# Onset of space-charge effects in strong-field photocurrents from nanometric
needle tips

Johannes Schötz  Department of Physics, Ludwig-Maximilians-Universität Munich,
D-85748 Garching, Germany  Max Planck Institute of Quantum Optics, D-85748
Garching, Germany  Lennart Seiffert  Institute for Physics, University of
Rostock, D-18051 Rostock, Germany  Ancyline Maliakkal  Department of Physics,
Ludwig-Maximilians-Universität Munich, D-85748 Garching, Germany  Max Planck
Institute of Quantum Optics, D-85748 Garching, Germany  Johannes Blöchl
Department of Physics, Ludwig-Maximilians-Universität Munich, D-85748
Garching, Germany  Max Planck Institute of Quantum Optics, D-85748 Garching,
Germany  Dmitry Zimin  Max Planck Institute of Quantum Optics, D-85748
Garching, Germany  Philipp Rosenberger  Department of Physics, Ludwig-
Maximilians-Universität Munich, D-85748 Garching, Germany  Max Planck
Institute of Quantum Optics, D-85748 Garching, Germany  Boris Bergues
Department of Physics, Ludwig-Maximilians-Universität Munich, D-85748
Garching, Germany  Max Planck Institute of Quantum Optics, D-85748 Garching,
Germany  Peter Hommelhoff  Laser Physics, Department of Physics, Friedrich-
Alexander-Universität Erlangen-Nürnberg, D-91058 Erlangen, Germany  Ferenc
Krausz  Department of Physics, Ludwig-Maximilians-Universität Munich, D-85748
Garching, Germany  Max Planck Institute of Quantum Optics, D-85748 Garching,
Germany  Thomas Fennel<EMAIL_ADDRESS>Institute for Physics,
University of Rostock, D-18051 Rostock, Germany  Department of Life, Light and
Matter, University of Rostock, D-18059 Rostock, Germany  Max-Born-Institute,
12489 Berlin, Germany  Matthias F. Kling<EMAIL_ADDRESS>Department of
Physics, Ludwig-Maximilians-Universität Munich, D-85748 Garching, Germany  Max
Planck Institute of Quantum Optics, D-85748 Garching, Germany

###### Abstract

Strong-field photoemission from nanostructures and the associated temporally
modulated currents play a key role in the development of ultrafast vacuum
optoelectronics. Optical light fields could push their operation bandwidth
into the petahertz domain. A critical aspect for their functionality in the
context of applications is the role of charge interactions, including space
charge effects. Here, we investigated the photoemission and photocurrents from
nanometric tungsten needle tips exposed to carrier-envelope phase-controlled
few-cycle laser fields. We report a characteristic step-wise increase in the
intensity-rescaled cutoff energies of emitted electrons beyond a certain
intensity value. By comparison with simulations, we identify this feature as
the onset of charge-interaction dominated photoemission dynamics. Our results
are anticipated to be relevant also for the strong-field photoemission from
other nanostructures, including photoemission from plasmonic nano-bowtie
antennas used in carrier-envelope phase-detection and for PHz-scale devices.

##  I Introduction

The interaction of light with nanostructures exhibits unique features [1]. In
plasmonic materials, the excitation of collective oscillations of the
electrons with respect to the lattice (i.e. plasmons) leads to a local near-
field that can be enhanced up to several orders of magnitude in intensity with
respect to the incident field. At the same time, the enhanced fields are
confined to the sharp geometrical features of the nanostructure, well below
the diffraction limit of light. These nanoplasmonic phenomena have found a
vast range of applications (see Ref. [1] for an overview) including
biochemical sensing and detection [2], near-field enhanced optical microscopy
with nanometer resolution (nanoscopy) [3], surface enhanced Raman spectroscopy
[4] with sensitivity down to the single molecule level [5], thermal cancer
treatment [6] and waveguiding of optical energy on the nanometer scale [7].

