# Issue 6, 2019

## Dose from secondary neutrons in the work of modern medical accelerators

## Dose from secondary neutrons in the work of modern medical accelerators

### A. V. Belousov$^1$, S. M. Varzar$^1$, M. V. Zheltonozhskaya$^1$, E. N. Lykova$^{1,2}$, A. P. Chernyeav$^{1,2}$

This paper presents a review of experiments and calculations performed to date on the study of secondary neutron fluxes at electron accelerators by different manufacturers and the identification of general patterns. The main differences between the construction of the three major manufacturers Varian, Elekta and Siemens are given. The article presents data on the flux density and the dose from neutrons for different accelerator models and different operation mode. Data analysis demonstrated that the dose from secondary neutrons must be taken into account, since its contribution can reach 2.04% with a maximum energy of up to 24 MeV. Therefore, when planning radiation therapy, it is necessary to evaluate the contribution to the absorbed dose of secondary neutron fluxes and, all other things being equal, select modes of operation with the lowest nominal energy for treating patients.

Show Abstract## Simulation of Random Coincidences in Whole Body 3D Total PET with GATE_v8.0

## Simulation of Random Coincidences in Whole Body 3D Total PET with GATE_v8.0

### A. Bardane, J. Tajmouati, A. Maghnouj, A. Dadouch, A. Didi, A. Mribah, A. El Hajami

Positron emission tomography (PET) is an important functional imaging technique of nuclear medicine used to determine metabolic processes in the body in order to locate and define the tumor . The most common correction method Coincidences is the real-time subtraction of a delayed coincidence channel, which does not add bias, but increases noise. These compromises depend on the injected activity, the local imaging environment and the reconstruction algorithm. Using full 3D simulations and ghost studies, we investigate how equivalent noise count rate gains from using a random noise coincidence estimation method result in an improved signal-to-noise ratio. The image SNR, however depends on the image reconstruction method. We validate that For fully 3D whole-body imaging simulated with GATE (tumor application by Geant4), a low-noise estimate of random coincidences improves SNR for sinograms and images by approximately 17%.

Show Abstract## MODEL OF CELL ACTIVATION THROUGH TNFR2 AND TLR4 RECEPTORS SIGNALING

## MODEL OF CELL ACTIVATION THROUGH TNFR2 AND TLR4 RECEPTORS SIGNALING

### V. A. Beloshapko$^1$, E. A. Generalov$^2$, L. V. Yakovenko$^2$

A mathematical model is suggested for description of translation of the cell activation signals generated by interactions of TLR4 and TNFR2 receptors with ligands. The theoretical background to the construction of the model is offered and the main simulation results are presented. The model takes into account the possibility of self-activation of the cell induced by polymerization of receptors, intersection of signal cascades that may result in depletion of substrates of translating proteins and binding sites on the DNA. The probability of the activation event has a local maximum at the last layer of the reaction graph. The process of cell activation is described by use nonlinear system of singularly perturbed differential equations. All requirements on solution existence have been satisfied and approximate solution has been derived. The boundary conditions type is of importance. Suitably, the probability density of signal transmission from TNFR2 to the cell's DNA has been specified on the membrane, and flow through the membrane has been set for the probability density of signal transmission from TLR4 to the cell's DNA. These obstacles necessitate the use of a special algorithm for analyzing nonlinear differential systems with a small parameter for different boundary conditions. The probability densities are qualitatively different themselves, have distinctive structure, emphasizing different ways of cell activation. The density functions of the probability of cell activation make it possible to determine approximately the distribution of the effectiveness of activation inhibitors over the reaction graph layers.

Show Abstract## Investigation on Concrete Neutron Shielding Properties filled by B4C, CdO and BN microparticles

## Investigation on Concrete Neutron Shielding Properties filled by B4C, CdO and BN microparticles

### M. Alipour, M. Kheradmand Saadi, a. rohani

In this study, compounds; which are highly absorbent for neutrons due to their high absorption cross-section, are used in different volume proportions within cubic geometry for concrete as the primary shielding substrate. For this purpose, these compounds were investigated using Monte-Carlo simulation method using the MCNP code. For achieving different volume percentages, the radius of the absorbent balls must vary from 200 µm(1%) to 750 µm (52%). The designed sample was exposure to an Am-Be neutron source with 5 Ci intensity. 37.5% of total activity of this source is Gamma emission. The goal of designing the geometry in this form is increasing the probability of interactions of fast and energetic neutrons which are moving along diffusion path inside the shield to decrease the speed and energy of these neutrons by inelastic scattering. The compounds have been investigated CdO, B4C, and BN; which are filled in serpentine concrete. According to the simulation results, based on the efficiency of various compounds and smooth production of these compounds and also the necessary costs for their production and acceptable descending process of equivalent dose, Boron Carbide and Boron Nitride compound exhibited satisfactory performance in reducing equivalent doses. So using these compounds as absorbent balls seems to be a reasonable choice.

