Transverse Instability Research Articles

Low-order modeling approach for the prediction of transverse combustion instabilities in multi-injector engines

This paper addresses the prediction of spontaneous self-sustained transverse combustion instabilities in multi-injector engines using a multi-dimensional non-linear low-order Eulerian model. The approach utilizes a physically aware response function that directly links pressure oscillations to fuel mass flow rate, independent of external data. This enables accurate capture of the behavior of shear coaxial injectors that have been proven to show a peculiar dynamics of cyclic fuel accumulation and release in response to acoustic waves. A NASA test case is employed as a reference, and a comprehensive analysis is conducted to investigate the behavior of the model. Firstly, a preliminary analysis is performed within a quasi-one-dimensional framework for a reduced single-injector configuration. This analysis provides insights into the influence of key parameters on the instability onset. Subsequently, the full-scale geometry is considered in a multi-dimensional framework, and the low-order solver is employed to analyze the thermo-acoustic behavior of the engine. The model successfully captures the instability dynamics, including temporal evolution, dominant frequency, and mode shapes. Sensitivity analyses are conducted to examine the impact of the model free parameters on the unstable modes. Additionally, the effect of introducing baffles as damping devices within the combustion chamber is investigated. The results highlight the model predictive capabilities and its potential for guiding the design and optimization of liquid rocket engines.

Collapse dynamics for two-dimensional space-time nonlocal nonlinear Schrödinger equations

The question of collapse (blow-up) in finite time is investigated for the two-dimensional (non-integrable) space-time nonlocal nonlinear Schrödinger equations. Starting from the two-dimensional extension of the well known AKNS q,r system, three different cases are considered: (i) partial and full parity-time (PT) symmetric, (ii) reverse-time (RT) symmetric, and (iii) general q,r system. Through extensive numerical experiments, it is shown that collapse of Gaussian initial conditions depends on the value of its quasi-power. The collapse dynamics (or lack thereof) strongly depends on whether the nonlocality is in space or time. A so-called quasi-variance identity is derived and its relationship to blow-up is discussed. Numerical simulations reveal that this quantity reaching zero in finite time does not (in general) guarantee collapse. An alternative approach to the study of wave collapse is presented via the study of transverse instability of line soliton solutions. In particular, the linear stability problem for perturbed solitons is formulated for the nonlocal RT and PT symmetric nonlinear Schrödinger (NLS) equations. Through a combination of numerical and analytical approaches, the stability spectrum for some stationary one soliton solutions is found. Direct numerical simulations agree with the linear stability analysis which predicts filamentation and subsequent blow-up.

Simplified expression for transverse mode instability threshold in high power fiber lasers.

In this work, we propose an analytical expression for calculating the transverse mode instability (TMI) threshold power, which clearly shows the role of various fiber parameters and system parameters. The TMI threshold expression is obtained by solving the heat conduction equation and the nonlinear coupling equation using the fundamental mode fitted by Gaussian functions. The calculation results of the proposed TMI threshold expression are consistent with the experimental phenomena and simulation results from the well-recognized theoretical model. The influence of some special parameters on the TMI threshold and the power scaling is also investigated. This work will be helpful for fiber design and TMI mitigation of high-power fiber lasers.

The stabilizing effect of collision on sheet instability in laser radiation pressure-based ion acceleration: A theoretical and simulation analysis

In the past decade, transverse instabilities in the ion acceleration process using the laser radiation pressure method have been a prominent topic of discussion. These instabilities caused by the coupling between quasi-static ions with oscillating electrons through the ponderomotive force lead to the creation of density ripples in the target, ultimately resulting in the breaking of the target. This article investigates the collisional effects on the instability characteristic through theoretical and two-dimensional PIC simulation analysis. In agreement with our simulation studies, theoretical results show that the collision term enhanced the ion acceleration by decreasing the ion density accumulation and temporal growth rate of instability.

Wakefields excited in the FCC-ee collimation system

The purpose of this paper is to calculate the longitudinal and transverse wakefields of the FCC collimators using the electromagnetic codes ECHO3D and IW2D. We cross-checked our results using CST particle studio for long bunches, and found them to be in good agreement. The obtained results show that the collimators give one of the highest contributions to the overall FCC-ee wake potentials. In particular, using the code PyHEADTAIL, we have found that the geometric contribution of the collimators' wakefield reduces significantly the transverse mode coupling instability threshold. Therefore, it is imperative to explore and implement solutions that effectively mitigate this wakefield source.