The demonstration that strong-field photoemission from nanometric needle tips
[8, 9] and nanospheres can be controlled by the electric field of the driving
laser [10, 11], and that the electron dynamics may be strongly modified by the
near-field decay [12, 13] has led to the development of attosecond nanophysics
as an independent research field [14, 15, 16, 17]. Nanotips illuminated by
few-cycle lasers have been used as sources of ultrashort electron pulses for
electron microscopy [18, 19, 20] or for the spatially-resolved detection of
the carrier-envelope phase (CEP) of a laser beam [21]. Significant progress
has been made in the direction of lightwave electronics [22, 23, 24], i.e.
electronics driven by optical fields on the PHz-scale. Based on plasmonic
nano-bowtie antennas, the CEP-detection using currents [25, 26, 27], a
potential PHz-scale diode [28] and recently on-chip field-resolved sampling of
optical waveforms [29] have been demonstrated.

It is typically argued that the small dimension of the nano-emission site
leads to highly divergent trajectories, justifying the neglect of charge
interaction [9, 30, 31]. On the other hand, for certain parameter ranges the
electron kinetic energy spectrum from nanometric needle tips with large apex
radii (r$\sim$100 nm) seems to be completely dominated by Coulomb interaction
[32, 33]. Clearly, the miniscule emission area makes nanometric needle tips
highly susceptible to space charge effects close to the emission surface.
Hence a systematic study of space-charge effects would be highly desirable and
of large importance for the ability to maximize the signal in applications
related to strong-field emission from nanostructures. Here, we present
intensity-dependent photoemission data from nanometric tungsten needle tips in
intense few-cycle laser fields recorded via both time-of-flight spectroscopy
and photocurrent measurements. By analysis of this data and comparison with
simulations, we identify a step-wise increase in the intensity re-scaled
cutoff energies of emitted electrons as the onset of charge interaction
dominated photoemission dynamics. The results are relevant for many related
studies.

##  II Experimental setup

The experimental setup is illustrated in Fig. 1. We obtained CEP-stable pulses
centered at 750 nm from a hollow-core fiber broadened Ti:sapphire laser system
(Spectra Physics, Femtopower Compact Pro HR/CEP) at 10 kHz repetition rate.
The pulses were compressed with a set of chirped mirrors (Ultrafast
Innovations, PC70) to 4.5 fs in full-width-at-half-maximum (FHWM) of the
intensity envelope, which was determined via the Dispersion Scan (d-scan)
technique [34]. A pair of fused silica wedges was used to control the
dispersion and the CEP of the pulses. The few-cycle pulses with controlled CEP
were focused onto a nanometric tungsten needle tip using an off-axis parabola
(OAP, f=10 cm). The needle tip was produced using wet chemical etching [35],
resulting in a typical apex radius of (40$\pm$20) nm. The emitted
photoelectrons were detected using a time-of-flight (TOF)-spectrometer (Stefan
Kaesdorf, ETF10) and a time-to-digital-converter (FAST ComTec, P7889). Due to
the vacuum-requirements for the electron spectra measurements and the
microchannel-plate detector of the spectrometer, the setup was placed in a
vacuum chamber. The photoemitted electrons also resulted in a photocurrent
from the nanotip. The photocurrent was amplified using a low-noise high-gain
transimpedance amplifier (FEMTO, DLPCA-200) and detected using a lock-in
amplifier (Zürich Instruments, HF2LI). For the measurements of the CEP-
dependence, the CEP of consecutive laser pulses was flipped between
$\phi_{\mathrm{0}}$ and $\phi_{\mathrm{0}}+\pi$ using the acousto-optic
programmable dispersive filter (Fastlite Dazzler) of the Ti:sapphire laser
system.

Figure 1:  Experimental setup: A linearly polarized few-cycle pulse at 750 nm
with controlled CEP (thick red line showing a cosine pulse for CEP = 0, and
thin red line showing a -cosine pulse for CEP = $\pi$) irradiates a tungsten
nanometric needle tip. OAP: off-axis parabola, TOF: time-of-flight
spectrometer. The CEP and dispersion are adjusted with fused silica wedges
(not shown). In addition to the kinetic energy spectrum of emitted electrons
measured using the TOF-spectrometer, the photocurrent from the tip is
recorded.

