A 10GHz Low-Jitter Cryogenic Phase-Locked Loop (PLL) For Quantum Applications
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79 ASTRONOMY AND ASTROPHYSICS↗
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Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors
Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr 2 Cu 2.75 Mo 0.25 O 7.54 (T c =84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO 2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO 2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Shapiro steps and stability of skyrmions interacting with alternating anisotropy under the influence of ac and dc drives
Here we use atomistic simulations to examine the sliding dynamics of a skyrmion in a two-dimensional system containing a periodic one-dimensional stripe pattern of variations between low and high values of the perpendicular magnetic anisotropy. The skyrmion changes in size as it crosses the interface between two anisotropy regions. On applying combined dc and ac driving in either parallel or perpendicular directions, we observe a wide variety of Shapiro steps, Shapiro spikes, and phase-locking phenomena. The phase-locked orbits have two-dimensional dynamics due to the gyrotropic or Magnus dynamics of the skyrmions and are distinct from the phase-locked orbits found for strictly overdamped systems. Along a given Shapiro step when the ac drive is perpendicular to the dc drive, the velocity parallel to the ac drive is locked while the velocity in the perpendicular direction increases with increasing drive to form Shapiro spikes. At the transition between adjacent Shapiro steps, the parallel velocity jumps up to the next step value, and the perpendicular velocity drops. The skyrmion Hall angle shows a series of spikes as a function of increasing dc drive, where the jumps correspond to the transition between different phase-locked steps. At high drives, the Shapiro steps and Shapiro spikes are lost. When both the ac and dc drives are parallel to the stripe periodicity direction, Shapiro steps appear, while if the dc drive is parallel to the stripe periodicity direction and the ac drive is perpendicular to the stripe periodicity, then there are only two locked phases, and the skyrmion motion consists of a combination of sliding along the interfaces between the two anisotropy values and jumping across the interfaces.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Magnetron R&D for high efficiency CW RF sources for industrial accelerators
The scheme of using high-efficiency magnetrons to drive radiofrequency accelerators has been demonstrated at 2450 MHz in CW mode *. Magnetron test stands at JLab and GA have been set up to further test the noise figure and the locking speed of the injection phase-lock method. For higher power applications, power combining experiments using a TM010 cavity-type combiner and a magic tee for the binary combiner while using a single clean injection signal has been carried out at 2450 MHz. The frequency pulling effect between the magnetron and a low-Q cavity has been shown to enhance the frequency locking bandwidth compared to the injection phase-lock alone. The principle has been studied by the equivalent circuit simulation, analytical model, and finally confirmed experimentally on the magnetrons. Due to the pandemic delay in 2020, the equivalent high power tests using a 75kW, 915MHz industrial magnetron will be done in 2021 and will be reported in a future paper.
Wang, H.↗
Disentangling Coexisting Structural Order Through Phase Lock-In Analysis of Atomic-Resolution STEM Data
As a real-space technique, atomic-resolution STEM imaging contains both amplitude and geometric phase information about structural order in materials, with the latter encoding important information about local variations and heterogeneities present in crystalline lattices. Such phase information can be extracted using geometric phase analysis (GPA), a method which has generally focused on spatially mapping elastic strain. Here we demonstrate an alternative phase demodulation technique and its application to reveal complex structural phenomena in correlated quantum materials. As with other methods of image phase analysis, the phase lock-in approach can be implemented to extract detailed information about structural order and disorder, including dislocations and compound defects in crystals. Extending the application of this phase analysis to Fourier components that encode periodic modulations of the crystalline lattice, such as superlattice or secondary frequency peaks, we extract the behavior of multiple distinct order parameters within the same image, yielding insights into not only the crystalline heterogeneity but also subtle emergent order parameters such as antipolar displacements. When applied to atomic-resolution images spanning large (~0.5 × 0.5 μm 2 ) fields of view, this approach enables vivid visualizations of the spatial interplay between various structural orders in novel materials.
