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Dynamic stabilization of the ablative Rayleigh-Taylor instability of a heavy ion fusion target induced by a beam wobbling system is studied. Using a sharp-boundary model and Courant-Synder theory, it is shown, with an appropriately chosen modulation waveform, that the instability can be sta- bilized in certain parameter regimes. It is found that the stabilization e ect has a strong dependence on the modulation frequency and the waveform. Modulation with frequency comparable to the instability growth rate is the most e ective in terms of stabilizing the instability. A modulation with two frequency components can result in a reduction of the growth rate larger than the sum of that due to the two components when applied separately.

The collective focusing concept in which a weak magnetic lens provides strong focusing of an intense ion beam pulse carrying a neutralizing electron background is investigated by making use of advanced particle-in-cell simulations and reduced analytical models. The original analysis by Robertson Phys. Rev. Lett. 48, 149 (1982) is extended to the parameter regimes of particular importance for several high-energy density physics applications. The present paper investigates (1) the effects of non-neutral collective focusing in a moderately strong magnetic field; (2) the diamagnetic effects leading to suppression of the applied magnetic field due to the presence of the beam pulse; and (3) the influence of a finite-radius conducting wall surrounding the beam cross-section on beam neutralization. In addition, it is demonstrated that the use of the collective focusing lens can significantly simplify the technical realization of the final focusing of ion beam pulses in the Neutralized Drift Compression Experiment-I (NDCX-I) , and the conceptual designs of possible experiments on NDCX-I are investigated by making use of advanced numerical simulations. 2011 American Institute of Physics

This study group was initiated to consider whether there were any ''show-stopper'' issues with accelerators for heavy-ion warm-dense matter (WDM) and heavy-ion inertial fusion energy (HIF), and to prioritize them. Showstopper issues would appear as limits to beam current; that is, the beam would be well-behaved below the current limit, and significantly degraded in current or emittance if the current limit were exceeded at some region of an accelerator. We identified 14 issues: 1-6 could be addressed in the near term, 7-10 are potentially attractive solutions to performance and cost issues but are not yet fully characterized, 11-12 involve multibeam effects that cannot be more than partially studied in near-term facilities, and 13-14 involve new issues that are present in some novel driver concepts. Comparing the issues with the new experimental, simulation, and theoretical tools that we have developed, it is apparent that our new capabilities provide an opportunity to re-examine and significantly increase our understanding of the number one issue--halo growth and mitigation.

In the currently envisioned configurations for heavy ion fusion, it is necessary to longitudinally compress the beam bunches by a large factor after the acceleration phase. Because the space-charge force increases as the beam is compressed, the beam size in the transverse direction will increase in a periodic quadrupole lattice. If an active control of the beam size is desired, a larger focusing force is needed to confine the beam in the transverse direction, and a non-periodic quadrupole lattice along the beam path is necessary. In this paper, we describe the design of such a focusing lattice using the transverse envelope equations. A drift compression and final focus lattice should focus the entire beam pulse onto the same focal spot on the target. This is difficult with a fixed lattice, because different slices of the beam may have different perveance and emittance. Four time-dependent magnets are introduced in the upstream of drift compression to focus the entire pulse onto the sam e focal spot. Drift compression and final focusing schemes are developed for a typical heavy ion fusion driver and for the Integrated Beam Experiment (IBX) being designed by the Heavy Ion Fusion Virtual National Laboratory.

A drift compression and final focus lattice for heavy ion beams should focus the entire beam pulse onto the same focal spot on the target. We show that this requirement implies that the drift compression design needs to satisfy a self-similar symmetry condition. For un-neutralized beams, the Lie symmetry group analysis is applied to the warm-fluid model to systematically derive the self-similar drift compression solutions. For neutralized beams, the 1-D Vlasov equation is solved explicitly, and families of self-similar drift compression solutions are constructed. To compensate for the deviation from the self-similar symmetry condition due to the transverse emittance, four time-dependent magnets are introduced in the upstream of the drift compression such that the entire beam pulse can be focused onto the same focal spot.

Results of three-dimensional numerical simulations of field-reversed configurations (FRCs) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs and the new FRC formation method by the counter-helicity spheromak merging. Kinetic simulations show nonlinear saturation of the n = 1 tilt mode, where n is the toroidal mode number. The n = 2 and n = 3 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to the ion spin-up in the toroidal direction. The ion toroidal spin-up is shown to be related to the resistive decay of the internal flux, and the resulting loss of particle confinement. Three-dimensional MHD simulations of counter-helicity spheromak merging and FRC formation show good agreement with results from the SSX-FRC experiment. Simulations show formation of an FRC in about 30 Alfven times for typical experimental parameters. The growth rate of the n = 1 tilt mode is shown to be significantly reduced compared to the MHD growth rate due to the large plasma viscosity and field-line-tying effects.