The digital lock-in amplifier was capable of demodulating the signal input at
several frequencies in parallel. For the first frequency, we chose the laser
repetition rate $f_{\mathrm{rep}}=10\,\mathrm{kHz}$ which resulted in a signal
proportional to the total photocurrent. The second frequency was the CEP-
flipping frequency $f_{\mathrm{CEP}}$ which was set to 5 kHz. We observed the
best signal to noise performance at the maximum gain of $10^{9}\,\mathrm{V/A}$
of the transimpedance amplifier even though the nominal gain bandwidth
($f_{\mathrm{-3dB}}$) was below 5 kHz, which slightly reduced the gain at 10
kHz. The conversion factor between signal amplitude and electrons per shot is
approximately given by
$0.6\,\mathrm{electrons}\cdot\mathrm{shot}^{-1}\mu\mathrm{V}^{-1}$. Our
experiments are conducted in the multi-electron emission regime with up to
several hundred electrons per shot. Similar conditions were found for the
nano-bowtie current experiments driven at MHz repetition rates [27]. Their
study indirectly indicates $10^{3}$ to $10^{4}$ electrons per shot per
nanostructure, based on the CEP-current per shot and nanostructure (0.11
electrons) and the ratio of CEP-current to total current ($10^{-4}$ to
$10^{-5}$). The results of our studies are thus of direct importance also in
related experiments where currents from nanostructures are measured.

##  III Results and discussion

The connection between the photocurrent emitted from and flowing through the
tip (and measured with the lock-in amplifier as discussed above - short ’the
photocurrent’) and the TOF measurements is established in Fig. 2, which shows
the intensity dependence of the number of detected electrons. In our
experiments, we observed no significant damage to the nanotip during the
measurement even at the highest intensities, as confirmed by the repeatability
of the measurements. Both photocurrent (blue crosses and dashed line) and TOF
(red triangles and solid line) measurements show a very similar evolution.
However, in the photocurrent, approximately a factor 70 more electrons are
detected. The main reason is likely the partial transmission of the TOF
spectrometer due to the acceptance angle of only around 2.5∘. We intentionally
did not make use of the lens in the TOF spectrometer in order to avoid
distortions of the spectra. From a rough estimate considering the emission
angle [9] we would expect a factor of 40, which is close to our observation.
This illustrates the advantage of the photocurrent approach to capture all
emitted electrons if this is required to characterize the dynamics which may
allow shorter measurement times. The total number of detected electrons per
shot in the photocurrent increases from below 5 at the lowest input power of
0.1 mW to above 3000 at 2 mW. The photocurrent may include slow, potentially
thermally emitted electrons that are not resolved in the TOF measurement. Most
importantly, the change of the slope in Fig. 2 towards a linear emission
regime is interpreted as a signature for the onset of substantial charge
interaction.

Figure 2:  Evidence of charge interaction in the recorded electron yield and
photocurrent measurement: TOF (red) and current (blue) count rate together
with the detected CEP dependence (light and dark gray, respectively). The
current curves have been scaled by a factor 1/70. The change in slope towards
linear emission indicates substantial charge interaction. The black lines
serve as a guide to the eye.

Figure 2 also shows the amplitude of the CEP-dependent modulation of the
photocurrent (dark gray crosses and dashed line) and the electron yield from
the TOF measurement (light gray triangles and solid line) by scanning the CEP
over 20 values between 0 and 2$\pi$. Note that the statistical error in the
TOF measurements is significantly higher (not shown for the sake of clarity of
the figure): on the order of the oscillations between consecutive datapoints,
since the measurements are affected by slow laser power drifts and
fluctuations unlike the photocurrent that is measured with a lock-in
amplifier. A ratio of CEP-dependent modulation signal to total count rate of
around $10^{-2}$ is measured, which is between one and two orders of magnitude
above what has been reported in other studies using nano-bowtie structures and
MHz repetition rate sources [26]. The reason could be twofold. Firstly, it has
been reported that in MHz repetition rate nanotip experiments the strong-field
emission is suppressed due to accumulative heating [36]. Secondly, we use
shorter input pulses and non-resonant field enhancement that translates into
enhanced near-fields with a pulse duration similar to the incident pulse.

