Picosecond timing planes for future collider detectors

We report experimental test-beam results on dielectric-loaded waveguide detectors that utilize microwave Cherenkov signals to time and characterize high energy particle showers. These results are used to validate models and produce high-fidelity simulations of timing plane systems that yield picosecond time tags and millimeter-level spatial coordinates for the shower centroid. These timing planes, based on the Askaryan effect in solid dielectrics, are most effective at the high center-of-momentum energies planned for the Future Circular Collider (FCC-hh). They will be of particular interest in the forward region due to their high radiation immunity. We use our beam test results and geant4 simulations to validate a hybrid microwave detector model, which is used to simulate a reference timing plane design for the FCC forward calorimeters. Our results indicate that 0.5–3 ps particle timing is possible for a wide range of collision products in the reference FCC hadron collider detector, even with current technology.

Figure 1

Top: waveforms for a single electron transit of a WR51 waveguide loaded with alumina. The estimate from vector potential theory is shown in blue, and data from an XF simulation are shown in red. Bottom: power spectral density for the two waveforms in the top pane. A causal passband filter has been applied to emphasize the ${TE}_{10}$ mode response for the two cases.

Figure 2

Upper left: a rendering of the dewar containing the ACE elements, and an expanded view of the 60-cm long active section, which includes three WR51 waveguide elements. Upper right: Dimensions in cm of the different portions of the experimental setup. Bottom: a geant4 simulation slice through the system from the beam pipe exit to the ACE elements within the dewar. This shows the charged portion of the electromagnetic shower for a bunch with ten electrons of 14.5 GeV energy each. Electrons are in red, positrons in blue, and each interaction vertex is marked with a yellow dot.

Figure 3

Profile slice of geant4 simulated flux of excess shower charge (due to the Askaryan effect) in each of the three ACE elements, along with fitted parameters for the double Lorentzian profiles. In this case, the “bins” are combined totals from two adjacent binned slices through the center, a 2D histogram of the charge passing through each 0.2-mm squared bin.

Figure 4

Similar to Fig. 3, but now without any gaps between the preshower tungsten block and detector elements.

Figure 5

Left column: FDTD-simulated electric fields for the as-built ACE element at a point just prior to the end of the waveguide. For these, the reflection from the shorted far end has been suppressed. Left top: the raw induced waveform with no $T{E}_{10}$ passband filtering imposed; blue is the $T{E}_{mn}$ transverse mode and red is the parasitic longitudinal mode. Left middle: same as left top, with a 5–8 GHz filter applied. Left bottom: power spectral density of each of the signals shown above. Right: the same sequence of signals is shown after coupling through the waveguide-to-coaxial adapter and now including the reflection from the shorted end. Imperfections in the impedance matching are included at each end to produce a realistic signal. The power spectra (right bottom) show a high degree of modulation due to the effects of the Fourier transform of the double pulse.

Figure 6

Composite image of the beam primary electron distribution arriving at the ePix 100 silicon detector, showing the pattern due to imperfect collimation of the beam arriving at End Station A. The vertical dashed lines show the location of the waveguide side wall inner edges.

Figure 7

For the same run shown in Fig. 6, we show the individual frame electron counts per bunch and a marginal histogram on the left, showing the distribution.

Figure 8

Coherent average of runs 268–292 (2400 ACE events), showing all three ACE waveform responses, including the reflection from the shorted end about 4 ns after the initial pulse, to showers generated by electron bunches with parameters similar to those shown in Figs. 6 and 7. The first two elements (in blue and red) had lower efficiency due to degradation in the coupling at liquid helium temperatures. The third element (green) retained its full design efficiency and is used for all amplitude-dependent estimates of absolute response.

Figure 9

Left: raw waveforms for a single event in run 312. Right: cross-correlation functions (CCF) with the signal templates. Slight offsets in the template reference time account for the lag differences in the CCF.

Figure 10

Coherent average of runs 311–330 (1,980 events), similar to Fig. 8 above. The average number of electrons per bunch in this sequence was $⟨N_e⟩=263$.

Figure 11

Top: a two-dimensional image of the amplitude of the time-domain response in the vicinity of the primary shower pulse. The vertical axis is offset relative to waveguide center, and the horizontal axis is time. Bottom: overlay of the waveforms for all offsets, labeled by their offset relative to center.

Figure 12

Cross-covariance coefficient for each channel 3 waveform in the offset data sample vs the CH3 template waveform.

Figure 13

Response function of the amplitude vs transverse offset from waveguide axis. The dashed curve shows the expected half-cosine response.

Figure 14

FDTD simulation of the delay between the dual outputs of a 1-m long waveguide with a shower core offset 75 mm from the center, as a function of the transverse position of the shower core.

Figure 15

Top: Two-dimensional histogram of relative shower energy vs measured delay for selected runs. The distribution at higher energies has a slightly different mean delay than the lower energy distribution. Bottom: a sum of two-Gaussian fit to the data, where the higher energies fit to a $\sim 1\text{−}\mathrm{ps}$ delay offset and a narrower timing distribution than the lower energies.

Figure 16

Single ACE element timing precision vs relative shower energy measured in our experiment.

Figure 17

Cutoff frequencies for alumina-loaded waveguides of 12.7-mm width and variable height.

Figure 18

FDTD simulation of dual WR51 waveguide modes arriving into a $2:1$ E-plane combiner.

