RF Phase Research Articles

Dry synovitis, a rare entity distinct from juvenile idiopathic arthritis

BackgroundDry synovitis (DS) is a rare entity as only a few cases have been reported to date. We describe the clinical features, radiological manifestations and course of DS in comparison with rheumatoid factor negative polyarticular juvenile idiopathic arthritis (RFneg-polyJIA).MethodsWe performed a multicenter retrospective collection of data of DS patients who presented with progressive joint limitations without palpable synovitis, absence of elevated acute phase reactants, negative ANA and RF, and imaging showing joint and/or osteochondral involvement. For comparative purposes, we included a cohort of RF neg-polyJIA patients.ResultsTwelve DS patients, 8F/4 M, with mean age at onset of 6.1 years, were included. Presenting signs comprised delayed motor development, functional limitations and/or progressive stiffness. Clinical examination showed symmetric polyarticular involvement with variable muscular atrophy. MRI showed mild, diffuse synovial involvement, without effusion. With time, signs of progressive osteochondral damage became evident, despite treatment. All patients were treated with low-dose corticosteroids and methotrexate. Anti-TNF agents were prescribed in five. The response was variable with limited joint mobility in 11/12, and need of joint replacement in 2. In comparison with a cohort of RFneg-polyJIA, DS patients presented higher number of joint involved (p = 0.0001) and contractures (p = 0.0001), less swelling (p = 0.0001) and prolonged diagnostic delay (p = 0.0001).ConclusionDS represents a unique juvenile-onset arthropathy, distinct from polyarticular JIA. Awareness among pediatricians is essential for early recognition and proper treatment. Further studies, including synovial pathology, immunology and genetics may contribute to a better understanding of this rare disorder of childhood.

A truncated twisted solenoid RF phase gradient transmit coil for TRASE MRI

Transmit array spatial encoding (TRASE) is an MR imaging technique that achieves k-space encoding through the use of phase gradients in the RF transmit field. Without requiring B0 gradient fields, TRASE MRI can be performed using significantly cheaper bi-planar permanent magnets or Halbach arrays. For TRASE encoding with these magnets, the twisted solenoid has been demonstrated as the most efficient RF transmit coil; however, this specific geometry results in a long coil with a relatively short imaging volume. We introduce a new truncated design to increase the usable imaging volume relative to the coil length. Based on simulations of optimal parameters, a 200 mm long, 100 mm inner diameter coil pair was constructed with an imaging volume 100 mm in length and 80 mm in diameter. The coil pair was tested using an un-shimmed 2.84 MHz Halbach array. Results indicate the truncated design can create a similar imaging volume and quality to the untruncated version whilst significantly reducing the length of the coil by as much as a half.

SwissFEL double bunch operation

SwissFEL has a unique capability, among the normal conducting linac-based light sources, to simultaneously serve two separate undulator lines (Aramis and Athos) up to the machine repetition rate of 100 Hz using the double bunch operation mode. It increases twice the experiments throughput of the facility with modest additional investment. Two electron bunches spaced 28 ns apart are extracted from the cathode by two laser pulses with individually controlled repetition rates. The bunches are accelerated up to about 3 GeV in the main linac using the same rf macropulse. After separation, one bunch serves the Athos soft x-ray beamline and the other is further accelerated to serve the hard x-ray beamline – Aramis. A fast and high-stability beam kicker separates the two bunches without disturbing the electron beam and consequently the x-ray lasing. The timing and control system sets hybrid machine modes utilizing independent operation of the two undulator lines with individually programmed repetition rates. Beam diagnostics and feedback systems have to operate with two closely spaced bunches where the two beams share the same machine path. The low-level rf system manipulates the rf amplitude and phase within a fraction of the rf macropulse to provide decoupling of the acceleration parameters of the first and the second bunch. This manuscript presents measurements that show that the bunch separation does not degrade FEL lasing stability.13 MoreReceived 7 July 2022Accepted 4 November 2022DOI:https://doi.org/10.1103/PhysRevAccelBeams.25.120701Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAccelerator/storage ring control systemsBeam diagnosticsBeam injection, extraction & transportBeam optics correction schemesBeam optics transportBeam processesBeam techniquesRadio frequency power sourcesAccelerators & Beams

Compact and efficient radio frequency digital feedback control system for accelerator applications

