%---------------------------------------------------------------% % CesrTA Phase I Report - % % Chapter - Studies of Electron Cloud Growth and Its Mitigation % % Section - Other Methods to Characterize EC Build-Up % % Section coordinator: John Sikora % % Page estimate: 12pp. % %---------------------------------------------------------------% \section[Other Methods to Characterize EC Build-Up]{Other Methods to Characterize EC Build-Up} \label{sec:ec_growth.ec_buildup_other} While the RFAs provide the largest number of detectors at \cesrta\, other techniques for measuring the electron cloud density are being used at a subset of locations. TE Wave and Shielded Pickup detectors provide data that is complimentary to that provided by the RFAs. The Shielded Pickups have a geometry that is similar to that of an RFA, but are designed to measure time resolved signals, while the RFAs measure integrated current. The TE Wave technique - where the electron cloud modulates a carrier transmitted through the beampipe - is sensitive to the cloud density in the center of the pipe, while both the RFA and Shielded Pickups measure the cloud current that is normal to the pipe surface. The comparison of data taken using these complimentary techniques should result in consistent measurements and modeling. % --- Subsection: TE Wave Studies \subsection{TE Wave Studies} \label{ssec:ec_growth.ec_buildup_other.tewave} As described in Section 2.3.2, TE wave measurements in CESR were performed in three regions of the ring, using several BPMs in each region. At the beginning of the \cesrta\ program electron cloud diagnostics in particle accelerator had only been demonstrated successfully in the PEP-II Low Energy Ring, just before that machine shutdown, in the arc of only a few measurements. A first objective of this program was therefore to investigate the technique in depth, understand its critical features and limits, and overall improve its theoretical model. Secondly, we worked on improving more technological aspects of the method. Finally, as already stated in Section 2.3.2, we are developing alternative uses of microwaves for electron cloud diagnostic purposes which allow overcoming some of the fundamental limits of the original technique emerged during our research. \subsubsection{TE Wave Transmission Measurements} \label{sssec:ec_growth.ec_buildup_other.tewave.transmission} \paragraph{Improvements to the theoretical model} The theoretical model of the TE wave measurement proposed by Caspers et al. in~\citep{ECLOUD04:89to94} only took into account the phase delay induced by the electron cloud on a propagating TE wave. Moreover, changes in the cloud density were supposed to have a simple sinusoidal evolution. Under such hypotheses the modulation sidebands amplitude, relative to the carrier $SB_c$, is simply given by \begin{equation} SB_c = \frac{{\Delta \Phi}}{{2}} \label{PM} \end{equation} if $\Delta \Phi$ is the modulation index, with only one upper and one lower sideband present for low index modulation, which is always the case with cloud densities normally encountered in particle accelerators. In the course of our experimental work, we encountered situations were amplitude modulation, and more in general simultaneous phase and amplitude modulations, were present. Additionally, the purely sinusoidal modulation model turned out to be an excessive abstraction in most cases, so that an effort to generalize the theory proved to be necessary. We summarize the result of our effort in the following subsections. \paragraph{AM/PM modulation} To increase the measurement sensitivity, it is good practice to choose the TE wave frequency in correspondence of a peak maximum in the beampipe transmission function. In most cases those peaks correspond to standing waves trapped by discontinuities in the vacuum chamber (~\citep{ECLOUD10:PST04}), may contain a simultaneous amplitude modulation component. The general formulation for an AM/PM modulation is reported in Ref.~\citep{PRSTAB13:071002}. If the standing wave has a narrow resonance (high quality factor $Q_0$), the modulation indexes are given by \begin{equation} \begin{array}{c} \Delta M = \frac{{Q_0^2}}{{2}} \left( \frac{ \omega _{p} }{ \omega _{res} } \right)^{4} \\ \Delta \Phi = Q_0 \left( \frac{{\omega_{p}}}{{\omega_{res}}} \right)^{2} \end{array} \label{AM/PM} \end{equation} where $\Delta M = \Delta \Phi^2/2$ is the amplitude modulation index and $\omega_{res}$ is the center frequency of the resonance. In the hypothesis $\omega_p<<\omega_{res}$ the modulation sidebands amplitude can be written as \begin{equation} SB_c \approx \Delta \Phi \left[1+\frac{{1}}{{2}} \left(\frac{{\Delta \Phi}}{{2}}\right)^2 \right] |F(\omega)| \label{modidx} \end{equation} where $|F(\omega)|$ is the Fourier transform of the cloud normalized density. In the case of a sinusoidal modulation we can compare Eqs.~\ref{PM}~and~\ref{modidx} and see that the corrective term in brackets accounts for the AM/PM modulation. \paragraph{Time evolution of the electron cloud density} From Eq.\ref{modidx} one can easily see that the temporal evolution of the electron cloud density is described by the function $F(\omega)$ in the frequency domain, which being the transform of a periodic function will be composed of discrete lines separated by the ring revolution frequency $\omega_{rev}$. In practical cases one usually observes a number of sidebands, even for small modulation depths, as shown in Fig.~\ref{fig:ec_growth:tew_meas_fig1}. A fairly good approximation can be obtained assuming that rise and fall times of the ECD are much shorter than the bunch train length, but still at least comparable with the bunch spacing. In such a case, which is often verified, a rectangular modulating function, with duty factor equal to the train length divided by the machine length, can obviously be seen as a more accurate representation than a sinusoidal one. \begin{figure} \centering \includegraphics[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_meas_fig1.jpg} \caption[Cancellation of modulation sidebands due to different bunch train lengths]{ Cancellation of modulation sidebands due to different bunch train lengths. Suppressed modulation sidebands due to the rectangular modulation function are indicated for various train lengths.\label{fig:ec_growth:tew_meas_fig1}} \end{figure} This hypothesis can find a degree of experimental verification by looking at the sidebands with different train lengths. Figure~\ref{fig:ec_growth:tew_meas_fig1} shows a detail of measurements in a dipole region of \cesrta\ with bunch trains of different lengths equal to one fourth, one fifth and one sixth of the ring circumference. One can see that correspondingly every fourth, fifth and sixth beam harmonic is suppressed. The general properties of the Fourier transform point out how this behavior is evidence of a strong rectangular modulation component. In such a case we can modify Eq.(\ref{PM}), by introducing a correction factor that takes into account the rectangular nature of the modulation and we have \begin{equation} \Delta \varphi = \frac{{1}}{{2}} \cdot \mbox{SB}_c\frac{{\pi}}{{\sin (t_b \omega_{rev}/2 )}} \label{rectmod} \end{equation} where $t_b$ is the bunch train length. Applying the \emph{Carson's Bandwidth Rule} \citep{LEPP:REU2009:BCarlson} an approximate evaluation of the ECD rise and fall times ($t_r$) is given by \begin{equation} t_r \approx \frac{{2}}{{3}} \frac{{2 \pi}}{{\omega_{rev} \cdot N_{SB}}} \label{carlsonform} \end{equation} where $N_{SB}$ is the number of visible sidebands. %\subsubsection{TE Wave Measurements} %\label{sssec:ec_growth.ec_buildup_other.tewave.measurements} \paragraph{Beampipe attenuation compensation} Experimental data showed a substantial difference in signal attenuation for different frequencies even on a relatively narrow frequency span such as the 390 kHz between TE wave frequency and first modulation sidebands. These difference need to be equalized in order to correctly evaluate the modulation depth and it is worth stressing that we frequently measured differences of several dB, which would easily cause errors as large as a factor of $2 \div 4$, if unaccounted for. Furthermore, the attenuation can change substantially with varying beam conditions, due principally to thermal effects, so that a continuous monitoring is necessary. To this end, we introduced an additional phase modulation, of known index, to the TE wave with sidebands near the sidebands generated by the electron cloud induced modulation. By comparing the sidebands height to what expected from theory, it is possible to evaluate the difference in attenuation between the TE wave and the sidebands frequencies at all times. An example of sideband measurement in the wiggler straight (L0) is shown in Fig.