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LONGITUDINAL RESISTIVE INSTABILITIES OF INTENSE COASTING BEAMS IN PARTICLE ACCELERATORS

Description: The effect of finite resistance in the vacuum-tank walls on the longitudinal stability of an intense beam of particles in an accelerator is investigated theoretically. We show that even if the particle frequency is an increasing function of particle energy, the wall resistance can render the beam unstable against longitudinal bunching. In the absence of frequency spread in the unperturbed beam, the instability occurs with a growth rate that is proportional to (N/{sigma}){sup 1/2}, where N is the number of particles in the beam and {sigma} is the conductivity of the surface material. By means of the Vlasov equation a criterion for beam stability is obtained. In the limit of highly conducting walls the criterion involves the frequency spread in the unperturbed beam, the number of particles N, the beam energy, geometrical properties of the accelerator, but not the conductivity {sigma}. A numerical example presented indicates that certain observations of beam behavior in the MURA 40-Mev-electron accelerator may be related to the phenomenon we investigated.
Date: September 29, 1964
Creator: Neil, V. Kelvin & Sessler, Andrew M.
Partner: UNT Libraries Government Documents Department

LONGITUDINAL RESISTIVE INSTABILITIES OF INTENSE COASTING BEAMS IN PARTICLE ACCELERATORS

Description: The longitudinal electromagnetic interaction of an intense coasting beam with itself, including the effect of a resistive vacuum tank, is investigated theoretically. It is shown that even in the range where the particle frequency is an increasing function of particle energy, the beam can be longitudinally unstable due to the resistivity of the vacuum tank walls. In the absence of frequency spread in the unperturbed beam the beam is shown to be always unstable against longitudinal bunching with a growth rate which depends upon (N/{sigma}){sup 1/2}, where N is the number of particles in the beam and {sigma} is the conductivity of the surface material. By means of the Vlasov equation, a criterion for stability of the beam is obtained; and shown in the limit of high-conductivity walls to involve the frequency spread in the unperturbed beam, the number of particles N, the beam energy, geometrical properties of the accelerator, but not the conductivity {sigma}. A numerical example is presented which indicates that certain observations of beam behavior in the MURA 40 MeV electron accelerator may be related to the phenomena investigated here.
Date: October 23, 1963
Creator: Neil, V. Kelvin & Sessler, Andrew M.
Partner: UNT Libraries Government Documents Department

Comparing new models of transverse instability with simulations

Description: Recently, Balbekov and Burov have produced an ordinary integro-differential equation that approximates the Vlasov equation for beams with wakefields and large space charge tune shift. The present work compares this model with simulations. In particular, the claim that certain types of transverse wakes cannot lead to mode coupling instabilities is explored.
Date: May 20, 2012
Creator: M., Blaskiewicz
Partner: UNT Libraries Government Documents Department

Generalized Kapchinskij-Vladimirskij Distribution and Envelope Equation for High-intensity Beams in a Coupled Transverse Focusing Lattice

Description: In an uncoupled lattice, the Kapchinskij-Vladimirskij (KV) distribution function first analyzed in 1959 is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high- intensity beams including self-fields in a self-consistent manner. The KV solution is generalized here to high-intensity beams in a coupled transverse lattice using the recently developed generalized Courant-Snyder invariant for coupled transverse dynamics. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space, determined by the generalized matrix envelope equation.
Date: November 20, 2009
Creator: Hong Qin, Moses Chung, and Ronald C. Davidson
Partner: UNT Libraries Government Documents Department

A three-dimensional kinetic theory of continuous-beam stability

Description: This work is a three-dimensional stability study based on the modal analysis for a continuous beam of 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 those modes sustainable by the cold beam is examined. We found two classes of coupling modes that would not exist if the longitudinal and the transverse perturbations are treated separately. The effects of wall impedance on beam stability is also studied and numerical examples are presented.
Date: January 1, 2003
Creator: Wang, T. F. (Tai-Sen F.)
Partner: UNT Libraries Government Documents Department

SOME EXACT RADIATION SOLUTIONS TO VLASOV'S EQUATIONS

Description: A class of exact solutions to the Vlasov equations which shows electromagnetic radiation is constructed, and a typical example discussed in some detail. Since velocities larger than c appear to be possibly of importance in these solutions, an exact radiating solution to the relativistic Vlasov equations is constructed, which, though much more specialized than the nonrelativistic solutions, shows that unphysically large velocities in the nonrelativistic solutions are not essential for the radiation there obtained. (auth)
Date: December 11, 1959
Creator: Biedenharn, L.C.
Partner: UNT Libraries Government Documents Department

THE CHAOTIC BEHAVIOR OF THE BUNCHED BEAM.