CEP-averaged photoelectron energy spectra measured by the TOF for various
local intensities are shown in Fig. 3 a. At low intensities (black curve), a
low-energy peak connected to a plateau is observed, reminiscent of the direct
electron and rescattering contributions of strong-field photoemission
corresponding to the 2 $U_{\text{p}}^{\text{loc}}$ and 10
$U_{\text{p}}^{\text{loc}}$-cutoffs, similar to e.g. Ref. [11]. Note that here
$U_{\text{p}}^{\text{loc}}$ is the local ponderomotive potential of the
enhanced near-field. Beyond the plateau, the spectra decrease rapidly but
still extend to quite high kinetic energy. This is measurable thanks to the
high dynamic range of the spectrometer. For each data set, the value of the
cutoff of the plateau is evaluated by fitting straight lines to the
logarithmic plot of the data below (orange) and above (green) the apparent
cutoff and determining their intersection point, as illustrated here for the
lowest input power shown. As the laser power is increased, the cutoff of the
plateau evolves into a peak structure (cf. gray curve in Fig. 3 a). The
formation of the peak is consistent with the typical structure of elastic
backscattering at higher intensity, where the underlying classical trajectory
picture becomes increasingly appropriate [37].

Figure 3:  Impact of charge interaction on the cutoff energies of recollision
electrons emitted from a nanometric tungsten needle tip: a) CEP-averaged
electron energy spectra for different laser input powers (as indicated). The
cutoff energies are defined via the intersection of linear fits of the data
below (orange line) and above (green line) the apparent cutoff of the
respective recollision plateaus (here visualized only for the lowest power).
b) Cutoff energies as function of near-field intensity (black circles).
Colored arrows indicate the cutoffs corresponding to the spectra in a). Gray
and red symbols show the cutoffs extracted from semi-classical M3C simulations
performed for the experimental parameters when ex- and including charge
interaction, respectively. Gray and black lines visualize the 10
$U_{\text{p}}^{\text{loc}}$ cutoff law as expected from the simple mans model
and a rescaled 16 $U_{\text{p}}^{\text{loc}}$ cutoff law. The scaling factor
between input laser power and local intensity is deduced from matching the
lowest three experimental cutoff values to the 10
$U_{\text{p}}^{\text{loc}}$-cutoff law.

Clear indications for the onset of considerable charge interaction effects are
found in both the power scaling of the yield in Fig. 2, which no longer
reflects the typical strongly non-linear yield increase with intensity but
grows nearly linearly, and the intensity scaling of the plateau cutoff (black
circles) shown in Fig. 3b. For the lowest intensities, a linear scaling of the
cutoff corresponding to the 10 $U_{\text{p}}^{\text{loc}}$-cutoff law (solid
gray line) is found. At a local intensity of about $7.5\times
10^{13}\,\mathrm{W/cm^{2}}$ a step-wise increase of the cutoffs is observed,
followed by an again nearly linear scaling corresponding to a modified cutoff-
law of about 16 $U_{\text{p}}^{\text{loc}}$ (solid black line). Both effects,
i.e. the nearly linear yield evolution with laser power and the increased
cutoff are consistent with previous results found for dielectric nanospheres
[38, 39]. According to these studies, ionization is limited by charge
separation at the surface. The capacitor-like field formed by the released
electrons and the residual ions remaining in the nanostructure quenches tunnel
ionization, leading to a nearly linear growth of the electron yield with
power. The additional energy gain is attributed to modified recollison
dynamics due to the trapping field resulting from the charge separation and
space charge repulsion among the electrons in the departing bunches [38, 39].

