Search Results (17 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 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.

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 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.

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.

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.

This paper describes a self-consistent kinetic model for the longitudinal dynamics of a long, coasting beam propagating in straight (linear) geometry in the z direction in the smooth-focusing approximation. Starting with the three-dimensional Vlasov-Maxwell equations, and integrating over the phase-space (x_⊥,p_⊥) transverse to beam propagation, a closed system of equations is obtained for the nonlinear evolution of the longitudinal distribution function F_b(z,p_z,t) and average axial electric field ⟨E_z^s⟩(z,t). The primary assumptions in the present analysis are that the dependence on axial momentum p_z of the distribution function f_b(x,p,t) is factorable, and that the transverse beam dynamics remains relatively quiescent (absence of transverse instability or beam mismatch). The analysis is carried out correct to order k_z²r_w² assuming slow axial spatial variations with k_z²r_w²≪1, where k_z∼∂/∂z is the inverse length scale of axial variation in the line density λ_b(z,t)=∫dp_zF_b(z,p_z,t), and r_w is the radius of the conducting wall (assumed perfectly conducting). A closed expression for the average longitudinal electric field ⟨E_z^s⟩(z,t) in terms of geometric factors, the line density λ_b, and its derivatives ∂λ_b/∂z,… is obtained for the class of bell-shaped density profiles n_b(r,z,t)=(λ_b/πr_b²)f(r/r_b), where the shape function f(r/r_b) has the form specified by f(r/r_b)=(n+1)(1-r²/r_b²)ⁿ for 0≤r<r_b, and f(r/r_b)=0 for r_b<r≤r_w, where n=0,1,2,…. The general kinetic formalism developed here is valid for the entire range of beam intensities (proportional to λ_b) ranging from low-intensity, emittance-dominated beams, to very-high-intensity, low-emittance beams.

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 3.2 GeV I^- and Cs⁺ ions. A large difference in cross section, up to a factor of 6, 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.

In plasmas with strongly anisotropic distribution functions (T_∥b/T_⊥b≪1) a Harris-like collective instability may develop if there is sufficient coupling between the transverse and longitudinal degrees of freedom. Such anisotropies develop naturally in accelerators and may lead to a deterioration of beam quality. This paper extends previous numerical studies [E. A. Startsev, R. C. Davidson, and H. Qin, Phys. Plasmas 9, 3138 (2002)] of the stability properties of intense non-neutral charged particle beams with large temperature anisotropy (T_⊥b≫T_∥b) to allow for nonaxisymmetric perturbations with ∂/∂θ≠0. The most unstable modes are identified, and their eigenfrequencies, radial mode structure, and nonlinear dynamics are determined. The simulation results clearly show that moderately intense beams with s_b=ω-^ _pb²/2γ_b²ω_β⊥²≳0.5 are linearly unstable to short-wavelength perturbations with k_z²r_b²≳1, provided the ratio of longitudinal and transverse temperatures is smaller than some threshold value. Here, ω-^ _pb²=4πn-^ _be_b²/γ_bm_b is the relativistic plasma frequency squared, and ω_β⊥ is the betatron frequency associated with the applied smooth-focusing field. A theoretical model is developed based on the Vlasov-Maxwell equations which describes the essential features of the linear stages of instability. Both the simulations and the analytical theory predict that the dipole mode (azimuthal mode number m=1) is the most unstable mode. In the nonlinear stage, tails develop in the longitudinal momentum distribution function, and the kinetic instability saturates due to resonant wave-particle interactions.