The digital feedback (DFB) setup employed in a low-level radio frequency (LLRF) control system is crucial to ensure RF field stability in accelerating cavities, thus guaranteeing successful operation. To this end, a novel in-house and multi-purpose prototype DFB setup was developed for multiple applications at the Japan Proton Accelerator Research Complex (J-PARC). Being efficient, low-cost, and compact is key to achieving a cost-effective system that fulfills the performance specifications. It also reduces the production and maintenance costs of future DFB setups. A field-programmable gate array (FPGA)-based design with a digital signal processing (DSP) function uses an analog in-phase/quadrature-phase (I/Q) demodulator for RF-to-baseband signal conversion and an I/Q modulator to generate RF power. This arrangement compensates for RF phase fluctuations and amplitude modulations by employing a proportional and integral (PI) feedback controller. In addition, systematic errors are minimized by applying a hardware-error-compensation process. The system was utilized to conduct high-power tests on the interdigital H-mode drift-tube linac (IH-DTL) cavity of a muon linac for short RF pulses. The setup was also tested on a buncher cavity (Buncher-2) in the J-PARC linac, achieving efficient performance for longer RF pulses. The stability of the RF accelerating field in the IH-DTL was achieved at ±0.25% peak-to-peak (pp) in amplitude and ±0.36 degree pp in phase. For the Buncher-2, the amplitude stability of ±0.18% pp and phase stability of ±0.13 degree pp were obtained. Therefore, this DFB setup can be used to conduct high-power tests of RF cavities and klystrons. This study discusses the design aspects of a cost-effective DFB system and reports high-power measurements.

Study of longitudinal phase space for typical beam injector via analytical method

Longitudinal phase space (LPS) manipulation for high-brightness electron beams is critical for successful development of photocathode injectors, especially those are expected to generate ultra-short bunches. Compared with commonly used schemes involving dedicated devices and complicated peripheral sub-systems, a convenient approach for LPS linearization, which is based on adjusting injecting RF phase, has advantages in the typical injectors those consisting of RF cavities and a drift tube. Therein, instead of conventional higher-order harmonic cavities, natural evolutions in the following drift space have been applied to compensate nonlinearity of the LPS from the injector. Since adequate characterizations for the LPS are of importance to promote the application of such approach, elaborate analytical derivations from a new view have been conducted to demonstrate the manipulation scheme, and numerical simulations have been performed to further validate the theoretical results. Contributions of inevitable phase slippages have also been analyzed via analytical and numerical methods. Additionally, to cross-check the analysis results, multi-particle simulations have been performed as well. All of the results indicate that the LPS of the typical injector can be linearized through the natural evolutions during the drifting process. Then such method presents to be a conceivable supplement to conventional LPS manipulation approaches.

Determination of lipophilicity and ionization of fentanyl and its 3‑substituted analogs by reversed-phase thin-layer chromatography

Lipophilicity and ionization constant of sixteen fentanyl analogues were investigated by reversed-phase thin-layer chromatography (RP-TLC). Fourteen compounds have nitrogen containing groups at C-3 position of the piperidine ring and two compounds are 3-carbomethoxy derivatives of fentanyl. Among them, five are diastereomeric cis/trans couples and six novel trans diastereomers. In addition, the lipophilicity and ionization constant of fentanyl were also determined by the same method, as a reference. The physicochemical property, lipophilicity, expressed as retention indices RM0, b, and C0, as well as PC1, was determined and correlated with in silico values. Ionization constants were determined on the basis of the relationships between analyte’s retention expressed as RF and mobile phase pH.Calculated structural descriptors together with the retention indices, were subjected to the principal component analysis – PCA and hierarchical cluster analysis – HCA, in order to provide basic insights into the similarities among the studied compounds. The blood – brain barrier (BBB) permeation was investigated in the function of experimentally obtained values of lipophilicity, polar surface area and molecular weight. In general, results of the present research corroborate well with previously determined antinociceptive activities of the investigated compounds, pointing out that besides the cis/trans isomerism, another set of important parameters should be taken into account when designing new derivatives of C-3 substituted fentanyl, especially lipophilicity, voluminosity and HBD/A character of the substituents. Accordingly, RP-TLC can be considered as a valuable asset in the ligand-based drug design.

