Search Results (7 total)

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 work is a three-dimensional stability study based on the modal analysis for a continuous beam with an axisymmetric Kapchinskij-Vladimirskij (KV) distribution. The analysis is carried out self-consistently within the context of linearized Vlasov-Maxwell equations and electrostatic approximation. The emphasis is on investigating the coupling between longitudinal and transverse perturbations in the high-intensity region. The interaction between the transverse modes supported by the KV distribution and the “usual transverse modes” is examined. We found two classes of “coupling modes” that would not exist if longitudinal and transverse perturbations are treated separately. We also found that some transverse modes can interact among themselves through longitudinal perturbation to cause instability. The effects of wall impedance on beam stability is also studied and numerical examples are presented.

This paper presents an analytical investigation of the transverse electron-proton (e-p) two-stream instability in a proton bunch propagating through a stationary electron background. The equations of motion, including damping effects, are derived for the centroids of the proton beam and the electron cloud by considering Lorentzian and Gaussian frequency spreads for the particles. For a Lorentzian frequency distribution, we derive the asymptotic solution of the coupled linear centroid equations in the time domain and study the e-p instability in proton bunches with nonuniform line densities. Examples are given for both uniform and parabolic proton line densities.

We studied the electrostatic field due to a charged-particle beam with uniform particle density propagating inside an rf-shielding cage (rf cage) constructed from evenly spaced conducting wires. The beam and the rf cage are surrounded by a ceramic beam pipe positioned inside a conducting pipe concentric with the beam and the rf cage. The space-charge impedances in the long wavelength regime are investigated by considering the electrostatic fields due to the longitudinal and transverse perturbations on the density of the charged-particle beam. Shielding effects due to the rf cage are discussed and simple formulas are derived for estimating the space-charge impedances. Numerical examples are given for illustration. Comparisons between analytical estimates and the results produced by the field-solver computer program MAFIA show good agreement.

This paper reports on an approach to investigate the dynamics of halo particles in mismatched charged-particle beams propagating through periodic-focusing channels using the particle-core model. The proposed method employs canonical transformations to minimize, in new phase-space variables, the flutter due to the periodic focusing to allow making stroboscopic plots. Applying this method, we find that in periodic-focusing systems, certain particles initially not in the halo region can be brought into resonance with the core oscillation to become halo particles.

The present analysis makes use of the Vlasov-Maxwell equations to develop a fully kinetic description of the electrostatic, electron-ion two-stream instability driven by the directed axial motion of a high-intensity ion beam propagating in the z direction with average axial momentum γ_bm_bβ_bc through a stationary population of background electrons. The ion beam has characteristic radius r_b and is treated as continuous in the z direction, and the applied transverse focusing force on the beam ions is modeled by F_foc^b=-γ_b  m_bω_βb⁰²  x_⊥ in the smooth-focusing approximation. Here, ω_βb⁰=const is the effective betatron frequency associated with the applied focusing field, x_⊥ is the transverse displacement from the beam axis, (γ_b-1)m_bc² is the ion kinetic energy, and V_b=β_bc is the average axial velocity, where γ_b=(1-β_b²  )^-1/2. Furthermore, the ion motion in the beam frame is assumed to be nonrelativistic, and the electron motion in the laboratory frame is assumed to be nonrelativistic. The ion charge and number density are denoted by +Z_be and n_b, and the electron charge and number density by -e and n_e. For Z_bn_b>n_e, the electrons are electrostatically confined in the transverse direction by the space-charge potential φ produced by the excess ion charge. The equilibrium and stability analysis retains the effects of finite radial geometry transverse to the beam propagation direction, including the presence of a perfectly conducting cylindrical wall located at radius r=r_w. In addition, the analysis assumes perturbations with long axial wavelength, k_z²r_b²≪1, and sufficiently high frequency that |ω/k_z|≫v_Tez and |ω/k_z-V_b|≫v_Tbz, where v_Tez and v_Tbz are the characteristic axial thermal speeds of the background electrons and beam ions. In this regime, Landau damping (in axial velocity space v_z) by resonant ions and electrons is negligibly small. We introduce the ion plasma frequency squared defined by ω-^ _pb²  =4πn-^ _bZ_b²e²/γ_bm_b, and the fractional charge neutralization defined by f=n-^ _e/Z_b  n-^ _b, where n-^ _b and n-^ _e are the characteristic ion and electron densities. The equilibrium and stability analysis is carried out for arbitrary normalized beam intensity ω-^ _pb²  /ω_βb⁰², and arbitrary fractional charge neutralization f, consistent with radial confinement of the beam particles. For the moderately high beam intensities envisioned in the proton linacs and storage rings for the Accelerator for Production of Tritium and the Spallation Neutron Source, the normalized beam intensity is typically ω-^ _pb²  /ω_βb⁰²≲ 0.1. For heavy ion fusion applications, however, the transverse beam emittance is very small, and the space-charge-dominated beam intensity is much larger, with ω-^ _pb²  /ω_βb⁰²≲ 2γ_b². The stability analysis shows that the instability growth rate Imω increases with increasing normalized beam intensity ω-^ _pb²  /ω_βb⁰² and increasing fractional charge neutralization f. In addition, the instability is strongest (largest growth rate) for perturbations with azimuthal mode number ℓ=1, corresponding to a simple (dipole) transverse displacement of the beam ions and the background electrons. For the case of overlapping step-function density profiles for the beam ions and background electrons, corresponding to monoenergetic ions and electrons, a key result is that there is no threshold in beam intensity ω-^ _pb²  /ω_βb⁰² or fractional charge neutralization f for the onset of instability. Finally, for the case of continuously varying density profiles with parabolic profile shape, a semiquantitative estimate is made of the effects of the corresponding spread in (depressed) betatron frequency on stability behavior, including an estimate of the instability threshold for the case of weak density nonuniformity.