Search Results (9 total)

Self-consistent Vlasov-Poisson simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel—both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of kinetic distributions commonly in use as initial Vlasov distributions in simulations of unbunched or weakly bunched beams with intense space-charge fields including the following: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various nonequilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of standard accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial kinetic distributions are constructed using transformations that preserve linear focusing, single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for noncontinuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulations that more precisely probe intrinsic stability properties and machine performance.

The transverse Vlasov equilibrium distribution function of an unbunched ion beam propagating in a continuous-focusing channel is specified by a function f_⊥(H_⊥), where H_⊥ is the single-particle Hamiltonian. In standard treatments of continuous-focusing equilibria in Vlasov-Poisson electrostatic models, it is assumed that a stable beam equilibrium specified by monotonic f_⊥(H_⊥) with ∂f_⊥(H_⊥)/∂H_⊥≤0 is axisymmetric (no variation in azimuthal angle, i.e., with ∂/∂θ=0). In this paper a simple, but rigorous, proof is presented that only axisymmetric equilibrium solutions are possible in Vlasov-Poisson models for any physical choice of f_⊥(H_⊥) with ∂f_⊥(H_⊥)/∂H_⊥≤0 if the confining boundary of the system (the beam pipe) is axisymmetric or if the geometry is radially unbounded.

A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij equations describing the transverse edge trajectory of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parametrizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to all physically achievable system parameters—including cases where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.

The High Current Experiment at Lawrence Berkeley National Laboratory is part of the U.S. program to explore heavy-ion beam transport at a scale representative of the low-energy end of an induction linac driver for fusion energy production. The primary mission of this experiment is to investigate aperture fill factors acceptable for the transport of space-charge-dominated heavy-ion beams at high intensity (line charge density ∼0.2  μC/m) over long pulse durations (4  μs) in alternating gradient focusing lattices of electrostatic or magnetic quadrupoles. This experiment is testing transport issues resulting from nonlinear space-charge effects and collective modes, beam centroid alignment and steering, envelope matching, image charges and focusing field nonlinearities, halo, and electron and gas cloud effects. We present the results for a coasting 1 MeV K⁺ ion beam transported through ten electrostatic quadrupoles. The measurements cover two different fill factor studies (60% and 80% of the clear aperture radius) for which the transverse phase space of the beam was characterized in detail, along with beam energy measurements and the first halo measurements. Electrostatic quadrupole transport at high beam fill factor (≈80%) is achieved with acceptable emittance growth and beam loss, even though the initial beam distribution is not ideal (but the emittance is low) nor in thermal equilibrium. We achieved good envelope control, and rematching may only be needed every ten lattice periods (at 80% fill factor) in a longer lattice of similar design. We also show that understanding and controlling the time dependence of the envelope parameters is critical to achieving high fill factors, notably because of the injector and matching section dynamics.

High current and low emittance are principal requirements for heavy-ion injection into a linac driver for inertial fusion energy. An electrostatic quadrupole injector is capable of providing these high charge density and low emittance beams. We have modified the existing 2-MV injector to reduce beam emittance and to double the pulse length. We characterize the beam delivered by the modified injector to the High Current Transport Experiment and the effects of finite rise time of the extraction voltage pulse in the diode on the beam head. We demonstrate techniques for mitigating aberrations and reducing beam emittance growth in the injector.

Stray electrons can arise in positive-ion accelerators for heavy-ion fusion or other applications as a result of ionization of ambient gas or gas released from walls due to halo-ion impact, or as a result of secondary-electron emission. We summarize the distinguishing features of electron-cloud issues in heavy-ion-fusion accelerators and a plan for developing a self-consistent simulation capability for heavy-ion beams and electron clouds (also applicable to other accelerators). We also present results from several ingredients in this capability. (1) We calculate the electron cloud produced by electron desorption from computed beam-ion loss, which illustrates the importance of retaining ion reflection at the walls. (2) We simulate the effect of specified electron-cloud distributions on ion beam dynamics. We consider here electron distributions with axially varying density, centroid location, or radial shape, and examine both random and sinusoidally varying perturbations. We find that amplitude variations are most effective in spoiling ion beam quality, though for sinusoidal variations which match the natural ion beam centroid oscillation or breathing-mode frequencies, the centroid and shape perturbations can also have significant impact. We identify an instability associated with a resonance between the beam-envelope “breathing” mode and the electron perturbation. We estimate its growth rate, which is moderate (compared to the reciprocal of a typical pulse duration). One conclusion from this study is that heavy-ion beams are surprisingly robust to electron clouds, compared to a priori expectations. (3) We report first results from a long-time-step algorithm for electron dynamics, which holds promise for efficient simultaneous solution of electron and ion dynamics.

