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Sheet beam model for intense space-charge: with application to Debye screening and the distribution of particle oscillation frequencies in a thermal equilibrium beam

Description: A one-dimensional Vlasov-Poisson model for sheet beams is reviewed and extended to provide a simple framework for analysis of space-charge effects. Centroid and rms envelope equations including image charge effects are derived and reasonable parameter equivalences with commonly employed 2D transverse models of unbunched beams are established. This sheet beam model is then applied to analyze several problems of fundamental interest. A sheet beam thermal equilibrium distribution in a continuous focusing channel is constructed and shown to have analogous properties to two- d three-dimensional thermal equilibrium models in terms of the equilibrium structure and Deybe screening properties. The simpler formulation for sheet beams is exploited to explicitly calculate the distribution of particle oscillation frequencies within a thermal equilibrium beam. It is shown that as space-charge intensity increases, the frequency distribution becomes broad, suggesting that beams with strong space-charge can have improved stability.
Date: January 10, 2011
Creator: Lund, Steven M.; Friedman, Alex & Bazouin, Guillaume
Partner: UNT Libraries Government Documents Department

Generation of Initial Kinetic Distributions for Simulation of Long-Pulse Charged Particle Beams with High Space-Charge intensity

Description: Self-consistent Vlasov-Poisson simulations of beams with high space-charge intensity often require specification of initial phase-space distributions that reflect properties of a beam that is well adapted to the transport channel--both in terms of low-order rms (envelope) properties as well as the higher-order phase-space structure. Here, we first review broad classes of kinetic distributions commonly in use as initial Vlasov distributions in simulations of unbunched or weakly bunched beams with intense space-charge fields including: the Kapchinskij-Vladimirskij (KV) equilibrium, continuous-focusing equilibria with specific detailed examples, and various non-equilibrium distributions, such as the semi-Gaussian distribution and distributions formed from specified functions of linear-field Courant-Snyder invariants. Important practical details necessary to specify these distributions in terms of usual accelerator inputs are presented in a unified format. Building on this presentation, a new class of approximate initial kinetic distributions are constructed using transformations that preserve linear-focusing single-particle Courant-Snyder invariants to map initial continuous-focusing equilibrium distributions to a form more appropriate for non-continuous focusing channels. Self-consistent particle-in-cell simulations are employed to show that the approximate initial distributions generated in this manner are better adapted to the focusing channels for beams with high space-charge intensity. This improved capability enables simulation applications that more precisely probe intrinsic stability properties and machine performance.
Date: April 3, 2007
Creator: Lund, Steven M.; Kikuchi, Takashi & Davidson, Ronald C.
Partner: UNT Libraries Government Documents Department

Truncated Thermal Equilibrium Distribution for Intense Beam Propagation

Description: An intense charged-particle beam with directed kinetic energy ({lambda}{sub b}-1)m{sub b}c{sup 2} propagates in the z-direction through an applied focusing field with transverse focusing force modeled by F{sub foc} = -{lambda}{sub b}m{sub b}{omega}{sub beta}{sup 2} {perpendicular} x {perpendicular} in the smooth focusing approximation. This paper examines properties of the axisymmetric, truncated thermal equilibrium distribution F(sub)b(r,p perpendicular) = A exp (-H Perpendicular/T perpendicular (sub)b) = (H perpendicular-E(sub)b), where A, T perpendicular (sub)b, and E (sub)b are positive constants, and H perpendicular is the Hamiltonian for transverse particle motion. The equilibrium profiles for beam number density, n(sub)b(r) = * d{sup 2}pF(sub)b(r,p perpendicular), and transverse temperature, T perpendicular (sub)b(r) = * d{sup 2}p(p{sup 2} perpendicular/2 lambda (sbu)bm (sub)b)F(sub)b(r,p perpendicular), are calculated self-consistently including space-charge effects. Several properties of the equilibrium profiles are noteworthy. For example, the beam has a sharp outer edge radius r(sub)b with n(sub)b(r greater than or equal to rb) = 0, where r(sub)b depends on the value of E(sub)b/T (sub)perpendicular(sub)b. In addition, unlike the choice of a semi-Gaussian distribution, F{sup SG}(sub)b = A exp (-p{sup 2}(sub)perpendicular/2lambda(sub)bm(sub)bTperpendicular(sub)b) = (r-r(sub)b), the truncated thermal equilibrium distribution F(sub)b(r,p) depends on (r,p) only through the single-particle constant of the motion Hperpendiuclar and is therefore a true steady-state solution (*/*t = 0) of the nonlinear Vlasov-Maxwell equations.
Date: February 26, 2003
Creator: Davidson, Ronald C.; Qin, Hong & Lund, Steven M.
Partner: UNT Libraries Government Documents Department

Characterization of Prototype Superconducting Magnetic Quadrupolesfor the High Current Transport Experiment

