Seth A. Veitzer

Simulating Electron Clouds in Heavy-Ion Accelerators

Contaminating clouds of electrons are a concern for most accelerators of positively charged particles, but there are some unique aspects of heavy-ion accelerators for fusion and high-energy density physics which make modeling such clouds especially challenging. In particular, self-consistent electron and ion simulation is required, including a particle advance scheme which can follow electrons in regions where electrons are strongly magnetized, weakly magnetized, and unmagnetized. The approach to such self-consistency is described, and in particular a scheme for interpolating between full-orbit (Boris) and drift-kinetic particle pushes that enables electron time steps long compared to the typical gyroperiod in the magnets. Tests and applications are presented: simulation of electron clouds produced by three different kinds of sources indicates the sensitivity of the cloud shape to the nature of the source; first-of-a-kind self-consistent simulation of electron-cloud experiments on the high-current experim...

Modeling ion-induced electrons in the High Current Experiment

A primary concern for high current ion accelerators is contaminant electrons. These electrons can interfere with the beam ions, causing emittance growth and beam loss. Numerical simulation is a main tool for understanding the interaction of the ion beam with the contaminant electrons, but these simulations then require accurate models of electron generation. These models include ion-induced electron emission from ions hitting the beam pipe walls or diagnostics. However, major codes for modeling ion beam transport are written in different programming languages and used on different computing platforms. For electron generation models to be maximally useful, researchers should be able to use them easily from many languages and platforms. A model of ion-induced electrons including the electron energy distribution is presented here, including a discussion of how to use the Babel software tool to make these models available in multiple languages and how to use the GNU Autotools to make them available on multipl...

Simulating electron cloud effects in heavy-ion beams

Stray electrons can be introduced in heavy ion fusion accelerators as a result of ionization of ambient gas or gas released from walls due to halo-ion impact, or as a result of secondary-electron emission. We summarize here results from several studies of electron-cloud accumulation and effects: (1) Calculation of the electron cloud produced by electron desorption from computed beam ion loss; the importance of ion scattering is shown; (2) Simulation of the effect of specified electron cloud distributions on ion beam dynamics. We find electron cloud variations that are resonant with the breathing mode of the beam have the biggest impact on the beam (larger than other resonant and random variations), and that the ion beam is surprisingly robust, with an electron density several percent of the beam density required to produce significant beam degradation in a 200-quadrupole system. We identify a possible instability associated with desorption and resonance with the breathing mode. (3) Preliminary investigations of a long-timestep algorithm for electron dynamics in arbitrary magnetic fields.

A comparison and benchmark of two electron cloud packages

We present results from precision simulations of the electron cloud (EC) problem in the Fermilab Main Injector using two distinct codes. These two codes are (i)POSINST, a F90 2D+ code, and (ii)VORPAL, a 2D/3D electrostatic and electromagnetic code used for self-consistent simulations of plasma and particle beam problems. A specific benchmark has been designed to demonstrate the strengths of both codes that are relevant to the EC problem in the Main Injector. As differences between results obtained from these two codes were bigger than the anticipated model uncertainties, a set of changes to the POSINST code were implemented. These changes are documented in this note. This new version of POSINST now gives EC densities that agree with those predicted by VORPAL, within {approx}20%, in the beam region. The root cause of remaining differences are most likely due to differences in the electrostatic Poisson solvers. From a software engineering perspective, these two codes are very different. We comment on the pros and cons of both approaches. The design(s) for a new EC package are briefly discussed.

Simulations of Dynamical Friction Including Spatially‐Varying Magnetic Fields

A proposed luminosity upgrade to the Relativistic Heavy Ion Collider (RHIC) includes a novel electron cooling section, which would use ∼55 MeV electrons to cool fully‐ionized 100 GeV/nucleon gold ions. We consider the dynamical friction force exerted on individual ions due to a relevant electron distribution. The electrons may be focussed by a strong solenoid field, with sensitive dependence on errors, or by a wiggler field. In the rest frame of the relativistic co‐propagating electron and ion beams, where the friction force can be simulated for nonrelativistic motion and electrostatic fields, the Lorentz transform of these spatially‐varying magnetic fields includes strong, rapidly‐varying electric fields. Previous friction force simulations for unmagnetized electrons or error‐free solenoids used a 4th‐order Hermite algorithm, which is not well‐suited for the inclusion of strong, rapidly‐varying external fields. We present here a new algorithm for friction force simulations, using an exact two‐body collis...