To substantiate that the observed cutoff enhancement is caused by charge
interaction, we performed semi-classical trajectory simulations for the
experimental parameters. We adapted our Mean-Field Mie Monte-Carlo (M3C)
model, previously utilized to study strong-field photoemission and attosecond
streaking at dielectric nanospheres [38, 40, 41, 42], for the description of
electron emission from a metallic nanotip. The details of the original
nanosphere model are described in [43]. In brief, the near-field of a
dielectric sphere is evaluated as a combination of the linear polarization
field caused by an incident laser pulse and additional non-linear
contributions from charge interaction that we treat as a mean-field in
electrostatic approximation. The latter includes both Coulomb interactions
among and the additional sphere polarization caused by the free charges, i.e.
liberated electrons and residual ions. Electron trajectories are generated by
Monte-Carlo sampling of ADK-type tunneling rates [44] and are propagated in
the local near-field by integrating classical equations of motion. For
electrons propagating in the material, we account for elastic electron-atom
collisions and inelastic collisions (impact ionization) via respective
scattering cross-sections. To describe the photoemission from a metallic
nanotip, we considered three key modifications. First, we allow tunneling only
from one half-sphere to mimic the apex of the nanotip. Second, we account for
the emerging image charges within the metal in the describtion of the mean-
field. Third, we use a Fowler-Nordheim type tunneling rate and consider a
workfunction of 6.5 eV for the oxidized tungsten nanotip similar to earlier
studies [11, 45, 46]. We note that the rate was scaled with a linear factor
for best agreement with the experimental data.

The cutoff energies extracted from M3C simulations with the mean-field turned
off and on are shown in Fig. 3 b) as gray and red symbols, respectively. The
simulations excluding the mean-field predict cutoffs following the 10
$U_{\text{p}}^{\text{loc}}$-law. When including the mean-field, cutoffs around
10 $U_{\text{p}}^{\text{loc}}$ are only obtained at low intensities where
ionization and thus charge-interaction-induced modifications of the local
near-fields are weak. At higher intensities, the cutoff converges to 16
$U_{\text{p}}^{\text{loc}}$ in close agreement with the experiment. Although
the transition between the two cutoff laws is less rapid than in the measured
data, the semiclassical model captures the main trends and thus confirms that
the observed step-like feature is a clear signature for the onset of charge
interaction dominated photoemission.

So far, most systematic studies focusing on charge interaction in strong-field
photoemission were performed on isolated nanospheres [10, 47, 38, 41]. In
these works, several effects could be identified by thorough analysis of the
experimental results and extensive numerical simulations. Despite the
differences in the strong-field photoemission process between nanometric
metallic needle tips and dielectric nanospheres, the similarity of the
observed charge-interaction effects, the strong reduction of the nonlinearity
of the photoemission process and the increase of the cutoff energy, are
striking.

Our measurements indicate that charge interaction starts to affect the
electron dynamics above a near-field intensity of $7.5\times
10^{13}\,\mathrm{W/cm^{2}}$ or around 1000 e-/shot for 4.5 fs pulses at 750 nm
and tungsten needle tips with a tip radius of around 40 nm. While the strong-
field tunneling photocurrent experiments on nano-bowties and triangles [25,
31, 48, 28, 29] focus mainly on the CEP-dependent current which is on the
order of one electron per shot, the total number of charges per shot is
typically several orders of magnitude higher [26, 31, 27] and therefore in a
similar regime as for our experiment. Our study also shows that despite the
clear charge interaction, waveform-dependent photocurrents can be measured,
which is important for the development of applications of field-controlled
currents. The discussion of charge interaction given here is therefore of high
relevance to these studies as well. Additionally, the higher kinetic energies
of electrons due to the charge interaction could prove useful in future
applications.