74 ATOMIC AND MOLECULAR PHYSICS↗
Linewidth narrowing and wideband frequency modulation of a DBR laser
We present a scheme to phase-lock a 240 mW, 852 nm distributed Bragg reflector (DBR) laser to a fixed-frequency narrow-linewidth laser with a rapidly tunable frequency offset near 9 GHz. The phase-lock is accomplished by electronic feedback on the beatnote between the two lasers. The frequency offset can be swept 200 MHz in 300 us, limited by the feedback loop bandwidth, allowing for its use in complex cooling and state preparation schemes needed in atomic physics experiments. Here, we find that the phase-lock reduces the linewidth of the DBR laser below its natural linewidth of ~400 kHz to ~100 kHz
47 OTHER INSTRUMENTATION↗
Asymmetric high energy dual optical parametric amplifier for parametric processes and waveform synthesis
We report on an asymmetric high energy dual optical parametric amplifier (OPA) which is capable of having either the idlers, signals, or depleted pumps, relatively phase locked at commensurate or incommensurate wavelengths. Idlers and signals can be locked on the order of 200 mrad rms or better, corresponding to a 212 as jitter at λ =2 µ m. The high energy arm of the OPA outputs a combined 3.5 mJ of signal and idler, while the low energy arm outputs 1.5 mJ, with the entire system being pumped with a 1 kHz, 18 mJ Ti:Sapphire laser. Both arms are independently tunable from 1080 nm-2600 nm. The combination of relative phase locking, high output power and peak intensity, and large tunability makes our OPA an ideal tool for use in difference frequency generation (DFG) in the strong pump regime, and for high peak field waveform synthesis in the near-infrared. To demonstrate this ability we generate terahertz radiation through two color waveform synthesis in air plasma and show the influence of the relative phase on the generated terahertz intensity. The ability to phase lock multiple incommensurate wavelengths at high energies opens the door to a multitude of possibilities of strong pump DFG and waveform synthesis.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Evaluating Methods for Measuring Grid Frequency in Low-Inertia Power Systems: Preprint
Accurate measurement of grid frequency is a critical component of reliable grid control. Traditionally, methods such as phase locked loops (PLLs) and discrete Fourier transforms (DFTs) have been used in inverters and phasor measurement units (PMUs) to measure frequency. However, as the percentage of inverter-based resources (IBRs) such as solar and wind has increased, these conventional frequency measurement methods are proving unable to guarantee reliable control in some cases. One challenge is measuring frequency during transient events, where there is a disruption in the steady state sinusoidal voltage. During these events, the underlying frequency of the grid may barely change, but measurement methods report a large spike in frequency due to the disrupted waveform. New methods must balance between suppressing spikes in frequency during faults, and providing fast, accurate, measurements in all other grid operation conditions, especially during events with high rate-of-change-of frequency (ROCOF), which are more prevalent in high-IBR power systems. This paper first surveys frequency measurement methods that have been proposed to reduce measurement errors during transient events. Then, both conventional and more novel frequency measurement methods are tested against an IEEE standard and industry recommendations, and their performance is evaluated for events simulated in PSCAD. Results quantify the trade-offs in performance during different grid conditions and lead to suggestions for the most appropriate frequency and ROCOF measurement methods for low inertia grids.
frequency↗
A 100 kW 1.3 GHz Magnetron System with Amplitude and Phase Control
Calabazas Creek Research, Inc., Fermilab, and Communications & Power Industries, LLC, developed a 100 kW peak, 10 kW average, 1.3 GHz, magnetron-based, RF system for driving accelerators. Efficiency varied between 81% and 87%. Phase locking uses a novel approach that provides fast amplitude and phase control when coupled into a superconducting accelerator cavity [1]. The system was successfully tested at Fermilab and produced 100 kW in 1.5 ms pulses at a repetition rate of 2 pps. A locking bandwidth of 0.9 MHz was achieved with a drive signal of 269 W injected through a 4 port circulator. The phase locking signal was 25 dB below the magnetron output power. The spectrum of the phase locked magnetron was suitable for driving accelerator cavities. Phase modulation was demonstrated to 50 kHz (the limit of the available driver source). The average power was limited by available conditioning time. Scaling indicates 42 kW of average power should be achievable. Estimated cost is less than $1/Watt of delivered RF power, exclusive of power supplies or modulators. System design and performance measurements will be presented.
