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A long-standing challenge in the design of a Heavy Ion Fusion power plant is that the ion beams entering the target chamber, which number of order a hundred, all need to be routed from one or two multi-beam accelerators through a set of transport lines. The beams are divided into groups, each of which has a unique arrival time and may have a unique kinetic energy. It is also necessary to arrange for each beam to enter the target chamber from a prescribed location on the periphery of that chamber. Furthermore, it has generally been assumed that additional constraints must be obeyed: that the path lengths of the beams in a group must be equal, and that any delay of “main-pulse” beams relative to “foot-pulse” beams must be provided by the insertion of large delay-arcs in the main beam transport lines. Here we introduce the notion of applying “differential acceleration” to individual beams or sets of beams at strategic stages of the transport lines. That is, by accelerating some beams “sooner” and others “later,” it is possible to simplify the beam line configuration in a number of cases. For example, the time delay between the foot and main pulses can be generated without resorting to large arcs in the main-pulse beam lines. It is also possible to use differential acceleration to effect the simultaneous arrival on target of a set of beams (e.g., for the foot-pulse) without requiring that their path lengths be precisely equal. We illustrate the technique for two model configurations, one corresponding to a typical indirect-drive scenario requiring distinct foot and main energies, and the other to an ion-driven fast-ignition scenario wherein the foot and main beams share a common energy.

The high-current experiment (HCX) at LBNL is a driver scale single beam injector that provides a 1 MeV K + ion beam current of 0.18 A for 5 μs. It transports high-current beams with large fill factor (ratio of the maximum beam envelope radius to the beam pipe radius) and low emittance growth that are required to keep the cost of the power plant competitive and to satisfy the target requirements of focusing ion beams to high-power density. Beam interaction with the background gas and walls desorbs electrons that can multiply and accumulate, creating an electron cloud. This ubiquitous effect grows at higher fill factors and degrades the quality of the beam. We review simulations and diagnostics tools used to measure electron production, accumulation and its properties.

We present simulations and analysis of the heating of warm dense matter foils by ion beams with ion energy less than one MeV per nucleon to target temperatures of order one eV. Simulations were carried out using the multi-physics radiation hydrodynamics code HYDRA and comparisons are made with analysis and the code DPC. We simulate possible targets for a proposed experiment at LBNL (the so-called Neutralized Drift Compression Experiment, NDCXII) for studies of warm dense matter. We compare the dynamics of ideally heated targets, under several assumed equation of states, exploring dynamics in the two-phase (fluid-vapor) regime.

For self-consistent ion-beam simulations including electron motion, it is desirable to be able to follow electron dynamics accurately without being constrained by the electron cyclotron timescale. To this end, we have developed a particle-advance that interpolates between full particle dynamics and drift motion. By making a proper choice of interpolation parameter, simulation particles experience physically correct parallel dynamics, drift motion, and gyroradius when the timestep is large compared to the cyclotron period, though the effective gyrofrequency is artificially low; in the opposite timestep limit, the method approaches a conventional Boris particle push. By combining this scheme with a Poisson solver that includes an interpolated form of the polarization drift in the dielectric response, the mover's utility can be extended to higher-density problems where the plasma frequency of the species being advanced exceeds its cyclotron frequency. We describe a series of tests of the mover and its application to simulation of electron clouds in heavy-ion accelerators.

Contamination from electrons is a concern for the solenoid-focused ion accelerators being developed for experiments in high-energy density physics (HEDP). These electrons are produced directly by beam ions hitting lattice elements and intercepting diagnostics, or indirectly by ionization of desorbed neutral gas, and they are believed responsible for time dependence of the beam radius, emittance, and focal distance seen on the solenoid transport experiment (STX) at Lawrence Berkeley National Laboratory. The electrostatic particle-in-cell code WARP has been upgraded to include the physics needed to simulate electron-cloud phenomena. We present preliminary self-consistent simulations of STX experiments suggesting that the observed time dependence of the beam stems from a complicated interaction of beam ions, desorbed neutrals, and electrons.