##  IV Conclusions

We have investigated the photoemission and photocurrents from nanometric
tungsten needle tips in CEP-controlled few-cycle laser fields. For multi-
electron emission, we identified two regimes, where initially the cutoff
energies of emitted electrons closely follow what is expected from near-field
enhanced backscattering dynamics. At the onset of charge interactions becoming
dominant in the emission process, we observed a step-wise increase in the
cutoff energies. The results are relevant also for the strong-field electron
emission from other nanostructures, including studies where ultrafast currents
from plasmonic bow-tie nanostructures have been used for CEP-detection and
PHz-scale optoelectronic devices.

## Acknowledgements

We acknowledge fruitful discussions with Matthew Weidman and support in the
fabrication of the nanometric needle tips by Mohammed Qahosh, Markus Bohn, and
Hirofumi Yanagisawa. T.F. acknowledges computing time provided by the North
German Supercomputing Alliance (HLRN, ID mvp00017).

## Funding

http://dx.doi.org/10.13039/501100001659,”Deutsche Forschungsgemeinschaft”, via
SPP QUTIF, LMUexcellent, and projects 389759512 and 398382624;
http://dx.doi.org/10.13039/501100000781,”European Research Council”, via
FETopen PetaCOM and FETlaunchpad FIELDTECH;
http://dx.doi.org/10.13039/501100004189,”Max-Planck-Gesellschaft”, via the
IMPRS for Advanced Photon Science and the Max-Planck Fellow program.

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# Installation, Commissioning and Performance of Phase Reference Line for
LCLS-II††thanks: This work was supported by the LCLS-II Project and the U.S.
Department of Energy, Contract DE-AC02-76SF00515

S.D. Murthy<EMAIL_ADDRESS>L. Doolittle  LBNL  Berkeley  CA 94720  USA
C. Xu  B. Hong  A. Benwell  J. Chen  SLAC  Stanford  CA 94309  USA

###### Abstract

Any cavity controller for a distributed system needs a Phase Reference Line
(PRL) signal from which to define phases of a cavity field measurement. The
LCLS-II PRL system at SLAC provides bidirectional (forward and reverse) phase
references at 1300 MHz to each rack of the LLRF system. The PRL controller
embedded with the Master Oscillator (MO) locks the average phase of the two
directions to the MO itself. Phase-averaging tracking loop is applied in
firmware which supports the feature of cancelling the phase drift caused by
changes in PRL cable length. FPGA logic moves the phase of digital LO to get
zero average phase of the two PRL signals. This same LO is used for processing
cavity pickup signals, thus establishing a stable reference phase for critical
cavity RF measurements. At low frequencies, open-loop PRL noise relative to
the LO distribution includes a strong environment and $1/f$ components, but
the closed-loop noise approaches the noise floor of the DSP. The implication
is that the close-in phase noise of the cavities will be dominated by the
chassis DAQ noise. The final out-of-loop phase noise relevant to machine
operations is that of the cavity field relative to the beam.

##  1 INTRODUCTION

To achieve their physics-driven goals, all accelerator RF sub-systems need a
stable phase reference. The primary job of the LLRF system is to hold the
amplitude and phase of each cavity’s voltage constant, where cavity phase is
defined relative to the phase reference signal. The LLRF hardware receives two
frequencies, LO (1320 ) and PRL (1300 MHz). Both of these signals are
generated by the MO subsystem. The specifications for cavity field stability
in LCLS-II are stringent by historical accelerator standards: 0.01∘ in phase
and $0.01\%$ in amplitude [1]. Careful analysis and design minimizes cavity
phase noise and drift.

A phase averaging reference line scheme has been used in the field before at
both SLAC [2] and Fermilab [3], to compensate for thermal drift in the cable
used to distribute phase information. The PRL design adopted for LCLS-II
starts from the same concept but uses digital techniques to perform the
averaging. When averaging is done using analog components, expert field setup
is needed because of sensitivity to amplitude imbalance. The LCLS-II system at
SLAC provides bidirectional (forward and reverse) references to each rack of
the LLRF system at 1300 MHz. By digitizing the two signal separately, more
diagnostics are possible, and the equivalent adjustments performed by
software.