Theoretical study on radiation effect on threshold of transverse mode instability of Yb-doped fiber amplifiers

<sec>Yb-doped fiber amplifiers and their applications in radiation environments have become more and more attractive in recent years. However, the radiation effect will cause damage to the Yb-doped fibers, which can give negative effect on the output properties of Yb-doped fiber amplifiers. In this work, the influence of radiation effect on the transverse mode instability (TMI) of Yb-doped fiber amplifier is studied. TMI can couple the single light from the fundamental mode to high-order mode, thereby degenerating the beam quality of fiber amplifier. TMI is considered a key limitation of power up-scaling of fiber amplifiers.</sec><sec>In this work, the radiation effect on the TMI is studied theoretically, and a formula of TMI threshold is presented by taking the radiation-induced attenuation (RIA), the most important radiation effect for the TMI, into account. The formula is deduced by introducing the loss of signal light induced by RIA into the formerly reported TMI-threshold formula which can be obtained by the linear stability analysis of the numerical model studying the TMI. Then, the relationship between the TMI and radiation dose is also given with the help of Power-Law describing the relationship between the RIA and radiation dose.</sec><sec>With the formula, the variations of TMI threshold with the radiation dose and RIA are studied. It is found, as expected, that the TMI threshold decreases monotonically with the increase of RIA or radiation dose. Nevertheless, it is unexpectedly found that, to some extent, the gain coefficient of fiber amplifiers will also affect the radiation effect on TMI threshold. The results reveal that the increase of gain coefficient will lower the sensitivity of TMI threshold to the radiation dose. However, it is also implied that the gain coefficient cannot be too large because it can also make the TMI threshold lowered. Therefore, in order to maintain a high TMI threshold in a radiation environment, sufficient radiation resistance of Yb-doped fiber is essential.</sec><sec>Because the RIA can affect not only the TMI threshold but also the output power or efficiency of Yb-doped fiber amplifier, the comparison between two effects of RIA is also discussed. It is found that the threshold of TMI is more sensitive to the radiation than to the output power or efficiency (see the figure attached below), which means that the TMI can exist in the irradiated Yb-doped fiber amplifier, although the output power is reduced because of RIA. This result can be verified by the experimental observation reported formerly. As a result, TMI can become a key limitation to the output power of Yb-doped fiber amplifier in radiation environments. The relevant results can provide significant guidance for the applications of Yb-doped fiber amplifiers in radiation environments.</sec>

Electron cloud build-up studies for FCC-ee

The Future Circular Collider (FCC) study is developing designs for a new research infrastructure to host the next generation of higher performance particle colliders to extend the research currently being conducted at the LHC. In particular, FCC-ee is an electron-positron collider, which is the first stage towards a 100 TeV proton-proton collider FCC-hh. FCC-ee may be affected by electron cloud (e-cloud) and the strongest effects are foreseen for the Z configuration, due to the highest number of bunches, which corresponds to the smallest bunch spacing. The presence of a large electron density in the beam pipe can limit the achievable performance of the accelerator through different effects like transverse instabilities, transverse emittance growth, particle losses, vacuum degradation and additional heat loads of the inner surface of the vacuum chambers. In the design phase, the goal is to suppress the e-cloud effects in FCC-ee and, therefore, a preliminary study to identify the parameters, which play a significant role in the e-cloud formation has been performed. In this paper, an extensive e-cloud simulation study is presented. In particular, the impact of the e-cloud is studied for different configurations, for example: for the electron and the positron beam; in the different elements of the particle accelerator; changing the beam chamber geometry; for different values of the Secondary Emission Yield (SEY); and for different beam parameters.