Research on 32-tupling frequency terahertz wave generation based on Mach-Zehnder modulators cascaded

A novel scheme to generate 32-tupling frequency terahertz waves by four Mach-Zehnder modulators (MZMs) cascaded is proposed. Four MZMs are divided into two groups linked in series and each group includes two MZMs connected in parallel. The output of the first group and second group of MZMs are ± 4nth and ± 8nth-order sideband signals, respectively. The 0th-order sideband can be cancelled by adjusting the splitting ratio of coupler; The ± 8th-order sidebands can be suppressed by adjusting the modulation index m of MZMs; The ± 8nth (n＞2) sidebands are negligible because of their very small amplitudes. Then the main components of output signal from the second group MZMs are ± 16th-order sidebands, which can generate 32-tupling frequency terahertz signal on the photodetector. The operation principle and simulation experiment of the proposed scheme is performed, and the optical sideband suppression ratio (OSSR) and radio frequency spurious suppression ratio (RFSSR) are obtained to be 53.7 dB, 53.34 dB and 47.7 dB, 47.39 dB, respectively. Simulation experiment values are very close to theoretical values and this demonstrates the feasibility of our scheme. The effects on the OSSR and RFSSR deviated from their designed values are investigated. When the deviations of modulation index, extinction ratio, DC bias, half-wave voltage, the insertion loss of MZM reach about ± 0.42 %, 82 %, ± 8.4 %, ± 1 %, 0.14 %, respectively, and when the deviations of initial phase of RF and splitting ratio of coupler reach about ± 1.3 % at 45°, ± 1.1 % at 90°, ± 2.27 %, respectively, the RFSSR are ≥ 15 dB, which satisfies the engineering applications

Photonic microwave frequency divider with a tunable division ratio and harmonic suppression capability

A photonic microwave frequency divider that is capable to realise tunable high order frequency division, is presented. It is based on injecting an RF phase modulated optical signal into an off-the-shelf DFB laser operating at period-N state. Optical frequency components with a frequency separation of 1/N times the input RF signal frequency are generated by the DFB laser. An optical bandpass filter can be employed to select two optical frequency components to be detected by a photodetector to obtain a divide-by-N RF signal without harmonic components. The proposed frequency divider can be operated over a wide frequency range and has high reconfigurability as it is free of electrical components. Experimental results demonstrate the realisation of frequency division operation with a tunable 1/2 to 1/5 division ratio for different input RF signal frequencies of 8 to 20 GHz by adjusting the DFB laser forward bias current. Over 35 dB harmonic component suppression is demonstrated. A proof-of-concept experiment is also set up to show the frequency divider based on an optically injected semiconductor laser is capable to operate at a high input RF signal frequency of 50 GHz and has a tunable high order division ratio of 1/2 to 1/8.

Coupled bunch mode zero correction using orbit measurements and rf system phase feedback

The target bandwidth of the Advanced Photon Source Upgrade (APS-U) fast orbit feedback (FOFB) is dc-1000 Hz where the synchrotron tune will be between 100 and 560 Hz. This overlap places coupled bunch mode 0 (CBM0) induced horizontal position offsets within the FOFB bandwidth range, affecting our ability to achieve APS-U goals for beam stability. In this article, we present a new feedback technique to damp CBM0 oscillations using the existent FOFB controller framework with no additional hardware and software requirements. Based on the theory of synchrotron oscillations, we developed a feedback algorithm that uses the beam horizontal position measurements at dispersive beam position monitors (BPM) as input and the low level rf (LLRF) phase as an actuator. We demonstrated via experiments in the present APS storage ring that this configuration can correct CBM0 oscillations, and also it can work simultaneously with orbit feedback used to damp ordinary betatron orbit. The simulation model for the proposed orbit to rf phase feedback system is implemented in matlab/simulink to guide us in the controller design. Simulation responses are in good agreement with measurements.

