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Computational Accelerator Physics
Yasuo Fukui: A Muon Cooling Ring with Lithium Lenses
  For the final muon cooling ring for a muon collider, a Higgs Factory, we designed a muon cooling ring with Lithium lens inserts. A normalized transverse equilibrium emittance around 0.3 mm*rad was obtained in a tracking simulation with hard edged magnet elements. The cooling capability of the muon ring with realistic magnet elements is also discussed.
Courtlandt Bohn: Collective Modes and Colored Noise as Beam-Halo Amplifiers
  We demonstrate how collective modes and colored noise conspire to produce beam halo with much larger amplitude than could be generated by either phenomenon separately. Collective modes are inherent to nonequilibrium beams. Colored noise arises from unavoidable machine transitions and/or errors and influences the internal space-charge force. Using lowest-order radial eigenmodes calculated self-consistently for a direct-current, cylindrically symmetric, warm-fluid Kapchinskij-Vladimirskij equilibrium, we compare and contrast halo dynamics involving collective modes against that involving a pure root-mean-square mismatch. The difference is dramatic; collective modes are centrally important to the dynamics of halo formation in real beams.
Michael Zeitlin: Complex Dynamics in Accelerator/Plasma Physics: Localized States, Zoo of Patterns, Control, Part I. Kinetic models: BBGKY, Vlasov-Maxwell/Poisson and all that
 i) An efficient approach is proposed for analysis of complex dynamics inaccelerator/plasma physics models based onthe full hierarchy of kinetic equations (BBGKY-like).Our calculations are based on variational and multiresolution approachesin the basis of polynomial algebrasof various localized bases.We construct the representation for hierarchy of distributionfunctions and dynamical variables via the exact multiscale decompositionin high-localizednonlinear eigenmodes. The corresponding cut-off of infinite hierarchy,reductions to finite dimensional subsets and accuracy of calculations arebased on the new multiscale metric structure of the whole Fock-like spaceof alldistribution functions. We demonstrate the existence ofenergy confinement/fusion in the small regions of the phase space.ii) A fast and efficient numerical-analytical approachis proposed for modeling the complex nonlinear collective behaviourin the various forms of the generalized Vlasov-Maxwell/Poisson systems (e.g., propagation of the intense charged particle beams).We compare our approach with previous ones, e.g.nonlinear delta F simulation and PIC modeling and demonstrateits advantages. As the particular limiting cases of our construction we have standard KV/Klimontovich distributions.The solutions are represented via the multiscale decomposition innonlinear high-localized eigenmodes, whichcorresponds to the full multiresolution expansion in all underlying hiddenscales. In contrast with different approaches wedo not use perturbation technique or linearization procedures.Numerical modeling shows the creation of different internalstructures from localized modes, which are related tostable/unstable type of behaviour and the correspondingpatterns (waveletons) formation. Reduced algebraical structure provides the pure algebraical control of stability/unstability scenario.Varioustypes of of patterns (chaotic and localized) are controlled i
Michael Zeitlin: Complex Dynamics in Accelerator/Plasma Physics: Localized States, Zoo of Patterns, Control, Part II. RMS Envelope Dynamics, Beam-Beam Interaction Models etc
i) We consider a few reductions from nonlinear Vlasov-like equations torms/rate equations (nonlinear models for dynamics of high-brightnessbeams) for second moments related quantities (with or withoutadditional equations or/and constraints for energy and emittance). Our analysis is based on variational--wavelet approach torational (in dynamical variables) approximations with possible related constraint equations. It allows to control contributions to spectrum fromeach scale ofunderlying multiscales and represent solutions via multiscale nonlinear eigenmodes expansions. Our approach provides the best convergenceproperties of the corresponding exact representations and does not useperturbations or/and linearization procedures. Reduced algebraicalstructure provides the pure algebraical control of stability/unstabilityscenario and appearance of different type of behaviour (chaotic vs.localized patterns) in space of parameters.ii)We consider modeling for strong-strong beam-beam interactions beyondthe standard perturbative methods.In our approach, based on projection methods and efficient functionalspace decomposition in localized bases with control of convergence for anonlinear and/or singular integral operators (Hilbert transform) based models, the full possible spectrum, partly discovered before(discrete coherent and possible incoherent oscillations),appears as the result ofthe exact multiresolution/multiscale fast convergent decomposition in the bases of high-localized exact nonlinear modes.The constructed solutions representthe full multiscale spectrum with contributions from all internal hiddenmodesfrom the slow to fast oscillating eigenmodes.The underlyingmethods provide some sort of the algebraical control of the spectrum andthe type of dynamical behaviour.
