Cutoff Layer Research Articles

Interaction between the core and the edge for ion cyclotron resonance heating based on artificial absorption plasma model

In numerical simulations of the ion cyclotron range of frequencies (ICRF) wave heating scheme, core solvers usually focus on wave propagation and absorption mechanisms within the core plasma region. However, the realistic scrape-off layer (SOL) plasma is usually simplified, making it difficult to have deeper understanding of wave propagation and absorption within the SOL. In this work, we employ a cold plasma assumption and an artificial absorption mechanism based on the approach of reference (Zhang et al 2022 Nucl. Fusion 62 076032), to study wave propagation and absorption in the realistic SOL plasma of the EAST. During the exponential decay of the total coupled power with respect to the toroidal mode numbers, several fluctuations are observed in the case of low collisional frequencies. The fluctuations may be caused by the cavity modes associated with specific toroidal mode numbers. Due to the presence of cut-off densities, the edge power losses and the total coupled power exhibit different behaviors before and after the cut-off layer is “open”. Furthermore, the simulation results obtained from the kinetic model in reference (Zhang et al 2022 Nucl. Fusion 62 076032) is discussed. This suggests that both the core-edge combined model and the artificial mechanism are capable of simulating wave propagation and absorption.

Development of ultra-short pulse reflectometry on the Experimental Advanced Superconducting Tokamak (EAST).

Microwave reflectometry is an invaluable diagnostic tool for measuring electron density profiles in large fusion devices. Density fluctuations near the plasma cutoff layer, particularly those that are time-varying on the timescale of the reflectometry measurement, can result in distortions in phase and/or amplitude of the reflected waveform, which present challenges to the accuracy of the reconstructed profile. The ultra-short pulse reflectometry (USPR) technique eliminates the time-varying issue in that reflectometry data are collected on a nanosecond timescale, essentially freezing the fluctuations in place. An X-mode dedicated 32-channel USPR system has been developed and installed on the EAST, covering the operation frequency range from 52 to 92GHz. This system enables high-resolution density profile measurements in the plasma pedestal and scrape-off layer, with resolutions reaching 5mm and 1 μs, respectively. Laboratory testing of the system performance has been conducted, demonstrating the potential of the USPR technique to provide accurate and high-temporal-resolution density profiles in challenging plasma environments.

Observation of Doppler shift modulated by the internal kink mode using conventional reflectometry in the EAST tokamak

In this paper we present a new experimental observation using a conventional reflectometry technique, poloidal correlation reflectometry (PCR), in the Experimental Advanced Superconducting Tokamak (EAST). The turbulence spectrum detected by the PCR system exhibits an asymmetry and induced Doppler shift during the internal kink mode (IKM) rotation phase. This Doppler shift is the target measurement of Doppler reflectometry, but captured by conventional reflectometry. Results show that the Doppler shift is modulated by the periodic changes in the effective angle between the probing wave and cutoff layer normal, but not by plasma turbulence. The fishbone mode and saturated long-lived mode are typical IKMs, and this modulation phenomenon is observed in both cases. Moreover, the value of the Doppler shift is positively correlated with the amplitude of the IKM, even when the latter is small. However, the positive and negative frequency components of the Doppler shift can be asymmetric, which is related to the plasma configuration. A simulated analysis is performed by ray tracing to verify these observations. These results establish a clear link between and IKM rotation, and are helpful for studying the characteristics of IKM and related physical phenomena.

Optimization of the collective Thomson scattering diagnostic for the GDT open magnetic trap

The collective Thomson scattering of high-power millimeter-wave radiation on plasma density fluctuations (CTS) is widely used for diagnosing the velocity distribution function of energetic ions in fusion plasma. In this paper, we discuss a non-standard scheme of CTS measurements, which exploits strong refraction of probing and scattered microwave beams when reflecting from the cut-off layer in dense plasma. The scheme may be realized with the existing CTS diagnostic system at the Gas-Dynamic Trap (GDT) facility, a large open magnetic trap operating at Budker Institute (Novosibirsk, Russia). This requires a minor upgrade of the available hardware and essentially increases the range of plasma densities allowed for CTS measurements, as well as its sensitivity and spatial resolution. A detailed study of CTS efficiency for different geometries and plasma conditions at GDT is performed by means of an advanced numerical model that allows for an accurate description of non-Gaussian beam scattering in inhomogeneous plasma. To perform this task, we develop a quasi-optical theory of scattering, which itself may be of general interest.