Figure 19

Comparison of amplitude spectra for the individual, combined, and square waveguide modes of the FDTD model.

Figure 20

A six-layer point design timing-plane detector using the methods we have described here.

Figure 21

Left: FCC-hh reference detector section view schematic, the forward $\mathrm{EMCAL}+\mathrm{HCAL}$ is in blue in the 17–19 m region. Right: a zoom of the forward calorimeters. ACE timing planes could be located just inside the dewar ahead of the EMCAL, and just after the EMCAL before the HCAL.

Figure 22

geant4-simulated time delay distributions of 100 GeV photon-initiated shower particles, through 3.5 radiation lengths of material, relative to the light travel time from the injection point, along with fits of a Weibull probability density. Each of the panels shows the delay spectrum and fit for one of the simulated waveguide elements, with alphanumeric indices giving their position in the six-element stack of three dual-waveguide detectors. Thus 1A and 1B are the individual waveguides in the first dual-element pair, with A in front and B in the rear relative to the shower propagation.

Figure 23

geant4-simulated time delay distributions of 100 GeV pion-initiated shower particles, through 1.7 nuclear interaction lengths of material, relative to the light travel time from the injection point, along with fits of a Weibull probability density. The geometry of the figure panes is similar to the previous figure.

Figure 24

Relative frequency spectral power for the time delay spectra shown previously. Left, for photon showers, and right, for pion showers.

Figure 25

Left column: distribution of throughgoing charged particles for a single realization of a photon shower transiting three layers of our timing plane. The remaining four columns show, from left to right, (1) the microwave signal at the left end of the ACE waveguide, (2) its cross-correlation with the template response function for the signal; (3) and (4), similar waveforms and CCFs for the microwave signal at the right end of the waveguides. From top to bottom, we show the signals and CCFs for each of the three layers, followed by the coherent sum in the bottom row.

Figure 26

Distributions of all times and time vs absorbed energy prior to the timing plane, for photons at 1 TeV and 100 GeV. Here our timing plane is between a preshower block and the forward EMCAL, with about 3.5 radiation lengths of material ahead of it.

Figure 27

Distributions of all times and time vs absorbed energy prior to the timing plane, for charged pions at 1 TeV and 100 GeV. Here our timing plane is between the forward EMCAL and HCAL, with about 1.7 nuclear interaction lengths of material ahead of it.

Figure 28

A simulation of the FCC-hh luminous region for a single event, based on the expected bunch sizes and interaction rate. The inset shows the core region, and the colors encode the time of the interaction at each vertex relative to the center time.

Figure 29

Timing results vs nuclear $Z$ for ions in our timing planes, where the signal is produced from microwave Cherenkov via the nuclear charge rather than the excess charge of a shower. Values above the bins in $Z$ indicate the fitted $1\sigma$ timing in picoseconds.

Figure 30

Excess TOF for particles or ions at 16.5 m relative to the interaction point, for various masses and energies over the range of the FCC-hh. The overlain text boxes show some specific examples of particles subject to TOF measurements. The energy scale starts at roughly, the limiting ACE threshold of $\sim 50\mathrm{GeV}$, and timing limits can achieve 1–3 ps with the current technology. Thus, the region to the lower right is currently inaccessible. For the timing of heavy ions, nuclear fragments, or long-lived stable BSM particles, the energy is total energy, not energy per nucleon, and the timing range extends from $\sim 1\mathrm{ps}$ to the limit where a new bunch arrives at 25 ns. Thus, for very heavy ions, the momentum precision will be parts in ${10}^4$ or better.

Figure 31

TOF for a heavy stable beyond-standard-model charged particle, in this case, the result of $R$-hadronization of a pair-produced top squark, as a function of the total particle energy, including the masses indicated in the legend.

Figure 32

Jet invariant mass spectrum from the HEPSIM simulations for 100-TeV collisions.

Figure 33

Top: total jet energy vs pseudorapidity for 100 TeV pythia8 jets. The vertical line indicates the forward region where our study is focused. Bottom: fraction of jet component particles that are expected to be above the ACE timing threshold as a function of pseudorapidity, again with the vertical division indicated the forward region. In each case, the color bars indicate the number of jets per bin in the histogram.

Figure 34

Top: Jet photon energy distribution vs $|\eta |$ with the forward region and energy threshold for ACE detection marked. Bottom: similar distribution for jet ${\pi }^{\pm }$. In both cases, the photons and pions are part of the 100 TeV pythia8 simulation introduced in Fig. 32 above. Color bars refer to counts per histogram bin.

Figure 35

TOF simulation for 100 TeV pythia8-simulated jet components with symbols denoting the particle type in each case, including the decays of the shorter-lived mesons and hyperons. The dashed and dot-dash lines provide lower bounds on the regions over which ACE can provide picosecond timing for either electromagnetic or hadronic showers for particles to the right and above the given lines. Quasistable particles appear to stack closely along diagonal lines corresponding to their momenta.

Figure 36

Distribution of pseudorapidity for $H\to \gamma \gamma$ at 14 and 100 TeV. Mean values of $|\eta |$ are also shown.

Figure 37

Daughter photon energy vs pseudorapidity for $H\to \gamma \gamma$ at 100 TeV. The box indicates the region covered by our baseline timing layer associated with the EMCAL.