Application of new simulation algorithms for modeling rf diagnostics of electron clouds

Traveling wave rf diagnostics of electron cloud build-up show promise as a non-destructive technique for measuring plasma density and the efficacy of mitigation techniques. However, it is very difficult to derive an absolute measure of plasma density from experimental measurements for a variety of technical reasons. Detailed numerical simulations are vital in order to understand experimental data, and have successfully modeled build-up. Such simulations are limited in their ability to reproduce experimental data due to the large separation of scales inherent to the problem. Namely, one must resolve both rf frequencies in the GHz range, as well as the plasma modulation frequency of tens of MHz, while running for very long simulations times, on the order of microseconds. The application of new numerical simulation techniques allow us to bridge the simulation scales in this problem and produce spectra that can be directly compared to experiments. The first method is to use a plasma dielectric model to measur...

Development and application of particle emission algorithms from cut-cell boundaries in the VORPAL EM-FDTD-PIC simulation tool

Recent advances to the electromagnetic solvers in the VORPAL FDTD-PIC simulation software have allowed us to maintain a finite-difference solution technique, while modeling conducting and dielectric boundary surfaces that cut through the grid at arbitrary angle, thus providing precise modeling of the electromagnetic volume. However, a remaining challenge is how to emit particles from these surfaces in a way that provides similar improved accuracy. We discuss our progress in cut-cell emission algorithms, and applications to practical problems.

Alternative modeling methods for plasma-based Rf ion sources

Rf-driven ion sources for accelerators and many industrial applications benefit from detailed numerical modeling and simulation of plasma characteristics. For instance, modeling of the Spallation Neutron Source (SNS) internal antenna H(-) source has indicated that a large plasma velocity is induced near bends in the antenna where structural failures are often observed. This could lead to improved designs and ion source performance based on simulation and modeling. However, there are significant separations of time and spatial scales inherent to Rf-driven plasma ion sources, which makes it difficult to model ion sources with explicit, kinetic Particle-In-Cell (PIC) simulation codes. In particular, if both electron and ion motions are to be explicitly modeled, then the simulation time step must be very small, and total simulation times must be large enough to capture the evolution of the plasma ions, as well as extending over many Rf periods. Additional physics processes such as plasma chemistry and surface effects such as secondary electron emission increase the computational requirements in such a way that even fully parallel explicit PIC models cannot be used. One alternative method is to develop fluid-based codes coupled with electromagnetics in order to model ion sources. Time-domain fluid models can simulate plasma evolution, plasma chemistry, and surface physics models with reasonable computational resources by not explicitly resolving electron motions, which thereby leads to an increase in the time step. This is achieved by solving fluid motions coupled with electromagnetics using reduced-physics models, such as single-temperature magnetohydrodynamics (MHD), extended, gas dynamic, and Hall MHD, and two-fluid MHD models. We show recent results on modeling the internal antenna H(-) ion source for the SNS at Oak Ridge National Laboratory using the fluid plasma modeling code USim. We compare demonstrate plasma temperature equilibration in two-temperature MHD models for the SNS source and present simulation results demonstrating plasma evolution over many Rf periods for different plasma temperatures. We perform the calculations in parallel, on unstructured meshes, using finite-volume solvers in order to obtain results in reasonable time.

Simulation of the Electron Flux Into the Main Injector Electron Cloud Retarding Field Analyzer Using Vorpal

We present results from precision simulations of the electron cloud (EC) in the Fermilab Main Injector (MI), focusing on the dynamics of the EC close to the Retarding Field Analyzer (RFA) detectors. Our simulations are based on the Vorpal plasma simulation package. We find that the presence of a parasitic, weak (few Gauss) magnetic field significantly alters the spatial distribution of electrons in the cloud. The detected flux can easily change by factors of two depending on the location of the RFA. Moreover, the growth rate of the EC is also sensitive to such magnetic fields. Therefore, we suggest to (i) upgrade the RFA preamplifier to  10 MHz bandwidth such that the change in EC growth rate during a complete MI bunch train can be detected; (ii) install a small solenoid (of  25 Gauss maximum) to optionally switch off the EC, and thereby cleanly establish the presence of low energy electrons in the pipe; and (iii) design an RFA that can be inserted in a  2 kGauss field, such that an EC signal can be seen in the environment that matters, i.e., in the MI dipoles.

Ion Solid Interaction And Surface Modification At RF Breakdown In High‐Gradient Linacs

Ion solid interactions have been shown to be an important new mechanism of unipolar arc formation in high‐gradient rf linear accelerators through surface self‐sputtering by plasma ions, in addition to an intense surface field evaporation. We believe a non‐Debye plasma is formed in close vicinity to the surface and strongly affects surface atomic migration via intense bombardment by ions, strong electric field, and high surface temperature. Scanning electron microscope studies of copper surface of an rf cavity were conducted that show craters, arc pits, and both irregular and regular ripple structures with a characteristic length of 2 microns on the surface. Strong field enhancements are characteristic of the edges, corners, and crack systems at surfaces subjected to rf breakdown.