43 PARTICLE ACCELERATORS↗
Complex Attosecond Waveform Synthesis at FEL FERMI
Free-electron lasers (FELs) can produce radiation in the short wavelength range extending from the extreme ultraviolet (XUV) to the X-rays with a few to a few tens of femtoseconds pulse duration. These facilities have enabled significant breakthroughs in the field of atomic, molecular, and optical physics, implementing different schemes based on two-color photoionization mechanisms. In this article, we present the generation of attosecond pulse trains (APTs) at the seeded FEL FERMI using the beating of multiple phase-locked harmonics. We demonstrate the complex attosecond waveform shaping of the generated APTs, exploiting the ability to manipulate independently the amplitudes and the phases of the harmonics. The described generalized attosecond waveform synthesis technique with an arbitrary number of phase-locked harmonics will allow the generation of sub-100 as pulses with programmable electric fields.
47 OTHER INSTRUMENTATION↗
Magnonic spontaneous oscillation induced by parametric pumping
Spontaneous dynamic systems have attracted significant attention for their rich underlying physics such as phase-locking and synchronization. In this work, we report a new mechanism of generating magnetic spontaneous oscillation via parametric pumping. By applying a pump tone to excite propagating spin waves in a yttrium iron garnet delay line, four-wave mixing converts the pump mode into two phase-autonomous propagating magnon modes, i.e. a spontaneous mode with nearly twice the wavenumber of the pump mode and an idler mode with nearly zero wavenumber. This allows us to reliably generate ultrasharp spin wave dynamics with broad frequency tunability from the pump and magnetic field. We show that the spontaneous mode can be phase-locked to a probe tone, similar to an auto-oscillator. Furthermore, the spontaneous dynamics can be used to implement a high-gain magnonic parametric amplifier with a gain up to 40 dB. Our results open a new avenue for studying nonlinear magnonics and synchronization physics in propagating magnon geometry and for developing new magnonic devices.
Li, Yi↗
PROGRESS ON MAGNETRON R&DS FOR INDUSTRIAL PARTICLE ACCELERATORS
The magnetron as an efficient RF source for a compact industrial SRF accelerator has been developed. The per-formance of injection phase lock on two independent magnetron transmitters operated at 915MHz, in CW mode with maximum power of 75kW each has been demon-strated to satisfy this application. This industrial type magnetron has AC transformer and the SCR rectifier on the DC anode power supply. Output power spectrum with phase locking can achieve noise reduction of -21.2 dBc at the 1st 60 Hz, -28.0 dBc at 1st 180 Hz with only -22.6 dBc injection power. Further control studies for 2×75 kW, 915 MHz power combing by WR975 magic-tee at Jefferson Lab (JLab) and for 4×1.2 kW, 2.45 GHz power combing by WR340 magic-tee at General Atomics (GA).
Rimmer, R.↗
Carrier and sampling frequency offset estimation for RF communication with crystal-less nodes
When the ultra-low power mm-scale sensor node does not have a crystal oscillator and phase-lock loop, it inevitably exhibits significant carrier frequency offset (CFO) and sampling frequency offset (SFO) with respect to the reference frequencies in the gateway. This disclosure enables efficient real-time calculation of accurate SFO and CFO at the gateway, thus the ultra-low power mm-scale sensor node can be realized without a costly and bulky clock reference crystal and also power-hungry phase lock loop. In the proposed system, the crystal-less sensor starts transmission with repetitive RF pulses with a constant interval, followed by the data payload using pulse-position modulation (PPM). A proposed algorithm uses a two-dimensional (2D) fast Fourier transform (FFT) based process that identifies the SFO and CFO at the same time to establish successful wireless communication between the gateway and crystal-less sensor nodes.
Kim, Hun-Seok↗
Proton Improvement Plan II (PIP-II) Clock and Timing
The PIP-II timing system is planned to be a two-part system consisting of a global timing system (referred to as ACLK) that provides high level, event-based timing for the whole Fermilab accelerator complex while the second part is a RF synchronized clock system unique to the PIP-II Linac itself (referred to as LCLK). The ACLK System will make use of an external 10 MHz GPS based signal source as a reference for its 650 MHz phase lock as it is the reference frequency for the TCLK output of the system (needed to support legacy hardware around complex). The LCLK System will use a PIP-II Linac RF reference (162.5 MHz) from the Linac LLRF system to allow beam synchronized event placement. Both the ACLK and LCLK systems will have a clock output with a data frame of 16 event bits + 32 data bits with frames broadcast at 650 MHz, phase locked to the 10MHz reference in the case of ACLK and the PIP-II LLRF sourced 162.5 MHz reference in the case of LCLK.
