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Ronald C. Davidson

Publications and source records attributed to Ronald C. Davidson.

16 recordsLinked to original sources
arXiv2016

Generalized Kapchinskij-Vladimirskij Distribution and Beam Matrix for Phase-Space Manipulations of High-Intensity Beams

In an uncoupled linear lattice system, the Kapchinskij-Vladimirskij (KV) distribution, formulated on the basis of the single-particle Courant-Snyder (CS) invariants, has served as a fundamental theoretical basis for the analyses of the equilibrium, stability, and transport properties of high-intensity beams for the past several decades. Recent applications of high-intensity beams, however, require beam phase-space manipulations by intentionally introducing strong coupling. In this Letter, we report the full generalization of the KV model by including all of the linear (both external and space-charge) coupling forces, beam energy variations, and arbitrary emittance partition, which all form essential elements for phase-space manipulations. The new generalized KV model yields spatially uniform density profiles and corresponding linear self-field forces as desired. The corresponding matrix envelope equations and beam matrix for the generalized KV model provide important new theoretical tools for the detailed design and analysis of high-intensity beam manipulations, for which previous theoretical models are not easily applicable.

physics.acc-ph↗
arXiv2016

On the structure of the two-stream instability -- complex G-Hamiltonian structure and Krein collisions between positive- and negative-action modes

The two-stream instability is probably the most important elementary example of collective instabilities in plasma physics and beam-plasma systems. For a warm plasma with two charged particle species based on a 1D warm-fluid model, the instability diagram of the two-stream instability exhibits an interesting band structure that has not been explained. We show that the band structure for this instability is the consequence of the Hamiltonian nature of the warm two-fluid system. Interestingly, the Hamiltonian nature manifests as a complex G-Hamiltonian structure in wave-number space, which directly determines the instability diagram. Specifically, it is shown that the boundaries between the stable and unstable regions are locations for Krein collisions between eigenmodes with different Krein signatures. In terms of physics, this rigorously implies that the system is destabilized when a positive-action mode resonates with a negative-action mode, and that this is the only mechanism by which the system can be destabilized. It is anticipated that this physical mechanism of destabilization is valid for other collective instabilities in conservative systems in plasma physics, accelerator physics, and fluid dynamics systems, which admit infinite-dimensional Hamiltonian structures.

physics.plasm-ph↗
arXiv2015

Short intense ion pulses for materials and warm dense matter research

We have commenced experiments with intense short pulses of ion beams on the Neutralized Drift Compression Experiment-II at Lawrence Berkeley National Laboratory, by generating beam spots size with radius r < 1 mm within 2 ns FWHM and approximately 10^10 ions/pulse. To enable the short pulse durations and mm-scale focal spot radii, the 1.2 MeV Li+ ion beam is neutralized in a 1.6-meter drift compression section located after the last accelerator magnet. An 8-Tesla short focal length solenoid compresses the beam in the presence of the large volume plasma near the end of this section before the target. The scientific topics to be explored are warm dense matter, the dynamics of radiation damage in materials, and intense beam and beam-plasma physics including selected topics of relevance to the development of heavy-ion drivers for inertial fusion energy. Here we describe the accelerator commissioning and time-resolved ionoluminescence measurements of yttrium aluminium perovskite using the fully integrated accelerator and neutralized drift compression components.

physics.acc-ph↗
arXiv2015

Field theory and weak Euler-Lagrange equation for classical particle-field systems

It is commonly believed as a fundamental principle that energy-momentum conservation of a physical system is the result of space-time symmetry. However, for classical particle-field systems, e.g., charged particles interacting through self-consistent electromagnetic or electrostatic fields, such a connection has only been cautiously suggested. It has not been formally established. The difficulty is due to the fact that the dynamics of particles and the electromagnetic fields reside on different manifolds. We show how to overcome this difficulty and establish the connection by generalizing the Euler-Lagrange equation, the central component of a field theory, to a so-called weak form. The weak Euler-Lagrange equation induces a new type of flux, called the weak Euler-Lagrange current, which enters conservation laws. Using field theory together with the weak Euler-Lagrange equation developed here, energy-momentum conservation laws that are difficult to find otherwise can be systematically derived from the underlying space-time symmetry.