We have commenced experiments with intense short pulses of ion beams on the Neutralized Drift Compression Experiment-II at Lawrence Berkeley National Laboratory, by generating beam spots size with radius r < 1 mm within 2 ns FWHM and approximately 10^10 ions/pulse. To enable the short pulse durations and mm-scale focal spot radii, the 1.2 MeV Li+ ion beam is neutralized in a 1.6-meter drift compression section located after the last accelerator magnet. An 8-Tesla short focal length solenoid compresses the beam in the presence of the large volume plasma near the end of this section before the target. The scientific topics to be explored are warm dense matter, the dynamics of radiation damage in materials, and intense beam and beam-plasma physics including selected topics of relevance to the development of heavy-ion drivers for inertial fusion energy. Here we describe the accelerator commissioning and time-resolved ionoluminescence measurements of yttrium aluminium perovskite using the fully integrated accelerator and neutralized drift compression components., 7 pages, 9 figures

The methods and codes employed in the US Heavy Ion Fusion program to simulate the beams in an Integrated Research Experiments (IRE) facility and a fusion driver are presented in overview. A new family of models incorporating accelerating module impedance, multi-beam, and self-magnetic effects is described, and initial WARP3D particle simulations of beams using these models are presented. Finally, plans for streamlining the machine-design simulation sequence, and for simulating beam dynamics from the source to the target in a consistent and comprehensive manner, are described.

Particle-in-cell simulations exploring the effects of transverse envelope resonances on the emittance of space-charge-dominated beams have been carried out using a new 2-D transverse “slice” model in the WARP particle-in-cell code. In this paper, we consider resonances between an applied quadrupole field error and harmonics of the asymmetric mismatch mode of beam envelope oscillation. We examine both acceleration and bunching, and show that rapid passage through a major resonance significantly reduces the attendant emittance growth.

For more than ten years [J. Bisognano, I. Haber, L. Smith, IEEE Trans. Nucl. Sci. NS-30, 2501 (1983)], the longitudinal wall impedance instability was thought to be a serious threat to the success of heavy-ion driven inertial confinement fusion. This instability is a “resistive wall” instability, driven by the impedance of the induction modules used to accelerate the beam. Early estimates of the instability growth rate predicted tens of e-folds due to the instability which would modulate the current and increase the longitudinal momentum spread and prevent focusing the ion beam on the small spot needed at the target. We have simulated this instability using an r−z particle-in-cell code which includes a model for the module impedance. These simulations, using driver parameters, show that growth due to the instability is smaller than in previous calculations. We have seen that growth is mainly limited to one head to tail transit by a space-charge wave. In addition, the capacitive component of the module imp...

A one-dimensional Vlasov-Poisson model for sheet beams is reviewed and extended to provide a simple framework for analysis of space-charge effects. Centroid and rms envelope equations including image-charge effects are derived and reasonable parameter equivalences with commonly employed 2D transverse models of unbunched beams are established. This sheet-beam model is then applied to analyze several problems of fundamental interest. A sheet-beam thermal equilibrium distribution in a continuous focusing channel is constructed and shown to have analogous properties to two- and three-dimensional thermal equilibrium models in terms of the equilibrium structure and Debye screening properties. The simpler formulation for sheet beams is exploited to explicitly calculate the distribution of particle oscillation frequencies within a thermal equilibrium beam. It is shown that as space-charge intensity increases, the frequency distribution becomes broad, suggesting that beams with strong space-charge can have improved stability relative to beams with weak space-charge.

A multi-dimensional discrete-particle simulation code, WARP, and its application to heavy-ion fusion beams is described. The code's 3D package combines features of an accelerator code and a particle-in-cell plasma simulation, and can efficiently track beams through many lattice elements and around bends. The code'sr, z package allows one to follow beams over very long times and models the accelerating module impedances. A number of applications are presented. These have led to an improved understanding of: beam equilibria, and the approach to equilibrium; longitudinal beam dynamics and stability; electrostatic quadrupole (ESQ) injector aberrations; bending and recirculation of space-charge-dominated beams; and the drift-compression process. The code is being used for accelerator design, as well as for theoretical investigations.