This paper makes use of the Vlasov-Maxwell equations to investigate collective excitations in an intense sheet beam, infinite in the y and z directions, propagating in the z direction with directed kinetic energy (γ_b-1)m_bc². The beam is confined in the x direction by the smooth-focusing force F→_foc=-γ_bm_bω_β⊥²xe→_x, and perfectly conducting walls are located at x=±x_w. A self-consistent water bag equilibrium f_b⁰ satisfying the steady-state (∂/∂t=0) Vlasov-Maxwell equations is shown to be exactly solvable for the beam density n_b⁰(x) and electrostatic potential φ⁰(x). A closed Schrödinger-like eigenvalue equation is derived, assuming small-amplitude perturbations (δf_b,δφ) about the self-consistent water bag equilibrium, and the eigenfrequency spectrum is shown to be purely real. The WKB approximation is employed to determine the eigenfrequency spectrum as a function of the normalized beam intensity s_b=ω-^ _pb²/γ_b²ω_β⊥², where ω-^ _pb²=4πn-^ _be_b²/γ_bm_b and n-^ _b=n_b(x=0) is the on-axis number density of beam particles.

Two-stream instabilities in intense charged particle beams, described self-consistently by the nonlinear Vlasov-Maxwell equations, are studied using a 3D multispecies perturbative particle simulation method. The recently developed Beam Equilibrium, Stability and Transport code is used to simulate the linear and nonlinear properties of the electron-proton (e-p) two-stream instability observed in the Proton Storage Ring (PSR) experiment for a long, coasting beam. Simulations in a parameter regime characteristic of the PSR experiment show that the e-p instability has a dipole-mode structure, and that the growth rate is an increasing function of beam intensity, but a decreasing function of the longitudinal momentum spread. It is also shown that the instability threshold decreases with increasing fractional charge neutralization and increases with increasing axial momentum spread of the beam particles. In the nonlinear phase, the simulations show that the proton density perturbation first saturates at a relatively low level and subsequently grows to a higher level. Finally, the nonlinear space-charge-induced transverse tune spread, which introduces a major growth-rate reduction effect on the e-p instability, is studied for self-consistent equilibrium populations of protons and electrons.

The Vlasov-Maxwell equations are used to investigate the nonlinear evolution of an intense sheet beam with distribution function f_b\(x,x^′,s\) propagating through a periodic focusing lattice κ_x\(s+S\)  =  κ_x\(s\), where S  =  const is the lattice period. The analysis considers the special class of distribution functions with uniform phase-space density f_b\(x,x^′,s\)  =  A  =  const inside of the simply connected boundary curves, x₊^′\(x,s\) and x_-^′\(x,s\), in the two-dimensional phase space \(x,x^′\). Coupled nonlinear equations are derived describing the self-consistent evolution of the boundary curves, x₊^′\(x,s\) and x_-^′\(x,s\), and the self-field potential ψ\(x,s\)  =  e_bφ\(x,s\)/γ_bm_bβ_b²c². 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_b\(x,s\)  =  const[n_b\(x,s\)]³. 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 \(x,x^′\) correspond to a pulsating parallelogram, to a cold beam in which the number density of beam particles, n_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.

The simultaneous forward and backward stimulated Brillouin scattering (SBS) of crossed laser beams is studied in detail. Analytical solutions are obtained for the linearized equations governing the transient phase of the instability and the nonlinear equations governing the steady state. These solutions show that backward SBS dominates the initial evolution of the instability, whereas forward SBS dominates the steady state. The analysis of this paper is verified by numerical simulation.

The trajectory and dephasing time of an electron accelerated by a circularly polarized laser pulse are determined analytically. The dephasing time is proportional to γ_P²l, where γ_P is the Lorentz factor associated with the pulse speed and l is the pulse length. The residual dependence of the dephasing time on pulse intensity and electron injection energy is studied in detail.

In this paper we use simple physical reasoning to deduce a formula for the ponderomotive force exerted by an intense laser pulse on an electron. We verify this formula numerically, for three cases of current interest, and analytically, using the method of multiple scales.

The acceleration of an electron by a circularly polarized laser pulse in a plasma is studied. It appears possible to increase significantly the energy of a preaccelerated electron. Although the pulse tends to generate a plasma wake, to which it loses energy, one can eliminate the wake by choosing the duration of the pulse judiciously.