Bradley  Shadwick: Thermal Effects in Intense Laser-Plasma Interactions
Intense laser-plasma interaction experiments access a unique physical regime wherein the plasma electrons experience highly relativistic motion while the temperature (or more correctly, momentum spread) is quite small and the plasma is effectively collisionless. To study this regime, we have recently developed a "warm" fluid model where the width of the distribution function is treated asymptotically. Unlike the collisional case, in this regime the plasma is not in local thermodynamic equilibrium and the pressure tensor can be strongly anisotropic. Using this model, we examine various experimentally relevantconfigurations, comparing the results of our new model with results of the traditional cold fluid approximation. A case of particular interest which we study in detail is that of a short-pulse pulse propagating in a laser wakefield accelerator, where the initial plasma temperature is on the order of 20eV. Within the quasi-static approximation, the warm-fluid equations for the momentum spread can be solved analytically. We find there is no significant heating of the plasma and that the anisotropy of both the pressure tensor and the distribution function is large. We compare these analytical results to numerical results fromboth warm and cold fluid models.

Xiangyun Chang: Compensation for bunch emittance in a magnetization and space-charge dominated beam
  In order to obtain sufficient cooling rates for the Relativistic Heavy Ion Collider (RHIC) electron cooling, a bunched beam with high bunch charge, high repetition frequency and high energy is required and it is necessary to use a “magnetized” beam, i.e., an electron beam with non-negligible angular momentum. Applying a longitudinal solenoid field on the cathode can generate such a beam, which rotates around its longitudinal axis in a field-free region. This paper suggests how a magnetized beam can be accelerated and transported from a RF photocathode electron gun to the cooling section without significantly increasing its emittance. The evolution of longitudinal slices of the beam under a combination of space charge, magnetization and energy spread is investigated, using paraxial envelope equations and numerical simulations. We find that we must modify the traditional method of compensating for emittance as used for normal non-magnetized beam with space charge to account for magnetization. The results of computer simulations of successful compensation are presented.Alternately, we show an electron bunch density distribution for which all slices propagate uniformly and which does not require emittance compensation
Xiangyun Chang: Design considerations for low field short photo-injected RF electron gun with high charge electron bunch followed by linac
  The RF field and space charge effect in a low field RF gun is given. The cell lengths are modified to have maximum accelerating efficiency. The modification introduces an extra RF field slice emittance. The phase space evolution of the following emittance compensation system is presented taking into account the chromatic effect. The emittance compensation mechanics for RF field and chromatic effect induced emittance is similar to that of compensating the space charge induced emittance. But the requirements are different to have best compensation for them. The beam waist is far in front of linac entrance to have best compensation for the RF field and chromatic effect induced emittance. For low field RF gun with high charge electron bunch this compensation is more important.
Dimitre Dimitrov: The IONPACK library of Ionization Algorithms for PIC Codes
  Impact and tunneling ionization physics play key roles in both beam-drivenand laser-driven plasma accelerator concepts [1,2,3]. The portable Clibrary IONPACK is being developed to encapsulate ionization algorithms,for use by particle-in-cell (PIC) codes written in Fortran or C/C++.For example, IONPACK is being used with the parallel VORPAL [4] code.We will discuss the ionization algorithms and their implementation, aswell as how IONPACK is linked with VORPAL. We will review previousvalidation of the algorithms via code benchmarking and comparisonwith experiment, and we will present recent VORPAL simulations ofrelevance to plasma-based particle accelerators.

[1] D.L. Bruhwiler et al., Phys. Rev. ST-AB 4, 101302 (2001).[2] D.L. Bruhwiler et al., Phys. Plasmas 10 (2003), p. 2022.[3] D.L. Bruhwiler et al., PAC Proc. (2003), p. 734.[4] C. Nieter and J.R. Cary, J. Comp. Phys. 196 (2004), p. 448.