Description: Using the self consistent Vlasov equation we discuss a wave dynamical system to describe the chaotic behavior of the bunched beam, present some results of the existence of the global solutions as the generalized functions. Disappearance of the first integral, and appearance of the wave packet chaos due to birth of the continuous spectrum in Vlasov system is studied. We propose a new concept of wave packet chaos to describe the chaotic behavior of the wave dynamical system.
Date: June 18, 2001
Creator: PARSA,Z. & ZADOROZHNY,V.
Partner: UNT Libraries Government Documents Department

Application of scaling properties of the Vlasov and the Fokker-Planck equations to improved macroparticle models

Description: Numerical simulations of cooling processes over minutes or hours of real time are usually carried out using direct solution of the Fokker-Planck equation. However, by using scaling rules derived from that equation, it is possible to use macroparticle representations of the beam distribution. Besides having applications for cooling alone, the macroparticle approach allows combining the cooling process with other dynamical processes which are represented by area-preserving maps. A time-scaling rule derived from the Vlasov equation can be used to adjust the time step of a map-based dynamics calculation to one more suitable for combining with a macroparticle Fokker-Planck calculation. The time scaling for the Vlasov equation is also useful for substantially more rapid calculations when a macroparticle model of a conservative multiparticle system requires a large number of macroparticles to faithfully produce the collective potential or when the model must simulate a long time period.
Date: July 12, 2001
Creator: MacLachlan, James A.
Partner: UNT Libraries Government Documents Department

Collective instabilities and halo formation of space-charge dominated beams in a particle-beam nonlinear-Dynamics approach

Description: Nonlinear dynamics deals with parametric resonances and diffusion, which are usually beam-intensity independent and rely on a particle Hamiltonian. Collective instabilities deal with beam coherent motion, where the Vlasov equation is frequently used in conjunction with a beam-intensity dependent Hamiltonian. The authors address the questions: Are the two descriptions the same? Are collective instabilities the results of encountering parametric resonances whose driving force is intensity dependent? The space-charge dominated beam governed by the Kapchinskij-Vladimirskij (K-V) envelope equation is used as an example.
Date: August 23, 2000
Creator: Ng, K.Y.
Partner: UNT Libraries Government Documents Department

Effects of bunch density gradient in high-gain free-electron lasers.

Description: The authors investigate effects of the bunch density gradient in self-amplified spontaneous emission (SASE), including the role of coherent spontaneous emission (CSE) in the evolution of the free-electron laser (FEL) process. In the exponential gain regime, the authors solve the coupled Maxwell-Vlasov equations and extend the linear theory to a bunched beam with energy spread. A time-dependent, nonlinear simulation algorithm is used to study the CSE effect and the nonlinear evolution of the radiation pulse.
Date: September 1, 1999
Creator: Huang, Z. & Kim, K.-J.
Partner: UNT Libraries Government Documents Department

Coherent spontaneous emission in high gain free-electron lasers.

Description: The authors investigate finite pulse effects in self-amplified spontaneous emission (SASE), especially the role of coherent spontaneous emission (CSE) in the start and the evolution of the free-electron laser (FEL) process. When the FEL interaction is negligible, they solve the one-dimensional Maxwell equation exactly and clarify the meaning of the slowly varying envelope approximation (SVEA). In the exponential gain regime, they solve the coupled Vlasov-Maxwell equations and extend the linear theory to a bunched beam with energy spread. A time-dependent, non-linear simulation algorithm is employed to study the CSE effect for a general beam distribution.
Date: April 14, 1999
Creator: muang, Z.
Partner: UNT Libraries Government Documents Department

Nonlinear Longitudinal Waves in High Energy Stored Beams

Description: We solve the Vlasov equation for the longitudinal distribution function and find stationary wave patterns when the distribution in the energy error is Maxwellian. In the long wavelength limit a stability criterion for linear waves has been obtained and a Korteweg-de Vries-Burgers equation for the relevant hydrodynamic quantities has been derived.
Date: July 26, 1999
Creator: Tzenov, Stephan I.
Partner: UNT Libraries Government Documents Department

