Steven M. Lund

Beam dynamics of the Neutralized Drift Compression Experiment-II, a novel pulse-compressing ion accelerator

Intense beams of heavy ions are well suited for heating matter to regimes of emerging interest. A new facility, NDCX-II, will enable studies of warm dense matter at ∼1 eV and near-solid density, and of heavy-ion inertial fusion target physics relevant to electric power production. For these applications the beam must deposit its energy rapidly, before the target can expand significantly. To form such pulses, ion beams are temporally compressed in neutralizing plasma; current amplification factors of ∼50–100 are routinely obtained on the Neutralized Drift Compression Experiment (NDCX) at the Lawrence Berkeley National Laboratory. In the NDCX-II physics design, an initial non-neutralized compression renders the pulse short enough that existing high-voltage pulsed power can be employed. This compression is first halted and then reversed by the beam’s longitudinal space-charge field. Downstream induction cells provide acceleration and impose the head-to-tail velocity gradient that leads to the final neutraliz...

Warm-fluid description of intense beam equilibrium and electrostatic stability properties

A nonrelativistic warm-fluid model is employed in the electrostatic approximation to investigate the equilibrium and stability properties of an unbunched, continuously focused intense ion beam. A closed macroscopic model is obtained by truncating the hierarchy of moment equations by the assumption of negligible heat flow. Equations describing self-consistent fluid equilibria are derived and elucidated with examples corresponding to thermal equilibrium, the Kapchinskij–Vladimirskij (KV) equilibrium, and the waterbag equilibrium. Linearized fluid equations are derived that describe the evolution of small-amplitude perturbations about an arbitrary equilibrium. Electrostatic stability properties are analyzed in detail for a cold beam with step-function density profile, and then for axisymmetric flute perturbations with ∂/∂θ=0 and ∂/∂z=0 about a warm-fluid KV beam equilibrium. The radial eigenfunction describing axisymmetric flute perturbations about the KV equilibrium is found to be identical to the eigenfunc...

Kinetic and collisional effects on the linear evolution of fast ignition relevant beam instabilities

The fast ignition scheme will involve the generation and transport of a relativistic electron beam, which may be subject to a number of instabilities that act to inhibit energy transport. This study will address the effects of collisions and the initial electron beam distribution on the linear evolution of these instabilities for theoretical distributions including the relativistic waterbag, the relativistic Maxwellian (Juttner), and the saddle point (low temperature) approximation of the relativistic Maxwellian. It will then be shown that a more physical distribution obtained from a 2D explicit particle-in-cell simulation of the laser-plasma interaction can be best modeled with a Juttner distribution, but well-approximated with a relativistic waterbag distribution. In sum, for all distributions of interest, collisions were found to have the ability to both suppress and enhance growth for the filamentary instability, while they only suppress growth for the two-stream instability.

INDUCTION ACCELERATOR ARCHITECTURES FOR HEAVY-ION FUSION

Abstract The approach to heavy-ion-driven inertial fusion studied most extensively in the US uses induction modulators and cores to accelerate and confine the beam longitudinally. The intrinsic peak-current capabilities of induction machines, together with their flexible pulse formats, provide a suitable match to the high peak-power requirement of a heavy-ion fusion target. However, as in the RF case, where combinations of linacs, synchrotrons, and storage rings offer a number of choices to be examined in designing an optimal system, the induction approach also allows a number of architectures, from which choices must be made. We review the main classes of architecture for induction drivers that have been studied to date. The main choice of accelerator structure is that between the linac and the recirculator, the latter being composed of several rings. Hybrid designs are also possible. Other design questions include which focusing system (electric quadrupole, magnetic quadrupole, or solenoid) to use, whether or not to merge beams, and what number of beams to use – all of which must be answered as a function of ion energy throughout the machine. Also, the optimal charge state and mass must be chosen. These different architectures and beam parameters lead to different emittances and imply different constraints on the final focus. The advantages and uncertainties of these various architectures will be discussed.

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...

Computational methods in the Warp code framework for kinetic simulations of particle beams and plasmas

