15c15 < % --- Subsection: Overview of Vacuum Chamber Studies --- > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Subsection: Overview of Vacuum Chamber Studies 17,47c17 < The buildup of high densities of low-energy electrons produced by the intense synchrotron radiation in < electron and positron storage rings has been under active study since it was identified as a limiting < factor in the operation of the KEKB collider in the 1990s\citep{PRL75:1526,IPAC10:TUPEB014}. < Extensive modeling efforts were developed < for the Large Hadron Collider as well~\citep{ECLOUD02:47to55,LHC:180}, leading to a series of ECLOUD workshops, < the most recent of which was held < at Cornell in 2010~\citep{ECLOUD10PROC}. Indeed, in retrospect, a number of puzzling resonant instability phenomena previously observed < have since been associated with the buildup of such electron clouds. Phenomena related to electron cloud < buildup have been reported at the Advanced Photon Source at ANL~\citep{PRSTAB6:034402}, < the Spallation Neutron Source at ORNL~\citep{EPAC08:TUPP043}, the Relativistic Hadron Collider at BNL~\citep{PRSTAB11:041002}, < the Proton Storage Ring at LANL~\citep{PAC03:ROAB003}, the \mbox{DA$\Phi$NE} $\Phi$-factory at the INFN-LNF in < Frascati~\citep{PAC05:FPAP001}, < PEP-II at SLAC~\citep{MBI97:170,PAC01:TPPH100}, the Tevatron Main Injector at FNAL~\citep{PAC07:THPAN117}, < and the CERN Proton Synchrotron~\citep{PRSTAB5:094401} and < Super Proton Synchrotron~\citep{BEAM07:202to208}. < The enhanced understanding of < electron cloud physics has identified the phenomenon as a primary limiting factor in the operation of < damping rings for future $e^+e^-$ linear colliders~\citep{PAC03:WOAA006,EPAC08:MOPP050,PAC05:ROPB001}. < The determining physical phenomena < governing the characteristics of the clouds are the generation of photoelectrons, their trajectories in the < transient and ambient electric and magnetic fields, and the secondary yield properties of the vacuum chamber. < Thus the RF structure of the beams, their intensities, the shape and dimensions of the vacuum chambers, and < especially the surface physics properties of those chambers affecting the production of electrons by < incident electrons are important factors in the rates of buildup and decay. A variety of mitigation < techniques have been experimentally studied and implemented in operating beamlines, such as the copper grids < in the LHC dipoles, the TiN coating in the PEP-II ring~\citep{NIMA551:187to199} and at the Spallation Neutron Source. The \cesrta\ < program includes the most extensive single project for the study of mitigation techniques to date, including < TiN, amorphous carbon, < diamond-like carbon coatings on aluminum chambers, grooves in copper chambers, clearing electrodes, and more. < Combined with an extensive array of retarding-field analyzers and shielded-pickup detectors, much has < been learned about the physics governing the local buildup of electron clouds. --- > The buildup of high densities of low-energy electrons produced by the intense synchrotron radiation in electron and positron storage rings has been under active study since it was identified in the mid-90's in the KEK Photon Factory (PF) when operated with a positron beam \cite{izawa-PRL95}. While this phenomenon did not present an operational limitation at the PF under nominal conditions, the observation raised immediate concerns for both B Factories, then under design, and triggered significant simulation efforts \citep{PRL75:1526} aimed at quantifying the phenomenon and designing mitigation techniques. Several years later, as the luminosity performance in the B Factories was pushed towards its specified goal, the electron cloud became at some point the most significant limitation. Mitigating this effect at both B Factories then became essential to reach, and then exceed, the design performance \cite{fukuma-BDNL48}. 48a19 > Almost concurrently with the above-mentioned developments at the PF and the B Factories, concerns arose in 1995-96, based on prior experience at the ISR, that electrons might spoil the LHC vacuum \cite{grobner-PAC97}. Early 1997 calculations showed that the LHC would be subject to an ECE \cite{zimm-LHCPR95}, chiefly because the beam emits copious synchrotron radiation upon traversing the dipole bending magnets, in analogy with \epem\ storage rings. Indeed, the LHC is the first proton storage ring ever built in which synchrotron radiation is significant: although the critical photon energy is only $\sim44$ eV at 7 TeV beam energy (as opposed to several keV's in typical \epem\ storage rings), this value is well above the work function of the chamber metal, hence photoemission inside the chamber is unavoidable. A straightforward calculation yields an estimate of 0.4 photons emitted per proton per dipole magnet traversal, also at 7 TeV beam energy. Although $\sim50\%$ of these photons have energies below the work function of the metal, the remaining 50\% lead to a substantial number of photoelectrons. Further calculations \cite{zimm-LHCPR95,furman-LHCPR180}, including the effects of secondary electron emission, quickly revealed the possibility of a substantial ECE. In the case of the LHC, the primary concern from the ECE is the power deposited by the electrons on the beam screen as they rattle around the chamber under the action of the beam; this power must be dissipated by the cryogenic system if the LHC superconducting magnets are to work according to specifications. Since the cryogenic system was designed before the discovery of the ECE's in the LHC, a significant ``crash program'' was launched in 1997 to better estimate the power deposition, to identify the conditions under which the cooling capacity might be exceeded, and to devise mitigation mechanisms if necessary \cite{ruggiero-frascati97}. As part of this effort, the ECE has been experimentally studied at the SPS and the PS at the high beam intensities required for nominal LHC operation \cite{EC-LHC-website} (recent experience at the LHC has confirmed the expectation of a significant ECE, even though the beam energy is presently only 3.5 TeV \cite{jimenez-chamonix2011}). This crash program at the LHC was almost certainly the single most comprehensive effort to understand the electron cloud in a hadron machine, and was comparable in scope to the present program at CESRTA for an \epem\ machine. 50c21,33 < % --- Subsection: Simulation Program --- > The above-mentioned ECE's are related to previously observed electron-proton dynamical effects such as beam-induced multipacting (BIM), first observed at the CERN proton storage ring ISR \cite{grobner-HEACC77} when operated with bunched beams. Closely related to BIM is trailing-edge multipacting observed at the LANL spallation neutron source PSR \cite{macek-PSR-status-ECLOUD04}, where electron detectors register a large signal during the passage of the tail of the bunch even for stable beams. All ECEs in \epem\ as well as in hadron storage rings have precursors in the e-p instabilities for bunched and unbunched beams first seen at BINP in the mid-60Õs \cite{dudnikov-PAC01-TPPH094}. > > The interest generated by the observations at the PF published in 1995 triggered a series of dedicated workshops the most recent of which was held at Cornell in 2010~\citep{ECLOUD10PROC}. The similarities of the ECE's in \epem\ and hadron storage rings is evidenced by the simultaneous and comparable participation, since 1997, of both communities in these workshops. Phenomena related to