The beams in a heavy-ion-beam-driven inertial fusion (HIF) accelerator are collisionless, nonneutral plasmas, confined by applied magnetic and electric fields. These space-charge-dominated beams must be focused onto small (few mm) spots at the fusion target, and so preservation of a small emittance is crucial. The nonlinear beam self-fields can lead to emittance growth, and so a self-consistent field description is needed. To this end, a multidimensional particle simulation code, warp [Friedman et al., Part. Accel. 37-38, 131 (1992)], has been developed and is being used to study the transport of HIF beams. The code’s three-dimensional (3-D) package combines features of an accelerator code and a particle-in-cell plasma simulation. Novel techniques allow it to follow beams through many accelerator elements over long distances and around bends. This paper first outlines the algorithms employed in warp. A number of applications and corresponding results are then presented. These applications include studies of: beam drift-compression in a misaligned lattice of quadrupole focusing magnets; beam equilibria, and the approach to equilibrium; and the MBE-4 experiment [AIP Conference Proceedings 152 (AIP, New York, 1986), p. 145] recently concluded at Lawrence Berkeley Laboratory (LBL). Finally, 3-D simulations of bent-beam dynamics relevant to the planned Induction Linac Systems Experiments (ILSE) [Fessenden, Nucl. Instrum. Methods Plasma Res. A 278, 13 (1989)] at LBL are described. Axially cold beams are observed to exhibit little or no root-mean-square emittance growth at midpulse in transiting a (sharp) bend. Axially hot beams, in contrast, do exhibit some emittance growth.

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For many issues relevant to acceleration and propagation of heavy-ion beams for inertial confinement fusion, understanding the behavior of the beam requires the self-consistent inclusion of the self-fields of the beams in multiple dimensions. For these reasons, the three-dimensional simulation code WAR93d A.Friedman[l] was developed. The code combines the particle-in-cell plasma simulation technique with a realistic description of the elements which make up an accelerator. In this paper, the general structure of the code is reviewed and details of two ongoing applications are presented along with a discussion of simulation techniques used. The most important results of this work are presented.

Abstract. The Warp co de, d evelo pe d for heavy -ion d riven iner tial fusion energy s t u dies, is u se d to m o d el high inte n sity ion (an d electro n) bea m s. Significant ca pa bility h a s bee n incor por a te d in War p, allowing n early all sectio n s of a n accelerator to be m o dele d, beginning with t he sou rce. Warp ha s a s its core a n explicit, t h ree -di me n sio nal, p a r ticle -in -cell m o del. Alongside t his is a rich se t of tools for d escribing t h e a p plied field s of t h e accelerator lattice, a n d e m be d de d con d uc ting s urfaces (which are ca p t u re d at s u b -grid resolu tio n). Also incor pora te d are m o dels with re d uce d di me nsionality: a n axisy m me t ric m o d el a n d a tra n sverse "slice" m o del. The code take s a dva ntage of m o de r n p rogra m ming tech niq ues, inclu ding o bject orie nta tion, p a r allelis m, a n d scripting (via Pytho n). It is a t t he forefro n t in t h e u se of t he co m p u ta tional tec hnique of a da p tive m e s h refine me n t, which ha s bee n p a r ticularly s uccessf ul in t h e area of diode a n d injector m o deling, bot h stea dy -st ate a n d timed e p e n de n t. In t he p r e se n ta tio n, so me of t he m ajor a s pects of War p will be overviewe d, especially t h o se t h a t co uld be u sef ul in m o d eling ECR so urces. Warp ha s bee n be nc h m a r ke d against bot h t heo ry a n d ex peri me n t. Recen t re sults will be p re se n te d s howing good agree me nt of War p with experi me n tal res ults fro m t he STS500 injector test s ta n d. Additional infor ma tion ca n be fou n d on t he web p age h t t p: / / hif.lbl.gov / t h eo ry /WARP_su m m a ry.ht ml.

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A multibeamlet approach to a high current ion injector, whereby a large number of beamlets are accelerated and then merged to form a single beam, offers a number of potential advantages over a monolithic single beam injector. These advantages include a smaller transverse footprint, more control over the shaping and aiming of the beam, and more flexibility in the choice of ion sources. A potential drawback, however, is a larger emittance. In this paper, we seek to understand the merging of the beamlets and how it determines the emittance. When the constraints imposed by beam propagation physics and practical engineering issues are included, the design is reduced to a few free parameters. We describe the physics design of a multibeamlet injector and produce a design for an example set of parameters. Extensive use of 2D and 3D particle simulations was made in understanding the injector. Design tolerances and sensitivities are discussed in general and in relation to the example.

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.