Numerical simulation of ultrashort-pulse reflectometry (USPR) on EAST

The microwave reflectometer is a popular non-intrusive plasma density diagnostic instrument on tokamaks that provides centimeter and millisecond level resolution. The ultrashort-pulse reflectometer (USPR) achieves plasma density measurement by emitting a chirped wave containing a broadband signal and measuring the time of flight from different frequency components. A USPR system is currently being built on EAST (Experimental Advanced Superconducting Tokamak) to meet the needs of diagnostic of the pedestal density evolution, such as high-frequency small edge-localized modes. In order to predict the density reconstruction of the EAST USPR system, this work presents a numerical simulation study of the beam propagation of the chirped wave of extraordinary waves (X-mode) in the plasma based on Python. The electron density profile has been successfully reconstructed by the reflection signal interpretation. The small gap between the right-hand cut-off layer and the electron cyclotron resonance layer, due to the low plasma density on the plasma edge, causes unexpected leakage from the transmitting microwave beam to the pedestal and the core region. This kind of ‘tunneling’ effect will cause the reflected signal to have energy loss in the low-frequency band. The study also discusses the influence of the poloidal magnetic field on the reflected signal. The spatial variation of the poloidal magnetic field will lead to the conversion between extraordinary (X) waves and ordinary (O) waves, which leads to energy loss in the reflected signals. The simulation results show that the ‘tunneling’ effect and the O-X mode conversion effect have little effect on the EAST USPR system. Therefore, the currently designed transmit power meets the working requirements.

W-band tunable, multi-channel, frequency comb Doppler backscattering diagnostic in the ASDEX-Upgrade tokamak

This article presents the design, implementation, and first data of a uniquely flexible, multi-channel, frequency comb Doppler backscattering diagnostic recently made operational in the ASDEX-Upgrade tokamak [A. Gruber and O. Gruber, Fusion Sci. Technol. 44, 569 (2003)]. It uses a double side-band signal fed into a ×6 frequency multiplier to produce a multiple-frequency output spectrum. Seven of these frequencies are simultaneously measured in the receiver via a two-step frequency down-conversion and traditional I/Q demodulation. The frequency comb spectrum is fully tunable to sit anywhere in the W-band. The inter-frequency separation is also uniquely tunable remotely between 0.1 and 6 GHz without any hardware changes. The diagnostic can be operated in both O and X-mode polarizations and at both oblique and normal incidence to the cutoff layer. The time evolution of backscattered signals, in excess of 30 dB, from seven distinct frequencies sampled simultaneously is presented across an L-to-H-mode confinement regime transition.

Investigation of phase modulation and propagation-route effect from unmatched large-scale structures for Doppler reflectometry measurement through 2D full-wave modeling

To interpret the common symmetric peaks caused by the large-scale structure in the complex S(f) spectrum from the heterodyne Doppler reflectometry (DR) measurement in EAST, a 2D circular-shaped O-mode full-wave model based on the finite-difference time-domain method is built. The scattering characteristics and the influences on the DR signal from various scales are investigated. When the structure is located around the cutoff layer, a moving radial or poloidal large-scale structure k θ ≲ k θ,match (k θ,match is the theoretic wavenumber of Bragg scattering) could both generate an oscillation phase term called ‘phase modulation’, and symmetrical peaks in the complex S(f) spectrum. It was found that the image-rejection ratio A −1/A +1 (A ±1 represents the amplitudes of ±1 order modulation peaks) could be a feasible indicator for experiment comparison. In the case when the structure is near the cutoff layer with the same arrangement as the experiment for the edge DR channel, the curve of A −1/A +1 versus k θ can be divided into three regions, weak asymmetrical range with k θ /k 0 ≲ 0.15 (k 0 is the vacuum wavenumber), harmonics range with 0.15 ≲ k θ /k 0 ≲ 0.4, and Bragg scattering range of 0.4 ≲ k θ /k 0 ≲ 0.7. In the case when the structure is located away from the cutoff layer, the final complex S(f) spectrum is the simple superimposing of modulation and Bragg scattering, and the modulation peaks have an amplitude response nearly proportional to the local density fluctuation, called the ‘propagation-route effect’. Under the H-mode experiment arrangement for the core DR, a critical fluctuation amplitude ∼ 1.3–4.1 ( refers to the pedestal large-scale structure amplitude and Amp(n e,Tur.@MSA) refers to turbulence amplitude at the main scattering area) is needed for the structure in the pedestal to be observed by the core DR measurement. The simulations are well consistent with the experimental results. These effects need to be carefully considered during the DR signal analyses as the injecting beam passes through the plasma region with large-scale structures.