electron cloud buildup have been reported (and in some cases been a performance-limiting factor) at the Advanced Photon Source at ANL~\citep{PRSTAB6:034402}, BEPC \cite{guo-PAC97}, the Spallation Neutron Source at ORNL~\citep{EPAC08:TUPP043}, the Relativistic Hadron Collider at BNL~\citep{PRSTAB11:041002}, the Proton Storage Ring at LANL~\citep{PAC03:ROAB003}, the \mbox{DA$\Phi$NE} $\Phi$-factory at the INFN-LNF in Frascati~\citep{PAC05:FPAP001}, PEP-II at SLAC~\citep{MBI97:170,PAC01:TPPH100}, the Tevatron Main Injector at FNAL~\citep{PAC07:THPAN117}, the CERN Proton Synchrotron~\citep{PRSTAB5:094401} and Super Proton Synchrotron~\citep{BEAM07:202to208} and the LHC \cite{jimenez-chamonix2011}. > > The enhanced understanding of electron cloud physics has identified the phenomenon as a primary potential limiting factor in the operation of damping rings for future \epem\ linear colliders~\citep{PAC03:WOAA006,EPAC08:MOPP050,PAC05:ROPB001}. The determining physical phenomena governing the characteristics of the clouds are the generation of photoelectrons, their trajectories in the > transient and ambient electric and magnetic fields, and the secondary electron yield properties of the vacuum chamber. Thus the RF structure of the beams, their intensities, the shape and dimensions of the vacuum chambers, and especially the surface physics properties of those chambers affect the production of electrons by incident electrons, and are therefore important factors in the rates of buildup and decay. A variety of mitigation techniques have been experimentally studied and implemented in operating beamlines, such as grooves on the chamber surface of the LHC arcs, the TiN coating in the PEP-II ring~\citep{NIMA551:187to199} and at the Spallation Neutron Source, and weak solenoidal magnetic fields at both B Factories \cite{kulikov-PAC01-TPPH100,funakoshi-PAC01-RPPH131}. > > The \cesrta\ program is almost certainly the single most extensive project for the study of mitigation techniques in \epem\ storage rings to date, including mitigation techniques based on low-emission coatings such as TiN, amorphous carbon and diamond-like carbon on aluminum chambers; grooves etched in copper chambers; clearing electrodes; and more. Combined with an extensive array of instrumentation and diagnostic tools such as retarding-field analyzers and shielded-pickup detectors, much has been learned to date about the physics governing the local buildup of electron clouds. > > In essentially all cases of practical interest, it is the secondary electron emission process that dominates the build-up of the electron cloud because this process leads to a compounding effect of the electron density under the action of successive bunches traversing the chamber: the more electrons are present in the chamber, the more electrons are generated upon striking the chamber walls. The CESRTA facility affords the unique and valuable possibility of studying the electron cloud formation and dissipation with a beam consisting of an almost arbitrary fill pattern and bunch intensity. This flexibility allows to tease out the contributions to the electron cloud due to photoemission from secondary electron emission. Short bunch trains (say, fewer than 10 bunches) lead to an electron cloud dominated by photoemission, while long bunch trains (say, more than 40) lead to an electron cloud dominated by secondary electron emission. As if this flexibility were not enough, CESRTA also allows the measurement of the electron cloud bunch by bunch, which provides another way to disentangle the two above-mentioned effects: the formation of the electron cloud at the beginning of the train is dominated by photoemission, while secondary emission dominates the formation towards the tail. In addition, an isolated ``witness bunch'' can be placed at varying distances from the end of the train, thus affording the possibility of studying the dissipation of the electron cloud as a function of time. > > > %%%%%%%%%%%%%%%%%%%%%%%%%%%%% --- Subsection: Simulation Program 54,57c37 < A broad-based program of developing, comparing and benchmarking electron cloud buildup simulation codes < was initiated in the \cesrta\ collaboration in 2008 and continues today. We have applied \cesrta\ input parameters < to the ECLOUD~\citep{ECLOUD04:143to152,PRSTAB5:121002}, CLOUDLAND~\citep{PRSTAB5:124402,KEK:INT2003:2}, < POSINST~\citep{MBI97:170,PRSTAB5:124404}, WARP/POSINST~\citep{PAC09:FR5RFP078} and PEHTS~\citep{PAC01:TPPH096} codes. --- > A broad-based program of developing, comparing and benchmarking electron cloud buildup simulation codes was initiated in the \cesrta\ collaboration in 2008 and continues today. We have used \cesrta\ parameters as input to the simulation codes ECLOUD~\citep{ECLOUD04:143to152,PRSTAB5:121002}, CLOUDLAND~\citep{PRSTAB5:124402,KEK:INT2003:2}, POSINST~\citep{MBI97:170,PRSTAB5:124404}, WARP/POSINST~\citep{PAC09:FR5RFP078} and PEHTS~\citep{PAC01:TPPH096}, and compared the results against measurements. By iterating this process, we are able to pin down parameters that are not well known and thereby make more reliable extrapolations to the future ILC damping rings. The main (indeed, the only) parameters that are not well known are those pertaining to the electronic surface properties, ie. photon reflectivity, photoemission and secondary electron emission. 58a39 > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 61,68c42 < Essential components of the codes are photoelectron < generation models, time-sliced calculations of macroparticle dynamics including beam kicks, the space charge force < from the cloud itself, and the Lorentz forces of ambient magnetic fields, the the model < describing the various components of the secondary yield. The ECLOUD and POSINST models use two-dimensional approximations < for the electric fields and have successfully reproduced a variety of coherent tune shift measurements, as well as < local RFA and shielded-pickup measurements. The CLOUDLAND~\citep{ECLOUD10:MOD05} and WARP/POSINST~\citep{PRSTAB14:041003} < codes have been used to model cloud buildup < in quadrupole, sextupole and wiggler magnets, providing information on the long-term trapping of electrons. --- > Essential components of the codes are photoelectron generation models, time-sliced calculations of macroparticle dynamics including beam kicks, the space charge force from the cloud itself, the Lorentz forces from ambient magnetic fields, and the models describing the various components of the secondary electron yield (SEY). The ECLOUD and POSINST models use two-dimensional approximations for the electric fields and have successfully reproduced a variety of coherent tune shift measurements, as well as local RFA and shielded-pickup measurements. These 2D codes are relatively fast, and are generally successful in predicting the features of the electron cloud in regions of the ring that are essentially 2D, namely field-free regions and long magnets, especially dipoles. The CLOUDLAND~\citep{ECLOUD10:MOD05} and WARP/POSINST~\citep{PRSTAB14:041003} codes are 3D and therefore far more computationally expensive, and have been used to model the electron cloud in essentially 3D regions such as quadrupole, sextupole and wiggler magnets, providing information on the long-term trapping of electrons. In addition, it should be pointed out the ECLOUD and POSINST are build-up codes, ie., in which the beam is a prescribed function of space and time, and therefore does not respond to the electron cloud. CLOUDLAND and WARP/POSINST, in addition to being 3D, have the option of describing the beam fully dynamically, so that the beam and the electron cloud respond to their mutual simultaneous influence. 