Show Abstract## Coherent $\pi^0$-photoproduction on the deuteron near threshold and the role of $D$-wave component of the deuteron wave function

## Coherent $\pi^0$-photoproduction on the deuteron near threshold and the role of $D$-wave component of the deuteron wave function

### E. M. Darwish, M. Saleh Yousef$^2$

Near-threshold coherent photoproduction of $\pi^0$-meson on the deuteron is investigated. Numerical results for the unpolarized differential and total cross sections, the linear photon $\Sigma$-asymmetry, the vector $T_{11}$ and tensor $T_{2M}$ ($M$=0,1,2) deuteron spin asymmetries, and the spin asymmetry $\tilde{T}_{20}$ of the total cross section are presented. The role of $D$-wave component of the deuteron wave function on these physical observables is studied. The calculations are based on the impulse approximation in which we use the realistic and high-precision Bonn $NN$ potential (full model) for the deuteron wave function and the unitary isobar MAID-2007 model for the elementary $\gamma N\to\pi N$ amplitude that describes well the threshold region. We have found that the $D$-wave component has a negligible effect on the unpolarized cross sections and the vector deuteron $T_{11}$-asymmetry at photon lab-energies close to threshold. On the contrary, we have obtained a significant role of the $D$-wave part of the deuteron wave function on the $\Sigma$, $T_{2M}$, and $\tilde{T}_{20}$ spin asymmetries. The results for the unpolarized differential cross section are compared to the experimental data from TAPS and a satisfactory agreement within the uncertainties has been obtained at forward pion angles. At backward pion angles, our results underestimate the experimental data and a disagreement has been found.

Show Abstract## Deterministic analysis of the Low Enriched Uranium SLOWPOKE-2 research reactor using DRAGON-5 and DONJON-5 codes system

## Deterministic analysis of the Low Enriched Uranium SLOWPOKE-2 research reactor using DRAGON-5 and DONJON-5 codes system

### O. Jai$^1$, O. EL HAJJAJI$^1$, T. EL BARDOUNI$^1$, A. Didi$^2$

This paper investigates the applicability of the DRAGON5 and DONJON5 code system to develop an accurate full-core model of the Moroccan 2 MW TRIGA Mark-II research reactor. The evaluated cross-section data library ENDFB.VII.1 with SHEM-295 group structure was used. A validation approach is applied to verify the consistency of the developed model. The results of the deterministic calculations based on ENDFB.VII.1/DRAGON5/DONJON5 scheme are compared with the experimental values available in the safety analysis report (SAR) as well as the Monte Carlo results. It was found that the DRAGON5 and DONJON5 code system results for core excess reactivity, critical size, reactivity worth of the five control rods, the power distribution and hot rod power peaking factor are in good agreement with measurements and the MCNP5 simulation values. Therefore, this study proves the capability of the DRAGON5 and DONJON5 code system to reliably simulate the TRIGA Type research reactors.

Show Abstract## Neutronic study of fuel depletion for the MNSR research reactor using DRAGON5 code

## Neutronic study of fuel depletion for the MNSR research reactor using DRAGON5 code

### J. Al Zain, O. El Hajjaji, T. EL BARDOUNI

The aim of this work is to study the fuel depletion of 30 kW miniature neutron source reactor (MNSR). Under operating conditions of two hours per day for five days a week at a peak thermal neutron flux of 1.0E+12 n/cm2:s, the estimated core life is 10 years ( 200 days) . The DRAGON5 code is utilizing to generate the fuel group constants and the infinite multiplication factor versus the MNSR reactor operating time, at different burn-up values. The amounts of uranium burnt up and plutonium produced in the reactor core are calculated using the DRAGON5 transport lattice code. The results are in good agreement with previous studies.

Show Abstract## Periodic solutions with the boundary layers in the modeling problem of anthropogenic pollution vertical transfer in the troposphere

## Periodic solutions with the boundary layers in the modeling problem of anthropogenic pollution vertical transfer in the troposphere

### A. L. Nechaeva, M. A. Davydova

We consider a periodic problem for the nonlinear transfer diffusion equation, which arise in the mathematical modelling of anthropogenic pollution vertical transfer in the lower troposphere. Model problem in the nondimensional variables is classified as the nonlinear singularly perturbed reaction-diffusion-advection problem, which is researched via the methods of asymptotic analysis. Using the boundary functions method and the asymtotic method of differential inequalities based on the comparison principle we construct the asymptotics of arbitrary-order accurasy with the subsequent justification of the constructions and the asymptotic Lyapunov stablility investigation for the periodic boundary layer solution. The results of the work are illustrated with an example, describing the concentration field of the substance linear flow.