43 PARTICLE ACCELERATORS↗
Nonlinear coupling of tearing modes in reversed field pinch plasmas with stepped pressure profiles
A theory of the three-wave coupling of triplets of tearing modes in toroidal pinches [i.e., either reversed field pinches (RFPs) or tokamaks] was proposed by R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)]. However, this theory only applies to toroidal pinches with negligible equilibrium plasma pressure gradients. Such a limitation is particularly inappropriate to RFPs. This paper generalizes the analysis of R. Fitzpatrick [Phys. Plasmas 6, 1168 (1999)] in order to take the equilibrium pressure gradient into account. However, for the sake of simplicity, a stepped pressure profile, rather than a continuous profile, is employed. In the limit in which the number of steps becomes very large, the results obtained from the generalized theory are presumably equivalent to those that would have been achieved using a continuous pressure profile. The generalized theory is used to investigate the formation of the characteristic toroidally localized pattern of phase-locked m = 1 and m = 0 tearing modes in RFP plasmas that is known as the “slinky” pattern. The incorporation of the equilibrium plasma pressure into the analysis is found to be of crucial importance when determining the properties of the pattern. This is the case because the plasma pressure controls the number of unstable m = 1 and m = 0 tearing modes, and also significantly affects the strength of three-wave coupling, as well as the phase relation between the phase-locked m = 1 and m = 0 modes.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Design of a Non-PLL Grid-Forming Inverter for Smooth Microgrid Transition Operation
This paper develops a controller for a grid-forming (GFM) inverter that is capable of operating as either a GFM or grid-feeding source that can improve the operation of a microgrid during on-off grid transitions through use of a novel synchronization approach. Furthermore, this controller avoids use of a phase-locked loop (PLL) and the inverter is able to synchronize with the grid with self-generated voltage and frequency. This prevents the inverter from replicating any grid voltage disturbances in its output—a key disadvantage of many grid-connected inverters that use a PLL. To enable fast synchronization, active synchronization control is adopted both during inverter start-up and microgrid reconnection operation and a method of coordinating synchronization of the inverter with a microgrid controller and grid interconnection circuit breaker is presented. Simulation results for multiple microgrid transition operations and unplanned islanding events demonstrate that the developed non-PLL grid-connected GFM inverter controller and synchronization method are effective in synchronizing the inverter and microgrid to the grid, avoiding phase jump during microgrid transition operation, and improving microgrid islanding transients versus a traditional configuration.
27 ARPA - Advanced Research Projects Agency-Energy↗
Decentralized Control of Cascaded H-Bridge Inverters for Medium-Voltage Grid Integration: Preprint
This paper introduces a fully decentralized control strategy that allows for individualized active and reactive power control of H-bridge inverters connected in series. After formulating a model of the system power flows, we outline a communications-free approach where each inverter can act on independent commands. Inverter-level feedback is accomplished locally via a measurement of current flowing through the stack. A key feature is the lack of any centralized control routines or phase-locked loop. In this framework, the reactive power control loops achieve voltage synchronization among the converters and the grid, and the active power control loops modulate the terminal voltage amplitudes that influence power delivery. Furthermore, pole placement via state feedback is used to ensure stability of voltage synchronization while also enabling tracking of bidirectional power commands. Simulations are presented to validate the proposed approach.
communication-free modular converter control↗
Design Power Control Strategies of Grid-Forming Inverters for Microgrid Application
This paper develops and compares two control schemes in the application control layer of a non-phase-locked loop (non-PLL) grid-forming (GFM) inverter to gain insight and understanding into how the two schemes affect the dynamic responses of GFM inverters and the transition operation of microgrids. The first scheme adopts power tracking based on an outer current loop in grid-connected mode and droop control in islanded mode, and the second uses droop control in both grid-connected and islanded modes. Analytical study is developed to compare the performance of these two strategies from various aspects, including fundamental differences, transition operation, power tracking, and P-Q capability with low point-of-common-coupling (PCC) voltages. Extensive simulation testing is carried out to validate the control performance of these two control strategies, and the simulation testing confirms the findings of the analytic study. Finally, the second strategy is recommended because of its superior control performance and ease of implementation. The analysis and results are useful in developing reliable control schemes for non-PLL GFM inverters because increasing numbers of inverters will work as non-PLL grid-forming sources in future grids because of their improved stability and reliability.
grid-forming↗