69a44 > %%%%%%%%%%%%%%%%%%%%%%%%% 73,91c48 < The components of the photoelectron generation model are the azimuthal location distribution of photoelectrons produced on the < wall of the vacuum chamber, the angular function governing their initial momentum direction, and their kinetic energy spectrum. < The code benchmarking project revealed that reconciliation of the time structure of density buildup in the ECLOUD and POSINST < codes for \cesrta\ conditions required a modification of the ECLOUD model for the angular distribution to match that employed by POSINST. < The simple model implemented at present uses a single energy-independent value for the quantum efficiency, < ignores the incident photon energy spectrum and generates an ad-hoc photoelectron energy distribution which must be re-tuned for < each set of beam conditions under study. < < While the modeling for the coherent tune measurements proved to be rather insensitive to the < assumed photoelectron energy distribution (see Section~\ref{sssec:ec_dynamics.observations.tunes.improv}), the local RFA measurements, and especially the time-resolved shielded-pickup pulse < shapes have been shown to impose strict constraints on the photoelectron generation model. These results are described in < Sect.~\ref{ssec:ec_growth.ec_buildup_other.spu} below. < < On the other hand, the modeling of the coherent tune shift measurements < depends critically on the azimuthal location distribution of the produced photoelectrons. As the bunch current increases, the < contribution from the dipole regions begins to dominate the total tune shift, since the cloud electrons are trapped on field lines < near the vertical plane of the beam. If photon reflection were to be ignored in the model, this dominant contribution would not < contribute at all, since no photoelectrons would be produced on the top or bottom of the beampipe. The \cesrta\ cloud modeling < effort thus required a substantial effort to develop a photon transport model, as described in Section~\ref{sssec:ec_growth.ec_buildup.simulation.photon_transport}. --- > The components of the photoelectron generation model are the azimuthal location distribution of photoelectrons produced on the wall of the vacuum chamber, the angular function governing their initial momentum direction, and their kinetic energy spectrum. The code benchmarking project revealed that reconciliation of the time structure of density buildup in the ECLOUD and POSINST codes for \cesrta\ conditions required a modification of the ECLOUD model for the angular distribution to match that employed by POSINST. 93,94c50 < The quantum efficiency is an empirical parameter in the cloud buildup codes, which is adjusted to find the best fit to the measurements. The reasonableness of these empirically determined values may be checked by comparing with direct measurements of the quantum efficiency. Since the quantum efficiency is a function of the energy of the absorbed photons, we need to know the photon energy spectrum to do this. This spectrum is provided by the photon transport simulations described in < Section~\ref{sssec:ec_growth.ec_buildup.simulation.photon_transport}. --- > The simple model implemented at present uses a single energy-independent value for the quantum efficiency, ignores the incident photon energy spectrum and generates an ad-hoc photoelectron energy distribution which must be re-tuned for each set of beam conditions under study. 96,104c52 < In connection with studies of electron cloud effects for the LHC, direct measurements~\citep{PRSTAB2:063201} have been made of the quantum efficiency, and the photoelectron energy spectrum, for VUV photons in the energy range up to about 120 eV. The measurements were made for a variety of surfaces, including aluminum. To estimate the relative quantum efficiency above 120 eV, we refer to tables of the photoabsorption cross section as a function of energy, as given in the Atomic Data and Nuclear Data Tables\citep[p.34]{ADNDT27:1to144}. The relative quantum efficiency obtained in this way for an aluminum surface is shown in Fig.~\ref{fig.EC_GrowthMitigation.qeff}. < < \begin{figure} < \centering < \includegraphics[width=3in]{EC_GrowthMitigation/figures/qeff1.pdf} < \includegraphics[width=3in]{EC_GrowthMitigation/figures/qeff2.pdf} < \caption[Relative quantum efficiency for an aluminum surface vs. photon energy]{\label{fig.EC_GrowthMitigation.qeff} < Relative quantum efficiency for an aluminum surface vs. photon energy. Left: energy range up to 0.5~keV. Right: energy range up to 10~keV. The L- and K-edges are evident at energies near 0.1~keV and 2~keV, respectively.} < \end{figure} --- > While the modeling for the coherent tune measurements proved to be rather insensitive to the assumed photoelectron energy distribution (see Section~\ref{sssec:ec_dynamics.observations.tunes.improv}), the local RFA measurements, and especially the time-resolved shielded-pickup pulse shapes have been shown to impose strict constraints on the photoelectron generation model. These results are described in Sect.~\ref{ssec:ec_growth.ec_buildup_other.spu} below. 106c54 < The information from Fig.~\ref{fig.EC_GrowthMitigation.qeff} can be folded with the photon energy spectrum from the photon transport simulations to estimate how the quantum efficiency might be expected vary for different beam energies, and at different points in the {\cesrta} ring. This provides additional information that is useful in constraining the quantum efficiency when comparing with {\cesrta} data, and in extrapolating electron cloud effects to future positron rings. --- > On the other hand, the modeling of the coherent tune shift measurements depends critically on the angle that describes the azimuthal location of the produced photoelectrons along the perimeter of the chamber cross section. As the bunch current increases, the contribution from the dipole regions begins to dominate the total tune shift, since the cloud electrons are trapped along the magnetic field lines near the vertical plane of the beam. If photon reflection were to be ignored in the model, this dominant contribution would not contribute at all, since no photoelectrons would be produced on the top or bottom of the beampipe (they would only be generated at the horizontal ``edge'' of the chamber, where the photon fan strikes). The \cesrta\ cloud modeling effort thus required a substantial effort to develop a photon transport model, as described in Section~\ref{sssec:ec_growth.ec_buildup.simulation.photon_transport}. 108c56,57 < Absolute quantum efficiencies, averaged over a VUV photon energy spectrum, were also measured in Ref.~\citep{PRSTAB2:063201}. These results were quite sensitive to the surface material and conditioning, but were in the range of 4\% to 11\%. Quantum efficiency values found for the best fits to the {\cesrta} data are roughly similar to these numbers. --- > The quantum efficiency, or photoelectric yield, is an empirical parameter in the cloud buildup codes, which is adjusted to find the best fit to the measurements. The reasonableness of these empirically determined values may be checked by comparing with direct measurements of the quantum efficiency. Since the quantum efficiency is a function of the energy of the absorbed photons, we need to know the photon energy spectrum to do this. This spectrum is provided by the photon transport simulations described in > Section~\ref{sssec:ec_growth.ec_buildup.simulation.photon_transport}. 