Search Results (87 total)

It is shown that the application of a weak solenoidal magnetic field along the direction of ion beam propagation through a neutralizing background plasma can significantly enhance the beam self-focusing for the case where the beam radius is small compared to the collisionless electron skin depth. The enhanced focusing is provided by a strong radial self-electric field that is generated due to a local polarization of the magnetized plasma background by the moving ion beam. A positive charge of the ion beam pulse becomes overcompensated by the plasma electrons, which results in the radial focusing of the beam ions. The expression for the self-focusing force is derived analytically and compared with the results of numerical simulations.

The Courant-Snyder theory gives a complete description of the uncoupled transverse dynamics of charged particles in electromagnetic focusing lattices. In this paper, the Courant-Snyder theory is generalized to the case of coupled transverse dynamics with two degrees of freedom. The generalized theory has the same structure as the original Courant-Snyder theory for one degree of freedom. The four basic components of the original Courant-Snyder theory, i.e., the envelope equation, phase advance, transfer matrix, and the Courant-Snyder invariant, all have their counterparts, with remarkably similar expressions, in the generalized theory presented here. In the generalized theory, the envelope function is generalized into an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are noncommutative. The generalized theory gives a new parametrization of the 4D symplectic transfer matrix that has the same structure as the parametrization of the 2D symplectic transfer matrix in the original Courant-Snyder theory. All of the parameters used in the generalized Courant-Snyder theory correspond to physical quantities of importance, and this parametrization can provide a valuable framework for accelerator design and particle simulation studies. A time-dependent canonical transformation is used to develop the generalized Courant-Snyder theory. Applications of the new theory to strongly and weakly coupled dynamics are given. It is shown that the stability of coupled dynamics can be determined by the generalized phase advance developed. Two stability criteria are given, which recover the known results about sum and difference resonances in the weakly coupled limit.

A random noise-induced beam degradation that could affect intense beam transport over long propagation distances has been experimentally investigated by making use of the transverse beam dynamics equivalence between an alternating-gradient focusing system and a linear Paul trap system. For the present study, machine imperfections in the quadrupole focusing lattice are considered, which are emulated by adding small random noise on the voltage waveform of the quadrupole electrodes in the Paul trap. It is observed that externally driven noise continuously increases the rms radius, transverse emittance, and nonthermal tail of the trapped charge bunch almost linearly with the duration of the noise. The combined effects of collective modes and colored noise are also investigated and compared with numerical simulations.

A random noise-induced beam degradation that can affect intense beam transport over long propagation distances has been experimentally studied by making use of the transverse beam dynamics equivalence between an alternating-gradient (AG) focusing system and a linear Paul trap system. For the present studies, machine imperfections in the quadrupole focusing lattice are considered, which are emulated by adding small random noise on the voltage waveform of the quadrupole electrodes in the Paul trap. It is observed that externally driven noise continuously produces a nonthermal tail of trapped ions, and increases the transverse emittance almost linearly with the duration of the noise.

Large-space-scale and long-time-scale plasma flow simulations are executed in order to study the spatial and temporal evolution of plasma parameters for two types of plasma sources used in the neutralized drift compression experiment (NDCX). The results help assess the charge neutralization conditions for ion beam compression experiments and can be employed in more sophisticated simulations, which previously neglected the dynamical evolution of the plasma. Three-dimensional simulations of a filtered cathodic-arc plasma source show the coupling efficiency of the plasma flow from the source to the drift region depends on geometrical factors. The nonuniform magnetic topology complicates the well-known general analytical considerations for evaluating guiding-center drifts, and particle-in-cell simulations provide a self-consistent evaluation of the physics in an otherwise challenging scenario. Plasma flow profiles of a ferroelectric plasma source demonstrate that the densities required for longitudinal compression experiments involving ion beams are provided over the drift length, and are in good agreement with measurements. Simulations involving azimuthally asymmetric plasma creation conditions show that symmetric profiles are nevertheless achieved at the time of peak on-axis plasma density. Also, the ferroelectric plasma expands upstream on the thermal expansion time scale, and therefore avoids the possibility of penetration into the acceleration gap and transport sections, where partial neutralization would increase the beam emittance. Future experiments on NDCX will investigate the transverse focusing of an axially compressing intense charge bunch to a sub-mm spot size with coincident focal planes using a strong final-focus solenoid. In order to fill a multi-tesla solenoid with the necessary high-density plasma for beam charge neutralization, the simulations predict that supersonically injected plasma from the low-field region will penetrate and partially fill the high-field region of the solenoid. Because of the magnetic mirroring effect, the on-axis plasma density in the solenoid depends on the injection velocity and magnetic field strength.