\ref{fig:ec_growth:tew_meas_fig2}, where we are measuring the sidebands generated by a 45-bunch positron train of 60 mA total current in a TE wave traveling along the Eastern half of the L0 wiggler straight. The relative amplitude of upper and lower sidebands (USB and LSB, respectively) have to be corrected for the difference in transmission function of the measuring system at the carrier and USB and LSB frequencies. This can be done with separate measurements, but we have recently introduced a calibration phase modulation of known index at a frequency close to the e-cloud modulation frequency, so that the transmission function is about equal to that for the nearby modulation sidebands. In this case the reference phase modulation index at 410 kHz was chosen to be 1 mrad, which should generate sidebands at -66 dBc. We observe lower values from which it is possible to infer the attenuation, with respect to the carrier frequency, at the USB and LSB frequencies (390 kHz). We calculate a correction factor equal to $\ -66.0-(-64.9)=-1.1~dB$\ for the LSB and, analogously, +6.4 dB for the USB. The corrected value for the LSB is -49.2 dBc and -48.3 dBc for the USB. It is worth noticing that, while before correction the two sidebands were rather different (6.6 dB), after the correction is applied their values are almost identical, as expected. \begin{figure} \centering \includegraphics[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_meas_fig2.jpg} \caption[Example of sidebands measurement in the wiggler straight] {Example of sidebands measurement in the wiggler straight. 45-bunch positron train of 60 mA total beam current with 14 ns bunch spacing, with reference modulation sidebands (1 mrad modulation depth at 410 kHz).\label{fig:ec_growth:tew_meas_fig2} } \end{figure} As previously stated, being able to continuously monitor the transmission function at the frequencies of interest is quite important during some experiments when beam and/or machine conditions undergo large variations. In such cases the transmission changes due mostly to thermal effects can disrupt the measurement as shown in Fig.\ref{fig:ec_growth:tew_meas_fig3}: While ramping the wigglers magnetic field, the emitted synchrotron radiation increase can change the beampipe transmission function at the sidebands frequency so that USB and LSB amplitudes actually appear to diverge during the experiment until correction is applied. \begin{figure} \centering \includegraphics[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_meas_fig3.pdf} \caption[Sideband levels relative to the carrier during wiggler ramp] { Sideband levels relative to the carrier during wiggler ramp in the L0 straight with (solid lines) and without (dashed) correction applied.\label{fig:ec_growth:tew_meas_fig3}} \end{figure} To estimate the ECD from the sidebands measured in Fig.\ref{fig:ec_growth:tew_meas_fig2}, we can use the average of the two sidebands -48.8 dBc. \subsubsection{TE Wave Resonance Measurements} \label{sssec:ec_growth.ec_buildup_other.tewave.resonance} As originally proposed, the TE wave technique was based on transmission and reception of microwaves from one point in the accelerator to another using the beampipe as a waveguide. Button detectors, normally used as part of the beam position monitor (BPM) system are used to couple microwaves in/out of the beampipe. In the presence of a plasma (the electron cloud), transmitted microwaves will be phase shifted and the ECD measured~\cite{PRL100:094801,PRSTAB11:094401,PRSTAB13:071002,PRSTAB14:012802}. However, in applying this technique to the data at \cesrta\, it was noticed that transmission through the beampipe does not have a flat frequency response. In fact, the large variations in response suggest the presence of resonant excitation of the beampipe rather than single pass transmission. This interpretation was confirmed by the response when exciting and receiving at the same location, where very large resonances are often seen. \paragraph{Reflections and Standing Waves} The beampipe at \cesrta\ was not designed to be a waveguide. In devices such as vacuum pumps, longitudinal slots were used to provide a reasonable vacuum connection, while minimizing the effect of beam-induced fields. However, these longitudinal slots present an obstacle to the propagation of a TE waves. A simple example was found at 43E in \cesrta\ where a BPM coupler/detector is located between two ion pumps (with slots). The response shown in Fig.~\ref{fig:ec_growth:tew_res_f1} is consistent with a waveguide of length $L$ having a cutoff frequency $f_c$ and $n$ half wavelengths in the distance $L$ between the pumps~\cite{ECLOUD10:PST06,ECLOUD10:PST04}. \begin{figure}[htb] \centering \includegraphics*[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_res_f1.eps} \caption{\label{fig:ec_growth:tew_res_f1} Sketch of 43E at \cesrta\, where a BPM Detector is located between two ion pumps with longitudinal slots. The measured resonances follow the expected \mbox{$f^2 = f_{c}^{2} + \left(\frac{nc}{2L} \right)^2$} of a rectangular cavity} \end{figure} The effect of dielectrics and plasmas on the resonant frequency of a cavity is well established~\cite{MAHeald1965:PlasDiagMicroW}. The effect of small dielectrics on resonant frequency is very useful in mapping the fields of accelerating cavities and plasma densities are routinely measured using resonant cavities~\cite{MAHeald1965:PlasDiagMicroW,PR106:196to199}. Perturbation techniques provide the following approximation for the shift in resonant frequency due to a dielectric in a resonant cavity~\cite{IEEEMMT49:918to923}. \begin{equation} \frac{\Delta \omega}{ \omega} = \frac{\displaystyle \int_{V} \left( 1 - \varepsilon_{r} \right) E_{0}^2 \,dV } {2 \displaystyle \int_{V} E_{0}^{2} \,dV } \label{dw:epsilon} \end{equation} The effective dielectric constant of a plasma has real and imaginary parts. The imaginary part gives a change in the Q of the resonance, the real part a change in its frequency. For low density plasmas ($\omega_{p} ^{2} \ll \omega ^{2} $) with a small collision frequency ($\nu \ll \omega$) and no magnetic field, the real part of the dielectric constant of a plasma can be written as~\cite{PR106:196to199}. \begin{equation} \varepsilon_r = \left[ 1 - \frac{\omega_{p}^{2}}{ \omega^2 \left( 1 + \left( \upsilon / \omega \right)^2 \right) } \right] \label{epsilon:omega_p} \end{equation} The plasma frequency $\omega _{p}$ is related to the electron cloud density by $ n_{e} = \omega _{p}^{2} \varepsilon _0 m / e^{2} $ \cite{MAHeald1965:PlasDiagMicroW}. Let the collision frequency be vanishingly small $\nu \rightarrow 0 $. The change in resonant frequency becomes. \begin{equation} \frac{\Delta \omega}{ \omega} \; = \; \frac{e^{2} }{2 \varepsilon _{0} m_{e} \omega ^{2} } \frac{ \displaystyle \int_{V} n_{e} E_{0}^{2}\,dV } { \displaystyle \int_{V} E_{0}^{2} \,dV } \label{TUPC170:Ne} \end{equation} If there are high local densities, they will not have an effect on $\Delta \omega$ where the cavity electric field is zero. On the other hand, if the density is uniform, $\Delta \omega$ is independent of the details of the electric field, since the same integral appears in the numerator and denominator~\cite{LEPP:REU2009:BCarlson}. An ECD of $10^{12}(m^{-3})$ would give a frequency shift of about 20~kHz. With a train of bunches in the storage ring, the electron cloud will grow and decay each time the bunch train passes a given point - at the revolution frequency $f_{rev}$ (390kHz at \cesrta\ ). The quantity $\Delta \omega$ is the modulation in the resonant frequency of the waveguide cavity produced by the electron cloud. We now need to determine the effect that this modulation has on the observed signals. \paragraph{Effect on Signals} For most of the TE Wave measurements made at \cesrta\, the resonant beampipe is driven at a fixed frequency and its response measured with a spectrum analyzer. The steady state solution for a driven oscillator is given in the following equations and illustrated in Fig.