Ion beam propagation in a background plasma is an important scientific issue for many practical applications. The process of ion beam charge and current neutralization is complex because plasma electrons move in strong electric and magnetic fields of the beam. Computer simulation images of plasma interaction with an intense ion beam pulse are presented.

Plasma neutralization of an intense ion pulse is of interest for many applications, including plasma lenses, heavy ion fusion, cosmic ray propagation, etc. An analytical electron fluid model has been developed to describe the plasma response to a propagating ion beam. The model predicts very good charge neutralization during quasi-steady-state propagation, provided the beam pulse duration {tau}{sub b} is much longer than the electron plasma period 2{pi}/{omega}{sub p}, where {omega}{sub p} = (4{pi}e{sup 2}n{sub p}/m){sup 1/2} is the electron plasma frequency and n{sub p} is the background plasma density. In the opposite limit, the beam pulse excites large-amplitude plasma waves. If the beam density is larger than the background plasma density, the plasma waves break. Theoretical predictions are compared with the results of calculations utilizing a particle-in-cell (PIC) code. The cold electron fluid results agree well with the PIC simulations for ion beam propagation through a background plasma. The reduced fluid description derived in this paper can provide an important benchmark for numerical codes and yield scaling relations for different beam and plasma parameters. The visualization of numerical simulation data shows complex collective phenomena during beam entry and exit from the plasma.

To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.

Properties of the multi-species electromagnetic Weibel and electrostatic two-stream instabilities are investigated for an intense ion beam propagating through background plasma. Assuming that the background plasma electrons provide complete charge and current neutralization, detailed linear stability properties are calculated within the framework of a macroscopic cold-fluid model for a wide range of system parameters.

The results presented here demonstrate that the Paul Trap Simulator Experiment (PTSX) simulates the propagation of intense charged particle beams over distances of many kilometers through magnetic alternating-gradient (AG) transport systems by making use of the similarity between the transverse dynamics of particles in the two systems. Plasmas have been trapped that correspond to normalized intensity parameters s = wp2 (0)/2wq2 * 0.8, where wp(r) is the plasmas frequency and wq is the average transverse focusing frequency in the smooth-focusing approximation. The measured root-mean-squared (RMS) radius of the beam is consistent with a model, equally applicable to both PTSX and AG systems that balances the average inward confining force against the outward pressure-gradient and space-charge forces. The PTSX device confines one-component cesium ion plasmas for hundreds of milliseconds, which is equivalent to over 10 km of beam propagation.

Results of three-dimensional hybrid simulations of the field-reversed configuration (FRC) are presented. Emphasis of this work is on the nonlinear evolution of magnetohydrodynamic (MHD) instabilities in kinetic FRCs. A wide range of ''bar s'' values is considered, where the ''bar s'' is the FRC kinetic parameter, which measures the number of ion gyroradii in the configuration. The linear and nonlinear stability of MHD modes with toroidal mode numbers n greater than or equal to 1 is investigated, including the effects of ion rotation, finite electron pressure, and weak toroidal field. Low-''bar s'' simulations show nonlinear saturation of the n = 1 tilt mode. The n greater than or equal to 2 rotational modes are observed to grow during the nonlinear phase of the tilt instability due to ion spin-up in the toroidal direction. Large-''bar s'' simulations show no saturation of the tilt mode, and there is a slow nonlinear evolution of the instability after the initial fast linear growth. Overall, the hybrid simulations demonstrate the importance of nonlinear effects, which are responsible for the saturation of instabilities in low-''bar s'' configurations, and also for the increase in FRC life-time compared to MHD models in high-''bar s'' configurations.