109a59,67 > In connection with studies of electron cloud effects for the LHC, direct measurements~\citep{PRSTAB2:063201} have been made of the quantum efficiency, and the photoelectron energy spectrum, for VUV photons in the energy range up to about 120 eV. The measurements were made for a variety of surfaces, including aluminum. To estimate the relative quantum efficiency above 120 eV, we refer to tables of the photoabsorption cross section as a function of energy, as given in the Atomic Data and Nuclear Data Tables\citep[p.34]{ADNDT27:1to144}. The relative quantum efficiency obtained in this way for an aluminum surface is shown in Fig.~\ref{fig.EC_GrowthMitigation.qeff}. > > \begin{figure} > \centering > \includegraphics[width=3in]{EC_GrowthMitigation/figures/qeff1.pdf} > \includegraphics[width=3in]{EC_GrowthMitigation/figures/qeff2.pdf} > \caption[Relative quantum efficiency for an aluminum surface vs. photon energy]{\label{fig.EC_GrowthMitigation.qeff} > Relative quantum efficiency for an aluminum surface vs. photon energy. Left: energy range up to 0.5~keV. Right: energy range up to 10~keV. The L- and K-edges are evident at energies near 0.1~keV and 2~keV, respectively.} > \end{figure} 110a69 > The information from Fig.~\ref{fig.EC_GrowthMitigation.qeff} can be folded with the photon energy spectrum from the photon transport simulations to estimate how the effective quantum efficiency might be expected vary for different beam energies, and at different points in the {\cesrta} ring. This provides additional information that is useful in constraining the quantum efficiency when comparing with {\cesrta} data, and in extrapolating electron cloud effects to future positron rings. 111a71,73 > Absolute quantum efficiencies, averaged over a VUV photon energy spectrum, were also measured in Ref.~\citep{PRSTAB2:063201}. These results were quite sensitive to the surface material and conditioning, but were in the range of 4\% to 11\%. Quantum efficiency values found for the best fits to the {\cesrta} data are roughly similar to these numbers. > > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 117c79 < The motivation for developing \texttt{SYNRAD3D} was to estimate the intensity and distribution of photon absorption sites, which are critical inputs to codes which model the growth of electron clouds. \texttt{SYNRAD3D} includes scattering from the vacuum chamber walls using X-ray data from an LBNL database~\citep{ADNDT54:181to342}. \texttt{SYNRAD3D} can handle any planar lattice and a wide variety of vacuum chamber profiles. --- > The motivation for developing \texttt{SYNRAD3D} was to estimate the intensity and distribution of photon absorption at various sites along the ring, which are critical inputs to codes which model the growth of electron clouds. \texttt{SYNRAD3D} includes scattering from the vacuum chamber walls using X-ray data from an LBNL database~\citep{ADNDT54:181to342}. \texttt{SYNRAD3D} can handle any planar lattice and a wide variety of vacuum chamber profiles. 119a82,83 > > %%%%%%%%%%%%%%%%%%%% 122c86,88 < \texttt{SYNRAD3D} uses Monte Carlo techniques to generate photons based on the standard synchrotron radiation formulas for dipoles, quadrupoles and wigglers, in the lattice of an accelerator. Any planar lattice can be handled. The lattice can be specified using Bmad, MAD, or XSIF formats. Photons are generated with respect to the particle beam's closed orbit, so the effect of variations in the orbit can be studied. In a linear accelerator lattice, since there is no closed orbit, the orbit is calculated from the user supplied initial orbit. The particle beam size is also taken into account when generating the photon starting positions. The emittance needed to calculate the beam size can be supplied by the user or is calculated from the standard radiation synchrotron radiation formulas. --- > \texttt{SYNRAD3D} uses Monte Carlo techniques to generate simulated photons based on the standard synchrotron radiation formulas for charged beam particles traversing dipoles, quadrupoles and wigglers, in the lattice of an accelerator. Any planar lattice can be handled. The lattice can be specified using Bmad, MAD, or XSIF formats. Photons are generated with respect to the particle beam's closed orbit, so the effect of variations in the orbit can be studied. In a linear accelerator lattice, since there is no closed orbit, the orbit is calculated from the user supplied initial orbit. The particle beam size is also taken into account when generating the photon starting positions. The emittance needed to calculate the beam size can be supplied by the user or is calculated from the standard radiation synchrotron radiation formulas. > > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 124c90 < Photons are tracked to the wall, where the probability of being scattered is determined by the angle of incidence and the energy of the photon. The model used to determine the scattering angle, which is taken from an X-ray database~\citep{ADNDT54:181to342}, is shown in Fig.~\ref{fig.EC_GrowthMitigation.Reflectivity_4nm}. This is for an aluminum vacuum chamber surface, but a model for a different surface could be used. --- > Simulated photons are tracked until they hit the wall, where the probability of being scattered is determined by their energy and angle of incidence. The model used to determine the scattering angle, which is taken from an X-ray database~\citep{ADNDT54:181to342}, is shown in Fig.~\ref{fig.EC_GrowthMitigation.Reflectivity_4nm} for the case of an aluminum vacuum chamber surface. A model for a different surface could also be used, as needed. 126,137c92 < For comparison, we also show in the figure the relative synchrotron radiation spectra for a 2~GeV beam in an arc dipole and a wiggler at < \cesrta. Also shown is a direct measurement~\citep{EUROTeV2005:013} of reflectivity at 5~$^{\circ}$ from an aluminum surface made at \texttt{DAPHNE}. < < Currently, only specular reflection is included, but diffuse scattering can also be simulated by altering the reflectivity model. < \begin{figure} < \centering < \includegraphics[width=6in]{EC_GrowthMitigation/figures/Reflectivity_4nm.pdf} < \caption{ \label{fig.EC_GrowthMitigation.Reflectivity_4nm} < Reflectivity model from LBNL X-ray database} < \end{figure} < \paragraph{Vacuum Chamber Model} < The vacuum chamber wall is characterized at a number of longitudinal positions by its cross-section. The cross section model is shown in Fig.~\ref{fig.EC_GrowthMitigation.Vcmodel}. As shown in the figure, antechambers can be included. A vacuum chamber wall cross-section may also be characterized using a piecewise linear outline. --- > For comparison, we also show in the figure the relative synchrotron radiation spectra for a 2~GeV beam in an arc dipole and a wiggler at \cesrta. Also shown is a direct measurement~\citep{EUROTeV2005:013} of the photon reflectivity at 5~$^{\circ}$ from an aluminum surface fabricated at \texttt{DAPHNE}. 138a94 > Currently, only specular reflection is included in \texttt{SYNRAD3D}, but diffuse scattering can also be simulated by altering the reflectivity model. 140,148c96,101 < In between the cross-sections, linear interpolation or triangular meshing can be used.