Description: Later phases of the High Current Transport Experiment (HCX) at LBNL will employ superconducting magnetic quadrupole lenses to focus an intense, heavy-ion beam over approximately 50 lattice periods (100 quadrupoles). Here they present a characterization of a baseline quadrupole design suitable for transporting a single, low-energy ({approx} 2 MeV), high-current ({approx} 800 mA) heavy-ion (K{sup +}) beam that will be provided from an existing injector and beam matching section. For optimal performance in this application, a compact quadrupole magnet providing high focusing strength and high field quality is required. The reference parameters that they have chosen take into account magnet development work by AML, LLNL, and MIT and result in a transport lattice well matched to programmatic needs with a lattice period of approximately 50 cm. The goal of this note is to introduce a common framework where the magnetic performance of different designs can be compared. In that regard, they try to avoid the details of an earlier parameter note [1] where provisions for tweaks in magnet excitation, cryostat assembly, etc. were discussed in fairly general terms. This note is not intended to be a final specification for the HCX quadrupoles to be constructed or to be the sole basis on which competing magnet designs will be compared. Other aspects such as prototype test results, economic considerations, and attractiveness within the context of ultimate applications in multi-beam drivers for heavy-ion fusion (i.e, compatibility with magnet arrays, etc.) will all factor in the selection of the appropriate design option. This note is organized as follows. Magnet characterizations including geometric and conductor parameters are given in Sec II. Performance parameters to be reported that quantify the magnet properties are outlined in Sec III. Supporting information is included in appendices. A reference coordinate system to be employed in field calculations is defined ...
Date: February 22, 2001
Creator: Lund, Steven M.; Sabbi, GianLuca & Seidl, Peter
Partner: UNT Libraries Government Documents Department

Emittance growth for the thermalization of space-charged nonuniformities

Description: Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. In general, injected particle distributions with systematic charge nonuniformities are not equilibria of the focusing channel and launch a broad spectrum of collective modes. These modes can phase-mix and have nonlinear wave-wave interactions which, at high space-charge intensities, results in a relaxation to a more thermal-like distribution characterized by a uniform density profile. This thermalization can transfer self-field energy from the initial space-charge nonuniformity to the local particle temperature, thereby increasing beam phase space area (emittance growth). In this paper, we employ a simple kinetic model of a continuous focusing channel and build on previous work that applied system energy and charge conservation to quantify emittance growth associated with the collective thermalization of an initial azimuthally symmetric, rms matched beam with a radial density profile that is hollowed or peaked. This emittance growth is shown to be surprisingly modest even for high beam intensities with significant radial structure in the initial density profile.
Date: March 1, 2001
Creator: Lund, Steven M.; Barnard, John J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Analytical study of envelope modes for a fully depressed beam in solenoidal and quadrupole periodic transport channels

Description: We present an analysis of envelope perturbations evolving in the limit of a fully space-charge depressed (zero emittance) beam in periodic, thin-lens focusing channels. Both periodic solenoidal and FODO quadrupole focusing channels are analyzed. The phase advance and growth rate of normal mode perturbations are analytically calculated as a function of the undepressed particle phase advance to characterize the evolution of envelope perturbations.
Date: May 2003
Creator: Bukh, Boris & Lund, Steven M.
Partner: UNT Libraries Government Documents Department

Efficient computation of matched solutions of the KV envelopeequation for periodic focusing lattices

Description: A new iterative method is developed to numerically calculate the periodic, matched beam envelope solution of the coupled Kapchinskij-Vladimirskij (KV) equations describing the transverse evolution of a beam in a periodic, linear focusing lattice of arbitrary complexity. Implementation of the method is straightforward. It is highly convergent and can be applied to all usual parameterizations of the matched envelope solutions. The method is applicable to all classes of linear focusing lattices without skew couplings, and also applies to parameters where the matched beam envelope is strongly unstable. Example applications are presented for periodic solenoidal and quadrupole focusing lattices. Convergence properties are summarized over a wide range of system parameters.
Date: January 3, 2006
Creator: Lund, Steven M.; Chilton, Sven H. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

Transverse centroid oscillations in solenoidially focused beam transport lattices

Description: Linear equations of motion are derived that describe small-amplitude centroid oscillations induced by displacement and rotational misalignments of the focusing solenoids in the transport lattice, dipole steering elements, and initial centroid offset errors. These equations are analyzed in a local rotating Larmor frame to derive complex-variable"alignment functions" and"bending functions" that efficiently describe the characteristics of the centroid oscillations induced by mechanical misalignments of the solenoids and dipole steering elements. The alignment and bending functions depend only on properties of the ideal lattice in the absence of errors and steering and have associated expansion amplitudes set by the misalignments and steering fields. Applications of this formulation are presented for statistical analysis of centroid deviations, calculation of actual lattice misalignments from centroid measurements, and optimal beam steering.
Date: August 1, 2008
Creator: Lund, Steven M.; Wootton, Christopher J. & Lee, Edward P.
Partner: UNT Libraries Government Documents Department

A core-particle model for periodically focused ion beams withintense space-charge