Dual-Output Microwave Photonic Frequency Up- and Down-Converter Using a 90° Optical Hybrid Without Filtering

A dual-output microwave photonic frequency up- and down-converter using a 90° optical hybrid without filtering is proposed. By using a dual-parallel Mach-Zehnder modulator and a Mach-Zehnder modulator in parallel to realize carrier suppressed single sideband and carrier suppressed double sideband modulation, respectively, with a 90° optical hybrid and 90° electrical hybrid coupler, this scheme can implement two functions: simultaneous up- and down-conversion signal generation, or high image rejection in down-conversion. Simulation results show that the proposed structure can achieve an up-conversion with a tunable range of 17–23 GHz or a down-conversion with a tunable range of 1–7 GHz, respectively, based on a fixed 8 GHz LO signal. The unwanted signal suppression ratio of desired signal is about 27.2 dB for up-conversion and 30.0 dB for down-conversion. In addition, we have tested and analyzed the conversion gain, noise figure and spurs free dynamic range of the system. For image rejection in down-conversion, we can achieve an image rejection ratio (IRR) about 65.2 dB. Moreover, the impact of the phase drift, RF frequency, amplitude and phase variation on IRR is discussed. Finally, the influence of half-voltage imbalance of the DPMZM sub-modulators on IRR is analyzed, and a compensation method is given.

Wideband Photonic Microwave Frequency Divider With Large Harmonic Suppression Capability

An all-optical photonic microwave frequency divider (PMFD) is presented. It is based on injecting an RF phase modulated optical signal into a semiconductor laser oscillating in the period-two state. New optical frequency components with frequency separation of half of the input RF signal frequency are generated at the laser output. A frequency divided signal can be obtained by the beating of these optical frequency components at a photodetector. Large harmonic suppression can be achieved by using an optical filter to select only two optical frequency components to be detected by the photodetector. The proposed PMFD is free of electrical components and does not suffer from the modulator bias drift problem. It has the potential to operate over a 100 GHz frequency range. System parameters required to realise divide-by-two frequency division operation for different input RF signal frequencies are investigated. Experimental results are presented for the novel PMFD, which demonstrate the generation of a 1/2 frequency component for different input RF signal frequencies by controlling the forward bias current of an off-the-shelf semiconductor laser, and which also show the important advantages of large harmonic suppression and high signal-to-noise ratio performance. Wide input RF signal power range and high output stability performance are also demonstrated experimentally.

The impact of respiratory motion on electromagnetic fields and specific absorption rate in cardiac imaging at 7T.

To present electromagnetic simulation setups for detailed analyses of respiration's impact on and E-fields, local specific absorption rate (SAR) and associated safety-limits for 7T cardiac imaging. Finite-difference time-domain electromagnetic field simulations were performed at five respiratory states using a breathing body model and a 16-element 7T body transceiver RF-coil array. and SAR are analyzed for fixed and moving coil configurations. SAR variations are investigated using phase/amplitude shimming considering (i) a local SAR-controlled mode (here SAR calculations consider RF amplitudes and phases) and (ii) a channel-wise power-controlled mode (SAR boundary calculation is independent of the channels' phases, only dependent on the channels' maximum amplitude). Respiration-induced variations of both amplitude and phase are observed. The flip angle homogeneity depends on the respiratory state used for shimming; best results were achieved for shimming on inhale and exhale simultaneously ( ). The results reflect that respiration impacts position and amplitude of the local SAR maximum. With the local-SAR-control mode, a safety factor of up to 1.4 is needed to accommodate for respiratory variations while the power control mode appears respiration-robust when the coil moves with respiration (SAR peak decrease: 9% exhale→inhale). Instead, a spatially fixed coil setup yields higher SAR variations with respiration. Respiratory motion does not only affect the distribution and hence the image contrast, but also location and magnitude of the peak spatial SAR. Therefore, respiration effects may need to be included in safety analyses of RF coils applied to the human thorax.

Millisecond burst extractions from synchrotrons using RF phase displacement acceleration

FLASH radiation therapy calls for the delivery of fast bursted spills of particles with dose delivery times of the order of milliseconds. The requirements overlap with fundamental physics experimental requests that are being studied at CERN, albeit at very different energy scales. In this contribution, a scheme for extracting millisecond bursts from synchrotrons is explored by controlling a third-integer resonant and chromatic extraction with RF phase displacement acceleration. The scheme would be implementable in existing medical and experimental synchrotron facilities. Using a model of the CERN Proton Synchrotron, both single-burst and multi-burst extractions are simulated. Results show that 80−90% of the total beam intensity is extracted in a single burst of 40−60ms. This would correspond to a ∼10ms burst in a typical medical synchrotron, namely the one outlined in the Proton Ion Medical Machine Study. A set of 3 consecutive bursts of 30ms was simulated in the Proton Synchrotron with optimised machine parameters.