Drift compression and final focus options for heavy ionfusion

Description: A drift compression and final focus lattice for heavy ion beams should focus the entire beam pulse onto the same focal spot on the target. The authors show that this requirement implies that the drift compression design needs to satisfy a self-similar symmetry condition. For un-neutralized beams, the Lie symmetry group analysis is applied to the warm-fluid model to systematically derive the self-similar drift compression solutions. For neutralized beams, the 1D Vlasov equation is solved explicitly and families of self-similar drift compression solutions are constructed. To compensate for the deviation from the self-similar symmetry condition due to the transverse emittance, four time-dependent magnets are introduced in the upstream of the drift compression such that the entire beam pulse can be focused onto the same focal spot.
Date: January 18, 2005
Creator: Qin, Hong; Davidson, Ronald C.; Barnard, John J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Phase segregation via Vlasov-Boltzmann particle dynamics

Description: In order to better understand and model the phase segregation of binary fluids we opted for a mesoscopic description that proves to be simplifying both conceptually and computationally. The system that we studied is a mixture of two kinds of particles. All particles interact with each other through strong short-range interactions modeled by hard spheres with the same mass and diameter. There is also a smooth long-range repulsion between particles of different kinds. At low overall densities and weak enough repulsion the natural dynamical description for this system is given in terms of two coupled, energy and momentum conserving Vlasov- Boltzmann equations, making it what we call a dynamical mean-field model. The computational scheme that we used is a combination of direct sim- ulation Monte Carlo (DSMC) and particle-in-the-cell (PIC) evolution, that inherits the efficiency and robustness of these two algorithms. The DSMC is a stochastic algorithm due to Bird that consistently incorporates the as- sumptions behind the Boltzmann equation into the particle dynamics. The method is essentially the following: the physical space is divided into a net- work of cells containing typically tens of particles and the free flow of the particles over a small time interval {Delta}t is followed by representative collisions among pairs of particles sharing the same cell. The typical linear dimension of a cell is a fraction of the mean free path between collisions. The PIC method for integrating the equations of motion was first used to deal with the l/r potential in plasma physics. It takes advantage of the simple form of the Vlasov potential, which is a product in Fourier space, by calculating the densities on a grid through some weighting, then the potentials and forces on the same grid, and finally interpolating the forces at the position of each particle. These two ...
Date: January 19, 1999
Creator: Bastea, S.
Partner: UNT Libraries Government Documents Department

COHERENT ELECTROMAGNETIC EFFECTS IN HIGH-CURRENT PARTICLE ACCELERATORS: I. INTERACTION OF A PARTICLE BEAM WITH AN EXTERNALLY DRIVEN RADIO-FREQUENCY CAVITY

Description: A calculation is made of the interaction of a beam of particles in an accelerator with the radio-frequency cavity that provides the accelerating mechanism of the machine. A Hamiltonian for synchrotron motion is employed that makes possible the simultaneous solution of Maxwell's equations and the Vlasov equation, so that a self-consistent distribution of particles in synchrotron phase space is determined. The effective voltage on the cavity due to the beam of charged particles is of the order of magnitude of the product of the total circulating current in the accelerator and the shunt impedance of the rf cavity. It has the net effect of producing a total voltage on the cavity which is both less than the applied voltage, and shifted in phase with respect to it. The increase in the stable phase angle required so the particles will remain in phase with the accelerating radio frequency is calculated. The decrease in total voltage and increase in stable phase angle result in a decrease in stable phase space available for acceleration, and convenient expressions are given for these quantities in terms of parameters of the accelerator. It is shown that the consequences of the induced voltage may be alleviated by increasing the voltage applied to the cavity.
Date: July 1, 1960
Creator: Neil, V. Kelvin & Sessler, Andrew M.
Partner: UNT Libraries Government Documents Department

Generalized Courant-Snyder Theory and Kapchinskij-Vladimirskij Distribution For High-intensity Beams In A Coupled Transverse Focusing Lattice