~\ref{fig:ec_growth:tew_res_f2}. \begin{eqnarray} x(t) & = & A_n sin(\omega t + \phi_n )\\ \nonumber \\ A_n & = & Q \frac{A}{[ (\omega_n^2 - \omega^2)^2 + \omega^4 ]^{1/2} } \\ \phi_n & = & tan^{-1} Q \frac{ (\omega_n^2 - \omega^2) }{ \omega^2 } \label{eq:ec_growth:tew_res_phi} \end{eqnarray} \begin{figure}[htb] \centering \includegraphics*[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_res_f2.eps} \caption{Steady state amplitude and phase response as the cavity resonant frequency changes from $\omega_0$ to $\omega_1$} \label{fig:ec_growth:tew_res_f2} \end{figure} To obtain a rough estimate of the ECD, a number of approximations will be made: that the steady state solution above applies, the drive frequency $\omega$ is close to resonance (this results primarily in phase modulation), the phase modulation, from Eq.~(\ref{eq:ec_growth:tew_res_phi}) using the measured $Q$ of about 3000, is small and a cw modulation would give a ratio of the first sideband to carrier amplitude of $\frac{1}{2} \Delta \phi$. Also, the phase modulation is not sinusoidal but modulated by the ECD, so a further approximation needs to be made. Let the duration of the ECD \textit{and its effect on the phase} be of fixed amplitude for the length of the bunch train and zero otherwise. Given these crude approximations, Fig.~\ref{fig:ec_growth:tew_res_f3} is a plot of the ECD measured in the wiggler region at 2~GeV during a wiggler ramp. The stored beam was a positron 45 bunch train spaced at 14~ns with a total current of 35~mA. \begin{figure}[htb] \centering \includegraphics*[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_res_f3.eps} \caption{Estimate of ECD during a ramp of wigglers} \label{fig:ec_growth:tew_res_f3} \end{figure} One concern with this approximation is that the beampipe cavity has damping time of about 500~$ns$. So the duration of the cloud and the damping time of the cavity are of the same magnitude. We are working on a more correct analysis that would include transient effects. For example, a step in the resonant frequency of the cavity at $t = 0$ would be described by. \begin{eqnarray} x(t < 0) &=& A_0 sin(\omega t + \phi_0 )\\ \nonumber \\ x(t \geq 0) & = & A_1 sin(\omega t + \phi_1 )\nonumber \\ & & + \; e^{-\gamma t} [A_0 sin(\omega _1 t + \phi_0) \nonumber \\ & & \; \; \; \; \; \; \; \; \; - A_1 sin(\omega _1 t + \phi_1) ] \label{eq:ec_growth:tew_res_t_gt_0} \end{eqnarray} For $t \gg 0$, the exponential vanishes and only the first term (steady state) remains. In the steady state solutions for $t < 0$ and $t \gg 0$ there is a difference both in the amplitude $A_0 \rightarrow A_1$ and in phase $\phi_0 \rightarrow \phi_1$. But, especially near the resonant frequency, the amplitude change will be quite small and the phase difference will dominate the signal. For small $t$ (and small $\Delta \omega$), the term in the brackets of Eq.~(\ref{eq:ec_growth:tew_res_t_gt_0}) appears to play the role of changing the phase from the initial $\phi_0$ to the new $\phi_1$ during the cavity damping time. \subsubsection{TE Wave Alternative Techniques} \label{sssec:ec_growth.ec_buildup_other.tewave.alternative} Finally, we give some other examples of measurements connected to alternative techniques we are developing. \paragraph{The Cutoff Resonance} Bench measurements were made using WR284 waveguide which has a cutoff frequency very similar to the beampipe of \mbox{CesrTA} near 2~GHz. A 4 meter long section was driven near its longitudinal center using buttons similar in geometry to those in \mbox{CesrTA}. Using metal blocks near the waveguide ends to generate reflections, cavity modes were excited. The $\Delta f \propto E^2$ of these modes were plotted vs. longitudinal position using a dielectric bead, making use of Eq.~(\ref{dw:epsilon}) and observing the shifts in resonant frequencies. For measurements with a uniform waveguide, the resonances showed $E^2$ varying as multiples of half wavelengths, including the lowest $n = 1$ mode. \begin{figure}[htb] \centering \includegraphics*[width=.48\textwidth,bb= 0 0 960 581]{EC_GrowthMitigation/figures/tew_res_f4.png} \caption{For bead pull measurements, a thin monofilament line varies the position of a dielectric bead in WR284 waveguide. The center flange has BPM-like buttons that are used to couple microwaves in/out of the waveguide. } \label{fig:ec_growth:tew_res_f4} \end{figure} However, a slight modification of the flange used at the drive point resulted in a significant change in the bead pull measurement of the lowest resonance as shown in Fig.~\ref{fig:ec_growth:tew_res_f5}. The inside width of the drive point flange was made 3mm wider than the waveguide. This portion of the flange is about 2cm long. The lowest `$n=1$' resonance was then shifted slightly below the cutoff frequency. But rather than a half-sine wave, it has a response consistent with an exponential decrease in $E$, as with an evanescent wave. \begin{figure}[htb] \centering \includegraphics*[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_res_f5.eps} \caption{The cutoff resonance was observed using a modified drive flange in a measurement with WR284 waveguide.} \label{fig:ec_growth:tew_res_f5} \end{figure} If excited in this mode, the response to ECD will occur over a distance of only about two meters and provide a very localized measurement, following Eq.~(\ref{TUPC170:Ne}). This can be a great advantage, especially when trying to cross calibrate with other localized ECD measurement techniques. There are many details about this cutoff mode that we need to understand. Primarily, we need to be able to tell - without performing a bead pull experiment in the storage ring - whether or not we have excited this resonance vs. the usual half wave $n = 1$ cavity mode. One indication should be the effect on the sequence of resonant frequencies and the extent to which they are different from $f^2 \propto n^2$. For example, the $n=1$ resonance should be lower than normally expected. At present, an extensive archive of resonant BPM measurements is available and efforts are underway (Ref~\citep{LEPP:REU2009:BCarlson,ECLOUD10:PST04,ECLOUD10:PST06}) for a full theoretical model of the relationship between sidebands amplitude and electron cloud density in these conditions. \paragraph{TE Magnetic Resonance} During measurements in the chicane in the L3 region we observed a strong enhancement in the modulation sidebands in correspondence of the upper hybrid resonance, when propagating a TE wave polarized with its electric field normal to the chicane magnetic field. \begin{figure} \centering \includegraphics[width=.48\textwidth]{EC_GrowthMitigation/figures/tew_meas_fig4.png} \caption[Modulation sideband amplitude near the upper hybrid resonance at two different frequencies]{Modulation sideband amplitude near the upper hybrid resonance at two different frequencies. Red and green traces correspond to opposite direction of propagation of the TE wave.