The Heavy-Ion Fusion Accelerator Research Program at Lawrence Berkeley Laboratory has proposed building a 10 MeV induction linac systems experiment, ILSE, to investigate accelerator physics and beam manipulations which are needed or desirable for an induction linac driver. This paper describes the experiments proposed for ILSE: transverse beam combining, drift compression, bending of space-charge-dominated beams, final focus, recirculation, and some studies of beam propagation in the environment of the reactor chamber.

A two‐year study of recirculating induction heavy ion accelerators as low‐cost driver for inertial‐fusion energy applications was recently completed. The projected cost of a 4 MJ accelerator was estimated to be about $500 M (million) and the efficiency was estimated to be 35%. The principal technology issues include energy recovery of the ramped dipole magnets, which is achieved through use of ringing inductive/capacitive circuits, and high repetition rates of the induction cell pulsers, which is accomplished through arrays of field effect transistor (FET) switches. Principal physics issues identified include minimization of particle loss from interactions with the background gas, and more demanding emittance growth and centroid control requirements associated with the propagation of space‐charge‐dominated beams around bends and over large path lengths. In addition, instabilities such as the longitudinal resistive instability, beam‐breakup instability and betatron‐orbit instability were found to be controllable with careful design.

NDCX-II project commencing at LBNL Alex Friedman, LLNL, and Joe Kwan, LBNL Construction is beginning on the second generation Neutralized Drift Compression eXperiment (NDCX-II), a new high-current, modest-kinetic-energy accelerator at Lawrence Berkeley National Laboratory (LBNL). The machine’s ion beams will enable studies of the poorly understood “warm dense matter” regime of temperatures around 10,000 K and densities near solid (as in the cores of giant planets). NDCX-II will also enable exploration of important issues in inertial- fusion target physics. These studies support the ultimate goal of using ion beams to heat deuterium/tritium fuel to ignition in a future inertial fusion power reactor (a role for which accelerators appear well suited). NDCX-II has received $11 M of funding from the American Recovery and Reinvestment Act; construction began in July, 2009, with completion of the initial 15-cell configuration anticipated in March, 2012. NDCX-II will accelerate a beam of 30-50 nanoCoulombs of Li + ions to 1.5-4 MeV and compress it into a nanosecond long pulse. The short, high-current pulse is important for applications requiring efficient stopping of ions for rapid heating of a small amount of matter. As with the existing NDCX-I, the new machine uses neutralized drift compression. In this process, the beam’s tail is given a higher velocity than its head, so that it shortens while it drifts in a plasma that provides electrons to cancel space-charge forces. The figure shows the layout of the machine. It will make extensive use of induction cells (accelerating elements) and other parts from the decommissioned Advanced Test Accelerator (ATA) at Lawrence Livermore National Laboratory (LLNL). It will be extensible and reconfigurable; in the configuration that has received the most emphasis, each pulse will deliver Li + ions at 3 MeV into a mm-diameter spot onto a thin-foil target. Pulse compression to ~ 1 ns begins in the accelerator and finishes in the drift compression line. NDCX-II employs novel beam dynamics to achieve unprecedented rapid pulse compression in a short ion accelerator. The 200 kV charged transmission line pulsed- power voltage sources from ATA, called “Blumleins”, can provide voltage pulses that are not longer than 70 ns. These are shown as blue cylinders in the figure. For them to be usable, it is necessary to reduce the ion bunch duration from its initial 500 ns. This shortening is accomplished in an initial stage of non-neutral drift compression, downstream of the injector and the first few induction cells (note the spaces between induction cells at the left end of the figure). Long-pulse voltage generators are used at the front end; Blumleins power the rest of the acceleration. Extensive particle-in-cell computer simulation studies have enabled an attractive physics design that meets the stringent cost goal. Snapshots from a simulation video are shown in the figure. Studies on a dedicated test stand are examining the ATA hardware and supporting the development of new pulsed solenoids that will provide transverse beam confinement. Applications of this facility will include studies of warm dense matter using uniform, volumetric ion heating of thin foil targets, and studies of ion energy coupling into an expanding plasma (such as that which occurs in an inertial fusion target). NDCX-II will also enable a better understanding of space- charge-dominated ion beam dynamics, and of beam behavior in a plasma. The machine will complement facilities at GSI in Darmstadt, Germany, but will employ lower ion kinetic energies and commensurately shorter stopping ranges in matter. NDCX-II will contribute to the long-term goal of electric power production via “Heavy-Ion inertial Fusion.” In inertial fusion, a target containing fusion fuel is heated by energetic driver beams, and undergoes a miniature thermonuclear explosion. The largest inertial confinement facility is Livermore’s National Ignition Facility (NIF). NIF is expected to establish the fundamental feasibility of fusion ignition on the laboratory scale. Heavy ion accelerators offer efficient conversion of input power into beam energy, are long-lived, and can use magnetic fields for final focusing onto a target. These attributes make them attractive candidates for a power plant. The beams in such a system will require manipulations similar to those being pioneered on NDCX-II. NDCX-II is sponsored by the U.S. Department of Energy’s Office of Fusion Energy Sciences. It is being developed by a collaboration known as the Virtual National Laboratory for Heavy Ion Fusion Science (HIFS-VNL), including LBNL, LLNL, and the Princeton Plasma Physics Laboratory (PPPL). Computer-aided-design of NDCX-II, and simulation of its ion beam. The ion source and injector are at left; voltage sources (blue) reside on a mezzanine; the induction cells are in yellow-orange; and the drift- compression line and target chamber are at right. The lower images (from a 3-D simulation video using the Warp code) show the beam at the injector and farther on, undergoing inductive acceleration. Further reading A recent article in the Berkeley Lab News is available at http://newscenter.lbl.gov/feature-stories/2009/10/14/warm-dense- matter ; see also references therein. The video can be viewed at http://hifweb.lbl.gov/public/movies/ICAP09. Joe Kwan is the NDCX-II project manager and Alex Friedman is the leader for the physics design. *This work was supported by the Director, Office of Science, Office of Fusion Energy Sciences, of the U.S. Department of Energy prepared by LBNL under Contract No. DE-AC02-05CH11231, by LLNL under Contract No. DE-AC52- 07NA27344, and by Princeton Plasma Physics Laboratory under contract No. DE-AC02-76CH-O3073.

