Search Results (12 total)

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.

The dispersion relation for the resistive hose instability in a charged particle beam with a flattop density profile is derived from the linearized Vlasov-Maxwell equations. Stability properties of the resistive hose instability where the perturbations are initiated at the beam entrance are investigated. In particular, the complex eigenfrequency Ω in the dispersion relation is expressed as a function of the real oscillation frequency ω of the excitation at the beam entrance. As expected, the growth rate ImΩ=Ω_i decreases rapidly as the conducting wall approaches the beam (r_w/r_b→1). The growth rate also decreases substantially as the frequency ratio ω/ν_c increases, where ν_c is the electron collision frequency. Stability properties for perturbations propagating through the beam pulse from its head to tail are also investigated. In this case, the growth rate Imω is calculated in terms of the real oscillation frequency Ω of each beam segment. It is shown that the resonance frequency Ω=Ω_r corresponding to the infinite growth rate detunes considerably from the betatron frequency ω_β of the beam particles. It is also found that the bandwidth corresponding to instability is narrow when the plasma electron collision time (1/ν_c) is long compared with the magnetic decay time (τ_d).

A novel high-gradient wake-field accelerator is presented in which the drive-beam current leaves behind a high-gradient wake field, accelerating the witness beam to very high energy. The theoretical analysis is based on Faraday’s law, which provides a second-order partial differential equation of the azimuthal magnetic field, under the assumption that με≫1. The accelerating field can be more than 1/2 GV/m in an appropriate choice of system parameters.

Modulation of the beam current has been observed during ion-focused-regime (IFR) transport of a high-power relativistic electron beam propagating through a low-density background plasma. In this experiment, a 1.7-MeV, 1-kA, rise-time-sharpened electron beam is transported in a KrF-excimer-laser–produced IFR channel in trimethylamine gas. The IFR channel is immersed in a low-density plasma-filled transport tube. We present experimental measurements and computer simulations demonstrating modulation of this high-current relativistic electron beam near the low-density background plasma frequency.

A theory of the magnetic field diffusion is developed in order to explain high-energy x-ray emission observed in vacuum spark plasmas. The acceleration mechanism is based on the intense induced electric field due to an abrupt inductance change when the plasma column expands from its pinch radius to a large radius. According to this magnetic field diffusion model, high-energy electrons are well collimated at the axis. In addition, the electron energy in this collimated flux can be easily more than 20 times the electrode voltage, which generates high-energy x-ray radiation by interaction with the dense plasma.

The influence of equilibrium self-field effects on the cyclotron-maser instability is investigated for an intense hollow electron beam, in connection with high-power gyrotron applications. The theoretical analysis is carried out within the framework of the linearized Vlasov-Maxwell equations, assuming that the beam thickness is much less than the mean radius of the beam. The electron orbit is calculated, including the important influence of strong self-fields. The formal dispersion relation for azimuthally symmetric electromagnetic perturbations is obtained. One of the most important features of the analysis is that the radial betatron frequency of an electron, which includes the equilibrium self-field effects, plays a pivotal role in stability behavior. Without ions, it is shown that the radial betatron frequency is always less than the electron cyclotron frequency. In this particular case, any deviation of the betatron frequency from the cyclotron frequency strongly stabilizes the instability. Moreover, it is also found that the self-dielectric effects of a very intense beam is negligibly small. Thus, electromagnetic waves of the vacuum transverse electric waveguide modes are very good approximations for perturbed fields in the cyclotron maser instability.

An expression for the relativistic ponderomotive Hamiltonian for magnetized particles of a cylindrical waveguide mode is derived. From this result, the equations of motion for the beam particles and the beam Vlasov susceptibility are obtained. The expression for the ponderomotive Hamiltonian is then taken in the limit of unmagnetized particles and used in an analysis of charged-particle-beam confinement by ponderomotive force due to a waveguide mode. Formulas for the rf power and energy density inside the waveguide needed to confine a beam with a given kinetic energy and current are then derived. Numerical estimates give reasonable values for the rf power and energy needed to confine a typical electron or ion beam.