Plasma position measurements by O-mode and X-mode reflectometry systems in tokamak plasmas.

Plasma Position Reflectometry (PPR) is planned to provide plasma position and shape information for plasma operation in future fusion reactors. Its primary function is to calibrate the drift of the magnetic signals due to the integral nature of magnetic measurement. Here, we attempt to measure plasma position using ordinary mode (O-mode) and extraordinary mode (X-mode) reflectometry systems on two tokamaks. A new physical model based on the phase shift is proposed to deduce the relative movement of the cut-off layer without density inversion. We demonstrate the plasma position measurements by absolute measurement from density profile inversion and relative measurement from phase shift. The combination of X-mode and O-mode reflectometers can minimize the limitations of single polarization reflectometry and further increase the accuracy of plasma position measurement. These results could provide an important technical basis for the further development of a real-time control system based on PPR.

A method for density fluctuation measurements using pulse reflectometry

An analytical 1D model based on the WKB approximation is used to study the properties of a short pulse reflectometry diagnostic in a magnetic fusion device. Expressions linking the pulse delay with the parameters of the turbulence near the cut-off layer are derived for both ordinary and extraordinary polarizations of the probing beam. These results are used to develop a method for measuring the turbulence amplitude and the radial correlation length. The analytical conclusions and the proposed method are validated using full-wave numerical modelling. The latter is also used to study the limitations of the method and potential experimental effects not included in the reduced model.

Mechanistic insight into developing a novel loose nanofiltration membrane for effective dye/salt separation by epigallocatechin gallate

Loose nanofiltration (LNF) membrane prepared by hydroxyl-based materials with excellent separation and antifouling properties has attracted great attention for treating textile wastewater. However, the construction and formation mechanism of the selective layer by using large polyphenol-based monomers was not well studied. Herein, a novel LNF membrane was fabricated by interfacial polymerization, in which a polyphenol named epigallocatechin gallate (EGCG) was employed as aqueous monomer to design the selective layer. The results illustrated that the formed polyester (PE) selective layer possessed a loose structure with smooth and hydrophilic surface. Notably, the EGCG with large molecular volume and polyphenol groups contributed to the larger molecular weight cut-off (MWCO) and hydrophilic PE layer with high permeability, whereas the small molecular trimesoyl chloride (TMC) accounted for the pore size reduction with low permeance. More importantly, the optimized EGCG-based LNF-4 membrane displayed a high water permeability of 41.7 LMH·bar−1, high rejection of dyes (98.5 % for Congo Red (CR), 93.4 % for Methyl Blue (MB), and 94.8 % for Evans Blue (EB), respectively) and low rejection of salt (7.4 % for NaCl). Besides, under 60 g/L salt content, a high retention of CR (93.0 %) and high permeation of NaCl (95.1 %) could be still maintained. Furthermore, the LNF-4 membrane had a superior fouling resistance towards CR and EB with flux recovery rate above 96.4 %. The excellent antibacterial property also made LNF-4 more competitive in practical applications. This work can provide a new strategy for fabrication of outstanding multifunctional LNF membranes by large molecular polyphenol monomers.

A new DRIE cut-off material in SOG MEMS process

The silicon on glasses process is a common preparation method of micro-electro-mechanical system inertial devices, which can realize the processing of thick silicon structures. This paper proposes that indium tin oxides (ITO) film can serve as a deep silicon etching cut-off layer because ITO is less damaged under the attack of fluoride ions. ITO has good electrical conductivity and can absorb fluoride ions for silicon etching and reduce the reflection of fluoride ions, thus reducing the foot effect. The removal and release of ITO use an acidic solution, which does not damage the silicon structure. Therefore, the selection of the sacrificial layer has an excellent effect in maintaining the shape of the MEMS structure. This method is used in the preparation of MEMS accelerometers with a structure thickness of 100 μm and a feature size of 4 μm. The over-etching of the bottom of the silicon structure caused by the foot effect is negligible. The difference between the simulated value and the designed value of the device characteristic frequency is less than 5%. This indicates that ITO is an excellent deep silicon etch stopper material.

