Fusion is a combining of atoms to form other atoms, which occurs when their nuclei get close enough to each other. The energy that powers the sun actually comes from nuclear fusion. The realization of fusion in laboratory conditions requires 1000 trillion watts of a charged particle beam over a period of approx. 10 billionth of a second (10 nanoseconds) to ignite a target of thermonuclear fuel. Due to natural repulsion of particles via Coulomb forces, beam space charge effects remain the key problem for designers of high intensity accelerators for heavy ion fusion. The subject of the RIKEN Symposium was to review the present understanding of space charge phenomena and to discuss possible solutions for unresolved problems.
This report describes modeling of intense electron and ion beams in the space charge dominated regime. Space charge collective modes play an important role in the transport of intense beams over long distances. These modes were first observed in particle-in-cell simulations. The work presented here is closely tied to the University of Maryland Electron Ring (UMER) experiment and has application to accelerators for heavy ion beam fusion.
The development of a high current, heavy-ion beam for inertial confinement fusion requires a detailed understanding of the behavior of the beam, including effects of the large self-fields. This necessity makes particle-in-cell (PIC) simulation the appropriate tool, and for this reason, the three-dimensional PIC/accelerator code WARP3d is being developed. WARP3d has been used extensively to study the creation and propagation of ion beams both to support experiments and for the understanding of basic beam physics. An overview of the structure of the code is presented along with a discussion of features that make the code an effective tool in the understanding of space-charge dominated beam behavior. A number of applications where WARP3d has played an important role is discussed, emphasizing the need of three-dimensional, first principles simulations. Results and comparisons with experiment are presented.
Heavy ion fusion requires injection, transport and acceleration of high current beams. Detailed simulation of such beams requires fully self-consistent space charge fields and three dimensions. WARP3D, developed for this purpose, is a particle-in-cell plasma simulation code optimized to work within the framework of an accelerator's lattice of accelerating, focusing, and bending elements. The code has been used to study several test problems and for simulations and design of experiments. Two applications are drift compression experiments on the MBE-4 facility at LBL and design of the electrostatic quadrupole injector for the proposed ILSE facility. With aggressive drift compression on MBE-4, anomalous emittance growth was observed. Simulations carried out to examine possible causes showed that essentially all the emittance growth is result of external forces on the beam and not of internal beam space-charge fields. Dominant external forces are the dodecapole component of focusing fields, the image forces on the surrounding pipe and conductors, and the octopole fields that result from the structure of the quadrupole focusing elements. Goal of the design of the electrostatic quadrupole injector is to produce a beam of as low emittance as possible. The simulations show that the dominant effects that increase the emittance are the nonlinear octopole fields and the energy effect (fields in the axial direction that are off-axis). Injectors were designed that minimized the beam envelope in order to reduce the effect of the nonlinear fields. Alterations to the quadrupole structure that reduce the nonlinear fields further were examined. Comparisons were done with a scaled experiment resulted in very good agreement.
This indispensable work offers a broad synoptic description of beams, applicable to a wide range of other devices, such as low-energy focusing and transport systems and high-power microwave sources. The monograph develops the material from the basic principles in a systematic way and discusses the underlying physics and validity of theoretical relationships, design formulas and scaling laws. Assumptions and approximations are clearly indicated throughout. This new, revised and updated edition has 10% additional content, and features, among others, a new chapter on beam physics research from 1993 to 2007, significant enhancement of chapter 6 on emittance variation, updated references and color image plates.
Over the past two years noteworthy experimental and theoretical progress has been made towards the top-level scientific question for the U.S. program in Heavy Ion Fusion Science and High Energy Density Physics: ''How can heavy ion beams be compressed to the high intensity required to create high energy density matter and fusion conditions''? [1]. New results in transverse and longitudinal beam compression, beam-target interaction, high-brightness transport, beam production, as well as a new scheme in beam acceleration will be reported. Longitudinal and Transverse Beam Compression: The Neutralized Transport Experiment (NTX) demonstrated transverse beam density enhancement by a factor greater than 100 when an otherwise space-charge dominated ion beam was neutralized by a plasma source [2]. This experiment was followed by the Neutralized Drift Compression Experiment (NDCX) in which an ion beam was longitudinally compressed by a factor of 50 [3]. This was accomplished by applying a linear head-to-tail velocity ''tilt'' to the beam, and then allowing the beam to drift through a meter-long neutralizing plasma. In both the transverse and longitudinal experiments, extensive 3-D simulations, using LSP, were carried out, and the agreement with experiments was excellent [4]. A three-dimensional kinetic model for longitudinal compression was developed, and it was shown that the Vlasov equation possesses a class of exact solutions for the problem [5]. Beam-Target Interaction: We have also made significant progress in identifying the unique role ion beams can play in heating material to warm dense matter (WDM) conditions. We have