In typical diagnostic applications, intense ion beams are intercepted by a conducting plate associated with devices used to measure beam phase-space projections. This results in the transverse space-charge field near the plate being shorted out, rendering simple envelope models with constant space-charge strength inaccurate. Here we develop corrected envelope models based on analytical calculations to account for this effect on the space-charge term of the envelope equations, thereby removing a systematic source of error in the equations and enabling more accurate comparisons with experiment. For common intense beam parameters, we find that the envelope correction occurs primarily in the envelope angles near the plate and that the effect can be large enough to degrade precision beam matching in periodic transport lattices. Results are verified with 3D self-consistent particle-in-cell simulations based on intense beam experiments associated with driver development for heavy-ion fusion.

The transverse evolution of the envelope of an intense, unbunched ion beam in a linear transport channel can be modeled for the approximation of linear self-fields by the Kapchinskij-Vladimirskij (KV) envelope equations. Here we employ the KV envelope equations to analyze the linear stability properties of so-called mismatch perturbations about the matched (i.e., periodic) beam envelope in continuous focusing, periodic solenoidal, and periodic quadrupole transport lattices for a coasting beam. The formulation is analyzed and explicit self-consistent KV distributions are derived for an elliptical beam envelope in a periodic solenoidal transport channel. This derivation extends previous work to identify emittance measures and Larmor-frame transformations to allow application of standard form envelope equations to solenoidal focusing channels. Perturbed envelope equations are derived that include driving sources of mismatch excitation resulting from focusing errors, particle loss, and beam emittance growth. These equations are solved analytically for continuous focusing and demonstrate a factor of 2 increase in maximum mismatch excursions resulting from sudden driving perturbations relative to adiabatic driving perturbations. Numerical and analytical studies are carried out to explore properties of normal mode envelope oscillations without driving excitations in periodic solenoidal and quadrupole focusing lattices. Previous work on this topic by Struckmeier and Reiser [Part. Accel. 14, 227 (1984)] is extended and clarified. Regions of parametric instability are mapped, new classes of envelope instabilities are found, parametric sensitivities are explored, general limits and mode invariants are derived, and analytically accessible limits are checked. Important, and previously unexplored, launching conditions are described for pure envelope modes in periodic quadrupole focusing channels.

An intense charged particle beam with directed kinetic energy (γ_b-1)m_bc² propagates in the z direction through an applied focusing field with transverse focusing force modeled by F_foc=-γ_bm_bω_β⊥²x_⊥ in the smooth-focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution F_b(r,p_⊥)=Aexp⁡(-H_⊥/T-^ _⊥b)⊕(H_⊥-E_b), where A, T-^ _⊥b, and E_b are positive constants, and H_⊥ is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, n_b(r)=∫d²pF_b(r,p_⊥), and transverse temperature, T_⊥b(r)=[n_b(r)]^-1∫d²p(p_⊥²/2γ_bm_b)F_b(r,p_⊥), 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_b with n_b(r≥r_b)=0, where r_b depends on the value of E_b/T-^ _⊥b. In addition, unlike the choice of a semi-Gaussian distribution, F_b^SG=Aexp⁡(-p_⊥²/2γ_bm_bT-^ _⊥b)⊕(r-r_b), the truncated thermal equilibrium distribution F_b(r,p) depends on (r,p) only through the single-particle constant of the motion H_⊥ and is therefore a true steady-state solution (∂/∂t=0) of the nonlinear Vlasov-Maxwell equations.