The Paul trap simulator experiment is a compact laboratory Paul trap that simulates a long, thin charged-particle bunch coasting through a kilometers-long magnetic alternating-gradient (AG) transport system by putting the physicist in the beam’s frame of reference. The transverse dynamics of particles in both systems are described by similar equations, including all nonlinear space-charge effects. The time-dependent quadrupolar electric fields created by the confinement electrodes of a linear Paul trap correspond to the axially dependent magnetic fields applied in the AG system. Results are presented for experiments in which the lattice period and strength are changed over the course of the experiment to transversely compress a beam with an initial depressed tune of 0.9. Instantaneous and smooth changes are considered. Emphasis is placed on determining the conditions that minimize the emittance growth and the number of halo particles produced by the beam compression process. Both the results of particle-in-cell simulations performed with the warp code and envelope equation solutions agree well with the experimental data.

The analytical studies show that the application of a small solenoidal magnetic field can drastically change the self-magnetic and self-electric fields of the beam pulse propagating in a background plasma. Theory predicts that when ω_ce∼ω_peβ_b, where ω_ce is the electron gyrofrequency, ω_pe is the electron plasma frequency, and β_b is the ion-beam velocity relative to the speed of light, there is a sizable enhancement of the self-electric and self-magnetic fields due to the dynamo effect. Furthermore, the combined ion-beam–plasma system acts as a paramagnetic medium; i.e., the solenoidal magnetic field inside the beam pulse is enhanced.

Longitudinal bunch compression of intense ion beams for warm dense matter and heavy ion fusion applications occurs by imposing an axial velocity tilt onto an ion beam across the acceleration gap of a linear induction accelerator, and subsequently allowing the beam to drift through plasma in order to neutralize its space-charge and current as the pulse compresses. The detailed physics and implications of acceleration gap effects and focusing aberration on optimum longitudinal compression are quantitatively reviewed using particle-in-cell simulations, showing their dependence on many system parameters. Finite-size gap effects are shown to result in compression reduction, due to an increase in the effective longitudinal temperature imparted to the beam, and a decrease in intended fractional tilt. Sensitivity of the focal plane quality to initial longitudinal beam temperature is explored, where slower particles are shown to experience increased levels of focusing aberration compared to faster particles. A plateau effect in axial compression is shown to occur for larger initial pulse lengths, where the increases in focusing aberration over the longer drift lengths involved dominate the increases in relative compression, indicating a trade-off between current compression and pulse duration. The dependence on intended fractional tilt is also discussed and agrees well with theory. A balance between longer initial pulse lengths and larger tilts is suggested, since both increase the current compression, but have opposite effects on the final pulse length, drift length, and amount of longitudinal focusing aberration. Quantitative examples are outlined that explore the sensitive dependence of compression on the initial kinetic energy and thermal distribution of the beam particles. Simultaneous transverse and longitudinal current density compression can be achieved in the laboratory using a strong final-focus solenoid, and simulations addressing the effects of focusing aberration in both directions are presented.

The transverse compression of a long charge bunch is investigated in the Paul trap simulator experiment (PTSX), which is a linear Paul trap that simulates the nonlinear transverse dynamics of an intense charged particle beam propagating through an equivalent kilometers-long magnetic alternating-gradient (AG) focusing system. Changing the voltage amplitude at fixed focusing frequency in the PTSX device corresponds to changing the field gradient of the quadrupole magnets with fixed axial periodicity in the AG transport system. In this work, we present experimental results on transverse compression of the charge bunch in which the amplitude of the applied oscillatory focusing voltage is changed instantaneously, and adiabatically. The experimental data are also compared with analytical estimates and 2D WARP particle-in-cell simulations.

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov-Maxwell equations are applied to high-intensity finite-length charge bunches, and a generalized δf particle simulation algorithm is developed for bunched beams with or without energy anisotropy. The nonlinear δf method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out under conditions corresponding to strong 3D nonlinear space-charge forces in the beam frame. For charge bunches with isotropic energy, finite bunch-length effects are clearly evident by the fact that the spectra for an infinitely long coasting beam and a nearly spherical charge bunch have strong similarities, whereas the spectra have distinctly different features when the bunch length is varied between these two limiting cases. For bunched beams with anisotropic energy, there exists no exact kinetic equilibrium because the particle dynamics do not conserve transverse energy and longitudinal energy separately. A reference state in approximate dynamic equilibrium has been constructed theoretically, and a quasi-steady state has been established in the simulations for the anisotropic case. Collective excitations relative to the reference state have been simulated using the generalized δf algorithm. In particular, the electrostatic Harris instability driven by strong energy anisotropy is investigated for a finite-length charge bunch. The observed growth rates are larger than those obtained for infinitely long coasting beams. However, the growth rate decreases for increasing bunch length to a value similar to the case of a long coasting beam. For long bunches, the instability is axially localized symmetrically relative to the beam center, and the characteristic wavelength in the longitudinal direction is comparable to the transverse dimension of the beam.