In plasmas with strongly anisotropic distribution functions, collective instabilities may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Our previous numerical and theoretical studies of intense charged particle beams with large temperature anisotropy [E. A. Startsev, R. C. Davidson and H. Qin, PRSTAB, 6, 084401 (2003); Phys. Plasmas 9, 3138 (2002)] demonstrated that a fast, electrostatic, Harris-like instability develops, and saturates nonlinearly, for sufficiently large temperature anisotropy (T{sub {perpendicular}b}/T{sub {parallel}b} >> 1). The total distribution function after saturation, however, is still far from equipartitioned. In this paper the linearized Vlasov-Maxwell equations are used to investigate detailed properties of the transverse electromagnetic Weibel-type instability for a long charge bunch propagating through a cylindrical pipe of radius r{sub w}. The kinetic stability analysis is carried out for azimuthally symmetric perturbations about a two-temperature thermal equilibrium distribution in the smooth-focusing approximation. The most unstable modes are identified, and their eigenfrequencies, radial mode structure and instability thresholds are determined. The stability analysis shows that, although there is free energy available to drive the electromagnetic Weibel instability, the finite transverse geometry of the charged particle beam introduces a large threshold value for the temperature anisotropy ((T{sub {perpendicular}b}/T{sub {parallel}b}){sup Weibel} >> (T{sub {perpendicular}b}/T{sub {parallel}b}){sup Harris}) below which the instability is absent. Hence, unlike the case of an electrically neutral plasma, the Weibel instability is not expected to play as significant a role in the process of energy isotropization of intense unneutralized charged particle beams as the electrostatic Harris-type instability.

Previous experiments on the Electron Diffusion Gauge showed that the diocotron mode damping increases with higher neutral gas filling pressure. Yet the energy dissipated from a rotating plasma by collisions with neutrals is predicted to excite the mode. To resolve this, experiments have been conducted to examine the coupling between expansion and the m=1 diocotron mode. Results from recent experiments have shown interesting phenomena: (1) The degree and sensitivity of mode growth is observed to be strongly dependent on filament conditions. Mode growth rates of nearly 20 sec{sup -1} have been observed even with negligible resistive drive. Specifically, at low filament bias voltages (and correspondingly low electron densities {approx}1-2 x 10{sup 7} electrons/cm), the mode growth is very sensitive to the heating voltage across the filament, even though changes in filament heating voltage barely affect the plasma expansion, the plasma density profile, the filament emission, or the resulting electron density. (2) At low neutral gas pressure (

The values of ion-atom ionization cross sections are frequently needed for many applications that utilize the propagation of fast ions through matter. When experimental data and theoretical calculations are not available, approximate formulas are frequently used. This paper briefly summarizes the most important theoretical results and approaches to cross section calculations in order to place the discussion in historical perspective and offer a concise introduction to the topic. Based on experimental data and theoretical predictions, a new fit for ionization cross sections is proposed. The range of validity and accuracy of several frequently used approximations (classical trajectory, the Born approximation, and so forth) are discussed using, as examples, the ionization cross sections of hydrogen and helium atoms by various fully stripped ions.

Stripping cross sections in nitrogen have been calculated using the classical trajectory approximation and the Born approximation of quantum mechanics for the outer shell electrons of 3.2GeV I{sup -} and Cs{sup +} ions. A large difference in cross section, up to a factor of six, calculated in quantum mechanics and classical mechanics, has been obtained. Because at such high velocities the Born approximation is well validated, the classical trajectory approach fails to correctly predict the stripping cross sections at high energies for electron orbitals with low ionization potential.

The Vlasov-Maxwell equations are used to investigate the nonlinear evolution of an intense sheet beam with distribution function f{sub b}(x,x{prime},s) propagating through a periodic focusing lattice k{sub x}(s+S) = k{sub x}(s), where S = const is the lattice period. The analysis considers the special class of distribution functions with uniform phase-space density f{sub b}(x,x{prime},s) = A = const inside of the simply connected boundary curves, x{prime}{sub +}(x,s) and x{prime}{sub -}(x,s), in the two-dimensional phase space (x,x{prime}). Coupled nonlinear equations are derived describing the self-consistent evolution of the boundary curves, x{prime}{sub +}(x,s) and x{prime}{sub -}(x,s), and the self-field potential {psi}(x,s) = e{sub b}{phi}(x,s)/{gamma}{sub b}m{sub b}{beta}{sub g}{sup 2}c{sup 2}. The resulting model is shown to be exactly equivalent to a (truncated) warm-fluid description with zero heat flow and triple-adiabatic equation-of-state with scalar pressure P{sub b}(x,s) = const x [n{sub b}(x,s)]. Such a fluid model is amenable to direct analysis by transforming to Lagrangian variables following the motion of a fluid element. Specific examples of periodically focused beam equilibria are presented, ranging from a finite-emittance beam in which the boundary curves in phase space (x,x{prime}) correspond to a pulsating parallelogram, to a cold beam in which the number density of beam particles, n{sub b}(x,s), exhibits large-amplitude periodic oscillations. For the case of a sheet beam with uniform phase-space density, the present analysis clearly demonstrates the existence of periodically focused beam equilibria without the undesirable feature of an inverted population in phase space that is characteristic of the Kapchinskij-Vladimirskij beam distribution.