Pre-conceptual studies of a travelling wave array antenna for the EAST

One of the primary problems of ion cyclotron range of frequency (ICRF) systems in magnetic confinement experiments is the coupling of a large amount of radio frequency wave power through the plasma cut-off layer within the voltage limits of the antenna system. Travelling wave array (TWA) antennas have higher coupling than conventional ICRF antennas, which is manifested in a sharp and optimized k // spectrum. As a pre-study of TWA applications in tokamaks, a TWA antenna with six consecutive straps and double-fin capacitors was conceptually designed for the experimental advanced superconducting tokamak (EAST). The antenna geometry was optimized to seek a low reflection coefficient for EAST ICRF heating scenarios. The design and simulation results of the TWA antenna are briefly presented. The results of the frequency sweep in vacuum show that a bandwidth of approximately 3 MHz with S 11 < −30 dB can be obtained. The peak of the k // power spectrum is adjusted to ∼3–4 m−1 at the frequency of 34–36 MHz. In addition, the properties of the power flow and the characteristics of the wave field are also discussed by modelling the plasma facing the TWA antenna using a cold plasma medium. The results in this study may provide some reference and guidance for the study of TWA antennas and other ICRF antennas in magnetic-confined fusion devices like EAST or the Chinese Fusion Engineering Test Reactor.

Ultrashort Pulse Reflectometry (USPR) diagnostic for EAST

Ultrashort Pulse Reflectometry (USPR) is a plasma diagnostic technique involving the propagation of ultrashort duration (∼few nsec) chirps which contain frequency components spanning large portions of the plasma density profile. Upon reflection, each frequency component reflects from a distinct density layer. The reflected wave packet is down-converted and passed through a multi-channel filter bank, with time-of-flight (TOF) measurements made on each of the filtered wave packets which are then used to reconstruct the electron density profile. Applied previously to the Sustained Spheromak Physics Experiment, UC Davis is updating this technique with higher power (>10X) sources, enhanced channel counts, and high speed customized TOF electronics. A 32 channel USPR system is being developed for the Experimental Advanced Superconducting Tokamak (EAST) device with frequencies spanning 52 to 92 GHz, reflecting from the right-hand plasma cut-off layer. The system will employ three monostatic transmit/receive horns each covering a different waveguide band. Each of the two higher frequency bands will have 8 distinct frequency channels, with the lowest frequency band, spanning 52 to 65 GHz, to have 16 receiver channels to better resolve the EAST scrape-off layer. With a pulse repetition rate of 1 MHz and simultaneous acquisition of all 32 TOF signals, electron density profiles may be obtained with time resolutions of as short as 3–6 µsec.

RF wave propagation simulation for ICRF antenna in EAST

ABSTRACT The propagation performance of radiofrequency (RF) waves excited by ICRF antenna in plasma has a great influence on the coupling effect. In this paper, the propagation characteristics of fast wave (FW) and slow wave (SW) under tokamak experimental condition are calculated, and the influence of angular frequency w 0, antenna power spectrum k// and tokamak total magnetic field B 0 is illustrated based on the typical operating parameters in EAST. By applying perfect matched layer (PML) boundary processing method to simulate single-pass absorption and using finite element method (FEM) to solve Maxwell equations in frequency domain, the propagation and coupling simulation of RF waves in cold plasma for EAST ICRF antenna in B-window were carried out to obtain the polarization characteristics of fields and the relationship between the coupling impedance and the gap length from antenna to the FW cut-off layer. The analysis results in this paper provide useful reference and guidance for the study of propagation coupling of ICRF waves in EAST and other magnetic confined fusion devices.

Overview of the ICRF antenna coupling experiments on EAST

Experimental verification of ion cyclotron range of frequencies (ICRF) wave coupling is crucial to gain insight into the physics of the improvement of ICRF antenna coupling. The progress of ICRF antenna coupling experiments on EAST has been reported since 2007. The dependence of the loading resistance on the target plasma parameters, operational regimes and synergic heating scenarios on EAST are reviewed. Results show that the antenna coupling resistance R c in L-mode regime meets the relation of R c ∝ exp(−1.5k ∥ x c), which is in good agreement with the simulation results with a perfectly matched layer method, where k ∥ is the dominant launched parallel wave number and x c is the distance of the ICRF antenna and fast wave cut-off layer. Low plasma current, gas puff in the magnetic connections with the ICRF antenna and lower hybrid wave/electron cyclotron heating are beneficial for improving ICRF antenna coupling. The antenna coupling has a strong response during large edge-localized modes (ELMs) but it becomes steady state during ELM free. The study of ICRF antenna coupling under various parameters is helpful to optimize the ICRF wave heating scenario and understand the physical mechanisms which influence the ICRF wave coupling in plasmas.