Show Abstract## Pairing of electrons in a Cooper pair as attraction of the oppositely directed quantum momentumes.

## Pairing of electrons in a Cooper pair as attraction of the oppositely directed quantum momentumes.

### A. I. Braginsky

The equations of state for the compensating interaction field, the distortion tensor, obtained from the translational invariance of the Lagrangian are investigated. In this model, the wave vector or quantum momentum of a particle is the interaction charge for the compensating distortion tensor. The article deals with the case when the quantum momentum of particles lie on the same line. It is shown that opposite quantum momentum are attracted as well as opposite electric charges. This explains the attraction of electrons with oppositely directed quantum momentum in Cooper pairs in the superconducting state.

Show Abstract## Analysis of nonlocal effect influence in plasmonics with Discrete Sources Method

## Analysis of nonlocal effect influence in plasmonics with Discrete Sources Method

### Yu. A. Eremin$^1$, I. V. Lopushenko$^2$

Mathematical problem of electromagnetic wave scattering by plasmonic dimer composed from two noble metal nanoparticles with size less than 10nm is considered in our work. Efficient Discrete Sources Method which allows to account for all features of such systems including particle shape and occurring nonlocal effects is used to develop mathematical models. It is shown that in case of incident waves that do not depend on azimuthal angle it is possible to approximate the problem solution with system of vertical dipoles on the particle's axis of symmetry. For the first time problem of dimer excitation by point charge in uniform straight motion in homogeneous medium is solved using the hybrid scheme of the Discrete Sources Method.

Show Abstract## Homotopy method for the calculation of the cylindrical waveguide guided waves with an impedance boundary

## Homotopy method for the calculation of the cylindrical waveguide guided waves with an impedance boundary

### A. A. Bykov

A mathematical model for a rectangular waveguide with an impedance boundary condition is formulated and substantiated. The model is based on the application of the Galerkin boundary method. It is assumed that the surface impedance is not a constant, but is given as a function of the coordinates on the surface. The solution is represented as a linear combination of coordinate functions, each of which exactly satisfies Maxwell's equations inside a cylindrical domain. The set of coordinate functions at the border forms a complete system. The coefficients are found from the condition of orthogonality of the surface residual to the system of a projection functions. Because of using the Galerkin method the projection functions coincide with the system of coordinate functions. To calculate the guided waves of a rectangular waveguide with an impedance boundary, a homotopy method is proposed and justified. The decomposition of the solution into a power series in a small parameter is also constructed.

Show Abstract## Features of the electronic exchange of ions with metal nanoclusters

## Features of the electronic exchange of ions with metal nanoclusters

### I. K. Gainullin

The article presents the results of a theoretical and computational study of the electron exchange of atomic particles with metal nanoclusters. For experimental studies of the electronic structure and surface reactivity of metal nanoclusters, scanning tunneling microscopy and electron exchange in the scattering of slow ions are actively used. Due to the complexity of direct experiments, computer simulation is an important tool for studying nanostructures. The results of the calculation of the eigenvalues of the electron wave function well describe the spatial distribution of the electron density on the surface of a nanocluster obtained using scanning tunneling microscopy. Due to the small size of the nanocluster, the electron energy inside it is quantized, and the spatial distribution of the electron density is discrete. The quantization of electron energy (discrete electron structure) significantly influences resonant electron processes, including the electron exchange of atomic particles with nanoclusters and electron tunneling in scanning tunneling microscopy. Using the model problem of electron tunneling from a negative ion to a nanocluster as an example, it was shown that the discrete electronic structure manifests itself in the form of a quantum-size effect of electron exchange and a non-monotonic dependence of the differential conductivity on the bias voltage. A quantitative explanation is also given of the experimentally registered effect of a strong (by an order of magnitude) increase in the probability of neutralization of alkali metal ions on metal nanoclusters, as compared with the case of a bulk metal.