The linear growth of the two-stream instability for a charged-particle beam that is longitudinally compressing as it propagates through a background plasma (due to an applied velocity tilt) is examined. Detailed, 1D particle-in-cell (PIC) simulations are carried out to examine the growth of the wave packet produced by a small amplitude density perturbation in the background plasma. Recent analytic and numerical work by Startsev and Davidson [Phys. Plasmas 13, 062108 (2006)] predicted reduced linear growth rates, which are indeed observed in the PIC simulations. Here, small-signal asymptotic gain factors are determined in a semianalytic analysis and compared with the simulation results in the appropriate limits. Nonlinear effects in the PIC simulations, including wave breaking and particle trapping, are found to limit the linear growth phase of the instability for both compressing and noncompressing beams.

The Paul Trap Simulator Experiment (PTSX) is a linear Paul trap whose purpose is to simulate the nonlinear transverse dynamics of intense charged particle beam propagation in periodic-focusing quadrupole magnetic transport systems. Externally created cesium ions are injected and trapped in the long central electrodes of the PTSX device. In order to have well-matched one-component plasma equilibria for various beam physics experiments, it is important to optimize the ion injection. From the experimental studies reported in this paper, it is found that the injection process can be optimized by minimizing the beam mismatch between the source and the focusing lattice, and by minimizing the number of particles present in the vicinity of the injection electrodes when the injection electrodes are switched from the fully oscillating voltage waveform to their static trapping voltage.

Heavy ion drivers for warm dense matter and heavy ion fusion applications use intense charge bunches which must undergo transverse and longitudinal compression in order to meet the requisite high current densities and short pulse durations desired at the target. The neutralized drift compression experiment (NDCX) at the Lawrence Berkeley National Laboratory is used to study the longitudinal neutralized drift compression of a space-charge-dominated ion beam, which occurs due to an imposed longitudinal velocity tilt and subsequent neutralization of the beam’s space charge by background plasma. Reduced theoretical models have been used in order to describe the realistic propagation of an intense charge bunch through the NDCX device. A warm-fluid model is presented as a tractable computational tool for investigating the nonideal effects associated with the experimental acceleration gap geometry and voltage waveform of the induction module, which acts as a means to pulse shape both the velocity and line density profiles. Self-similar drift compression solutions can be realized in order to transversely focus the entire charge bunch to the same focal plane in upcoming simultaneous transverse and longitudinal focusing experiments. A kinetic formalism based on the Vlasov equation has been employed in order to show that the peaks in the experimental current profiles are a result of the fact that only the central portion of the beam contributes effectively to the main compressed pulse. Significant portions of the charge bunch reside in the nonlinearly compressing part of the ion beam because of deviations between the experimental and ideal velocity tilts. Those regions form a pedestal of current around the central peak, thereby decreasing the amount of achievable longitudinal compression and increasing the pulse durations achieved at the focal plane. A hybrid fluid-Vlasov model which retains the advantages of both the fluid and kinetic approaches has been implemented to describe the formation of pedestals in the current profiles. The comparison between the experimental measurements and the various theoretical models is excellent.

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 to +150  keV was measured using a PLIA input voltage waveform of -21 to +12  kV. Ion pulses accelerated by 150 keV, and bunching by a factor of 4 were simultaneously achieved. The measured longitudinal phase space and current waveform of the accelerated beam are in good agreement with 3D particle-in-cell simulations.

The single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant, a fundamental concept in accelerator physics, is fundamentally a result of the corresponding symmetry admitted by the harmonic oscillator equation with linear time-dependent frequency. It is demonstrated that the Lie algebra of the symmetry group for the oscillator equation with time-dependent frequency is eight dimensional, and is composed of four independent subalgebras. A detailed analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. As an application to accelerator physics, the symmetries of the envelope equation enable a fast numerical algorithm for finding matched solutions without using the conventional iterative Newton’s method, where the envelope equation needs to be numerically integrated once for every iteration, and the Jacobi matrix needs to be calculated for the envelope perturbation.

Heavy ion drivers for heavy ion fusion and high energy density physics applications use space-charge-dominated ion beams which must undergo longitudinal bunch compression in order to meet the requisite beam intensities desired at the target. The Neutralized Drift Compression Experiment-1A (NDCX-1A) at Lawrence Berkeley National Laboratory is used to determine the effective limits of neutralized drift compression, which occurs due to an imposed longitudinal velocity tilt on the drifting beam and subsequent neutralization of the beam’s space charge with background plasma. The accurate and temporally resolved measurement of the ion beam’s current and pulse length, which has been longitudinally compressed to a few nanoseconds duration at its focal plane, is a critical diagnostic. This paper describes the design and experimental results for a fast and accurate ion beam probe, which reliably measures the absolute beam current in the presence of high density plasma at the focal plane as a function of time. A particle-in-cell code has been used to model the propagation of the intense ion beam and to design the diagnostic probe.