physics.plasm-ph↗
arXiv2015

Spectral and structural stability properties of charged particle dynamics in coupled lattices

It has been realized in recent years that coupled focusing lattices in accelerators and storage rings have significant advantages over conventional uncoupled focusing lattices, especially for high-intensity charged particle beams. A theoretical framework and associated tools for analyzing the spectral and structural stability properties of coupled lattices are formulated in this paper, based on the recently developed generalized Courant-Snyder theory for coupled lattices. It is shown that for periodic coupled lattices that are spectrally and structurally stable, the matrix envelope equation must admit matched solutions. Using the technique of normal form and pre-Iwasawa decomposition, a new method is developed to replace the (inefficient) shooting method for finding matched solutions for the matrix envelope equation. Stability properties of a continuously rotating quadrupole lattice are investigated. The Krein collision process for destabilization of the lattice is demonstrated.

physics.acc-ph↗
arXiv2015

Analytical methods for describing charged particle dynamics in general focusing lattices using generalized Courant-Snyder theory

The dynamics of charged particles in general linear focusing lattices with quadrupole, skew-quadrupole, dipole, and solenoidal components, as well as torsion of the fiducial orbit and variation of beam energy is parameterized using a generalized Courant-Snyder (CS) theory, which extends the original CS theory for one degree of freedom to higher dimensions. The envelope function is generalized into an envelope matrix, and the phase advance is generalized into a 4D symplectic rotation, or an U(2) element. The 1D envelope equation, also known as the Ermakov-Milne-Pinney equation in quantum mechanics, is generalized to an envelope matrix equation in higher dimensions. Other components of the original CS theory, such as the transfer matrix, Twiss functions, and CS invariant (also known as the Lewis invariant) all have their counterparts, with remarkably similar expressions, in the generalized theory. The gauge group structure of the generalized theory is analyzed. By fixing the gauge freedom with a desired symmetry, the generalized CS parameterization assumes the form of the modified Iwasawa decomposition, whose importance in phase space optics and phase space quantum mechanics has been recently realized. This gauge fixing also symmetrizes the generalized envelope equation and express the theory using only the generalized Twiss function β.The generalized phase advance completely determines the spectral and structural stability properties of a general focusing lattice. For structural stability, the generalized CS theory enables application of the Krein-Moser theory to greatly simplify the stability analysis. The generalized CS theory provides an effective tool to study coupled dynamics and to discover more optimized lattice design in the larger parameter space of general focusing lattices.

physics.acc-ph↗
arXiv2015

One-dimensional kinetic description of nonlinear traveling-pulse (soliton) and traveling-wave disturbances in long coasting charged particle beams

This paper makes use of a one-dimensional kinetic model to investigate the nonlinear longitudinal dynamics of a long coasting beam propagating through a perfectly conducting circular pipe with radius $r_{w}$. The average axial electric field is expressed as $\langle E_{z}\rangle=-(\partial/\partial z)\langleϕ\rangle=-e_{b}g_{0}\partialλ_{b}/\partial z-e_{b}g_{2}r_{w}^{2}\partial^{3}λ_{b}/\partial z^{3}$, where $g_{0}$ and $g_{2}$ are constant geometric factors, $λ_{b}(z,t)=\int dp_{z}F_{b}(z,p_{z},t)$ is the line density of beam particles, and $F_{b}(z,p_{z},t)$ satisfies the 1D Vlasov equation. Detailed nonlinear properties of traveling-wave and traveling-pulse (solitons) solutions with time-stationary waveform are examined for a wide range of system parameters extending from moderate-amplitudes to large-amplitude modulations of the beam charge density. Two classes of solutions for the beam distribution function are considered, corresponding to: (a) the nonlinear waterbag distribution, where $F_{b}=const.$ in a bounded region of $p_{z}$-space; and (b) nonlinear Bernstein-Green-Kruskal (BGK)-like solutions, allowing for both trapped and untrapped particle distributions to interact with the self-generated electric field $\langle E_{z}\rangle$. .