Gwenael Fubiani: Studies of space charge effects in ultrashort electron bunches
  Laser driven accelerators are capable of producing multi nC, multi MeV electron beams with transverse and longitudinal sizes on the order of microns. We present theoretical studies of the transport of such electron bunches in vacuum. The effects of space charge forces and energy spread on longitudinal and transverse bunch properties are evaluated for various bunch lengths, energies and amount of charge. We provide a comprehensive summary and limitations of analytical methods available for the simulation of the wide variety of beam distributions generated by plasma-based accelerators: (i) high charges (~1 nC), large energy spreads (100 %) compact electron bunches produced by the self-modulated laser-wakefield-accelerator, e.g., where the laser pulse size is many times the plasma wavelength. (ii) lower charges (~ 10 pC), small energy spreads (~ 2-5 %) compact electron bunches produced by the colliding pulse laser-wakefield-accelerator regime where two counterpropagationg laser pulses (the drive pulse is resonnant) are used to inject electrons into the wakefield. The various methods discussed are respectively: envelope equations, semi-analytical approach using ellipsoidal shells, poisson solver and a 3-D point-to-point interaction code.
Min Hur: Averaged-PIC simulation of laser-plasma interaction: pulse amplification by Raman backscattering and wake field generation by two counterpropagating lasers.
  An average particle-in-cell code (aPIC), based on an eikonal formalism hasbeen developed [1] to simulate laser-plasma interactions.The dominant laser modes are described by their wave envelopes, avoidingthe need to resolve the laser frequency.Appropriately time-averaged equations describe the particle motion. Thecode is fully kinetic, and thus includes critical physics such as particletrapping and Landau damping.The code has been initially employed to study Raman backscatteramplification [2,3] of ultra-intense pulses, where the dominant forces onthe particles are the ponderomotive force of the beat-wave and theself-consistent plasma electric field. The code agrees well, in theappropriate regimes, with the results from three-wave equations andparticle-in-cell (PIC) simulations (XOOPIC).The effects of plasma temperature on RBS amplification are studied. Ramanbackscatter amplification is proposed as a successor technology to chirpedpulse amplification. If realized, it should have important applications inhigh-energy density science. The low-noise implementation of a movingwindow with an incoming radiation pulse and finite plasma temperaturerequires some numerical subtleties which will be discussed.1. M.S. Hur, et al, submitted for publication2. V.M. Malkin, G. Shvets, and N.J. Fisch, Phys. Plasmas 7, 2232 (2000).3. G. Shvets, N.J. Fisch, A. Pukhov, and J. Meyer-ter-Vehn, Phys. Rev. E60, 2218 (1999).
Amit Kesar: Time and frequency domain models for Smith-Purcell Radiation from a two dimensional charge moving above a short grating
  The Smith-Purcell radiation (SPR) formed by an electron bunch traveling above a grating is important for determining bunch characteristics as well as a coherent source in the THz regime. The SPR from a two dimensional bunch moving above a finite length grating is studied theoretically by two independent models: a finite-difference time-domain (FDTD) simulation and an electric-field integral equation (EFIE) method. A total-field/scattered-field approach was used in the FDTD model to simulate the bunch free-space fields incident on the grating. A numerical example is presented by an ~18 MeV, 50 pC/mm, 200 micron bunch traveling 0.6 mm above a 2.1 mm period echelle grating. Good agreement is obtained between the two models. It is shown that the EFIE method provides the same results as the van den Berg model for an infinitely long, periodic grating. Applications and limitations of these models are discussed.
Chiping Chen: Center-of-Mass Dynamics and Space-Charge Limit of a Finite-Size Bunched Beam
  We derive the space-charge limit for a train of periodic finite-size charged bunches which are slightly displaced from the axis of a circular, perfectly conducting pipe. The general calculation assumes that the bunches, while periodic, may have arbitrary radial and longitudinal density distributions with respect to the beam axis. We present results for a few specific distributions, as well as the limits of unbunched and single bunch beams. Finally, we show how the bunched beam space-charge limit along with the radial rms envelope equation for a bunched beam is applied to predict operational limits of periodic permanent magnet (PPM) focusing klystrons that are being developed for the Next Linear Collider.