Ê Linear interpolation is faster but is best suited for convex chamber shapes. < \begin{figure} < \centering < \includegraphics[width=6in]{EC_GrowthMitigation/figures/Vcmodel.pdf} < \caption{ \label{fig.EC_GrowthMitigation.Vcmodel} < Vacuum chamber model} < \end{figure} < \paragraph{Example 1: Photon Emission in a Dipole} < As the first example, we consider the \cesrta\ ring with a 5.3~GeV positron beam, and use \texttt{SYNRAD3D} to simulate photon emission only in the arc dipole at B12W. The vacuum chamber is a simple ellipse. The photons are generated only in the upstream end of this dipole but propagate downstream and can scatter. --- > \begin{figure} > \centering > \includegraphics[width=6in]{EC_GrowthMitigation/figures/Reflectivity_4nm.pdf} > \caption{\label{fig.EC_GrowthMitigation.Reflectivity_4nm} > Photon reflectivity model from LBNL X-ray database~\citep{ADNDT54:181to342}.} > \end{figure} 150c103,105 < In Fig.~\ref{fig.EC_GrowthMitigation.2d_trajects}, we show a collection of photon trajectories, projected onto the bend plane. Photons generated by the beam in B12W strike the B12W vacuum chamber a short distance downstream. Some are absorbed here, but most scatter and strike the vacuum chamber further downstream, in B13W. More are absorbed here, but many others scatter again. --- > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% > \paragraph{Vacuum Chamber Model} > The vacuum chamber wall is characterized by the chamber cross-section at a number of longitudinal positions along the ring. The cross section model is shown in Fig.~\ref{fig.EC_GrowthMitigation.Vcmodel}. As shown in the figure, antechambers can be included. A vacuum chamber wall cross-section may also be characterized using a piecewise linear outline. 151a107 > In between two consecutive longitudinal positions, linear interpolation or triangular meshing can be used. Linear interpolation is faster but is best suited for convex chamber shapes. 154,158c110,114 < \centering < \includegraphics[width=6in]{EC_GrowthMitigation/figures/2d_trajects} < \caption[Photon trajectories from B12W: projections onto bend plane.]{\label{fig.EC_GrowthMitigation.2d_trajects} < Photon trajectories from B12W: projections onto bend plane. The red dots at the lower right are the photon source (the radiating beam in a section of the dipole). Black lines are photon trajectories, and blue dots are photon absorption sites. The green lines in the lower right are the edges of the vacuum chamber in B12W; the red lines are the edges in a straight section, and the green lines on the left are the edges of the vacuum chamber in the next dipole, B13W. The geometry has been distorted for purposes of illustration.} < \end{figure} --- > \centering > \includegraphics[width=6in]{EC_GrowthMitigation/figures/Vcmodel.pdf} > \caption{ \label{fig.EC_GrowthMitigation.Vcmodel} > Vacuum chamber model} > \end{figure} 160,179c116,118 < \begin{figure} < \centering < \includegraphics[width=6.5in]{EC_GrowthMitigation/figures/3d_trajects} < \caption[Photon trajectories from B12W in three dimensions.]{ \label{fig.EC_GrowthMitigation.3d_trajects} < Photon trajectories from B12W in three dimensions. The photon source is on the right. Black lines are trajectories, and blue dots are photon absorption sites. The transverse geometry has been distorted from an ellipse to a circle, and the longitudinal dimension has been rectified and divided by 10, for purposes of illustration.} < \end{figure} < These photon trajectories in three dimensions are shown in Fig.~\ref{fig.EC_GrowthMitigation.3d_trajects}. Photons from the source (on the right) propagate and strike the vacuum chamber. Blue dots represent absorption sites. For this simple example, in which the photon source is localized longitudinally, the absorption site locations tend to be clumped in several clusters (at the location of downstream dipoles), with decreasing intensity as we get further from the source. < \begin{figure} < \centering < \includegraphics[width=3in]{EC_GrowthMitigation/figures/Photon_reflections} < \includegraphics[width=3in]{EC_GrowthMitigation/figures/Photon_energy} < \caption[Reflection distribution (left) and energy distribution (right)]{ \label{fig.EC_GrowthMitigation.Phot_refl_ener} < Reflection distribution (left) and energy distribution (right). The mean number of reflections is 5.1} < \end{figure} < \begin{figure} < \centering < \includegraphics[width=5.8in]{EC_GrowthMitigation/figures/3d_photon_position} < \caption{\label{fig.EC_GrowthMitigation.3d_phot_pos} < Distribution of photon absorption sites around the vacuum chamber perimeter} < \end{figure} --- > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% > %%%%%%%%%%%%%%% Miguel has read up to this point %%%%%%%%%%%%%%%%%%%%%% > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 181c120,122 < Other features of the photon scattering and absorption process are shown in Fig.~\ref{fig.EC_GrowthMitigation.Phot_refl_ener} and Fig.~\ref{fig.EC_GrowthMitigation.3d_phot_pos}. --- > %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% > \paragraph{Example 1: Photon Emission in a Dipole} > As the first example, we consider the \cesrta\ ring with a 5.3~GeV positron beam, and use \texttt{SYNRAD3D} to simulate photon emission only in the arc dipole at B12W. The vacuum chamber is a simple ellipse. The photons are generated only in the upstream end of this dipole but propagate downstream and can scatter. 183,192c124,166 < \begin{figure} < \centering < \includegraphics[width=6in]{EC_GrowthMitigation/figures/photon_plot_sfinal} < \caption[Distribution of photon absorption sites vs. longitudinal position]{\label{fig.EC_GrowthMitigation.phot_plot_s} < Distribution of photon absorption sites vs. longitudinal position, for different magnetic environments. The origin for the longitudinal coordinate is the center of the L0 straight section. The ring circumference is about 760~m.} < \end{figure} < \begin{figure} < \centering < \includegraphics[width=6in]{EC_GrowthMitigation/figures/photon_plot_perimeter} < \caption[Distribution of photon absorption sites vs. scaled perimeter along the vacuum chamber]{\label{fig.EC_GrowthMitigation.phot_plot_perim} --- > In Fig.~\ref{fig.EC_GrowthMitigation.2d_trajects}, we show a collection of photon trajectories, projected onto the bend plane. Photons generated by the beam in B12W strike the B12W vacuum chamber a short distance downstream. Some are absorbed here, but most scatter and strike the vacuum chamber further downstream, in B13W. More are absorbed here, but many others scatter again. > > > \begin{figure} > \centering > \includegraphics[width=6in]{EC_GrowthMitigation/figures/2d_trajects} > \caption[Photon trajectories from B12W: projections onto bend plane.]{\label{fig.EC_GrowthMitigation.2d_trajects} > Photon trajectories from B12W: projections onto bend plane. The red dots at the lower right are the photon source (the radiating beam in a section of the dipole). Black lines are photon trajectories, and blue dots are photon absorption sites. The green lines in the lower right are the edges of the vacuum chamber in B12W; the red lines are the edges in a straight section, and the green lines on the left are the edges of the vacuum chamber in the next dipole, B13W. The geometry has been distorted for purposes of illustration.} > \end{figure} > > \begin{figure} > \centering > \includegraphics[width=6.5in]{EC_GrowthMitigation/figures/3d_trajects} > \caption[Photon trajectories from B12W in three dimensions.]{ \label{fig.EC_GrowthMitigation.3d_trajects} > Photon trajectories from B12W in three dimensions. The photon source is on the right. Black lines are trajectories, and blue dots are photon absorption sites. The transverse geometry has been distorted from an ellipse to a circle, and the longitudinal dimension has been rectified and divided by 10, for purposes of illustration.