Experimental Research on Abnormal Transverse Mode Instability in High-Power Fiber Lasers

Experimental Research on Abnormal Transverse Mode Instability in High-Power Fiber Lasers

Brightness enhancement on a narrow-linewidth fiber Bragg grating-based master oscillator power amplification fiber laser

Abstract In this paper, we have experimentally demonstrated a high-power and high-brightness narrow-linewidth fiber amplifier seeded by an optimized fiber oscillator. In order to improve the temporal stability, the fiber oscillator consists of a composite fiber Bragg grating-based cavity with an external feedback structure. By optimizing the forward and backward pumping ratio, the nonlinear effects and stimulated Raman scattering-induced mode distortion of the fiber amplifier are suppressed comprehensively, accompanied with the simultaneous improvement of beam quality and output power. The laser brightness is enhanced further by raising the threshold of transverse mode instability by approximately 1.0 kW by coiling the gain fiber with a novel curvature shape. Finally, a 6 kW narrow-linewidth laser is achieved with beam quality (M2) of approximately 1.4. The laser brightness doubled compared to the results before optimization. To the best of our knowledge, it is the highest brightness narrow-linewidth fiber laser based on a one-stage master oscillator power amplification structure.

Accurate Modeling of Transverse Mode Instability in Thulium-doped Optical Fiber Amplifiers

Accurate Modeling of Transverse Mode Instability in Thulium-doped Optical Fiber Amplifiers

Simulations and measurements of the transverse mode coupling instability in the LHC

Simulations and measurements of the transverse mode coupling instability in the LHC

Polarization-resolved mode evolution in TMI-limited Yb-doped fiber amplifiers using a novel high-speed Stokes polarimeter.

In this work we have developed a high-speed Stokes polarimeter method based on simultaneous 4-channel imaging with a high-speed camera. Thus, current speed limitations of imaging polarimeters for wavelengths around 1 µm can be overcome, allowing a sub-ms polarization-resolved characterization of transverse mode instability (TMI). Additionally, the Stokes parameters of each individual mode are calculated by a simultaneous 4-beam mode reconstruction algorithm during post-processing and can be analyzed with unprecedented temporal resolution. We demonstrate the measurement capabilities of this polarimeter setup by characterizing TMI of a large-mode-area Yb-doped polarization maintaining (PM) fiber amplifier with 30 kHz video frame rate. Upon thorough characterization, we have found for the first time that at the onset of TMI in a PM fiber, the modal polarization states begin to oscillate on circular and elliptical trajectories at the same frequencies as the modal energy transfer occurs. The ability to measure the modal polarization states with sub-ms temporal resolution is key to developing a fundamental understanding and subsequently possible mitigation strategies of TMI in PM-fiber lasers.

Mitigation of transverse mode instability by modal birefringence in polarization-maintaining fibers

The effect of transverse mode instability (TMI) poses a fundamental obstacle for a further scaling of diffraction-limited, high-power fiber laser systems. In this work we present a theoretical and experimental study on the mitigation of TMI by modal birefringence in a polarization maintaining (PM) fiber. With the help of comprehensive simulations, we show that the thermally-induced refractive index grating responsible for TMI can be modified and washed out when light is coupled with a polarization input angle detuned from the main axes of the fiber. To confirm the theoretical predictions, we have designed and manufactured an Yb-doped large-mode-area PM fiber. Using this fiber, we have systematically investigated the dependence of the TMI threshold on the polarization input angle of the seed laser. We experimentally demonstrate that when the polarization input angle of the seed is aligned at 50° with respect to the slow-axis, the TMI threshold increases by a factor of 2, verifying the theory and the numerical simulations. A high speed polarization mode-resolved analysis of the output beam is presented, which reveals that at the onset of TMI both polarization axes fluctuates simultaneously.

10kW tandem pumping fiber amplifier with good beam quality based on tapered ytterbium-doped fiber.

In this paper, we established a high power tandem pumped fiber amplifier based on tapered ytterbium-doped fiber (TYDF). The TYDF is developed in-house with a core/inner cladding diameter of 30/250 µm at the small-core region and 48/400 µm at the large-core region. The key parameters of the amplifier in a co-pumped and counter-pumped configuration are experimentally investigated, such as slope efficiency, stimulated Raman scattering (SRS) threshold, and beam quality evolution. Up to 10.28 kW laser free of SRS or transverse mode instability is obtained from the counter-pumped amplifier, and the beam quality factor M2 is 2.29, which is significantly improved compared with the 48/400 µm uniform YDF. To the best of our knowledge, this is the highest average output power achieved so far based on the TYDF. This work could provide a solution for balancing the SRS suppression and high order modes control in high power tandem pumped YDF lasers.

