudinal space charge and provide validation against macroparticle simulations.

Modeling microbunching from shot noise using Vlasov solvers

Unlike macroparticle simulations, which are sensitive to unphysical statistical fluctuations when the number of macroparticles is smaller than the bunch population, direct methods for solving the Vlasov equation are free from sampling noise and are ideally suited for studying microbunching instabilities evolving from shot noise. We review a 2D (longitudinal dynamics) Vlasov solver we have recently developed to study the microbunching instability in the beam delivery systems for X-ray FELs and present an application to FERMI@Elettra. We discuss, in particular, the impact of the spreader design on microbunching.

Vlasov solver for longitudinal dynamics in beam delivery systems for x-ray free electron lasers

Direct numerical methods for solving the Vlasov equation offer some advantages over macroparticle simulations, as they do not suffer from the consequences of the statistical fluctuations inherent in using a number of macroparticles smaller than the bunch population. Unfortunately, these methods are more time consuming and generally considered impractical in a full 6D phase space. However, in a lower-dimension phase space they may become attractive if the beam dynamics is sensitive to the presence of small charge-density fluctuations and a high resolution is needed. In this paper we present a 2D Vlasov solver for studying the longitudinal beam dynamics in single-pass systems of interest for x-ray FELs, where characterization of the microbunching instability stemming from self-field amplified noise is of particular relevance.

Macroparticle simulation studies of a proton beam halo experiment

We report macroparticle simulations for comparison with measured results from a proton beam halo experiment in a 52-quadrupole periodic-focusing channel. An important issue is that the input phase-space distribution is not experimentally known. Three different initial distributions with different shapes predict different beam profiles in the transport system. Simulations have been fairly successful in reproducing the core of the measured matched-beam profiles and the trend of emittance growth as a function of the mismatch factor, but underestimate the growth rate of halo and emittance for mismatched beams. In this study, we find that knowledge of the Courant-Snyder parameters and emittances of the input beam is not sufficient for reliable prediction of the halo. Input distributions with greater population in the tails produce larger rates of emittance growth, a result that is qualitatively consistent with the particle-core model of halo formation in mismatched beams.

Systematic comparison of position and time dependent macroparticle simulations in beam dynamics studies

Macroparticle simulation plays an important role in modern accelerator design and operation. Most linear rf accelerators have been designed based on macroparticle simulations using longitudinal position as the independent variable. In this paper, we have done a systematic comparison between using longitudinal position as the independent variable and using time as the independent variable in macroparticle simulations. We have found that, for an rms-matched beam, the maximum relative moment difference for second, fourth moments and beam maximum amplitudes between these two types of simulations is $0.25%$ in a 10 m reference transport system with physical parameters similar to the Spallation Neutron Source linac design. The maximum $z$-to- $t$ transform error in the space-charge force calculation of the position dependent simulation is about $0.1%$ in such a system. This might cause a several percent error in a complete simulation of a linac with a length of hundreds of meters. Furthermore, the error may be several times larger in simulations of mismatched beams. However, if such errors are acceptable to the linac designer, then one is justified in using position dependent macroparticle simulations in this type of linac design application.

The origins of electrical resistivity in magnetic reconnection: Studies by 2D and 3D macro particle simulations

This article argues the roles of electrical resistivity in magnetic reconnection, and also presents recent 3D particle simulations of coalescing magnetized flux bundles. Anomalous resistivity of the lower-hybrid-drift (LHD) instability, and collisionless effects of electron inertia and/or off-diagonal terms of electron pressure tensor are thought to break the frozen-in state that prohibits magnetic reconnection. Studies show that, while well-known stabilization of the LHD instability in high-beta plasma condition makes anomalous resistivity less likely, the electron inertia and/or the off-diagonal electron pressure tensor terms make adequate contributions to break the frozen-in state, depending on strength of the toroidal magnetic field. Large time and space scale particle simulations show that reconnection in magnetized plasmas proceeds by means of electron inertia effect, and that electron acceleration results instead of Joule heating of the MHD picture. Ion inertia contributes positively to reconnection, but ion finite Larmor radius effect does negatively because of charge separation of ions and magnetized electrons. The collisionless processes of the 2D and 3D simulations are similar in essence, and support the mediative role of electron inertia in magnetic reconnection of magnetized plasmas.

Ion acceleration and direct ion heating in three-component magnetic reconnection.

Ion acceleration and direct ion heating in magnetic reconnection were experimentally observed during counterhelicity merging of two plasma toroids. Plasma ions are accelerated up to the order of the Alfv\'en speed through contraction of reconnected field lines with three components. The significant ion heating (from 10 up to 200 eV) is attributed to direct conversion of magnetic energy into ion thermal energy, in agreement magnetohydrodynamic and macroparticle simulations.

Macro-particle simulations of collisionless magnetic reconnection

The basic process of collisionless reconnection is studied in terms of coalescence of two flux bundles using an implicit particle simulation of two-dimensions. As the toroidal electric field is generated by magnetic induction, an elongated current sheet whose width is a few electron skin depths is formed. Sub-Alfvénic plasma outflow off the reconnection region is generated in the poloidal plane which spreads within the dual fans originating at the X-point. Significant toroidal acceleration and streaming of the electrons without direct thermalization is observed in the current sheet. The electron parallel transport is proved to enhance the reconnection rate by comparing the implicit and hybrid-particle simulations; in the latter the electrons are spatially frozen to the ions. The reconnection rate is insensitive to finite Larmor radii of the ions in the regime where the magnetic flux merges constantly in time. The simulation results support that the collisionless reconnection is mediated by the electron inertia.

Guiding-center simulation of toroidal plasmas

A new computer simulation method for axisymmetric toroidal plasmas is developed. The method comprises two separate physical models representing different components of an experimental plasma. The first model is an MHD fluid equilibrium representation; the technique devised for the solution of this equilibrium is faster than any currently in common use. The second model is a macroparticle representation which uses guiding-center formalism for the particles' velocities and positions; consequently, the timestep used by this model may be many times longer than those possible for conventional macroparticle simulations. A new computer, code, GUIDON, which incorporates in these models a solution for self-consistent magnetic fields, is presented. Special features of the guiding-center model are discussed in detail. Results of simulations using GUIDON are also presented.