Sum-Rate Maximization in Two-Way MIMO Cooperative Networks With an Energy Harvesting Relay

This study considers a two-way amplify-and-forward relay system wherein two users exchange information with the assistance of an energy-harvesting MIMO relay node. With two-time-slot transmission, the relay receives the transmitted signal from both users in the first time-slot and splits it into two parts for information forwarding and energy harvesting, respectively, in accordance with a particular power splitting ratios. The phases of the RF signals used for energy harvesting at each relay antenna are shifted before being combined to achieve the highest power. Meanwhile, the RF signals used for information forwarding are passed through a linear precoder and then broadcast to the users in the second time-slot. We aim to optimize the power splitting ratios, precoding matrix, and RF phase shifting factors such that the sum-rate is maximized. Since joint optimization is intractable, the parameters are partitioned into three sub-optimization problems. For each parameter, a sub-optimal solution is derived in a (semi-)closed form. It shows numerically that the proposed sub-optimal solutions for the optimal phase shift and power split ratio are close to the global optimal solutions. Moreover, the proposed solution for the precoding matrix outperforms the so-called ’General Power Iterative’ algorithm proposed in the literature.

Phase-cycled balanced SSFP imaging for non-contrast-enhanced functional lung imaging.

To introduce phase-cycled balanced SSFP (bSSFP) acquisition as an alternative in Fourier decomposition MRI for improved robustness against field inhomogeneities. Series 2D dynamic lung images were acquired in 5 healthy volunteers at 1.5 T and 3T using bSSFP sequence with multiple RF phase increments and compared with conventional single RF phase increment acquisitions. The approach was evaluated based on functional map homogeneity analysis, while ensuring image and functional map quality by means of SNR and contrast-to-noise ratio analyses. At both field strengths, functional maps obtained with phase-cycled acquisitions displayed improved robustness against local signal losses compared with single-phase acquisitions. The coefficient of variation (mean± SD, across volunteers) measured in the ventilation maps resulted in 29.7 ± 2.6 at 1.5T and 37.5 ± 3.1 at 3T for phase-cycled acquisitions, compared with 39.9 ± 5.2 at 1.5T and 49.5 ± 3.7 at 3T for single-phase acquisitions, indicating a significant improvement ( ) in ventilation map homogeneity. Phase-cycled bSSFP acquisitions improve robustness against field inhomogeneity artifacts and significantly improve ventilation map homogeneity at both field strengths. As such, phase-cycled bSSFP may serve as a robust alternative in lung function assessments.

Study of the third-order parametric resonance induced by RF phase modulation and its effectiveness in improving injection efficiency

The on-axis swap-out injection scheme is promising for diffraction-limited storage rings, mainly because it can significantly reduce the requirement of dynamic aperture. However, this scheme requires the injection of full-charge bunches. Therefore, it may suffer from the reduction of injection efficiency caused by the so-called “injection transient instability” when high-charge bunches are needed. The idea of implementing RF modulation in a booster before extraction, driving the second-order parametric resonance to suppress the “injection transient instability” in the storage ring, was proposed and demonstrated previously. Here, we mainly present studies of third-order parametric resonance driven by RF phase modulation. Derivation of the modulated Hamiltonian around the third-order parametric resonance, the coordinates of both stable and unstable fixed points, and the ‘island tune’ are presented in detail. To double check the correctness of the theoretical results, numerical tests and tracking studies were carried out and presented. Furthermore, the results from comprehensive simulations are presented to demonstrate the improvement of injection efficiency by the proper settings of the RF phase modulation.

Optical Radio-Frequency Phase Measurement With an Internal-State Rydberg Atom Interferometer

We realize and model an internal-state Rydberg atom interferometer for measurement of phase and intensity of radio-frequency (rf) electromagnetic waves. A phase reference is supplied to the atoms via a modulated laser beam, enabling atomic measurement of the rf wave's phase without a rf reference wave. The rf and optical fields give rise to closed interferometric loops within the atoms' internal Hilbert space. In our experiment, we construct interferometric loops in the state space ${6{P}_{3/2},90{S}_{1/2},91{S}_{1/2},90{P}_{3/2}}$ of cesium and employ them to measure phase and intensity of a 5-GHz rf wave in a room-temperature vapor cell. Electromagnetically induced transparency on the $6{S}_{1/2}$ to $6{P}_{3/2}$ transition serves as an all-optical interferometer probe. The rf phase is measured over a range of $\ensuremath{\pi}$, and a sensitivity of 2 mrad is achieved. Measurements of rf phase and amplitude at submillimeter optical spatial resolution are demonstrated.