An intense charged-particle beam with directed kinetic energy ({lambda}{sub b}-1)m{sub b}c{sup 2} propagates in the z-direction through an applied focusing field with transverse focusing force modeled by F{sub foc} = -{lambda}{sub b}m{sub b}{omega}{sub beta}{sup 2} {perpendicular} x {perpendicular} in the smooth focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution F(sub)b(r,p perpendicular) = A exp (-H Perpendicular/T perpendicular (sub)b) = (H perpendicular-E(sub)b), where A, T perpendicular (sub)b, and E (sub)b are positive constants, and H perpendicular is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, n(sub)b(r) = * d{sup 2}pF(sub)b(r,p perpendicular), and transverse temperature, T perpendicular (sub)b(r) = * d{sup 2}p(p{sup 2} perpendicular/2 lambda (sbu)bm (sub)b)F(sub)b(r,p perpendicular), are calculated self-consistently including space-charge effects. Several properties of the equilibrium profiles are noteworthy. For example, the beam has a sharp outer edge radius r(sub)b with n(sub)b(r greater than or equal to rb) = 0, where r(sub)b depends on the value of E(sub)b/T (sub)perpendicular(sub)b. In addition, unlike the choice of a semi-Gaussian distribution, F{sup SG}(sub)b = A exp (-p{sup 2}(sub)perpendicular/2lambda(sub)bm(sub)bTperpendicular(sub)b) = (r-r(sub)b), the truncated thermal equilibrium distribution F(sub)b(r,p) depends on (r,p) only through the single-particle constant of the motion Hperpendiuclar and is therefore a true steady-state solution (*/*t = 0) of the nonlinear Vlasov-Maxwell equations.

New computational results are presented which advance the understanding of the stability properties of the Field-Reversed Configuration (FRC). We present results of hybrid and two-fluid (Hall-MHD) simulations of prolate FRCs. The n = 1 tilt instability mechanism and growth rate reduction mechanisms are investigated in detail including resonant particle effects, finite Larmor radius and Hall stabilization, and profile effects. It is shown that the Hall effect determines the mode rotation and the change in the linear mode structure in the kinetic regime; however, the reduction in the growth rate is mostly due to finite Larmor radius effects. Resonant wave-particle interactions are studied as a function of (a) elongation, (b) the kinetic parameter S*, which is proportional to the ratio of the separatrix radius to the thermal ion Larmor radius, and (c) the separatrix shape. It is demonstrated that, contrary to the usually assumed stochasticity of the ion orbits in the FRC, a large fraction of the orbits are regular in long configurations when S* is small. A stochasticity condition is found, and a scaling with the S* parameter is presented. Resonant particle effects are shown to maintain the instability in the large gyroradius regime regardless of the separatrix shape.

In this paper, a 3-D nonlinear perturbative particle simulation code (BEST) [H. Qin, R.C. Davidson and W.W. Lee, Physical Review Special Topics on Accelerators and Beams 3 (2000) 084401] is used to systematically study the stability properties of intense nonneutral charged particle beams with large temperature anisotropy (T{sub {perpendicular}b} >> T{sub {parallel}b}). The most unstable modes are identified, and their eigen frequencies, radial mode structure, and nonlinear dynamics are determined for axisymmetric perturbations with {partial_derivative}/{partial_derivative}{theta} = 0.

Neutralization of the ion beam charge and current is an important scientific issue for many practical applications. The process of ion beam charge and current neutralization is complex because the excitation of nonlinear plasma waves may occur. Computer simulation images of plasma neutralization of the ion beam pulse are presented.

This paper develops a clear procedure for solving the nonlinear Vlasov-Maxwell equations for a one-component intense charged particle beam or finite-length charge bunch propagating through a cylindrical conducting pipe (radius r = r(subscript)w = const.), and confined by an applied focusing force. In particular, the nonlinear Vlasov-Maxwell equations are Lorentz-transformed to the beam frame ('primed' variables) moving with axial velocity relative to the laboratory. In the beam frame, the particle motions are nonrelativistic for the applications of practical interest, already a major simplification. Then, in the beam frame, we make the electrostatic approximation which fully incorporates beam space-charge effects, but neglects any fast electromagnetic processes with transverse polarization (e.g., light waves). The resulting Vlasov-Maxwell equations are then Lorentz-transformed back to the laboratory frame, and properties of the self-generated fields and resulting nonlinear Vlasov-Maxwell equations in the laboratory frame are discussed.