Increasing the efficiency of heat and mass exchange in an improved rotary film evaporator for concentration of fruit-and-berry puree

An improved model of a rotary film evaporator with a cutting blade having a reflective surface and equipped with an autonomous heating system which is fed by a power supply from Peltier elements. The reflective surface of the advanced cutting blade had an area of 0.06 m 2 and was heated by a flexible film resistive electric heater of radiating type with a ~15...20 W power supply. This solution provides additional heating and mixing and helps to capture the cut-off layer of puree while reducing the useful surface of the working chamber by 7 %. Most evaporators have a low heat transfer coefficient reducing the energy content of the process and final quality of the product. The heat exchange efficiency can be increased by improving the design of the film-forming element of the rotary film evaporator. The use of the proposed cutting blade with a reflective surface enables an increase in the heat transfer coefficient by approximately 20 % compared to the basic rectangular blade design. When comparing the calculated data, it can be concluded that the main indicator of resource efficiency, namely specific energy consumption for heating a unit volume of product in the RFE amounts to 408 kJ/kg compared to 1,019 kJ/kg with the basic vacuum evaporator which means a 1.97 times consumption reduction. The duration of heat treatment in the RFE is 60 s compared to 1 h in the basic VE which shows a significant reduction of raw material exposure to high temperatures. The obtained data show the effectiveness of engineering and technological solutions. The engineering and technological component of any heat and mass exchange processes, in particular the concentration of fruit-and-berry raw materials, is the main component in the production of semi-finished food products of a high degree of readiness

Energy expenditure on ground cutting by continuous action buckets to form the underlying layer of the road

Introduction. To solve the problem of accelerating the construction of roads, improving their quality, it is advisable to use a continuous action unit to form a underlying layer. In general, energy costs for the construction of roads are a significant share occupied by work aimed at cutting and transporting the ground. The working bodies of existing technical means carry out mainly energy-intensive cutting of the ground, which theoretically can be likened to cutting a punch. The energy costs of ground cutting can be significantly reduced by the use of blade cutting. In the bucket of the continuous action unit to form a underlying layer of roads provides the use of working bodies, cutting the ground with blades of knives. The process of filling the bucket with cut soil, the forces attached to the bucket, and the total amount of energy spent on cutting the ground with the buckets of the continuous action unit to form the underlying layer are considered. The method of research. The method of constructions to detect the kinematics of filling the bucket with the cut ground is given. The method of calculation is given: the path of the ground on the bottom of the bucket case when it is filled; the resulting force of force projections in the longitudinal-vertical, cross-vertical and horizontal plane attached to the bucket; moments attached to the bucket in a longitudinal-vertical and horizontal plane, when the bucket is empty and full. The formulas for calculating the total energy on the movement of the bucket when cutting the ground without taking into account the energy costs of the cutting process and determining the total energy costs of cutting the ground by one cubic meter of continuous action buckets to form the underlying layer of roads are given. Results. On the basis of the developed method, the conditional path of the ground along the bottom of the bucket case was calculated, the resulting forces of force projections in the longitudinal-vertical, cross-vertical and horizontal plane attached to the bucket were revealed. The moments attached to the bucket in the longitudinal-vertical and horizontal plane, when the bucket is empty and full, have been determined. The total energy for moving the bucket during ground cutting is calculated without taking into account the energy costs of the cutting process. The total energy costs of cutting the ground by one cubic meter of continuous action buckets to form the underlying layer of roads have been determined. Conclusion. During the filling of the bucket of the unit of continuous action to form the underlying layer of roads cut off soil is twisted and shift of the cut-off layer, which contribute to its destruction into fragments. In a cross-vertical plane, the bucket is balanced. The moment attached to the bucket in the longitudinal-vertical plane is balanced by elements of the structure of the unit. The total energy on moving the bucket when cutting the ground, without taking into account the energy costs of the cutting process, includes energy costs: to accelerate the ground with a bucket, to overcome the friction of the bottom plane of the bucket on the ground, to the additional horizontal force to move the bucket, caused by friction in the elements of the structure. It is u_k≈13 kJ/m3. Theoretically reasonable total energy costs for ground cutting of one cubic meter by the buckets of the continuous action unit to form the underlying layer of roads〖u 〗 (k-gr) ≈109 kJ/m.