} > \end{figure} > These photon trajectories in three dimensions are shown in Fig.~\ref{fig.EC_GrowthMitigation.3d_trajects}. Photons from the source (on the right) propagate and strike the vacuum chamber. Blue dots represent absorption sites. For this simple example, in which the photon source is localized longitudinally, the absorption site locations tend to be clumped in several clusters (at the location of downstream dipoles), with decreasing intensity as we get further from the source. > \begin{figure} > \centering > \includegraphics[width=3in]{EC_GrowthMitigation/figures/Photon_reflections} > \includegraphics[width=3in]{EC_GrowthMitigation/figures/Photon_energy} > \caption[Reflection distribution (left) and energy distribution (right)]{ \label{fig.EC_GrowthMitigation.Phot_refl_ener} > Reflection distribution (left) and energy distribution (right). The mean number of reflections is 5.1} > \end{figure} > \begin{figure} > \centering > \includegraphics[width=5.8in]{EC_GrowthMitigation/figures/3d_photon_position} > \caption{\label{fig.EC_GrowthMitigation.3d_phot_pos} > Distribution of photon absorption sites around the vacuum chamber perimeter} > \end{figure} > > Other features of the photon scattering and absorption process are shown in Fig.~\ref{fig.EC_GrowthMitigation.Phot_refl_ener} and Fig.~\ref{fig.EC_GrowthMitigation.3d_phot_pos}. > > \begin{figure} > \centering > \includegraphics[width=6in]{EC_GrowthMitigation/figures/photon_plot_sfinal} > \caption[Distribution of photon absorption sites vs. longitudinal position]{\label{fig.EC_GrowthMitigation.phot_plot_s} > Distribution of photon absorption sites vs. longitudinal position, for different magnetic environments. The origin for the longitudinal coordinate is the center of the L0 straight section. The ring circumference is about 760~m.} > \end{figure} > \begin{figure} > \centering > \includegraphics[width=6in]{EC_GrowthMitigation/figures/photon_plot_perimeter} > \caption[Distribution of photon absorption sites vs. scaled perimeter along the vacuum chamber]{\label{fig.EC_GrowthMitigation.phot_plot_perim} 194,195c168,169 < \end{figure} < In Fig.~\ref{fig.EC_GrowthMitigation.Phot_refl_ener}(left), a histogram of the number of photons, vs. the number of reflections, is presented. Many photons suffer no reflections, that is, they are absorbed as soon as they hit the vacuum chamber, but most are reflected several times before being absorbed. The mean number of reflections is 5.4. --- > \end{figure} > In Fig.~\ref{fig.EC_GrowthMitigation.Phot_refl_ener}(left), a histogram of the number of photons, vs. the number of reflections, is presented. Many photons suffer no reflections, that is, they are absorbed as soon as they hit the vacuum chamber, but most are reflected several times before being absorbed. The mean number of reflections is 5.4. 197c171 < In Fig.~\ref{fig.EC_GrowthMitigation.Phot_refl_ener}(right), a histogram of the number of photons, vs. photon energy, is presented. This is strongly peaked at zero but has a long tail out to at least 5~keV. --- > In Fig.~\ref{fig.EC_GrowthMitigation.Phot_refl_ener}(right), a histogram of the number of photons, vs. photon energy, is presented. This is strongly peaked at zero but has a long tail out to at least 5~keV. 199c173 < In Fig.~\ref{fig.EC_GrowthMitigation.3d_phot_pos}, a two dimensional histogram of the number of photons, vs. location of the absorption site on the vacuum chamber perimeter, is presented. This is is peaked at the outside edge of the vacuum chamber, where the direct photon strikes occur, but there is long tail extending around the entire surface of the vacuum chamber, due to the reflected photons. --- > In Fig.~\ref{fig.EC_GrowthMitigation.3d_phot_pos}, a two dimensional histogram of the number of photons, vs. location of the absorption site on the vacuum chamber perimeter, is presented. This is is peaked at the outside edge of the vacuum chamber, where the direct photon strikes occur, but there is long tail extending around the entire surface of the vacuum chamber, due to the reflected photons. 203,204c177,178 < \paragraph{Example 2: Photon Emission throughout the Ring} < For the second example, photon emission throughout the \cesrta\ ring from a 2.1~GeV positron beam is simulated. The vacuum chamber is again a simple ellipse. --- > \paragraph{Example 2: Photon Emission throughout the Ring} > For the second example, photon emission throughout the \cesrta\ ring from a 2.1~GeV positron beam is simulated. The vacuum chamber is again a simple ellipse. 206c180 < In Fig.~\ref{fig.EC_GrowthMitigation.phot_plot_s}, the distribution of photon absorption sites around the ring is shown, sorted by the type of magnetic environment in which the absorption occurs. This information is important for simulations of electron cloud growth, which is strongly influenced by the magnetic environment. --- > In Fig.~\ref{fig.EC_GrowthMitigation.phot_plot_s}, the distribution of photon absorption sites around the ring is shown, sorted by the type of magnetic environment in which the absorption occurs. This information is important for simulations of electron cloud growth, which is strongly influenced by the magnetic environment. 210c184 < In Fig.~\ref{fig.EC_GrowthMitigation.phot_plot_perim}, we see the distribution of photon absorption sites vs. scaled perimeter along the vacuum chamber, again sorted by the type of magnetic environment in which the absorption occurs. --- > In Fig.~\ref{fig.EC_GrowthMitigation.phot_plot_perim}, we see the distribution of photon absorption sites vs. scaled perimeter along the vacuum chamber, again sorted by the type of magnetic environment in which the absorption occurs. 216,217c190,191 < \paragraph{Summary} < As part of the Bmad software library, a program called \texttt{SYNRAD3D} has been written to track synchrotron radiation photons generated in storage rings. \texttt{SYNRAD3D} includes scattering from the vacuum chamber walls using X-ray data from an LBNL database. It can handle any planar lattice and a wide variety of vacuum chamber profiles. Two examples of the application of this program to radiation in \cesrta\ have been shown and discussed. --- > \paragraph{Summary} > As part of the Bmad software library, a program called \texttt{SYNRAD3D} has been written to track synchrotron radiation photons generated in storage rings. \texttt{SYNRAD3D} includes scattering from the vacuum chamber walls using X-ray data from an LBNL database. It can handle any planar lattice and a wide variety of vacuum chamber profiles. Two examples of the application of this program to radiation in \cesrta\ have been shown and discussed. 