For every offset frequency from DC up to the closed-loop cavity bandwidth, the
LLRF system locks the cavity phase using combination of LO and PRL sources. At
low frequencies (below a few kHz), the PRL contribution dominates, so the
information it provides (after averaging) needs to have minimum phase drifts
[5].

##  2 DESIGN

###  2.1 Phase Reference System

A Voltage Controlled Oscillator (VCO) drives the remote end (far from the MO)
of the physical PRL cable to generate a forward phase reference signal at 1300
MHz. In the MO rack, that forward signal is actively reflected to generate the
reverse wave on the physical PRL cable. A phase lock circuit pins the average
of those two signals to the phase of the MO itself, creating the reflectometer
technique [4]. The block diagram of the phase averaging portion of the PRL is
shown in Fig. 1. At any arbitrary point on the phase reference line, the
directional coupler couples out the forward and reverse signals. The distance
from the coupler to the MO determines the amount of phase difference. The
forward and reverse signals are sent to the LLRF chassis to perform digital
phase averaging.

Figure 1: LCLS-II phase averaging technique.

###  2.2 Installation

The overall LCLS-II linac with 35 1.3 GHz cryomodules, spread out over 600
meters, is divided into segments, from L0 near the gun (a single cryomodule)
to the long (20 cryomodules) L3 for the final on-crest energy boost. LH refers
to the 3.9 GHz energy linearizer (two cryomodules). The PRL is divided up into
three segments: L0+L1+LH, L2, and L3. The MO and most PRL support electronics
are located between LH and L2. The phase-averaging feature described here is
only used in the L0+L1+LH and L2 segments. The unidirectional L3 segment is
driven based on an analog phase averager tap on the L2 PRL. Out-of-loop
diagnostics can measure the consistency between the L0+L1+LH and L2 segments.

As part of the original (2016) system design, the coaxial cable connection
from the PRL coupler to the LLRF rack and the cable connection from the
cryomodule to the LLRF racks are installed to be from the same cable roll with
matching electrical lengths. This is so that they exhibit the same amount of
phase drift due to temperature swings. Also, Time-Domain Reflectometer (TDR)
is used to check any faults in these cables. Fig. 2 shows the physical
installation of the PRL at cryomodules 8 and 9.

Figure 2: Physical PRL installation.

During this setup, PRL amplitude was attenuated to approximately -10 dBFS at
each chassis to reduce the effect of any crosstalk at the digitizer.

###  2.3 Cavity Phase Measurement Firmware

A phase-averaging tracking loop is applied in firmware to eliminate the phase
drift caused by the change in PRL cable length. Both the forward and reverse
reference signals are first downconverted and digitized by the LLRF system,
and further digitally downconverted to baseband. These complex-number values
are multiplied by the PRL gains and summed together to get an average phase,
canceling drifts as previously described. This phase is integrated and passed
to the digital downconverter shared between cavity and PRL signals, forming a
tracking phase-locked loop. The phase-averaging module can be easily enabled
and disabled under software control. When it is disabled, the reference phase
is driven to zero, and the system operates using the LO as a virtual phase
reference. The above computation of phase-averaging adds four cycles of
pipelining delays from the input to the averaged phase and uses a total of 2
multipliers (one for each pair of input) and 2 adders (adding each product and
integrator).

The PRL gain registers are calculated and set by the software, based on the
tracking bandwidth, nominal phase offset, actual phase offset, forward and
reverse PRL signal strengths. The reason to have a nominal offset is that the
setup process can be able to consistently choose one of the two possible
values (180∘ apart) for forward/reverse offset that will bring those two
signals into phase alignment. Either selection will work, but it’s important
to choose the same one across reboots. The actual phase offset is the final
phase offset that will be subtracted and added to the forward and reverse
reference signals respectively. The forward and reverse PRL amplitudes along
with the bandwidth are used to calculate the gain amplitudes. Finally, the PRL
gain values are calculated based on the gain amplitude and the actual phase
offset.