\label{fig:ec_growth:tew_meas_fig4}} \end{figure} Figure \ref{fig:ec_growth:tew_meas_fig4} shows the change in modulation sideband amplitude when the chicane magnetic field is changed so that the TE wave frequency corresponds to the upper hybrid frequency $\omega_{uh}=\sqrt{\omega_p^2+\omega_{cycl}^2}$ for the electron cloud plasma. Because in all practical situations, for a wave above cutoff, $\omega_p<<\omega_{cycl}$ making the evaluating the plasma frequency from the upper hybrid frequency measurement problematic, we are currently studying the phenomenon for waves below cutoff. Preliminary results give us the hope of being able to effectively turn on and off transmission between two BPMs by applying a relatively small dipole magnetic field to the portion of vacuum chamber between them. This could be easily achievable by employing external air-coil magnets, for instance. At that point, the evaluation of the electron cloud density in that region would essentially reduce to the measurement of a resonance peak. \subsubsection{TE Wave Modeling} \label{sssec:ec_growth.ec_buildup_other.tewave.modeling} % --- Subsection: Shielded Pickup Studies \subsection{Shielded Pickup Studies} \label{ssec:ec_growth.ec_buildup_other.spu} \subsubsection{Measurements} \label{sssec:ec_growth.ec_buildup_other.spu.measurements} Time-resolved shielded-pickup measurements provide time structure information on cloud development, in contrast to the time-integrated RFA measurements~\citep{ECLOUD10:PST03}. However, they have relatively primitive energy selection, since they have no retarding grid and position segmentation is more coarse, the charge-collecting electrodes being of diameter 18 mm. Data has been recorded with biases of 0 and $\pm 50 {\rm{V}}$ relative to the vacuum chamber. The studies described here address exclusively the data a with bias $+50$~V in order to avoid contributions to the signal from secondary electrons escaping the pickup. Such secondaries generally carry kinetic energy insufficient to escape a 50~V bias. This choice of bias obviously provides sensitivity to cloud electrons which enter the port holes with low kinetic energy. The front-end readout electronics comprise RF amplifiers with $50~{\Omega}$ input impedance and a total voltage gain of 100. Digitized oscilloscope traces are recorded with 0.1~ns step size. \paragraph{Two Bunch Data} The data shown in Fig.~\ref{fig:ec_growth:spu_meas_twobunch_pos} was taken with two bunches of equal positron currents, 36ns apart. With a ring revolution period of 2.5~{$\mu$}s, the cloud has presumably fully decayed by the time of the arrival of the first bunch. This first bunch produces a fairly small signal in the detector. The signal from the second bunch is much larger, not because it has produced more photoelectrons, but because its electric field kicks electrons that were produced by the first bunch into the detector. \begin{figure}[htbp] % figure placement: here, top, bottom, or page \begin{minipage}[t]{.48\textwidth} \begin{center} \includegraphics[width=\textwidth]{EC_GrowthMitigation/figures/spu_meas_twobunch_pos.eps} \caption{\label{fig:ec_growth:spu_meas_twobunch_pos} Shielded pickup signal from two bunches of positrons spaced at 36~ns } \end{center} \end{minipage} \hfill \begin{minipage}[t]{.48\textwidth} \begin{center} \includegraphics[width=\textwidth]{EC_GrowthMitigation/figures/spu_meas_twobunch_ele.eps} \caption{\label{fig:ec_growth:spu_meas_twobunch_ele} The signal from two bunches of electrons spaced at 20~ns } \end{center} \end{minipage} \end{figure} Another feature of the plot in Fig.~\ref{fig:ec_growth:spu_meas_twobunch_ele} is the presence of what is presumed to be a small direct beam signal. The geometry of the detector holes give reasonably good – but not complete – isolation from the electromagnetic field of the beam. This signal provides a convenient fiducial that can be used to measure the time-of-flight of cloud electrons. For example, notice that the peak of the signal from the first bunch occurs about 15ns after its direct beam signal. Given the detector geometry, most of these electrons must be coming from the floor of the beampipe – a distance of 5cm – which would require an energy of roughly 30~eV. After the passage of the second positron bunch in Fig.~\ref{fig:ec_growth:spu_meas_twobunch_pos}, the cloud electrons enter the detector almost immediately. Since this is a positron beam, the electrons kicked into the detector must come from below the beam height in the chamber, at least 2.5cm from the detector. These initial electrons must have energies of many hundreds of eV and originate close to the beam. Fig.~\ref{fig:ec_growth:spu_meas_twobunch_ele} is the signal produced by two electron bunches spaced at 20~ns. Notice that the signal from the first bunch is not visible (except for the direct beam signal) and that the signal from the second bunch has a faster rise time than that of a positron beam. \paragraph{Two Bunches with Different Spacings} The much larger signal after the passage of the second bunch suggests that this signal is dominated by cloud electrons that are already in the pipe and are being kicked into the detector. This kick has an effective duration that is set by the sum of the length of the bunch and the size of the button, about 120~ps. So the second bunch signal is effectively a sample of the electron cloud in the chamber at the time of the second bunch's transit. Following this idea, pairs of bunches with equal currents were injected with different spacings. The result was a mapping of the electron cloud density produced by the first bunch as a function of time as the second bunch samples the cloud. In Fig.~\ref{fig:ec_growth:spu_meas_multi_pos}, a number of these measurements are plotted on the same time scale, showing the decay of the cloud. \begin{figure} % figure placement: here, top, bottom, or page \centering \includegraphics[width=\textwidth]{EC_GrowthMitigation/figures/spu_meas_multi_pos.eps} \caption{ \label{fig:ec_growth:spu_meas_multi_pos} Overlay of two bunch data with spacings in multiples of 4~ns at 2.1~GeV with an aluminum chamber} \end{figure} \paragraph{Single Bunch with Solenoid} When the solenoid surrounding the shielded pickup is energized, there is a noticeable effect on the detector signal that generally depends on the sign of the magnetic field. The four plots in Fig.~\ref{fig:ec_growth:spu_meas_bscan} show the signal vs. solenoid field for 15E, 15W, both with positron and electron beams. In the top left plot of Fig.~\ref{fig:ec_growth:spu_meas_bscan} there is a large signal when the sign of the magnetic field positive. This positive magnetic field is such that primary electrons produced at the outside wall would be directed upward into the detector. It is likely that this signal is due to the synchrotron light stripe in the mid-plane of the beampipe producing a concentration of photoelectrons along that stripe. The magnetic field that gives the largest signal, -14~G, can be used to estimate the electron energy at ~150eV. So when used with a solenoid, the 15E detector seems to function as a crude spectrometer with an electron bunch. However, data from positrons at 15E or either beam at 15W is inconsistent with this simple interpretation. So while there is hope that the use of a solenoid field can give useful information about electron energies, there are inconsistencies in data interpretation that need to be resolved through more careful modeling. \begin{figure} % figure placement: here, top, bottom, or page \begin{minipage}[t]{.48\textwidth} \begin{center} \includegraphics[width=\textwidth]{EC_GrowthMitigation/figures/spu_meas_bscan_15E_ele.eps} \end{center} \end{minipage} \hfill \begin{minipage}[t]{.48\textwidth} \begin{center} \includegraphics[width=\textwidth]{EC_GrowthMitigation/figures/spu_meas_bscan_15E_pos.eps} \end{center} \end{minipage} \vspace{.01\textwidth} \begin{minipage}[t]{.48\textwidth} \begin{center} \includegraphics[width=\textwidth]{EC_GrowthMitigation/figures/spu_meas_bscan_15W_ele.eps} \end{center} \end{minipage} \hfill \begin{minipage}[t]{.48\textwidth} \begin{center} \includegraphics[width=\textwidth]{EC_GrowthMitigation/figures/spu_meas_bscan_15W_pos.eps} \end{center} \end{minipage} \caption{\label{fig:ec_growth:spu_meas_bscan} Pickup signal vs. solenoid field with a single bunch } \end{figure} \subsubsection{Shielded Pickup Modeling} \label{sssec:ec_growth.ec_buildup_other.spu.modeling} \paragraph{Sensitivity to Photoelectron Energy Distribution} The upper row of Fig.