Bench test of microwave imaging reflectometry system for EAST tokamak

Microwave Imaging Reflectometry (MIR) has been developed for measuring two-dimensional electron density fluctuations on many Tokamaks. A MIR system with 96 pixels (12 poloidal × 8 radial) has been fabricated for EAST tokamak. In the paper, we present the evaluation results in laboratory bench test with details, including performance of the electronic system and optics. With an artificial target as the real plasma cutoff layer, it has been proved that the EAST MIR system has the capability to reconstruct the correct corrugated shape of cutoff layer.

570 Myocardial deformation imaging after STEMI: can we better predict one-year mortality and heart failure development?

Abstract Prognosis after STEMI is still challenging. One-year mortality ranges between 10-12% and the incidence of heart failure (HF) is between 4% and 28%. Early and accurate identification of high-risk patients necessitates therapy intensification. Aim this study is a part of PREDICT-VT study (NCT03263949). The aim was to test whether deformation imaging based on spackle tracking echocardiography predict MACE (total mortality, HF hospitalization and NYHA class ≥3 development) better than conventional echocardiography and clinical parameters. Methods in 264 consecutive pts enrolled in PREDICT-VT study early echocardiography (5 ± 2 days after pPCI) was done including LA and multilayer LV deformation analysis with longitudinal (L), radial (R) and circumferential (C) strain (S; %) and strain rate (SR, 1/sec). LV index of post systolic shortening for longitudinal (PSS LS) and circumferential (PSS CS) strain were calculated as average of PSS over 18 LV segments. Results 198 patients completed 1-year follow-up and 22 patients (11.1%) experienced MACE. Significant echo, clinical and laboratory predictors with the ROC analysis are listed in the table according to AUC . Conclusion peak systolic longitudinal and to a lesser degree peak systolic circumferential deformation predict mortality and HF development after pPCI better than conventional echo and even clinical parameters. From diastolic parameters only radial SR during atrial contraction was better MACE predictor compared to conventional echocardiography. AUC p Cut-off Senz Spec Peak systolic LS epicardial layer 0.757 &amp;lt;0.001 -11 75 63 Radial SR during atrial contraction 0.754 &amp;lt;0.001 -0.63 65 80 Peak systolic LS mid-wall layer 0.750 &amp;lt;0.001 -12.58 80 60 PSS LS endocardial layer 0.744 &amp;lt;0.001 0.1409 70 61 Peak systolic CS endocardial layer 0.744 &amp;lt;0.001 -18.08 70 67 Wall Motion Score Index 0.740 0.001 1.53 70 70 Peak systolic CS mid-wall layer 0.730 0.001 -13.66 80 60 Peak radial LV strain 0.722 0.001 14.08 80 60 Creatine kinase peak level 0.698 0.003 2155 64 73 LV EF 0.692 0.004 47.5 67 60 TAPSE 0.685 0.015 1.95 75 60 LA strain 0.676 0.012 18.33 63 64 Killip class 0.644 0.028

DETAILS’ REPAIR OF CONSTRUCTION AND ROAD MACHINES: FLUCTUATIONS’ MODELLING

Introduction. Hole details are quite widely used in structures of construction and road machines. The specialists apply boring for draft, semi-fair, and in some cases for fair processing of such surfaces. This type of processing is often followed by the negative nature of oscillatory processes that leads to decrease in accuracy and in the surface quality. The paper studies the possibility of the calculation method’s usage in oscillatory processes, which allows assigning the cutting modes by providing required output parameters.Materials and methods. The authors used the double-support beam as a design model of a boring cutter. The solution of the fluctuations’ modeling came down to definition of point movements, which corresponded to cutter top (points of application equally effective cutting forces). The authors made the definition of movements with use of Mor integrals. Therefore, the paper considered the impact of chip formation and separation due to perturbing forces.Results. The authors carried out the calculation of forces’ values in cutting with use of the degree dependences. Moreover, the authors accepted the formation’s frequency as the frequency of the perturbing influenced structure. The frequency of the chip formation was defined on the basis of estimated dependences, which connected parameters of the tool, the cut-off layer and modes of cutting. As a result, the author received the implementations of oscillatory processes and studied the influence of different factors on vibration amplitude.Discussion and conclusions. The authors make assessment of the received results’ adequacy by comparison with experimental data. The error doesn’t exceed 20%. The developed model considers geometrical parameters of the tool (a departure, plate corners, etc.), the modes of cutting both mechanical properties of the processed material and parameters of the chip formation. The model can be used both at design of boring operations and by optimization of the cutting modes for the purpose of productivity increase.