The linearized Vlasov-Poisson equations are used to investigate the electrostatic stability properties of nonrelativistic non-neutral electron flow in a planar diode with cathode located at x=0 and anode at x=d. The electron layer is immersed in a uniform applied magnetic field B₀e^_z, and the equilibrium flow velocity V_yb⁰(x) is in the y direction. Stability properties are calculated for perturbations about the choice of self-consistent Vlasov equilibrium f_b⁰(H,P_y)=(n^_b/2πm)δ (H)δ(P_y), which gives an equilibrium with uniform electron density (n^_b=const) extending from the cathode (x=0) to the outer edge of the electron layer (x=x_b). Assuming flute perturbations (∂/∂z=0) of the form δφ(x,y,t)=δφ^_k(x)exp(iky -iωt), the eigenvalue equation for δφ^_k(x) is simplified and solved analytically for long-wavelength, low-frequency perturbations satisfying kx_b≪1 and ‖ω-kV_d‖²≪ω_v²≡ω_c² -ω^_pb². This gives a quadratic dispersion relation for the complex oscillation frequency ω. Defining μ=ω^_pb²/ω_v² and g=d/(d-x_b), it is shown that the necessary and sufficient condition for instability (Imω>0) is given by (1+μ+g)(μ+g)>2(1+μ)(1+μ/4  )². It is found that the maximum growth rate in the unstable region can be substantial. For example, for d=2x_b and g=2, the maximum growth rate is (Imω)_max≃0.25(kx_b)ω_c, which occurs for μ≃2.3.

A high-current annular electron beam in an accelerator is subject to various instabilities. A general fluid-Maxwell theory of the diocotron instability is developed for an infinitely long and azimuthally symmetric annular electron beam propagating along an external magnetic field. In contrast with the treatment used in the conventional diocotron instability, the assumptions of tenuous electron beam and strong magnetic field have been eliminated. Furthermore, the restriction of infinite axial wavelength perturbation has been removed and the approximation of ω∼ckβ is no longer applied. Instead, we conduct full electromagnetic perturbation in the macroscopic cold-fluid description of plasma dynamics with the beam parameters of general interest. In the special case of a sharp-boundary density profile, the diocotron instability which dominates in the low-frequency region is investigated in a broad range of beam parameters and geometries. The results are significantly different from that obtained from the conventional diocotron instability; the kink mode can be destabilized and the growth rates are much larger for every azimuthal mode.

Use is made of the macroscopic cold-fluid Poisson equations to investigate the electrostatic stability properties of nonrelativistic, non-neutral electron flow in a cylindrical diode with applied magnetic field B₀e^_z. The cathode is located at r=a and the anode is located at r=b. Space-charge-limited flow with E_r⁰(r=a)=0 is assumed. Detailed stability properties are investigated analytically and numerically for electrostatic flute perturbations with ∂/∂z=0. Particular emphasis is placed on the influence of the neutral anode plasma on stability behavior assuming uniform cathode electron density (n^_b) extending from the cathode (r=a) to r=r_b, and uniform anode plasma density (n^_e=Z_in^_i) extending from r=r_p to the anode (r=b). Depending on the cathode electron density (as measured by s_b=ω^ _pb²/ω_ce²), the anode plasma density (as measured by s_e=ω^ _pe²/ω_ce²), the diode aspect ratio, etc., it is found that there can be a strong coupling of the anode plasma to the cathode electrons, and a concomitant large influence on detailed stability behavior for both the high-frequency (electron-driven) and low-frequency (ion-driven) branches. Detailed stability properties are investigated over a wide range of cathode electron density, anode plasma density, diode aspect ratio, etc.

The equilibrium properties of a relativistic non-neutral electron layer confined in a magnetically insulated cylindrical diode are investigated within the framework of the steady-state (∂/∂t=0) Vlasov-Maxwell equations. The analysis is carried out for an infinitely long cylindrical electron layer with axis of symmetry parallel to an applied magnetic field B₀e→^_z, which provides radial confinement of the electrons. The theoretical analysis is specialized to the class of self-consistent Vlasov equilibria f_b⁰(x→,p→) in which all electrons have the same canonical angular momentum (P_θ=P₀=const) and the same energy (H=mc²), i.e., f_b⁰=(n^_bR_c/2πm)δ(H-mc² )δ(P_θ-P₀). One of the most important features of the analysis is that the closed analytic expressions for the self-consistent electrostatic potential φ₀(r) and the θ component of vector potential A₀(r) are obtained. Moreover, all essential equilibrium quantities, such as electron density profile n_b⁰(r), total magnetic field B_0z(r), perpendicular temperature profile T_⊥b⁰(r), etc., can be calculated self-consistently from these potentials. As a special case, the equilibrium properties of a planar diode are investigated in the limit of large aspect ratio, further simplifying the functional form of the electrostatic and vector potentials. Detailed equilibrium properties are investigated numerically for a cylindrical diode over a broad range of system parameters, including diode voltage V₀, cathode electric field, electron density n^_b at the cathode, diode polarity, and applied magnetic field B₀.

The filamentation instability of the electron and positron colliding beams in a storage ring is investigated within the framework of the Vlasov-Maxwell equations, and a closed algebraic dispersion relation for the complex eigenfrequency ω is obtained. It is shown that the typical growth rate of instability is a substantial fraction of the electron plasma frequency ω_pe. For parameters characterizing the recent colliding-beam experiments at DESY, the instability threshold is marginally satisfied.