Description: The Courant-Snyder (CS) theory and the Kapchinskij-Vladimirskij (KV) distribution for high-intensity beams in a uncoupled focusing lattice are generalized to the case of coupled transverse dynamics. The envelope function is generalized to an envelope matrix, and the envelope equation becomes a matrix envelope equation with matrix operations that are non-commutative. In an uncoupled lattice, the KV distribution function, first analyzed in 1959, is the only known exact solution of the nonlinear Vlasov-Maxwell equations for high-intensity beams including self-fields in a self-consistent manner. The KV solution is generalized to high-intensity beams in a coupled transverse lattice using the generalized CS invariant. This solution projects to a rotating, pulsating elliptical beam in transverse configuration space. The fully self-consistent solution reduces the nonlinear Vlasov-Maxwell equations to a nonlinear matrix ordinary differential equation for the envelope matrix, which determines the geometry of the pulsating and rotating beam ellipse. These results provide us with a new theoretical tool to investigate the dynamics of high-intensity beams in a coupled transverse lattice. A strongly coupled lattice, a so-called N-rolling lattice, is studied as an example. It is found that strong coupling does not deteriorate the beam quality. Instead, the coupling induces beam rotation, and reduces beam pulsation.
Date: July 18, 2011
Creator: QIn, Hong & Davidson, Ronald
Partner: UNT Libraries Government Documents Department

Meshless Solution of the Vlasov Equation Using a Low Discrepancy Sequence

Description: A good method for solving the nonlinear Vlasov equation is the semi-Lagrangian algorithm, in which the phase space density is represented by its values on a fixed Cartesian grid with interpolation to off-grid points. At each time step, orbits are followed backward from grid points. Since this method is expensive with phase space dimension D > 2, we seek a more efficient discretization of the density. Taking a cue from the theory of numerical quadrature in high dimensions, we explore the idea of replacing the grid by scattered data sites from a low-discrepancy (quasirandom) sequence. We hope to see a reduction in the required number of sites, especially for D > 2. In our first implementation we follow forward orbits rather than backward, and work only with D = 2. We are able to reduce the number of sites by a factor of 8, at least for a limited time of integration. A much bigger reduction is expected in higher dimensions.
Date: January 28, 2009
Creator: Warnock, R.L.; /SLAC; Ellison, J.A.; Heinemann, K.; Zhang, G.Q. & U., /New Mexico
Partner: UNT Libraries Government Documents Department

A New Class of Non-Linear, Finite-Volume Methods for Vlasov Simulation

Description: Methods for the numerical discretization of the Vlasov equation should efficiently use the phase space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order, non-linear, finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls oscillations is presented. The method is fourth-order in space and time in well-resolved regions, but smoothly reduces to a third-order upwind scheme as features become poorly resolved. The new scheme is applied to several standard problems for the Vlasov-Poisson system, and the results are compared with those from other finite-volume approaches, including an artificial viscosity scheme and the Piecewise Parabolic Method. It is shown that the new scheme is able to control oscillations while preserving a higher degree of fidelity of the solution than the other approaches.
Date: November 24, 2009
Creator: Banks, J W & Hittinger, J A
Partner: UNT Libraries Government Documents Department

Longitudinal Motion in High Current Ion Beams - a Self-Consistent Phase Space Distribution With an Envelope Equation

Description: Many applications of particle acceleration, such as heavy ion fusion, require longitudinal bunching of a high intensity particle beam to extremely high particle currents with correspondingly high space charge forces. This requires a precise analysis of longitudinal motion including stability analysis. Previous papers have treated the longitudinal space charge force as strictly linear, and have not been self-consistent; that is, they have not displayed a phase space distribution consistent with this linear force so that the transport of the phase space distribution could be followed, and departures from linearity could be analyzed. This is unlike the situation for transverse phase space where the Kapchinskij-Vladimirskij (K-V) distribution can be used as the basis of an analysis of transverse motion. In this paper we derive a self-consistent particle distribution in longitudinal phase space which is a solution of the Vlasov equation and derive an envelope equation for this solution. The solution is developed in Section II from a stationary solution of the Vlasov equation derived in Section I.
Date: March 1, 1979
Creator: Neuffer, D.
Partner: UNT Libraries Government Documents Department

Study of Bunch Instabilities By the Nonlinear Vlasov-Fokker-Planck Equation

Description: Instabilities of the bunch form in storage rings may be induced through the wake field arising from corrugations in the vacuum chamber, or from the wake and precursor fields due to coherent synchrotron radiation (CSR). For over forty years the linearized Vlasov equation has been applied to calculate the threshold in current for an instability, and the initial growth rate. Increasing interest in nonlinear aspects of the motion has led to numerical solutions of the nonlinear Vlasov equation, augmented with Fokker-Planck terms to describe incoherent synchrotron radiation in the case of electron storage rings. This opens the door to much deeper studies of coherent instabilities, revealing a rich variety of nonlinear phenomena. Recent work on this topic by the author and collaborators is reviewed.
Date: July 11, 2006
Creator: Warnock, Robert L.
Partner: UNT Libraries Government Documents Department