Simple and All-Optical In-Phase and Quadrature Phase Generation Techniques

New microwave photonic signal processing structures for generating in-phase and quadrature phase RF signals are presented. They are based on designing the bias angles of a dual-drive Mach Zehnder modulator (DDMZM) or a dual-parallel Mach Zehnder modulator (DPMZM) to introduce a specific phase shift to the optical carrier and using a wavelength division multiplexer to separate the lower and upper RF modulation sidebands. The optical carrier beat with the sidebands in a pair of photodetectors generate two output RF signals with a quadrature phase difference. The two proposed structures are simple, low cost and free of electrical components. The upper operating frequency of the two microwave photonic signal processors is only limited by the optical modulator bandwidth. Experimental results demonstrate the proposed microwave photonic signal processing structures have the ability to generate in-phase and quadrature phase signals with small phase and amplitude imbalance, over a wide frequency range.

Efficient phase-cycling strategy for high-resolution 3D gradient-echo quantitative parameter mapping.

Magnetization-prepared (MP) gradient-echo (GRE) sequences suffer from signal contaminations from T1 recovery during the readout train, which can be eliminated by paired RF phase cycling (PC) at the cost of doubling the scan time. The objective of this study was to develop and validate a novel unpaired PC strategy to eliminate the time penalty for high-resolution quantitative parameter mapping in 3D MP-GRE sequences. Based on the observation that the contaminating T1 recovery signal along the GRE readout train is independent of magnetization preparation, its impact can be eliminated using a novel curve-fitting approach with complex-valued data without needing paired PC acquisitions. Four new unpaired PC schemes were compared with two traditional paired PC schemes in both phantom and in vivo human knee studies at 3 T using a MP angle-modulated partitioned k-space spoiled gradient-echo snapshots (MAPSS) T1ρ mapping sequence. In the phantom study, all methods resulted in consistent T1ρ measurements (∆T1ρ < 0.5%) at the center slice when B0 /B1 values were uniform. Results were not consistent when off-center slices with nonideal B0 /B1 were included. Two unpaired PC schemes had comparable or significantly improved quantitative accuracy and scan-rescan reproducibility compared with the paired PC schemes. There was no significant T1ρ quantitative variability increase or spatial fidelity loss using the new unpaired PC schemes. Unpaired PC schemes also had different T1ρ spectral responses at different B0 frequency offsets, which can potentially be exploited to reduce sensitivity to B0 field inhomogeneities. The human knee study results were consistent with the phantom study findings. In conclusion, an unpaired PC strategy potentially allows more accurate quantitative parameter mapping with halved scan time compared with the paired PC approach to eliminate signal contaminations from T1 recovery. It therefore offers additional flexibility in SNR optimization, spatial resolution improvement, and choice of imaging sampling points to obtain more accurate quantitative parameter mapping.

Results of the first implementation of RF phase signature matching at LANSCE

The LINAC at the Los Alamos Neutron Science Center (LANSCE) has been utilizing the Delta-t method to match the RF cavities to the design acceleration parameters since its commissioning in 1972. The differences in time-of-flight between two subsequent Beam Position and Phase Monitors (BPPMs) are measured with both accelerated and drifting beams, depending on the whether the module is set to on or off. The algorithm optimizes the module amplitude and phase via iterative measurements if the initial phase is in the vicinity of the design value. With an upgrade to a faster readout system, a scan over the whole RF cavity phase range requires relatively less time than the classical optimization procedure. The Phase Scan Signature Matching (PSSM) method provides a time-efficient method that ensures the phase selection lands on the bunching side and empowers future analyses to build module-specific models. The PSSM also utilizes a direct model to determine the correct amplitude to sub-percent level instead of using linearized matrices. Furthermore, lacking a reliable energy measurement method in the LINAC, we measure the beam phases at two downstream locations to increase the precision of energy measurements. In this letter, we also discuss the sensitivities of PSSM, error propagation, and the implementation results for the 2019 and 2020 beam cycles.