~\ref{fig:shapesbefore} shows examples of shielded pickup signals for two bunches of 5.3~GeV positrons (left) and electrons (right) separated by 14~ns. The population of the first bunch is 1.3E11e while that of the trailing bunch varies up to a similar value. The trailing bunch accelerates cloud particles into the detector, producing the second signal. The arrival time and structure of the earlier signal corresponds to photoelectrons produced at the time of bunch passage on the lower chamber wall. The kick from the positron bunch accelerates such photoelectrons toward the detector, whereas in the case of an electron beam the signal electrons must carry sufficient kinetic energy to overcome the repulsion of the beam bunch. The lower row of Fig.~\ref{fig:shapesbefore} shows an initial attempt to model the case of two 1.3E11e bunches using the electron cloud simulation code ECLOUD~\citep{ICFABDNL33:14to24}. \begin{figure*} \centering \includegraphics*[width=80mm]{EC_GrowthMitigation/figures/positrons_spu.eps} \includegraphics*[width=80mm]{EC_GrowthMitigation/figures/electrons_spu.eps}\\ \includegraphics*[width=75mm]{EC_GrowthMitigation/figures/positrons_ecloud.eps} \hspace{3mm} \includegraphics*[width=75mm]{EC_GrowthMitigation/figures/electrons_ecloud.eps} \caption[SPU signals vs. initial modeling results]{\label{fig:shapesbefore} Upper row: shielded pickup signals produced by two 5.3~GeV positron (left) and electron (right) bunches separated by 14~ns. The leading bunch population is 1.3E11e . The population of the second bunch varies up to a similar value. Lower row: initial ECLOUD model results exhibiting discrepancies with the measured signals which are quite dramatic in the case of the electron beam.} \end{figure*} The calculation of cloud kinematics including space charge forces and beam kicks determines arrival times, momentum vectors and charges of the macroparticles reaching the upper surface of the chamber at the positions of the pickups. This early attempt at simulating the observed signals included a rather crude model of the port hole acceptance, leading to poor approximation of the magnitude of the signal, but it was sufficient to diagnose the obviously discrepancy with the observed signals. The positron case shows moderate time structure differences, but the modeling of the electron beam kick exhibited a dramatic discrepancy. The arrival times of the observed signals indicate photoelectron production on the lower wall of the chamber, which is effected in the simulation via a reflectivity parameter distributing 20\% of the photoelectrons uniformly in azimuth. The prompt signal from each electron bunch corresponds to photoelectrons produced on the upper wall repelled into the detector during the bunch passage. The photoelectrons produced on the lower wall in the ECLOUD simulation are similarly reabsorbed, and these are the ones needed to produce the observed signal! In other words, the measurement shows that photoelectrons of sufficient energy to overcome the repulsion of the beam bunch must be present. The photoelectron energy distribution in this original default model is common to many successful simulations of a wide variety of experimental observations~\citep{ICFABDNL33:14to24,PAC09:FR5RFP044,IPAC10:TUPD024}, namely a Gaussian with average and rms values of 5~eV limited by truncation to positive values. Figure~\ref{fig:pe} compares such a distribution (blue) to a power-law modification adequately reproducing the observed signal shapes (red). Low-energy and high-energy regions are shown normalized on logarithmic scales to illustrate the dramatically higher energies needed. \begin{figure} \centering \includegraphics*[width=65mm]{EC_GrowthMitigation/figures/pe.eps} \caption[Modifying the modeled photoelectron energy distributions]{\label{fig:pe} Low- and high-energy regions of the photoelectron energy distributions used to model the measured signals shown in Fig.~\ref{fig:shapesbefore}. The original low-energy distribution shown in blue results in dramatic discrepancy with the signals observed in the case of an electron beam. The modified distribution shown in red provides good agreement with the observed signals.} \end{figure} This new high-energy distribution was determined by matching single-bunch models to the measured signals for various electron bunch currents as shown in Fig.~\ref{fig:shapesafter}. The measured signals for a single bunch of 5.3~GeV electrons are shown in the left column. A bunch current of 1~mA corresponds to a bunch population of 1.6E10e. \begin{figure*} \centering \includegraphics*[width=140mm]{EC_GrowthMitigation/figures/RedBlackPlots2.eps} \caption[Comparison of SPU signals to ECLOUD with adjusted photoelectron energies]{\label{fig:shapesafter} Comparison of measured single bunch signals for various electron bunch currents (left column) to the ECLOUD model (right column) after improving the modeled photoelectron energy distributions.} \end{figure*} The model successfully reproduces the increase of signal magnitude with bunch current. While some time structure discrepancies remain, the improvement relative to the results shown in Fig.~\ref{fig:shapesbefore} is remarkable. The overall normalization of the modeled signals is proportional to the assumed reflectivity value, which in this case was 20\%. In addition, the model also exhibits a prompt signal arising from photoelectrons produced nearby the detector repelled into it during the passage of the bunch, increasing with bunch current similarly to the observed signals. \paragraph{Detailed Photoelectron Energy Modeling using Bunch Current Scans} A detailed model of the photoelectron kinetic energy distribution for photoelectrons produced by reflected photons can be obtained by exploiting SPU data recorded for different bunch current levels. The early SPU signal from the leading bunch for a positron beam is largely due to photoelectrons produced on the bottom of the vacuum chamber. This is the closest production point where the beam kick attracts the photoelectrons toward the SPU. Thus the size and shape of the leading bunch signal is determined by the reflected photon rate, azimuthal distribution, the quantum efficiency for producing photoelectrons, the kinetic energy distribution of the photoelectrons and the strength of the attractive beam kick for a positron beam. In particular, the arrival time distribution determines the shape. By modeling the shape for different strengths of beam kick, we can extract the photoelectron energy distribution. An example of such an analysis is shown in Fig.~\ref{fig:currentscan}. Note that the signal begins just a few nanoseconds after bunch passage even for weak beam kicks, indicating that high-energy photoelectrons were produced (hundreds of eV). This level of modeling accuracy was achieved with a photoelectron energy distribution, consisting of the sum of two power law distributions each parameterized by values of $P_1$, $P_2$, and $E_0$: \begin{equation} f(E_{pe}) \propto \frac {E^{P_1}_{pe}} {\strut \left(1+ \strut \frac{E_{pe}}{\strut E_0}\right)^{P_2}} \end{equation} where the parameter $E_0$ is related to the value of the energy at the maximum of the distribution $E_{peak}$ by \begin{equation} E_0 = E_{peak} \frac {P_2-P_1} {P_1} \end{equation} The high-energy component (22\%) has a peak energy of 80 eV and an asymptotic power of 4.4 ($P_1=4$, $P_2=8.4$). Its contribution to the signal is shown as yellow circles in Fig.~\ref{fig:powerlaws}. The low-energy component (78\%) has a peak energy of 4 eV and an asymptotic power of 2 ($P_1=4$, $P_2=6$). It's contribution to the signal is shown as pink triangles. The combined energy distribution is shown on three horizontal scales in Fig.