Investigation of gain-filtering Yb-doped fibers with different gain-dopant doping ratios for high power amplifier

We presented an investigation on gain-filtering Yb-doped fiber for the mitigation of transverse mode instability (TMI). The gain-filtering Yb-doped fibers were fabricated by modified chemical vapor deposition (MCVD) combined with solution doping technique. Four gain-dopant diameter ratio fibers, entailing 100% doping, ∼73% doping, Gaussian doping, and ∼57% doping, presented similar parameters with the core/inner cladding diameter of ∼30/400 μm and core numerical aperture (NA) of ∼0.061. The laser performances of four fibers were demonstrated by a bidirectional pumping all-fiber amplifier. The TMI thresholds of 100%-doped, ∼73%-doped, Gaussian-doped, and ∼57%-doped fibers, were measured to be ∼1753 W, ∼3089 W, ∼3048 W, and over 3301 W, corresponding to the M2 factors of ∼1.52, ∼1.40, ∼1.45, and ∼1.32, respectively. The experimental results indicated that by reasonably tailoring the gain-dopant doping diameter, better gain-filtering effect was manifested, exactly as higher TMI threshold and more superior beam quality. This contribution could provide an effective approach for obtaining high-brightness Yb-doped fiber amplifiers based on gain-filtering effect.

Bifurcations and synchrony in a ring of delayed Wilson–Cowan oscillators

Ring structures are crucial in network neuroscience, enabling the integration of neural information through closed loop circuits within feedback systems. Here, we use numerical bifurcation analysis to explore time delay effects on a ring of delay-coupled Wilson–Cowan masses. Investigating a low-dimensional ‘self-coupled’ version of the aforementioned system, we uncover the bifurcation structure of the synchronization manifold, and unveil a diverse array of dynamic synchronization patterns that emerge as a consequence of Hopf branch crossings and subsequent higher-order bifurcations. Analysis of the full system reveals transverse instabilities in the synchronized state for large regions of parameter space, with the ring network architecture promoting various dynamics depending on the balance between coupling strength and delay time. Under weak coupling, emergent oscillations are generally synchronous or anti-phase synchronous, with transitions between them triggered by a torus bifurcation of a periodic orbit. Regions of synchronous and anti-phase synchronous solutions are delineated by weakly chaotic borders due to the breakdown of the torus. As coupling strength increases, the bifurcation diagram displays more overlapped branching structure, resulting in increasingly complicated, multistable dynamics.

Experimental and numerical investigation of transverse combustion instability in a rectangle multi-injector rocket combustor

Rocket engines are prone to suffer from transverse combustion instabilities, manifesting as periodic oscillations in pressure and heat release rate. Self-excited transverse instabilities in a rectangle multi-injector rocket combustor powered by n-C12H26 and O2, are investigated experimentally and numerically in this paper. Transverse combustion instabilities are captured during repeatable experiments, while dynamic characteristics in the combustion chamber and driving mechanisms of instabilities are analyzed via numerical simulation based on stress-blended eddy simulation. Dynamic mode decomposition analysis reveals coupling behaviors between the transverse mode in the combustion chamber and longitudinal mode in the oxidizer post, resulting in propellant mass flow rate oscillations. Substantial evidence demonstrates that the intensities of heat release rate near the end walls are higher than that detected around the chamber center due to its intense coupling to the local first transverse (1W) acoustic mode. Flow field animations indicate strong deflection of oxygen posts and liquid particles by a transverse moving gas mixture leading to flame interactions and collision between adjacent share injectors. The propellant injected into the chamber does not burn immediately and is transported to the combustor end wall. Propellant mixing performance is significantly enhanced during interactions between acoustic pressure and end wall, causing a sudden heat release near 1W pressure anti-node, thereby strengthening pressure oscillations. Finally, a combustion instability driving mechanism associated with propellant mass flow rate oscillations, and interactions between unsteady acoustic pressure and heat release rate is proposed. The insights obtained from this work can aid comprehension of transverse combustion instabilities encountered by rocket engines.