HIFAN 1757 HEAVY ION FUSION SCIENCE VIRTUAL NATIONAL LABORATORY, 3rd QUARTER 2009 MILESTONE REPORT, Upgrade plasma source configuration and carry out initial experiments. Characterize improvements in focal spot beam intensity by S. Lidia, A. Anders, F.M. Bieniosek, A. Faltens, W. Greenway, J.Y. Jung, T. Katayanagi, B.G. Logan, C.W. Lee, M. Leitner, P. Ni, A. Pekedis, M. J. Regis, P. K. Roy, P. A. Seidl, W. Waldron Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA J.J. Barnard, A. Friedman, D. Grote, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA M. Dorf, E. Gilson Princeton Plasma Physics Laboratory Accelerator Fusion Research Division Ernest Orlando Lawrence Berkeley National Laboratory University of California June 2009 This work was supported by the Director, Office of Science, Office of Fusion Energy Sciences, of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

Intense beams of heavy ions offer a very attractive tool for fundamental research in high energy density physics and inertial fusion energy science. These applications build on the significant recent advances in the generation, compression and focusing of intense heavy ion beams in the presence of a neutralizing background plasma. Such beams can provide uniform volumetric heating of the target during a time-scale shorter than the hydrodynamic response time, thereby enabling a significant suite of experiments that will elucidate the underlying physics of dense, strongly-coupled plasma states, which have been heretofore poorly understood and inadequately diagnosed, particularly in the warm dense matter regime. The innovations, fundamental knowledge, and experimental capabilities developed in this basic research program is also expected to provide new research opportunities to study the physics of directly-driven ion targets, which can dramatically reduce the size of heavy ion beam drivers for inertial fusion energy applications. Experiments examining the behavior of thin target foils heated to the warm dense matter regime began at the Lawrence Berkeley National Laboratory in 2008, using the Neutralized Drift Compression Experiment - I (NDCX-I) facility, and its associated target chamber and diagnostics. The upgrade of this facility, called NDCX-II, will enable an excitingmore » set of scientific experiments that require highly uniform heating of the target, using Li{sup +} ions which enter the target with kinetic energy in the range of 3 MeV, slightly above the Bragg peak for energy deposition, and exit with energies slightly below the Bragg peak. This document briefly summarizes the wide range of fundamental scientific experiments that can be carried out on the NDCX-II facility, pertaining to the two charges presented to the 2008 Fusion Energy Science Advisory Committee (FESAC) panel on High Energy Density Laboratory Plasmas (HEDLP). These charges include: (1) Identify the compelling scientific opportunities for research in fundamental HEDLP that could be investigated using existing and planned facilities in support of the Office of Fusion Energy Sciences and the National Nuclear Security Administration/Defense Program missions; and (2) Identify the scientific issues of implosion and target design that need to be addressed to make the case for inertial fusion energy as a potential future energy source. Compelling research opportunities of high intellectual value that can be carried out on the NDCX-II experimental facility are briefly summarized below, grouped into four main research areas. Page 4 lists several national and internationally-attended user workshops that have provided much of the input for the experimental campaigns describe below. More detailed information can be provided upon request.« less