identified promising accelerator, beam, and target configurations, as well as new experiments on material properties. It is shown that the target temperature uniformity can be maximized if the ion energy at target corresponds to the maximum in the energy loss rate dE/dX [6]. Ions of moderate energy (a few to tens of MeV) may be used. The energy must be deposited in times much shorter than the hydrodynamic expansion time (ns for metallic foams at 0.01 to 0.1 times solid density). Hydrodynamic simulations [7] have confirmed that uniform conditions with temperature variations of less than a few per cent can be achieved. High-Brightness Transport: Unwanted electrons can lead to deleterious effects for high-brightness ion beam transport. We are studying electron accumulation in quadrupole and solenoid beam transport systems. Electrons can originate from background gas ionization, from beam-tubes struck by ions near grazing incidence, and from end-walls struck by ions near normal incidence [8]. In parallel with the experimental campaign, we have developed and implemented in WARP 3D a new approach to large time-step advancement of electron orbits, as well as a comprehensive suite of models for electrons, gas, and wall interactions [9]. If sufficient electrons are accumulated within the beam, severe distortion of the beam phase space can result. Simulations of this effect have reproduced the key features observed in the experiments. Beam Production: The merging-beamlet injector experiment recently completed demonstrates the feasibility of a compact, high-current injector for heavy ion fusion drivers. In our experiment, 119 argon ion beamlets at 400 keV beam energy were merged into an electrostatic quadrupole channel to form a single beam of 70 mA. The measured unnormalized transverse emittance (phase space area) of 200-250 mm-mrad for the merged beam met fusion driver requirement. These measurements are in good agreement with our particle-in-cell simulations using WARP3D [10]. We have also completed the physics design of a short-pulse injector suitable for WDM studies. Beam Acceleration: A new concept for acceleration, the Pulse Line Ion Accelerator PLIA [11], offers the potential of a very low cost accelerator for WDM studies. It is based on a traveling wave structure, using a simple geometry with a helical conductor. We have obtained experimental verification of the predicted PLIA beam dynamics. Measured energy gain, longitudinal phase space, and beam bunching are in good agreement with WARP3D simulations. Computational Models and Simulator Experiments: The pioneering merger of Adaptive Mesh Refinement and particle-in-cell methods [12] underlies much of the recent success of WARP3D. BEST, the Beam Equilibrium Stability and Transport code was optimized for massively parallel computers and applied to studies of the collective effects of 3D bunched beams [13] and the temperature-anisotropy instability [14]. Space-charge-dominated beam physics experiments relevant to long-path accelerators were carried out on the recently completed University of Maryland Electron Ring, and on the Paul Trap Simulator Experiment at PPPL.
Inertial confinement fusion driven by beams of heavy ions is an attractive route to controlled fusion. In the U.S., induction accelerators are being developed as {open_quotes}drivers{close_quotes} for this process. This paper is divided into two main sections. In the first section, the concept of induction-accelerator driven heavy-ion fusion is briefly reviewed, and the U.S. program of experiments and theoretical investigations is described. In the second, a {open_quotes}taxonomy{close_quotes} of space-charge-dominated beam physics issues is presented, accompanied by a brief discussion of each area.
A non-perturbing electron beam diagnostic system for measuring the charge distribution of an ion beam is developed for Heavy Ion Fusion (HIF) beam physics studies. Conventional diagnostics require temporary insertion of sensors into the beam, but such diagnostics stop the beam, or significantly alter its properties. In this diagnostic a low energy, low current electron beam is swept transversely across the ion beam; the measured electron beam deflection is used to infer the charge density profile of the ion beam. The initial application of this diagnostic is to the Neutralized Transport Experiment (NTX), which is exploring the physics of space-charge-dominated beam focusing onto a small spot using a neutralizing plasma. Design and development of this diagnostic and performance with the NTX ion beamline is presented.
The current U.S. approach for a driver for inertial confinement fusion power production is a heavy-ion induction accelerator; high-current beams of heavy ions are focused onto the fusion target. The space-charge of the high-current beams affects the behavior more strongly than does the temperature (the beams are described as being ''space-charge dominated'') and the beams behave like non-neutral plasmas. The particle simulation code WARP has been developed and used to study the transport and acceleration of space-charge dominated ion beams in a wide range of applications, from basic beam physics studies, to ongoing experiments, to fusion driver concepts. WARP combines aspects of a particle simulation code and an accelerator code; it uses multi-dimensional, electrostatic particle-in-cell (PIC) techniques and has a rich mechanism for specifying the lattice of externally applied fields. There are both two- and three-dimensional versions, the former including axisymmetric (r-z) and transverse slice (x-y) models. WARP includes a number of novel techniques and capabilities that both enhance its performance and make it applicable to a wide range of problems. Some of these have been described elsewhere. Several recent developments will be discussed in this paper. A transverse slice model has been implemented with the novel capability of including bends, allowing more rapid simulation while retaining essential physics. An interface using Python as the interpreter layer instead of Basis has been developed. A parallel version of WARP has been developed using Python.