Optimization and demonstration of a bidirectional output linear-cavity fiber laser with a record high power of 2 × 4 kW

The bidirectional output fiber laser can achieve two laser outputs from a single resonant cavity, which can reduce the volume and cost of high-power fiber laser systems and has good application prospects in the industry. In this work, we demonstrated a bidirectional output fiber laser oscillator structure, and a total output power of 8 kW at the 2 ports × 4 kW level was achieved experimentally for the first time. In order to suppress stimulated Raman scattering (SRS) and transverse mode instability (TMI), the double cladding ytterbium-doped fiber with a core/cladding diameter of 30/400 µm, a pair of matched output coupler fiber Bragg gratings (OCFBG) with a 3 dB bandwidth of 2 nm, and the pump source with wavelength-stabilized 981 nm laser diodes (LDs) were employed. The effect of the coiling method and diameter of the active fiber on the optical-to-optical (O-O) efficiency and TMI threshold were studied intensively. The comparison of laser performance with a unidirectional output oscillator was further exploited, and results indicated that the bidirectional output fiber laser oscillator possessed a higher O-O efficiency and TMI threshold. By optimizing the fiber coiling diameter and coiling method, we finally achieved a total laser output power of 8169 W (3769 W at end A and 4400 W at end B), with an efficiency of 74.6% and beam quality of M2A ∼ 2.13, M2B ∼ 2.36, while the total output power achieved by unidirectional output structure was only 5805 W with signs of TMI. To the best of our knowledge, it is the highest output power of the bidirectional output fiber laser.

Numerical Prediction of the Streamwise Fluidelastic Instability

Abstract Recent experimental investigations have shown that tube arrays can become unstable in the streamwise direction. This is contrary to the long-held notion that fluidelastic instability is only a concern in the direction transverse to the flow. The possibility of the streamwise fluidelastic instability (SFEI) as a potential threat to the integrity of tube bundles was confirmed by the recent failures of newly installed replacement steam generators. A number of investigations were conducted to uncover the nature of this mechanism. A theoretical framework was developed by Hassan and Weaver (2016, “Modeling of Streamwise and Transverse Fluidelastic Instability in Tube Arrays,” ASME J. Pressure Vessel Technol., 138(5), p. 051304) to model streamwise fluidelastic instability in a bundle of flexible tubes. The model utilized a simple time lag expression for the flow channel area perturbation. The current work aims at developing a numerical model to precisely predict the flow perturbation characteristics in a tube bundle due to streamwise tube motion. Flow simulations were carried out for single phase fluid flow in a parallel triangle tube bundle array with 1.2, 1.5, and 1.7 pitch to diameter ratios. The numerical model was validated against numerical and experimental results available in the fluidelastic instability literature. Simulations were carried out for a range of reduced flow velocities. The model results showed that the upstream flow perturbation magnitude and phase are different from those obtained downstream of the moving tube. The obtained flow perturbation characteristics were implemented in the Hassan and Weaver (2016, “Modeling of Streamwise and Transverse Fluidelastic Instability in Tube Arrays,” ASME J. Pressure Vessel Technol., 138(5), p. 051304) model and the streamwise FEI threshold was predicted.

Research of Transverse Mode Instability in High-Power Bidirectional Output Yb-Doped Fiber Laser Oscillators

Bidirectional output fiber laser oscillators can realize two high-power laser outputs employing only a single-laser resonant cavity and hold the advantages of being low cost and of compact size. However, like other fiber lasers, their power improvement is limited by transverse mode instability (TMI). To achieve higher power output, in this paper, the characteristics and corresponding suppression method of the TMI in bidirectional output fiber laser oscillators were investigated for the first time. Firstly, the TMI threshold was obtained when the fiber laser oscillator was pumped by 976 nm LDs and 981 nm LDs, separately, and the difference between the two pumping conditions was researched in detail. After that, a comparison study between the bidirectional and unidirectional output fiber laser oscillators pumped by 981 nm LDs was carried out. In the experiment, the effect of pump distribution on the TMI threshold was also considered. The results show that the TMI threshold of the bidirectional-output laser pumped by 981 nm LDs is much higher than that pump by 976 nm LDs, which means that the effective TMI suppression methods in the unidirectional output laser are also applicable in the bidirectional output laser. In addition, it is found that the TMI threshold of a bidirectional output fiber laser is much lower than that of a unidirectional output fiber laser.