Description: A core-particle model is derived to analyze transverse orbits of test particles evolving in the presence of a core ion beam that has uniform density within an elliptical cross-section. The model can be applied to both quadrupole and solenoidal focused beams in periodic or aperiodic lattices. Efficient analytical descriptions of electrostatic space-charge fields external to the beam core are derived to simplify model equations. Image charge effects are analyzed for an elliptical beam centered in a round, conducting pipe to estimate model corrections resulting from image charge nonlinearities. Transformations are employed to remove coherent flutter motion associated with oscillations of the ion beam core due to rapidly varying, linear applied focusing forces. Diagnostics for particle trajectories, Poincare phase-space projections, and single-particle emittances based on these transformations better illustrate the effects of nonlinear forces acting on particles evolving outside the core. A numerical code has been written based on this model. Example applications illustrate model characteristics. The core-particle model described has recently been applied to identify physical processes leading to space-charge transport limits for an rms matched beam in a periodic quadrupole focusing channel. Further characteristics of these processes are presented here.
Date: August 28, 2006
Creator: Lund, Steven M.; Barnard, John J.; Bukh, Boris; Chawla, SurgreevR. & Chilton, Sven H.
Partner: UNT Libraries Government Documents Department

Survey of Collective Instabilities and Beam-Plasma Interactions in Intense Heavy Ion Beams

Description: This paper presents a survey of the present theoretical understanding based on advanced analytical and numerical studies of collective processes and beam-plasma interactions in intense heavy ion beams for applications to ion-beam-driven high energy density physics and heavy ion fusion. The topics include: discussion of the conditions for quiescent beam propagation over long distances; and the electrostatic Harris instability and the transverse electromagnetic Weibel instability in highly anisotropic, intense one-component ion beams. In the longitudinal drift compression and transverse compression 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 multispecies electromagnetic Weibel instability, and collective excitations in the presence of a solenoidal magnetic field. The effects of a velocity tilt on reducing two-stream instability growth rates are also discussed. Operating regimes are identified where the possible deleterious effects of collective processes on beam quality are minimized.
Date: June 19, 2008
Creator: Davidson, Ronald C.; Dorf, Mikhail A.; Kaganovich, Igor D.; Qin, Hong; Startsev, Edward A.; Rose, David V. et al.
Partner: UNT Libraries Government Documents Department

Simulations of beam emittance growth from the collectiverelaxation of space-charge nonuniformities

Description: Beams injected into a linear focusing channel typically have some degree of space-charge nonuniformity. For unbunched beams with high space-charge intensity propagating in linear focusing channels, Debye screening of self-field interactions tends to make the transverse density profile flat. An injected particle distribution with a large systematic charge nonuniformity will generally be far from an equilibrium of the focusing channel and the initial condition will launch a broad spectrum of collective modes. These modes can phase-mix and experience nonlinear interactions which result in an effective relaxation to a more thermal-equilibrium-like distribution characterized by a uniform density profile. This relaxation transfers self-field energy from the initial space-charge nonuniformity to the local particle temperature, thereby increasing beam phase space area (emittance growth). Here they employ two-dimensional electrostatic particle in cell (PIC) simulations to investigate the effects of initial transverse space-charge nonuniformities on the equality of beams with high space-charge intensity propagating in a continuous focusing channel. Results are compared to theoretical bounds of emittance growth developed in previous studies. Consistent with earlier theory, it is found that a high degree of initial distribution nonuniformity can be tolerated with only modest emittance growth and that beam control can be maintained. The simulations also provide information on the rate of relaxation and characteristic levels of fluctuations in the relaxed states. This research suggests that a surprising degree of initial space-charge nonuniformity can be tolerated in practical intense beam experiments.
Date: May 1, 2004
Creator: Lund, Steven M.; Grote, David P. & Davidson, Ronald C.
Partner: UNT Libraries Government Documents Department

Beam Energy Scaling on Ion-Induced Electron Yield from K+ Impacton Stainless Steel

Description: Electron clouds limit the performance of many major accelerators. Significant quantities of electrons result when halo ions are lost to beam tubes, generating gas which can be ionized and ion-induced electrons that can multiply and accumulate, causing degradation or loss of the ion beam. In order to understand the physical mechanisms of ion-induced electron production, experiments studied the impact of 50 to 400 keV K{sup +} ions on stainless steel surfaces near grazing incidence, using the 500 kilovolts Ion Source Test Stand (STS-500) at LLNL. The experimental electron yield scales with the electronic component (dE{sub e}/dx) of the stopping power. A theoretical model is developed, using TRIM code to evaluate dE{sub e}/dx at several depths in the target, to estimate the electron yield, which is compared with the experimental results.
Date: January 1, 2006
Creator: Kireeff Covo, Michel; Molvik, Arthur; Friedman, Alex; Westenskow,Glen; Barnard, John J.; Cohen, Ronald et al.
Partner: UNT Libraries Government Documents Department