This firmware setup applies only to the L0, L1, LH, and L2 sections of the
Linac. The L3 system is simpler, since there’s only one PRL input to each
rack. There is no need for any intricate offset considerations. To simplify
deployment, the same firmware is used in both cases. In L3, we just lock to
the single input (forward) with zero phase. The two PRL gain registers
handling reverse signals get set to zero, and the two others depend only on
the forward signal strength and desired tracking bandwidth.

##  3 Commissioning and Performance

The commissioning of the LCLS-II SRF system is currently ongoing at SLAC.
Changes to firmware/software while testing on the real PRL cables is
inevitable. One such change included adding guard bits to the phase-averaging
firmware module to reduce rounding errors.

Figure 3: Phase noise power spectral density. Figure 4: Cumulative phase noise
plot.

A LLRF chassis was installed in the MO rack to monitor the upstream and
downstream signals of each of the PRLs, so four RF signals in total (L0+L1
forward and reverse signals, L2 forward and reverse signals). The jitter
between the two reference lines is 0.0073∘ rms, with energy between 60 Hz and
1 kHz as shown in Fig. 3. The rms jitter on these individual reference lines
L0+L1 and L2 are 0.0061∘ and 0.0094∘ respectively. In the cumulative phase
noise plot shown in Fig. 4, an artificial 0.1 Hz high-pass filter is applied
before integrating, to avoid pathologies at DC. Due to the physical location
of this chassis and the supporting couplers and cables, many error terms will
be smaller here than in the "real" LLRF racks. This includes the noise from
the PRL and noise of the measurement system itself. Fig. 5 shows how the PRL
cables to the LLRF chassis stretch over the long term due to temperature
fluctuations. A defective coupler (since replaced) for cryomodule 9 rack A
shows unusually large phase drifts.

Figure 5: Phase drift of cables over the long term.

The maximum achievable tracking loop bandwidth is 300 kHz (limited by the
firmware design), and the system has been tested at 10 kHz. Acquired noise
spectra show the transition between high frequencies (PRL noise is unchanged)
to low frequencies (noise is reduced by the PRL gain). At low frequencies,
open-loop PRL noise relative to the LO distribution system includes a clear
1/f component. At low frequencies, closed-loop noise (in-loop error)
approaches -150 dBrad2/Hz representing the noise floor of the DSP as shown in
Fig. 6.

Figure 6: Noise spectrum of the phase-averaging tracking loop (open and
closed-loop).

##  4 CONCLUSION

The phase reference line was successfully installed at the LCLS-II to provide
a stable reference phase for the LLRF system measurements. The (correctable)
phase drift of the PRL cables over a long period has a span of about 2∘. At
low frequencies, closed-loop noise (in-loop error) approaches the noise floor
of the DSP, and the measured jitter between the two reference lines easily
meets the performance requirements. The full out-of-loop performance
measurement of the system will only be possible further along in the
accelerator commissioning, when the phase noise of the beam relative to
cavities can be measured.

## References

  * [1] P. Emma, “LCLS-II Physics Requirement Document: Linac Requirements”, LCLSII-2.4-PR-0041-R2.
  * [2] J. Frisch, D. Brown, E. Cisneros, “The RF Phase Distribution and Timing System for the NLC” in 20th International Linac Conference, Monterey, California, August 2000.
  * [3] B. Chase, E. Cullerton,  “1.3 GHz Phase Averaging Reference Line for Fermilab’s NML ASTA Program”, Beams-doc-3806-v2.
  * [4] C. Xu, J. Frisch, B. Hong, S. Smith, L. Ruckman, “LCLS-II Phase Reference System” in Low-Level Radio Frequency Workshop, Barcelona, Spain, October 2017.
  * [5] L. Doolittle, “LLRF Sensitivity to LO and PRL Noise in LCLS-II”, LCLSII-2.7-EN-0640.