This milestone has been accomplished. The Heavy Ion Fusion Science Virtual National Laboratory (HIFS-VNL) has developed and implemented an initial beam-in-plasma implicit modeling capability in Warp; has carried out tests validating the behavior of the models employed; has compared the results of electrostatic and electromagnetic models when applied to beam expansion in an NDCX-I relevant regime; has compared Warp and LSP results on a problem relevant to NDCX-I; has modeled wave excitation by a rigid beam propagating through plasma; and has implemented and begun testing a more advanced implicit method that correctly captures electron drift motion even when timesteps too large to resolve the electron gyro-period are employed. The HIFS-VNL is well on its way toward having a state-of-the-art source-to-target simulation capability that will enable more effective support of ongoing experiments in the NDCX series and allow more confident planning for future ones.

Intense ion beams are difficult to maintain as non-neutral plasmas. Experiments and simulations are used to study the complex interactions between beam ions and (unwanted) electrons. Such ''electron clouds'' limit the performance of many accelerators. To characterize electron clouds, a number of parameters are measured including: total and local electron production and loss for each of three major sources, beam potential versus time, electron line-charge density, and gas pressure within the beam. Electron control methods include surface treatments to reduce electron and gas emission, and techniques to remove electrons from the beam, or block their capture by the beam. Detailed, self-consistent simulations include beam-transport fields, and electron and gas generation and transport; these compute unexpectedly rich behavior, much of which is confirmed experimentally. For example, in a quadrupole magnetic field, ion and dense electron plasmas interact to produce multi-kV oscillations in the electron plasma and distortions of the beam velocity space distribution, without the system becoming homogeneous or locally neutral.

In a first beam dynamics validation experiment for a new Pulse Line Ion Acceleration (PLIA) concept, the predicted energy amplification and beam bunching were experimentally observed. Beam energy modulation of -80 keV to +150 keV was measured using a PLIA input voltage waveform of -21 kV to +12 kV. Ion pulses accelerated by 150 keV, and bunching by a factor of four were simultaneously achieved. The measured longitudinal phase space and current waveform of the accelerated beam are in good agreement with 3-D particle-in-cell simulations.

Electron clouds limit the performance of many major accelerators and storage rings. Significant quantities of electrons result when halo ions are lost to beam tubes, generating gas which can be ionized and ion-induced electrons that can multiply and accumulate, causing degradation or loss of the ion beam. In order to understand the physical mechanisms of ion-induced electron production, experiments studied the impact of 50 to 400 keV K{sup +} ions on stainless steel surfaces near grazing incidence, using the 500 kV Ion Source Test Stand (STS-500) at LLNL. The experimental electron yield scales with the electronic component (dE{sub e}/dx) of the stopping power and its angular dependence does not follow l/cos({theta}). A theoretical model is developed, using TRIM code to evaluate dE{sub e}/dx at several depths in the target, to estimate the electron yield, which is compared with the experimental results. The experiment extends the range of energy from previous works and the model reproduces the angular dependence and magnitude of the electron yield.