234,238c208,212 < \item Determine if the macroparticle has hit in the azimuthal region where one of the RFA collectors exists. \\ < \item Calculate an efficiency (probability of passing through the beam pipe hole) based on the incident angle and energy of the particle. \\ < \item Determine if the macroparticle has enough energy to make it past the retarding field. \\ < \item Deposit the appropriate amount of charge on the grid and collector. \\ < \item Do a ``voltage scan" by repeating this process for several different values of retarding voltage \\ --- > \item Determine if the macroparticle has hit in the azimuthal region where one of the RFA collectors exists. \\ > \item Calculate an efficiency (probability of passing through the beam pipe hole) based on the incident angle and energy of the particle. \\ > \item Determine if the macroparticle has enough energy to make it past the retarding field. \\ > \item Deposit the appropriate amount of charge on the grid and collector. \\ > \item Do a ``voltage scan" by repeating this process for several different values of retarding voltage \\ 250,251c224,225 < \includegraphics*[width=\linewidth]{EC_GrowthMitigation/figures/h1_15E_c23_data_3d_pub.eps} %{avcols_15E_Al_TiN2_Carbon.eps} < \caption{\label{fig:rfa_data_example} Data: Carbon coated drift chamber, 1x45x1.25mA e+, 5.3 GeV, 14ns} --- > \includegraphics*[width=\linewidth]{EC_GrowthMitigation/figures/h1_15E_c23_data_3d_pub.eps} %{avcols_15E_Al_TiN2_Carbon.eps} > \caption{\label{fig:rfa_data_example} Data: Carbon coated drift chamber, 1x45x1.25mA e+, 5.3 GeV, 14ns} 257,260c231,234 < % \centering < \includegraphics*[width=\linewidth]{EC_GrowthMitigation/figures/h1_15E_c23_sim_3d_pub.eps} %{avcols_15E_Al_TiN2_Carbon.eps} < \caption{\label{fig:rfa_sim_example} Simulation: Carbon coated drift chamber, 1x45x1.25mA e+, 5.3 GeV, 14ns} < \end{minipage} --- > % \centering > \includegraphics*[width=\linewidth]{EC_GrowthMitigation/figures/h1_15E_c23_sim_3d_pub.eps} %{avcols_15E_Al_TiN2_Carbon.eps} > \caption{\label{fig:rfa_sim_example} Simulation: Carbon coated drift chamber, 1x45x1.25mA e+, 5.3 GeV, 14ns} > \end{minipage} 268,270c242,244 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/trampoline_wig1w_2585.eps} %{ipac_tramp_combined.eps} < \caption[Resonant enhancement in wiggler data]{\label{fig:tramp_example} Resonant enhancement in wiggler data, 1x45x1.25 mA e+, 2.1GeV. Note that there are 12 collectors, so collector 6 is one of the central ones. Also note that the grid signal is divided by 12.} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/trampoline_wig1w_2585.eps} %{ipac_tramp_combined.eps} > \caption[Resonant enhancement in wiggler data]{\label{fig:tramp_example} Resonant enhancement in wiggler data, 1x45x1.25 mA e+, 2.1GeV. Note that there are 12 collectors, so collector 6 is one of the central ones. Also note that the grid signal is divided by 12.} 277,279c251,253 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/TUPD022f5.eps} %{ipac_tramp_combined.eps} < \caption[Resonant spike location at different bunch spacings]{\label{fig:tramp_spacing} Resonant spike location at different bunch spacings, 1x45x1.25 mA e+, 5GeV. Only the signal in the central collector is plotted} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/TUPD022f5.eps} %{ipac_tramp_combined.eps} > \caption[Resonant spike location at different bunch spacings]{\label{fig:tramp_spacing} Resonant spike location at different bunch spacings, 1x45x1.25 mA e+, 5GeV. Only the signal in the central collector is plotted} 291,294c265,268 < \centering < %\includegraphics*{EC_GrowthMitigation/figures/integrated_model_posinst.eps} < \includegraphics*{EC_GrowthMitigation/figures/integrated_model_example.png} < \caption{\label{fig:int_model} POSINST simulation showing resonant enhancement, 1x45x1.2 mA e+, 2.1GeV, 14ns, central collector} --- > \centering > %\includegraphics*{EC_GrowthMitigation/figures/integrated_model_posinst.eps} > \includegraphics*{EC_GrowthMitigation/figures/integrated_model_example.png} > \caption{\label{fig:int_model} POSINST simulation showing resonant enhancement, 1x45x1.2 mA e+, 2.1GeV, 14ns, central collector} 315,317c289,291 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/B15W_2983_pub_fix2.eps} %{thin15w_2615_2.eps} < \caption{\label{fig:drift_example} Example voltage scan: TiN coated drift RFA, 1x45x1.25mA, 5.3GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/B15W_2983_pub_fix2.eps} %{thin15w_2615_2.eps} > \caption{\label{fig:drift_example} Example voltage scan: TiN coated drift RFA, 1x45x1.25mA, 5.3GeV, 14ns} 378,381c352,355 < \centering < %\includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_neg_pub.eps} %{avcols_15E_Al_TiN2_Carbon.eps} < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/neg3_comparison_notitle.eps} < \caption{\label{fig:neg_rfa} NEG RFA comparison, 1x20 e+, 5.3GeV, 14ns} --- > \centering > %\includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_neg_pub.eps} %{avcols_15E_Al_TiN2_Carbon.eps} > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/neg3_comparison_notitle.eps} > \caption{\label{fig:neg_rfa} NEG RFA comparison, 1x20 e+, 5.3GeV, 14ns} 390,395c364,369 < %\begin{minipage}{1.0\textwidth} < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/run2983_slac4_pub.eps} %{slac4_2615_2.eps} < \caption{\label{fig:dipole_example} Typical Al dipole RFA measurement: 1x45x1.25mA e+, 5.3GeV, 14ns} < %\vspace{1cm} < %\end{minipage} --- > %\begin{minipage}{1.0\textwidth} > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/run2983_slac4_pub.eps} %{slac4_2615_2.eps} > \caption{\label{fig:dipole_example} Typical Al dipole RFA measurement: 1x45x1.25mA e+, 5.3GeV, 14ns} > %\vspace{1cm} > %\end{minipage} 400,403c374,377 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_1x20_slac.eps} %{avcols_slac_5_6_2010.eps} < \caption{\label{fig:dipole_compare}Dipole RFA comparison, 1x20 e+, 5.3GeV, 14ns} < % \end{minipage} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_1x20_slac.eps} %{avcols_slac_5_6_2010.eps} > \caption{\label{fig:dipole_compare}Dipole RFA comparison, 1x20 e+, 5.3GeV, 14ns} > % \end{minipage} 411,413c385,387 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/run1912_slac4_bifurcate_pub.eps} %{slac4_2615_2.eps} < \caption{\label{fig:bifurcate} Bifurcation of peak density in a Al dipole: 1x20 e+, 5.3GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/run1912_slac4_bifurcate_pub.eps} %{slac4_2615_2.eps} > \caption{\label{fig:bifurcate} Bifurcation of peak density in a Al dipole: 1x20 e+, 5.3GeV, 14ns} 420,422c394,396 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/chicane_scan_1418.eps} %{slac4_2615_2.eps} < \caption[RFA signal as a function of chicane magnetic field]{\label{fig:chicane_scan} RFA signal as a function of chicane magnetic field: 1x45x1mA e+, 5GeV, 4ns. Cyclotron resonances are observed every 89G. Note that the Aluminum chamber signal is divided by 20.} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/chicane_scan_1418.eps} %{slac4_2615_2.eps} > \caption[RFA signal as a function of chicane magnetic field]{\label{fig:chicane_scan} RFA signal as a function of chicane magnetic field: 1x45x1mA e+, 5GeV, 4ns. Cyclotron resonances are observed every 89G. Note that the Aluminum chamber signal is divided by 20.