~\ref{fig:pe_energyspectrum}. \begin{figure} \begin{minipage}[t]{0.45\linewidth} \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/comp_113_113_0.eps} \caption[Bunch current scan data and model]{\label{fig:currentscan} Modeled and measured leading SPU signals for bunch currents of 1, 2, 3 and 4 mA/bunch. The dramatically varying amplitudes and shapes are successfully reproduced by tuning the modeled photoelectron energy distribution as described in the text. } \end{minipage} \hspace{1cm} \begin{minipage}[t]{0.45\linewidth} \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/comp_114_114_29751.eps} \caption[ECLOUD model power law contributions to the photoelectron energy distribution]{\label{fig:powerlaws} Two power-law contributions to the modeled photoelectron energy distribution. The yellow circles show the contribution to the signal from the high-energy photoelectron component, and the magenta triangles the low-energy contribution. The combined result is shown in blue.} \end{minipage} \end{figure} \begin{figure} \centering \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/primarype_29748.eps} \caption[ECLOUD model photoelectron energy distribution]{\label{fig:pe_energyspectrum} Modeled photoelectron energy spectrum resulting from the weighted contribution of the two power laws } \end{figure} This analysis presents an opportunity to relate the obtained photoelectron energy distribution to the incident synchrotron energy spectrum and thus derive an estimate of the energy dependence of the quantum efficiency. For example, the power law contributions have been determined in this manner for 2.1~GeV positron beams, showing that the high-energy tails are greatly reduced~\citep{LEPP:REU2011:RPBadman}. These studies also allow us to draw qualitative conclusions on the photoelectron energy distributions for various coatings, as described below in the section on vacuum chamber comparisons under under the same beam conditions and radiation environment. Since these studies pertain to photoelectrons produced by reflected synchrotron radiation photons, the incident photon energy spectrum is a convolution of the critical energy at the source and the energy dependence of the reflection process. Detailed work on modeling reflected photon trajectories is underway~\citep{ECLOUD10:PST08,IPAC11:WEPC141}. \paragraph{Cloud Lifetime Studies Using Witness Bunches} While the awareness of the sensitivity of the shielded pickup measurements to the parameters of photoelectron production was largely motivated by inadequacies of the model discovered in its application to recent measurements, the original intended use of these time-resolved cloud measurements was to provide a quantitative estimate of the elastic yield parameter in the secondary electron yield model. A similar investigation was performed at RHIC~\citep{EPAC06:MOPCH135}. The basic concept is that the mature cloud long after passage of any beam bunch is dominated by low-energy electrons which suffer predominantly elastic interactions with the vacuum chamber wall. The elastic yield parameter describes the ratio of outgoing to incoming macroparticle charge in probabilistic models~\citep{PRSTAB5:124404}, and carries a value typically \mbox{0.5-0.7}, determining the decay time of the cloud density, typically around 100~ns. High-energy electrons of more than 100~eV, produced by synchrotron radiation, beam kicks, or the rediffused component of the secondary yield process, undergo primarily the so-called ``true'' secondary yield process, in which the produced secondary carries only a few electron volts of kinetic energy, resulting in the dominance of low-energy electrons late in the cloud development. Figure~\ref{fig:seypop} shows an ECLOUD secondary yield population curve typical of the shielded pickup signal simulations.The true secondary yield maximum at 400~eV ranges from a minimum of 0.9 to a maximum of 1.5 owing to the dependence on incident angle. At low energy the yield value is dominated by the elastic interactions with the chamber wall. This case exhibits an elastic yield parameter of 0.55. \begin{figure*} \centering \includegraphics*[width=120mm]{EC_GrowthMitigation/figures/sey_population.eps} \caption[Secondary yield population curve]{\label{fig:seypop} Secondary yield population curve typical of the ECLOUD model for the shielded pickup signals. The upper plot shows the yield value (ratio of secondary macroparticle charge to that of the incident charge) as a function of the incident kinetic energy. At low energy the yield value is dominated by the elastic interaction with the chamber wall. This case exhibits an elastic yield parameter of 0.55. The lower plot shows the incident energy distribution. The elastic and rediffused components are shown in green and blue, respectively. The sum of all three components, true, elastic and rediffused, is shown in red. Since the three colors are plotted on top of each other, the upper plot shows primarily blue at low energy, even though the elastic process dominates, as is seen in the lower plot. } \end{figure*} The witness bunch experimental method consists of generating a cloud with a leading bunch, then accelerating cloud electrons into the shielded pickup detector with a trailing bunch at various delay times. Table~\ref{tab:witness_bunch_data_sets} shows the witness bunch data sets which were recorded from March, 2010 through June, 2011. Additional data sets with delay times restricted to 14~ns and 84~ns at bunch currents of 1, 2, 4, 6, and 8~mA were also taken for systematic checks of the modeling. \begin{table}[htpb] \centering \caption{\label{tab:witness_bunch_data_sets} Shielded pickup witness bunch data sets recorded from March, 2010 through June, 2011. Note that the various cloud-mitigating coatings (TiN, a-carbon, and diamond-like carbon) were swapped into the different radiation environments at 15E and 15W. Data sets with differing total radiation dose were obtained as well. Two vacuum chambers with a-carbon coatings were studied, providing information on production reproducibility.} \vspace*{1ex} \begin{tabular}{ccccccc} \hline\hline Date & Species & Beam Energy & Bunch Current & 15E/W & Mitigation & Bunch Spacing \\ & & (GeV) & (mA) & & Technique & (ns) \\ \hline 03/27/2010 & Positrons & 5.3 & 5 & W & a-Carbon (1) & 14-84 \\ & & & & E & TiN \\ & Electrons & & 5 & W & a-Carbon (1) & 14-70 \\ & & & & E & TiN \\ \hline 05/09/2010 & Positrons & 2.1 & 3 & W & Al & 4-140 \\ & & & & E & a-Carbon (2) \\ & Electrons & & 3 & W & Al & 4-20 \\ & & & & E & a-Carbon (2) \\ \hline 05/17/2010 & Positrons & 5.3 & 3 & W & Al & 4-100 \\ & & & & E & a-Carbon (2) \\ & Electrons & & 3 & W & Al & 4-100 \\ & & & & E & a-Carbon (2) \\ \hline 05/19/2010 & Electrons & 2.1 & 1 & W & Al & 4-120 \\ & & & & E & a-Carbon (2) \\ \hline 12/24/2010 & Positrons & 5.3 & 3, 5 & W & TiN & 14-84 \\ & & & & E & a-Carbon (2) \\ & Electrons & & 3, 5 & W & TiN & 14-84 \\ & & & & E & a-Carbon (2) \\ \hline 04/07/2011 & Positrons & 5.3 & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ & Electrons & & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ \hline 04/16/2011 & Positrons & 2.1 & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ 04/17/2011& Electrons & & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ \hline 06/11/2011 & Positrons & 2.1 & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ 06/12/2011 & Electrons & & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ \hline 06/18/2011 & Positrons & 5.3 & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ & Electrons & & 3, 5 & W & TiN & 14-84 \\ & & & & E & DL Carbon \\ \hline \hline \end{tabular} \end{table} The magnitude and time structure of the signal from the leading bunch is determined by the reflective properties of the vacuum chamber and by the energy-dependent quantum efficiency, as described in the preceding section. The signal induced by the witness bunch has a contribution similar to that of the leading bunch added to the contribution from the existing cloud kicked into the detector. The latter contribution is sensitive to the cloud density and the spatial and kinematic distributions of the cloud electrons. Figure~\ref{fig:al} shows the results of six sets of simulations with various values for the elastic yield parameter $\delta_0$. In each of the six plots, eleven two-bunch (5.3~GeV, 4.8E10e positrons each) pickup signals are superposed, whereby the delay of the witness bunch varies from 12 to 100~ns. The modeled signals are shown with the statistical error bars corresponding to the number of macroparticles contributing to the signal. The magnitudes of the modeled signals at large witness bunch delay clearly show the dependence on the elastic yield parameter $\delta_0$ as it is varied from 0.05 to 0.75. The most consistent description of the measured signals is given by a value of $\delta_0=0.75$. This value can be compared to the value of $\delta_0=0.5$ used in the modeling of \cesrta\ coherent tune shift measurements as described in Refs.