Clouds of stray electrons are ubiquitous in particle accelerators and frequently limit the performance of storage rings. Earlier measurements of electron energy distribution and flux to the walls provided only a relative electron cloud density. We have measured electron accumulation using ions expelled by the beam. The ion energy distribution maps the depressed beam potential and gives the dynamic cloud density. Clearing electrode current reveals the static background cloud density, allowing the first absolute measurement of the time-dependent electron cloud density during the beam pulse.

The Warp code, developed for heavy‐ion driven inertial fusion energy studies, is used to model high intensity ion (and electron) beams. Significant capability has been incorporated in Warp, allowing nearly all sections of an accelerator to be modeled, beginning with the source. Warp has as its core an explicit, three‐dimensional, particle‐in‐cell model. Alongside this is a rich set of tools for describing the applied fields of the accelerator lattice, and embedded conducting surfaces (which are captured at sub‐grid resolution). Also incorporated are models with reduced dimensionality: an axisymmetric model and a transverse “slice” model. The code takes advantage of modern programming techniques, including object orientation, parallelism, and scripting (via Python). It is at the forefront in the use of the computational technique of adaptive mesh refinement, which has been particularly successful in the area of diode and injector modeling, both steady‐state and time‐dependent. In the presentation, some of the major aspects of Warp will be overviewed, especially those that could be useful in modeling ECR sources. Warp has been benchmarked against both theory and experiment. Recent results will be presented showing good agreement of Warp with experimental results from the STS500 injector test stand. Additional information can be found on the web page http://hif.lbl.gov/theory/WARP_summary.html.

A set of experiments has been performed on the High-Current Experiment (HCX) facility at LBNL, in which the ion beam is allowed to collide with an end plate and thereby induce a copious supply of desorbed electrons. Through the use of combinations of biased and grounded electrodes positioned in between and downstream of the quadrupole magnets, the flow of electrons upstream into the magnets can be turned on or off. Properties of the resultant ion beam are measured under each condition. The experiment is modeled via a full three-dimensional, two species (electron and ion) particle simulation, as well as via reduced simulations (ions with appropriately chosen model electron cloud distributions, and a high-resolution simulation of the region adjacent to the end plate). The three-dimensional simulations are the first of their kind and the first to make use of a timestep-acceleration scheme that allows the electrons to be advanced with a timestep that is not small compared to the highest electron cyclotron period. The simulations reproduce qualitative aspects of the experiments, illustrate some unanticipated physical effects, and serve as an important demonstration of a developing simulation capability.

LBNL-54716 HIFAN 1303 Experimental study of electron effects in heavy-ion beams •A.W. MOLVIK a , •With F.M. BIENIOSEK b , D. Baca b , R.H. COHEN a , A. FRIEDMAN a , M.A. FURMAN b , b. LBNL E.P. LEE b , S.M. LUND a , L. PROST b , P.A. SEIDL b , J-L. VAY b . a. LLNL •Heavy-Ion Fusion Virtual National Laboratory HIF-VNL Presented to International workshop in physics of high energy density in matter, session on gas/electron cloud effects in high-ion-current accelerators Waldemar-Petersen-Haus, Hirschegg, Austria Feb. 2-7, 2003 AWM 1 The Heavy Ion Fusion Virtual National Laboratory

The transverse dynamics of a nearly-monoenergetic particle beam are described by the evolution of the 4D distribution f(x,y,x',y'), where x and y are the transverse spatial coordinates and x' {triple_bond} p{sub x}/p{sub z} and y' {triple_bond} p{sub y}/p{sub z} are the corresponding momentum components divided by the longitudinal momentum component. In present-day experimental practice, such beams are often diagnosed by passing them through an axially-separated pair of slits parallel to the y axis. This selects for x and x' and integrates over y and y'. A sequence of pulses (with the slits at various x positions) yields a 2D projection of the beam phase space, f(x,x'). Another scanner might yield f(y,y') or, using crossed slits, f(x,y). The challenge is that a small set of such 2D scans does not uniquely specify f(x,y,x',y'); correlations in planes other than those measured are unknown. We have developed Monte-Carlo methods and formulated physically-motivated constraints to synthesize a ''reasonable'' set of particles having 2D projectional densities consistent with the experimental data. Such a set may be used to initialize simulations of the downstream beam. The methods and their performance on model problems are described.