} 432,434c406,408 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/run2983_quad_pub2.eps} %{quad1909.eps} < \caption{\label{fig:quad_example} Quadrupole RFA measurement: 1x45x1.25mA e+, 5.3GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/run2983_quad_pub2.eps} %{quad1909.eps} > \caption{\label{fig:quad_example} Quadrupole RFA measurement: 1x45x1.25mA e+, 5.3GeV, 14ns} 439,441c413,415 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_quad_Al_TiN_20_pub.eps} %{avcols_quad_Al_TiN_20.eps} < \caption{\label{fig:quad_compare} Quadrupole mitigation comparison, 1x20 e+, 5.3GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_quad_Al_TiN_20_pub.eps} %{avcols_quad_Al_TiN_20.eps} > \caption{\label{fig:quad_compare} Quadrupole mitigation comparison, 1x20 e+, 5.3GeV, 14ns} 448,450c422,424 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/quad_trapping_pub2.eps} < \caption{\label{fig:quad_trap} Long term cloud buildup in a quadrupole: 1x45x1mA e+, 5.3GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/quad_trapping_pub2.eps} > \caption{\label{fig:quad_trap} Long term cloud buildup in a quadrupole: 1x45x1mA e+, 5.3GeV, 14ns} 461,463c435,437 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/wig1w_2585_pub3.eps} %{wig1w2585.eps} < \caption{\label{fig:cu_wig} Cu Wiggler RFA measurement: 1x45x1.25mA e+, 2.1GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/wig1w_2585_pub3.eps} %{wig1w2585.eps} > \caption{\label{fig:cu_wig} Cu Wiggler RFA measurement: 1x45x1.25mA e+, 2.1GeV, 14ns} 468,470c442,444 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_wig2wb_pub.eps} %{wigcompare4.eps} < \caption{\label{fig:wig_compare} Wiggler mitigation comparison: 1x45 e+, 2.1GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/avcols_wig2wb_pub.eps} %{wigcompare4.eps} > \caption{\label{fig:wig_compare} Wiggler mitigation comparison: 1x45 e+, 2.1GeV, 14ns} 479,481c453,455 < \centering < \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/wiggler_ramp_9_21_10_pub.eps} %{wigcompare4.eps} < \caption{\label{fig:wig_ramp} Wiggler ramp measurement: 1x45x.75mA e+, 2.1GeV, 14ns} --- > \centering > \includegraphics*[width=0.5\textwidth]{EC_GrowthMitigation/figures/wiggler_ramp_9_21_10_pub.eps} %{wigcompare4.eps} > \caption{\label{fig:wig_ramp} Wiggler ramp measurement: 1x45x.75mA e+, 2.1GeV, 14ns} 488,490c462,464 < \item We have found beam pipe coatings (TiN, Carbon, and NEG) to be effective at mitigating the cloud in drifts. < \item TiN coating was also found to be effective in a dipole and quadrupole; using a grooved and coated chamber in a dipole is even more effective. < \item In a wiggler, a clearing electrode appears to be the most effective mitigation technique. --- > \item We have found beam pipe coatings (TiN, Carbon, and NEG) to be effective at mitigating the cloud in drifts. > \item TiN coating was also found to be effective in a dipole and quadrupole; using a grooved and coated chamber in a dipole is even more effective. > \item In a wiggler, a clearing electrode appears to be the most effective mitigation technique. 519c493 < \chi^2 = (\mathbf{y} - \mathbf{X} \, \mathbf{\beta})^T \: \mathbf{W} \: (\mathbf{y} - \mathbf{X} \, \mathbf{\beta}) --- > \chi^2 = (\mathbf{y} - \mathbf{X} \, \mathbf{\beta})^T \: \mathbf{W} \: (\mathbf{y} - \mathbf{X} \, \mathbf{\beta}) 524c498 < \mathbf{\beta} = (\mathbf{X}^T \, \mathbf{W} \, \mathbf{X})^{-1} \: \mathbf{X}^T \: \mathbf{W} \, \mathbf{y} --- > \mathbf{\beta} = (\mathbf{X}^T \, \mathbf{W} \, \mathbf{X})^{-1} \: \mathbf{X}^T \: \mathbf{W} \, \mathbf{y} 615c589,603 < \centering --- > \centering > > \caption{\label{tab:param_result_al} Best fit parameters- Aluminum chamber} > \begin{tabular}{ccc} > %\toprule > \hline \hline > %\textbf{Parameter} & \textbf{Nominal Value} & \textbf{Best Fit Value} \\ > Parameter & Nominal Value & Best Fit Value \\ > %\midrule > \hline > dtspk & 1.8 & 2.2 $\pm$ .1 \\ > P1epk & .5 & .42 $\pm$ .03 \\ > P1rinf & .2 & .20 $\pm$ .02 \\ > E0epk & 310 & 334 $\pm$ 20 \\ > queffp & .1 & .10 $\pm$ .02 \\ 617,619d604 < \caption{\label{tab:param_result_al} Best fit parameters- Aluminum chamber} < \begin{tabular}{ccc} < %\toprule 621,633c606,607 < %\textbf{Parameter} & \textbf{Nominal Value} & \textbf{Best Fit Value} \\ < Parameter & Nominal Value & Best Fit Value \\ < %\midrule < \hline < dtspk & 1.8 & 2.2 $\pm$ .1 \\ < P1epk & .5 & .42 $\pm$ .03 \\ < P1rinf & .2 & .20 $\pm$ .02 \\ < E0epk & 310 & 334 $\pm$ 20 \\ < queffp & .1 & .10 $\pm$ .02 \\ < < \hline \hline < %\bottomrule < \end{tabular} --- > %\bottomrule > \end{tabular} 639c613,628 < \centering --- > \centering > > \caption{\label{tab:param_result} Best fit parameters- coated chambers} > \vspace*{1ex} > \begin{tabular}{cccc} > %\toprule > \hline \hline > %\textbf{Parameter} & \textbf{Nominal} & \textbf{Best Fit- TiN} & \textbf{Best Fit- C} \\ > Parameter & Nominal & Best Fit- TiN & Best Fit- C \\ > %\midrule > \hline > dtspk & .8 & .59 $\pm$ .02 & .64 $\pm$ .04\\ > P1epk & .5 & .040 $\pm$ .002 & .049 $\pm$ .007 \\ > P1rinf & .2 & .20 $\pm$ .01 & .17 $\pm$ .02 \\ > E0epk & 500 & 500 $\pm$ 30 & 410 $\pm$ 60 \\ > queffp & .1 & .090 $\pm$ .006 & .08 $\pm$ .01 \\ 641,644d629 < \caption{\label{tab:param_result} Best fit parameters- coated chambers} < \vspace*{1ex} < \begin{tabular}{cccc} < %\toprule 646,658c631,632 < %\textbf{Parameter} & \textbf{Nominal} & \textbf{Best Fit- TiN} & \textbf{Best Fit- C} \\ < Parameter & Nominal & Best Fit- TiN & Best Fit- C \\ < %\midrule < \hline < dtspk & .8 & .59 $\pm$ .02 & .64 $\pm$ .04\\ < P1epk & .5 & .040 $\pm$ .002 & .049 $\pm$ .007 \\ < P1rinf & .2 & .20 $\pm$ .01 & .17 $\pm$ .02 \\ < E0epk & 500 & 500 $\pm$ 30 & 410 $\pm$ 60 \\ < queffp & .1 & .090 $\pm$ .006 & .08 $\pm$ .01 \\ < < \hline \hline < %\bottomrule < \end{tabular} --- > %\bottomrule > \end{tabular} 661c635 < %ek0phel & 5 & 4.6 $\pm$ .41 \\ --- > %ek0phel & 5 & 4.6 $\pm$ .41 \\ 667,671c641,645 < \item Repeating the analysis for other surface types \\ < \item Continuing work on quantifying errors and correlations in the parameters \\ < \item Repeating the analysis for RFAs in magnetic fields, including dipoles, quadrupoles, and wigglers \\ < \item Comparing with other local cloud measurements, such as shielded pickups \\ < \item Incorporating a more complete description of photoelectron emission \\ --- > \item Repeating the analysis for other surface types \\ > \item Continuing work on quantifying errors and correlations in the parameters \\ > \item Repeating the analysis for RFAs in magnetic fields, including dipoles, quadrupoles, and wigglers \\ > \item Comparing with other local cloud measurements, such as shielded pickups \\ > \item Incorporating a more complete description of photoelectron emission \\ 792,794c766,768 < TiN-Al samples.]{Repeated measurements of SEY as a function of energy for < TiN-Al samples in the horizontal station (left) and the $45^\circ$ < station (right). --- > TiN-Al samples.]{Repeated measurements of SEY as a function of energy for > TiN-Al samples in the horizontal station (left) and the $45^\circ$ > station (right). 842c816 < The ``fresh'' sample in the $45^\circ$ station started with a peak --- > The ``fresh'' sample in the $45^\circ$ station started with a peak 946,953c920,927 < energy for a diamond-like carbon-coated aluminum sample.]{SEY as a < function of incident electron energy for a diamond-like < carbon-coated aluminum sample. The blue circles correspond to a < ``continuous'' scan in energy (5 seconds for each energy, with all 9 < grid points; Point 5 is shown). The red squares correspond to a < ``discrete'' scan in energy (3 to 4 minutes waiting period with the < electron beam deflected away from the point of interest before each < measurement; only Point 9 was measured). --- > energy for a diamond-like carbon-coated aluminum sample.]{SEY as a > function of incident electron energy for a diamond-like > carbon-coated aluminum sample. The blue circles correspond to a > ``continuous'' scan in energy (5 seconds for each energy, with all 9 > grid points; Point 5 is shown). The red squares correspond to a > ``discrete'' scan in energy (3 to 4 minutes waiting period with the > electron beam deflected away from the point of interest before each > measurement; only Point 9 was measured). 1009,1010c983,984 < energy for amorphous carbon-coated stainless steel sample. < \label{fig:grow_mitig.aCang}} --- > energy for amorphous carbon-coated stainless steel sample. > \label{fig:grow_mitig.aCang}} 1063c1037 < cloud bombardment is the main source of processing. --- > cloud bombardment is the main source of processing. \ No newline at end of file