~\citep{PAC09:FR5RFP044,IPAC10:TUPD024}, where the measurements had much less discriminating sensitivity to the elastic yield. \begin{figure*} \centering \includegraphics*[width=52.5mm]{EC_GrowthMitigation/figures/lifetime_20100517_15w_1.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100517_15w_2.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100517_15w_3.eps}\\ \includegraphics*[width=52.5mm]{EC_GrowthMitigation/figures/lifetime_20100517_15w_4.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100517_15w_5.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100517_15w_6.eps} \caption[Witness bunch study with the uncoated aluminum chamber.]{\label{fig:al} Witness bunch study with the uncoated aluminum chamber. Eleven two-bunch scope traces are superposed in each of the six plots, whereby the delay of the witness bunch ranges from 12 to 100~ns. The modeled signals are shown with the statistical error bars corresponding to the number of macroparticles contributing to the signal. The magnitudes of the modeled signals at large witness bunch delay clearly show the dependence on the elastic yield parameter $\delta_0$ as it is varied from 0.05 to 0.75. The most consistent description of the measured signals is given by a value of $\delta_0=0.75$.} \end{figure*} Figure~\ref{fig:tin} shows a similar study, but for a titanium-nitride-coated aluminum chamber. For each of the six values assumed for the elastic yield, thirteen two-bunch (5.3~GeV, 8.0E10e positrons each) pickup signals are superposed, whereby the delay of the witness bunch is varied from 14 to 84~ns. The optimal value for the elastic yield is clearly less than the value determined for the uncoated aluminum chamber, with $\delta_0 = 0.05$ providing the best description of the measurements. \begin{figure*} \centering \includegraphics*[width=52.5mm]{EC_GrowthMitigation/figures/lifetime_20100327_15e_1.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100327_15e_2.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100327_15e_3.eps}\\ \includegraphics*[width=52.5mm]{EC_GrowthMitigation/figures/lifetime_20100327_15e_4.eps} % \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100327_15e_5.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100327_15e_17386_5.eps} \includegraphics*[width=50mm]{EC_GrowthMitigation/figures/lifetime_20100327_15e_6.eps} \caption[Witness bunch study with the titanium-nitride-coated aluminum chamber.]{\label{fig:tin} Witness bunch study with the titanium-nitride-coated aluminum chamber. The smooth curves are the digitized shield pickup signals. Six two-bunch scope traces are superposed in each of the six plots, whereby the delay of the witness bunch ranges from 14 to 84~ns. The magnitudes of the modeled signals at large witness bunch delay clearly show the dependence on the elastic yield parameter $\delta_0$ as it is varied from 0.05 to 0.95. The most consistent description of the measured signals is given by a value of $\delta_0=0.05$. } \end{figure*} These comparisons show a number of intriguing discrepancies. The leading bunch signal shape exhibits the need for further tuning of the photoelectron energy distribution. The signal widths tend to be wider than observed. In addition, such a low value of 0.9 for the secondary yield of an uncoated aluminum surface cannot be easily understood, since the tune shifts measurements require an average value around the CESR ring of about 1.8. A wide variety of systematic studies have been undertaken since the ECLOUD'10 workshop, discovering sensitivity to many detailed characteristics of the cloud. For example, the signal widths for early witness signals depend strongly on the azimuthal production distribution of photoelectrons, as was observed by implementing in ECLOUD the distributions calculated by the photon-tracing reflectivity model for the CESR ring described in Ref.~\citep{ECLOUD10:PST08}. Nonetheless, the dramatic improvements in consistency obtained via such systematic studies have not changed the quantitative conclusions concerning the sensitivity to the value for the elastic yield. Generally one can say that the choice of peak true secondary yield value relative to the effective reflectivity value determines the ratio of the early witness bunch signal magnitudes to that from the leading bunch. However, for witness bunches late enough that the signal magnitude becomes comparable to that of the leading bunch, there is little sensitivity to the true secondary yield. Instead, those signal magnitudes are determined by the value assumed for the elastic yield. \paragraph{In situ comparisons of custom vacuum chambers} One fruitful analysis strategy has proved to be the comparison of SPU signals in chambers which have been swapped into the same location in the CESR ring and studied under identical beam conditions~\citep{IPAC11:WEPC135}. The two regions in CESR equipped with SPU detectors differ in radiation environment, since the dominant source points are in dipole magnets of differing strengths. At 5.3~GeV, for example, the source dipole field is 3~kG (2~kG) in the west (east) region for a positron beam, resulting in a critical energy of 5.6~keV (3.8~keV). In addition, the situation with regard to reflected radiation is different. By comparing SPU signals recorded at the same place in the ring with the same beam energy, bunch spacing and bunch population, many systematic contributions to the comparisons are avoided, and relatively simple changes to the modeling suffice to quantify the different properties of the vacuum chambers. Figure~\ref{fig:carbon} shows such a comparison for an a-C-coated chamber in May and December 2010 for two 5.3~GeV 28-ns-spaced bunches each carrying $4.8\times10^{10}$ positrons, corresponding to a bunch current of 3~mA. \begin{figure} \centering \includegraphics*[width=120mm]{EC_GrowthMitigation/figures/WEPC135_f1.eps} \caption[ECLOUD modeling for conditioning effect in a-Carbon]{\label{fig:carbon} Shielded pickup signals measured in an a-C-coated chamber in May (blue dotted line) and December (red dotted line) of 2010 for two 5.3~GeV, 28-ns-spaced bunches each carrying $4.8\times10^{10}$ positrons. The ECLOUD model optimized for the May data is shown as blue circles, the error bars showing the signal macroparticle statistical uncertainties. } \end{figure} During the intervening time interval, CESR had operated at high current as an X-ray research facility, with the consequence that synchrotron radiation dose on the chamber had increased by a factor of about 20, from $8.1{\times}10^{23}$ to $1.8{\times}10^{25}$~$\gamma$/m. Also shown is the ECLOUD model optimized to reproduce the May measurement. Since the signal from the leading bunch arises from photoelectrons produced on the bottom of the vacuum chamber~\citep{ECLOUD10:PST09,PAC11:WEP142,IPAC11:WEPC135}, careful tuning of