Under conditions which arise commonly in space-charge-dominated beam applications, the applied focusing, bending, and accelerating fields vary rapidly with axial position, while the self-fields (which are, on average, comparable in strength to the applied fields) vary smoothly. In such cases it is desirable to employ timesteps which advance the particles over distances greater than the characteristic scales over which the applied fields vary. Several related concepts are potentially applicable: sub-cycling of the particle advance relative to the field solution, a higher-order time-advance algorithm, force-averaging by integration along approximate orbits, and orbit-averaging. We report on our investigations into the utility of such techniques for systems typical of those encountered in accelerator studies for heavy-ion beam-driven inertial fusion.

By manipulating a set of ion beams upstream of a target, it is possible to arrange for a smoother deposition pattern, so as to achieve more uniform illumination of the target. A uniform energy deposition pattern is important for applications including ion-beam-driven high energy density physics and heavy-ion beam-driven inertial fusion energy (“heavy-ion fusion”). Here, we consider an approach to such smoothing that is based on rapidly “wobbling” each of the beams back and forth along a short arc-shaped path, via oscillating fields applied upstream of the final pulse compression. In this technique, uniformity is achieved in the time-averaged sense; this is sufficient provided the beam oscillation timescale is short relative to the hydrodynamic timescale of the target implosion. This work builds on two earlier concepts: elliptical beams applied to a distributed-radiator target [D. A. Callahan and M. Tabak, Phys. Plasmas 7, 2083 (2000)] and beams that are wobbled so as to trace a number of full rotations ar...

WARPrz is a 2.5 dimensional, cylindrically symmetric, electrostatic, particle‐in‐cell code. It is part of the WARP family of codes which has been developed to study heavy ion fusion driver issues. WARPrz is being used to study the longitudinal dynamics of heavy ion beams including a longitudinal instability that is driven by the impedance of the LINAC accelerating modules. This instability is of concern because it can enhance longitudinal momentum spread; chromatic abhoration in the lens system restricts the amount of momentum spread allowed in the beam in the final focusing system. The impedance of the modules is modeled by a continuum of resistors and capacitors in parallel in WARPrz. We discuss simulations of this instability including the effect of finite temperature and reflection of perturbations off the beam ends. We also discuss intermittency of axial confining fields (‘‘ears’’ fields) as a seed for this instability.

Analysis of the dynamics of a space charge dominated beam in a lattice of electrostatic focusing structures requires a full three‐dimensional code that includes self‐consistent space charge fields and the fields from the complex conductor shapes. The existing WARP3d code, a particle simulation code which has been developed for HIF applications, contains machinery for handling particles in three‐dimensional fields. A successive overrelaxation field solver with subgrid‐scale placement of boundaries for rounded surfaces and four‐fold symmetry has been added to the code. The electrostatic quadrupole (ESQ) injector for the ILSE accelerator facility being planned at Lawrence Berkeley Laboratory is shown as an application. The issue of concern is possible emittance degradation because the focusing voltages are a significant fraction of the particles’ energy and because there are significant nonlinear fields arising from the shapes of the quadrupole structures.

The three-dimensional particle-in-cell (3-D PIC) simulation code WARP is used to study positron confinement in antihydrogen traps. The magnetic geometry is close to that of a UC Berkeley experiment conducted, with electrons, as part of the ALPHA collaboration [W. Bertsche et al., AIP Conf. Proc. 796, 301 (2005)]. In order to trap antihydrogen atoms, multipole magnetic fields are added to a conventional Malmberg-Penning trap. These multipole fields must be strong enough to confine the antihydrogen, leading to multipole field strengths at the trap wall comparable to those of the axial magnetic field. Numerical simulations reported here confirm recent experimental measurements of reduced particle confinement when a quadrupole field is added to a Malmberg-Penning trap. It is shown that, for parameters relevant to various antihydrogen experiments, the use of an octupole field significantly reduces the positron losses seen with a quadrupole field. A unique method for obtaining a 3-D equilibrium of the positrons in the trap with a collisionless PIC code was developed especially for the study of the antihydrogen trap; however, it is of practical use for other traps as well.