physics.acc-ph↗
arXiv2004

Scaling and Formulary cross sections for ion-atom impact ionization

The values of ion-atom ionization cross sections are frequently needed for many applications that utilize the propagation of fast ions through matter. When experimental data and theoretical calculations are not available, approximate formulas are frequently used. This paper briefly summarizes the most important theoretical results and approaches to cross section calculations in order to place the discussion in historical perspective and offer a concise introduction to the topic. Based on experimental data and theoretical predictions, a new fit for ionization cross sections is proposed. The range of validity and accuracy of several frequently used approximations (classical trajectory, the Born approximation, and so forth) are discussed using, as examples, the ionization cross sections of hydrogen and helium atoms by various fully stripped ions.

physics.atom-ph↗
arXiv2004

Analytical Solutions for the Nonlinear Longitudinal Drift Compression (Expansion) of Intense Charged Particle Beams

To achieve high focal spot intensities in heavy ion fusion, the ion beam must be compressed longitudinally by factors of ten to one hundred before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.

physics.acc-ph↗
arXiv2003

Comparison of quantum mechanical and classical trajectory calculations of cross sections for ion-atom impact ionization of negative - and positive -ions for heavy ion fusion applications

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

physics.atom-ph↗
arXiv2003

Renormalization Group Reduction of the Henon Map and Application to the Transverse Betatron Motion in Cyclic Accelerators

The renormalization group method is applied to the study of discrete dynamical systems. As a particular example, the Henon map is considered as applied to describe the transverse betatron oscillations in a cyclic accelerator or storage ring possessing a FODO-cell structure with a single thin sextupole. A powerful renormalization group method is developed that is valid correct to fourth order in the perturbation amplitude, and a technique for resolving the resonance structure of the Henon map is also presented. This calculation represents the first successful application of a renormalization group method to the study of discrete dynamical system in a unified manner capable of reducing the dynamics of the system both far from and close to resonances, thus preserving the symplectic symmetry of the original map.

nlin.SI↗
arXiv2002

Solitary Waves in an Intense Beam Propagating Through a Smooth Focusing Field

Based on the Vlasov-Maxwell equations describing the self-consistent nonlinear beam dynamics and collective processes, the evolution of an intense sheet beam propagating through a periodic focusing field has been studied. In an earlier paper [1] it has been shown that in the case of a beam with uniform phase space density the Vlasov-Maxwell equations can be replaced exactly by the macroscopic warm fluid-Maxwell equations with a triple adiabatic pressure law. In this paper we demonstrate that starting from the macroscopic fluid-Maxwell equations a nonlinear Schroedinger equation for the slowly varying wave amplitude (or a set of coupled nonlinear Schroedinger equations for the wave amplitudes in the case of multi-wave interactions) can be derived. Properties of the nonlinear Schroedinger equation are discussed, together with soliton formation in intense particle beams.

physics.acc-ph↗
arXiv2001

Hamiltonian Formalism for Solving the Vlasov-Poisson Equations and Its Applications to Periodic Focusing Systems and the Coherent Beam-Beam Interaction

A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new Hamiltonian that contains slowly varying terms only. The formalism has been applied to the dynamics of an intense beam propagating through a periodic focusing lattice, and to the coherent beam-beam interaction. A stationary solution to the transformed Vlasov equation has been obtained.

physics.acc-ph↗
arXiv2001

Hamiltonian Formalism for Solving the Vlasov-Poisson Equations and Its Application to the Coherent Beam-Beam Interaction

A Hamiltonian approach to the solution of the Vlasov-Poisson equations has been developed. Based on a nonlinear canonical transformation, the rapidly oscillating terms in the original Hamiltonian are transformed away, yielding a new Hamiltonian that contains slowly varying terms only. The formalism has been applied to the coherent beam-beam interaction, and a stationary solution to the transformed Vlasov equation has been obtained.

physics.acc-ph↗
arXiv2001

Macroscopic Fluid Approach to the Coherent Beam-Beam Interaction

Building on the Radon transform of the Vlasov-Poisson equations, a macroscopic fluid model for the coherent beam-beam interaction has been developed. It is shown that the Vlasov equation, expressed in action-angle variables, can be reduced to a closed set of hydrodynamic (fluid) equations for the beam density and current velocity. The linearized one dimensional equations have been analysed, and explicit expressions for the coherent beam-beam tuneshifts are presented.

physics.acc-ph↗