the energy distribution and quantum efficiency (QE) for photoelectrons produced by reflected photons is required to reproduce the size and shape of the signal. The signal from the witness bunch includes additionally the contribution from secondary EC electrons accelerated into the SPU detector by the witness-bunch kick. The modeled witness signal is therefore crucially dependent on the SEY and production kinematics. Since conditioning affects both signals similarly, we can conclude that the change is in the QE rather than in the SEY. The December measurement is reproduced by a 50\% decrease in the modeled QE for photoelectron production. A reduction in the SEY of 25\% is inconsistent with the observed effect, since the modeled leading bunch signal remains unchanged. Guided by the above comparisons, we can assess conditioning effects in the TiN- and DL-carbon-coated chambers in similar fashion. Figure~\ref{fig:tincond} compares the SPU signals for two $8\times10^{10}~e^+$ bunches in the TiN-coated chamber in April and June 2011, with accumulated synchrotron radiation doses of $5.9{\times}10^{24}$ and $1.1{\times}10^{25}$~$\gamma$/m, corresponding to integrated beam currents up to more than 730 amp-hours. Changes in the QE and SEY are less than a few percent. The conditioning effects in the DL-carbon-coated vacuum chamber are quite different, as shown in Fig.~\ref{fig:dlc}. \begin{figure} \begin{minipage}[t]{0.45\linewidth} \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/WEPC135_f2.eps} \caption[SPU signals showing conditioning effects for TiN coating]{\label{fig:tincond} SPU signals showing conditioning effects in the TiN-coated aluminum vacuum chamber } \end{minipage} \hspace{1cm} \begin{minipage}[t]{0.45\linewidth} \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/WEPC135_f3.eps} \caption[SPU signals showing conditioning effects for a diamond-like carbon coating]{\label{fig:dlc} SPU signals showing conditioning effects in the aluminum vacuum chamber coated with DL carbon } \end{minipage} \end{figure} Conditioning effects are clearly observed for a radiation dose increasing from $6.6{\times}10^{24}$ to $1.3{\times}10^{25}$~$\gamma$/m, corresponding to 370 and 730~amp-hours. Remarkably, the size and risetime of the signal from the leading bunch increased, indicating that the QE for photoelectrons produced by reflected photons increased somewhat, and that more photoelectrons were produced at higher kinetic energies. Despite the increase in photoelectron production, the signal from the witness bunch decreased, showing that the conditioned SEY is significantly lower. Future modeling efforts will provide quantitative estimates for these changes. The method of in situ comparison of custom vacuum chambers can also be used to compare the characteristics of different mitigation techniques. Figure~\ref{fig:al_tin} compares signals from a TiN-coated aluminum chamber and an uncoated chamber with a factor of ten lower synchrotron radiation dose. The shape and size of the leading bunch signal show that the quantum efficiency for producing photoelectrons from reflected photons is much lower for the TiN coating. The secondary yield is also significantly smaller. A comparison between TiN and amorphous carbon coatings is shown in Fig.~\ref{fig:acarbon_tin}. The later, smaller signal from the leading bunch from the a-carbon chamber shows that the quantum efficiency is lower, particularly for high-energy photoelectrons. However, the similar magnitudes of the signals from the witness bunch indicate that the secondary yield for TiN is somewhat smaller than that for a-carbon. Further modeling promises to provide quantitative results for these qualitative observations. \begin{figure} \begin{minipage}[t]{0.45\linewidth} \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/comp_103_0_3.eps} \caption[SPU signals comparing uncoated aluminum to TiN]{\label{fig:al_tin} SPU signals exhibiting the difference in cloud buildup characteristics between a TiN-coated aluminum chamber and an uncoated aluminum chamber with a factor of ten lower synchrotron radiation dose } \end{minipage} \hspace{1cm} \begin{minipage}[t]{0.45\linewidth} \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/comp_104_0_3.eps} \caption[SPU signals comparing a-carbon and TiN coatings]{\label{fig:acarbon_tin} SPU signals exhibiting the difference in cloud buildup characteristics between a-carbon-coated and TiN-coated aluminum chambers } \end{minipage} \end{figure} \paragraph{Use of a Weak Solenoidal Magnetic Field} One type of measurement which has been obtained with the shielded-pickup detectors is illustrated schematically in Fig.~\ref{fig:bpsketch}. The vacuum chambers have been outfitted with windings to approximate a solenoidal field in the region of the cloud with magnitude up to 40~G. Since signal contributions require nearly vertical arrival angles, the centers of the corresponding circular trajectories for any given magnetic field value lie in the horizontal plane of the ports. The three trajectories originating at the primary impact point of the synchrotron radiation and leading to the center of each electrode thus select different regions of photoelectron energy and production angle, as shown. \begin{figure} \centering \includegraphics*[width=70mm]{EC_GrowthMitigation/figures/beampipe_sketch_wall.eps} \caption{\label{fig:bpsketch} Vacuum chamber wall cross section with circular trajectories of photoelectrons contributing to the pickup signals.} \end{figure} Experiments to date have shown that the $40$~G field magnitude range suffices to cover the full energy range of the photoelectrons produced by a 2.1~GeV beam (${\rm E}_{\rm critical} \approx 300$~eV) (i.e. no pickup signal is observed for field values of 0 and 40~G), in contrast to the case of a 5.3~GeV beam (${\rm E}_{\rm critical} \approx 5$~keV), where photoelectron energies suffice to produce an observable signal even at 40~G. Furthermore, reversal of the solenoidal field provides information on the production of photoelectrons at a point on the vacuum chamber opposite the primary source point and thus relevant to the reflective characteristics of the vacuum chamber wall. This paper does not discuss in detail the measurements obtained with solenoidal field, which remain under analysis, but instead concentrates on an alternative method to measure photoelectron energy. \paragraph{Summary} The shielded pickup detectors installed in the CESR ring in 2010 have begun providing a wide variety of time-resolved measurements of electron-cloud-induced signals. Measurements with custom vacuum chambers incorporating cloud mitigation techniques such as carbon and titanium-nitride coatings have been obtained and compared to the case of an uncoated aluminum chamber. Weak solenoidal magnetic fields have been employed to study photoelectron production kinematics. A model for the shielded pickup acceptance has been developed in the context of the electron cloud simulation code ECLOUD. The shielded pickup data have proved remarkably sensitive to model parameters poorly constrained by any other experimental means, such as the azimuthal production distribution for photoelectrons and their energy distributions. The measurements with 5.3~GeV electron and positron beams indicate the need for a high-energy component previously absent in the photoelectron generation model. In addition, the design purpose of the shielded pickup detectors has been experimentally confirmed, as the cloud lifetime has been accurately measured using witness bunches at various delays. Sensitivity to the elastic yield parameter in the secondary yield model has been shown to be less than 0.05 and remarkably robust against variation of other model parameters. Data taken with an uncoated aluminum chamber provide a best estimate for the elastic yield of about 0.75. The cloud lifetime studies in a titanium-nitride-coated aluminum chamber exclude such a high value, yielding an optimal value of 0.05.