The transverse compression and dynamics of an intense beam propagating through an alternating-gradient quadrupole lattice, plays an important role in many accelerator physics applications. Typically, the compression can be achieved by means of increasing the focusing strength of the lattice along the beam propagation direction. However, beam propagation through the lattice transition region inevitably leads to a certain level of beam mismatch and halo formation. In this work we present a detailed analysis of these phenomena using the envelope equations in the smooth-focusing approximation, which describe the average effects of an alternating-gradient lattice, and full particle-in-cell numerical simulations using the WARP code, taking into account the effects of the alternating-gradient quadrupole field. Simulations are presented for both space-charge–dominated beams, and beams with a moderate space-charge strength.

For the motion of a charged particle in a uniform, time-dependent axial magnetic field B(t)e_z, it is shown that there is an exact magnetic-moment invariant of the particle dynamics M, to which the adiabatic magnetic-moment invariant μ=mv_⊥²/2B is asymptotic when the time scale of the magnetic field variation is much slower than the gyroperiod. The connection between the exact invariant M and the adiabatic invariant μ enables us to characterize in detail the robustness of the adiabatic magnetic-moment invariant μ.

The classical electrostatic Harris instability is generalized to the case of a one-component intense charged particle beam with anisotropic temperature including the important effects of finite transverse geometry and beam space charge. For a long, coasting beam, the eigenmode code bEASt have been used to determine detailed 3D stability properties over a wide range of temperature anisotropy and beam intensity. A simple theoretical model is developed which describes the essential features of the linear stage of the instability. Both the simulations and the analytical theory clearly show that moderately intense beams are linearly unstable to short-wavelength perturbations provided the ratio of the longitudinal temperature to the transverse temperature is smaller than some threshold value. The delta-f particle-in-cell code BEST has been used to study the detailed nonlinear evolution and saturation of the instability.

Longitudinal compression of a velocity-tailored, intense neutralized K⁺ beam at 300 keV, 25 mA has been demonstrated. The compression takes place in a 1–2 m drift section filled with plasma to provide space-charge neutralization. An induction cell produces a head-to-tail velocity ramp that longitudinally compresses the neutralized beam, enhancing the beam peak current by a factor of 50 and producing a pulse duration of about 3 ns. This measurement has been confirmed independently with two different diagnostic systems.

A kinetic model based on the Vlasov equation is used to describe the axial drift compression and transverse focusing of an intense ion charge bunch propagating along the axis of a solenoidal focusing field B^sol(x). The space charge and current of the ion charge bunch are assumed to be completely neutralized by the electrons provided by a dense background plasma. In the absence of self-field forces, the Vlasov equation is solved exactly for general initial distribution function f_b(x,v,0), using the method of characteristics. It is shown that the Vlasov equation possesses a class of exact, dynamically evolving solutions f_b(W_⊥,W_z), where W_⊥ and W_z are transverse and longitudinal constants of the motion. Detailed dynamical properties of the charge bunch are calculated during axial compression and transverse focusing for several choices of distribution function f_b(W_⊥,W_z).

The authors disagree with Dr. D. V. Pestrikov’s assertion that “the results obtained in the commented paper are not true,” based on how Volterra’s integral equations are treated in the paper. The authors would agree, for clarity, that the equal sign (=) in Eqs. (34), (36), and (38) in the paper be replaced by some special symbol or the approximate sign (≈) to indicate the omission of initial conditions. These and similar changes together with the revision to an error found by the authors have been published in a recent erratum.

This paper presents a survey of the present theoretical understanding of collective processes and beam-plasma interactions affecting intense heavy ion beam propagation in heavy ion fusion systems. In the acceleration and beam transport regions, the topics covered include discussion of the conditions for quiescent beam propagation over long distances; the electrostatic Harris-type instability and the transverse electromagnetic Weibel-type instability in strongly anisotropic, one-component non-neutral ion beams; and the dipole-mode, electron-ion two-stream instability driven by an (unwanted) component of background electrons. In the plasma plug and target chamber regions, collective processes associated with the interaction of the intense ion beam with a charge-neutralizing background plasma are described, including the electrostatic electron-ion two-stream instability, the electromagnetic Weibel instability, and the resistive hose instability. Operating regimes are identified where the possible deleterious effects of collective processes on beam quality are minimized.

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 nonperiodic 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 same focal spot. Drift compression and final focusing schemes are developed for a typical heavy ion fusion driver and for the integrated beam experiment being designed by the Heavy Ion Fusion Virtual National Laboratory.