The Warp code (and its framework of associated tools) was initially developed for particle-in-cell simulations of space-charge-dominated ion beams in accelerators, for heavy-ion-driven inertial fusion energy, and related experiments. It has found a broad range of applications, including nonneutral plasmas in traps, stray electron clouds in accelerators, laser-based acceleration, and the focusing of ion beams produced when short-pulse lasers irradiate foil targets. We summarize novel methods used in Warp, including: time-stepping conducive to diagnosis and particle injection; an interactive Python-Fortran-C structure that enables scripted and interactive user steering of runs; a variety of geometries (3-D x, y, z; 2-D r, z; 2-D x, y); electrostatic and electromagnetic field solvers; a cut-cell representation for internal boundaries; the use of warped coordinates for bent beam lines; adaptive mesh refinement, including a capability for time-dependent space-charge-limited flow from curved surfaces; models for accelerator lattice elements (magnetic or electrostatic quadrupole lenses, accelerating gaps, etc.) at user-selectable levels of detail; models for particle interactions with gas and walls; moment/envelope models that support sophisticated particle loading; a drift-Lorentz mover for rapid tracking through regions of strong and weak magnetic field; a Lorentz-boosted frame formulation with a Lorentz-invariant modification of the Boris mover; an electromagnetic solver with tunable dispersion and stride-based digital filtering; and a pseudospectral electromagnetic solver. Warp has proven useful for a wide range of applications, described very briefly herein. It is available as an open-source code under a BSD license. This paper describes material presented during the Prof. Charles K. (Ned) Birdsall Memorial Session of the 2013 IEEE Pulsed Power and Plasma Science Conference. In addition to our overview of the computational methods used in Warp, we summarize a few aspects of Neds contributions to plasma simulation and to the careers of those he mentored.

Numerical simulation of intense-beam experiments at LLNL and LBNL

We present intense-beam simulations with the WARP code that are being carried out in support of the Heavy-Ion Fusion experimental programs at Lawrence Livermore National Laboratory (LLNL) and Lawrence Berkeley National Laboratory (LBNL). The WARP code is an electrostatic particle-in-cell code with an extensive hierarchy of simulation capabilities. Two experiments are analyzed. First, simulations are presented on an 80 keV, 2 mA K‘ bent transport channel at LLNL that employs an alternating-gradient lattice of magnetic quadrupoles for beam focusing and electric dipoles for beam bending. Issues on dispersion-induced changes in beam quality on the transition from straight- to bent-lattice sections are explored. The second experiment analyzed is a 2 MeV, 800 mA, driver-scale injector and matching section at LBNL that is based on a K‘ source and an alternating-gradient lattice of electrostatic quadrupoles biased to accelerate, focus, and match the beam. Issues on beam quality, space-charge waves, and beam hollowing are explored. Published by Elsevier Science B.V.

Overview of US heavy ion fusion research

Significant experimental and theoretical progress has been made in the U.S. heavy ion fusion program on high-current sources, injectors, transport, final focusing, chambers and targets for high energy density physics (HEDP) and inertial fusion energy (IFE) driven by induction linac accelerators. One focus of present research is the beam physics associated with quadrupole focusing of intense, space-charge dominated heavy-ion beams, including gas and electron cloud effects at high currents, and the study of long-distance-propagation effects such as emittance growth due to field errors in scaled experiments. A second area of emphasis in present research is the introduction of background plasma to neutralize the space charge of intense heavy ion beams and assist in focusing the beams to a small spot size. In the near future, research will continue in the above areas, and a new area of emphasis will be to explore the physics of neutralized beam compression and focusing to high intensities required to heat targets to high energy density conditions as well as for inertial fusion energy.

Integrated experiments for heavy ion fusion

Author(s): Barnard, J.J.; Ahle, L.E.; Bieniosek, F.M.; Celata, C.M.; Davidson, R.C.; Henestroza, E.; Friedman, A.; Kwan, J.W.; Logan, B.G.; Lee, E.P.; Lund, S.M.; Meier, W.R.; Sabbi, G.-L.; Seidl, P.A.; Sharp, W.M.; Shuman, D.B.; Waldron, W.L.; Qin, H.; Yu, S.S.

Recent progress in the simulation of heavy ion beams

Production of electric power by using a beam of heavy ions to ignite an inertially-confined fusion target requires the focusing of high-power beams onto a small spot several meters distant from the final lens system. Beams with the necessary intensity generally behave like warm nonneutral bounded plasmas where beam kinetic temperatures are sufficiently high that a cold-plasma description can be inadequate for describing the collective space-charge modes. In view of the complexity of the self-consistent nonlinear dynamics, analytic study has largely been limited to the singular Kapchinskij–Vladimirskij (K–V) distribution. Numerical simulations, primarily using the WARP [D. P. Grote, A. Friedman, I. Haber, W. Fawley, and J. L. Vay, Nucl. Instrum. Methods Phys. Res. A 415, 428 (1998)] particle-in-cell (PIC)/accelerator code, have been employed to identify the degree to which the analytic results, especially the predictions of unstable modes, are applicable to realistic beam distributions. During extensive benchmarking of the code against experiments at Lawrence Berkeley National Laboratory, Lawrence Livermore National Laboratory, and the University of Maryland, a particular feature of the beam which has been seen in both experiment and simulation is the launching, in the source region, of collective warm-plasma oscillations similar to those predicted on the basis of the K–V analysis.