At the November 14-15, 2000, meeting of the Fusion Energy Sciences Advisory Committee, a Panel was set up to address questions about the Theory and Computing program, posed in a charge from the Office of Fusion Energy Sciences (see Appendix A). This area was of theory and computing/simulations had been considered in the FESAC Knoxville meeting of 1999 and in the deliberations of the Integrated Program Planning Activity (IPPA) in 2000. A National Research Council committee provided a detailed review of the scientific quality of the fusion energy sciences program, including theory and computing, in 2000.

Measurements of the expansion rate of pure-electron plasmas have been performed on the Electron Diffusion Gauge (EDG) device at background helium gas pressures in the 5 x 10(superscript -8) Torr to 1 x 10(superscript -5) Torr range, where plasma expansion due to electron-neutral collisions dominates over plasma expansion due to trap asymmetries. It is found that the expansion rate, defined as the time rate of change of the particles' mean-square radius, scales approximately linearly with pressure and inversely as the square of the magnetic field strength in this regime, in agreement with classical predictions.

The propagation of a high-current finite-length ion beam in a cold pre-formed plasma is investigated. The outcome of the calculation is the quantitative prediction of the degree of charge and current neutralization of the ion beam pulse by the background plasma. The electric magnetic fields generated by the ion beam are studied analytically for the nonlinear case where the plasma density is comparable in size with the beam density. Particle-in-cell simulations and fluid calculations of current and charge neutralization have been performed for parameters relevant to heavy ion fusion assuming long, dense beams with el >> V(subscript b)/omega(subscript b), where V(subscript b) is the beam velocity and omega subscript b is the electron plasma frequency evaluated with the ion beam density. An important conclusion is that for long, nonrelativistic ion beams, charge neutralization is, for all practical purposes, complete even for very tenuous background plasmas. As a result, the self-magnetic force dominates the electric force and the beam ions are always pinched during beam propagation in a background plasma.

The intense ion beams in a heavy ion Inertial Fusion Energy (IFE) driver and fusion chamber are non-neutral plasmas whose dynamics are largely dominated by space charge. We propose to develop a ''source-to-target'' Heavy Ion Fusion (HIF) beam simulation capability: a description of the kinetic behavior of this complex, nonlinear system which is both integrated and detailed. We will apply this new capability to further our understanding of key scientific issues in the physics of ion beams for IFE. The simulations will entail self-consistent field descriptions that require interprocessor communication, but are scalable and will run efficiently on terascale architectures. This new capability will be based on the integration of three types of simulations, each requiring terascale computing: (1) simulations of acceleration and confinement of the space-charge-dominated ion beams through the driver (accelerator, pulse compression line, and final focusing system) which accurately describe their dynamics, including emittance growth (phase-space dilution) effects; these are particle-in-cell (PIC) models; (2) electromagnetic (EM) and magnetoinductive (Darwin) simulations which describe the beam and the fusion chamber environment, including multibeam, neutralization, stripping, beam and plasma ionization processes, and return current effects; and (3) highly detailed simulations (6f, multispecies PIC, continuum Vlasov), which can examine electron effectsmore » and collective modes in the driver and chamber, and can study halo generation with excellent statistics, to ensure that these effects do not disrupt the focusability of the beams. The code development will involve: (i) adaptation of existing codes to run efficiently on multi-SMP computers that use a hybrid of shared and distributed memory; (ii) development of new and improved numerical algorithms, e.g., averaging techniques that will afford larger timesteps; and (iii) incorporation of improved physics models (e.g., for self-magnetic, module impedance, atomic physics, and multibeam effects) that will be made practical by the terascale capability. The codes will be linked using scripting tools for intercommunication and code steering, ''workspace'' tools for heterogeneous computations, and self-describing data files (e.g., NetCDF).« less

The macroscopic warm-fluid model developed by Lund and Davidson [Phys.Plasmas 5, 3028 (1998)] is used in the smooth-focusing approximation to investigate detailed stability properties of an intense charged particle beam with pressure anisotropy, assuming small-amplitude electrostatic pertubations about a waterbag equilibrium.