Show Abstract## CURRENT LIMITATIONS FOR THE HOLLOW ELECTRON BEAMS IN THE TUBES OF ELECTRON VACUUM DEVICES IN MILLIMETER RANGE

## CURRENT LIMITATIONS FOR THE HOLLOW ELECTRON BEAMS IN THE TUBES OF ELECTRON VACUUM DEVICES IN MILLIMETER RANGE

### V. Y. Rodyakin$^1$, V. M. Pikunov$^1$, V. N. Aksenov$^2$

The conditions for ensuring the equilibrium steady state of a high-density annular electron flow transported in cylindrical span channels and focused by a uniform magnetic field are investigated. The results of numerical calculations of the limiting current, the limitation of which is due to the longitudinal braking of electrons by the forces of the space charge in the conditions of equilibrium transverse magnetic focusing during the transportation of beams of different configurations in klystron-type devices are presented. Estimates of the limitation of the working length of the device associated with the excitation of the diocotron instability are given. The calculation results are compared with the data obtained using the quasi-three-dimensional Arsenal-MSU program and approximate analytical formulas of other authors.

Show Abstract## Effect of 4H-SiC target temperature under ion irradiation on the distribution profile of Al+ ions

## Effect of 4H-SiC target temperature under ion irradiation on the distribution profile of Al+ ions

### A. A. Shemukhin$^{1,2,4}$, A. P. Evseev$^{1,2}$, A. V. Kozemyako$^2$, B. '. Merzuk$^2$, V. I. Egorkin$^5$, Yu. S. Fedotov$^3$, A. V. Danilov$^3$, V. S. Chernysh$^{1,2}$

4H-SiC was irradiated with Al+ ions at an energy of 190 keV. The depth profiles of implanted aluminum were obtained using the secondary ion mass spectrometry method; a comparison was made with profiles calculated in the SRIM program. Using Rutherford backscattering in channeling mode, we studied the amorphization of the crystal structure after ion implantation in the target at room temperature and 400 ◦C. The fluence of 1015cm−2 was shown to completely disorder the crystal structure under irradiation of a room temperature target. It was found that after ion irradiation of a target heated to 400 ◦C, the penetration depth of the embedded impurity increases. An increase in the target temperature during irradiation leads to the recombination of a significant number of simple defects and the restoration of the crystal structure. The topography of the samples before and after ion irradiation was compared.

Show Abstract## Physical bases of neuroaesthetics

## Physical bases of neuroaesthetics

### A. M. Zotov$^1$, P. V. Korolenko$^{1,2}$, A. Yu. Mishin$^1$, Yu. V. Ryzhikova$^1$

A section of neuroaesthetics that explains the beauty of fractals is considered. The analysis was performed using physical and cognitive representations. Arguments in favor of spatial frequencies selection in the cerebral cortex are given. Special attention is paid to the problem of the stability of scaling characteristics ratio an object and its Fourier transform. The detected stability of Fourier transforms scaling indicates the possibility of faster signals processing in specialized areas of the brain. Fast Fourier processing of visual signals creates a feeling of comfort and causes a sense of beauty when contemplating a fractal object. The obtained results make it possible to physically substantiate the effectiveness of the use in medicine of visual art therapy. In addition, numerical simulation data allow us to give a physical interpretation of some provisions of modern aesthetics.

Show Abstract## Multi-Frequency Terahertz Quantum-Cascade Laser for Atmospheric Probing and Revelin of Small Impurities

## Multi-Frequency Terahertz Quantum-Cascade Laser for Atmospheric Probing and Revelin of Small Impurities

### V. N. Aksenov$^1$, A. A. Angeluts$^1$, P. M. Solyankin$^2$, A. P. Shkurinov$^1$, I. A. Ozheredov$^1$, A. V. Balakin$^1$, S. V. Ivanov$^2$

A multi-frequency terahertz radiation source based on quantum-cascade lasers is described. The prospects of its application for the study of atmospheric phenomena, the creation of lidars and the remote sensing equipment are discussed. The influence of radiation attenuation in atmosphere for three frequency ranges is studied with the help of proposed terahertz source. The estimates of the laser spectral line width influence on terahertz radiation attenuation coefficient measurements in the atmosphere are obtained.

Show Abstract## Electron-vibrational interaction in thiophene-phenylene co-oligomer and its relation to the Raman spectrum

## Electron-vibrational interaction in thiophene-phenylene co-oligomer and its relation to the Raman spectrum

### A. Yu. Sosorev

Electron-vibrational interaction plays the key role in limiting charge mobility in organic semiconductors. In this study, we address theoretically the electron-vibrational interaction in 5,5’-diphenyl-2,2’-bithiophene (PTTP), which belongs to the popular family of thiophene-phenylene co-oligomers (TPCOs). TPCOs are actively studied for application in organic optoelectronic devices due to their promising charge-transport and luminescent properties. Electron-vibrational interaction in PTTP is than compared to that in the model organic semiconductor - anthracene. We have revealed the contributions of various vibrational modes to the reorganization energy of the PTTP molecule, and have shown that these contributions correlate with the Raman intensities of the modes. Specifically, it is found that in both spectra for PTTP, dominating vibration is the Я-mode at ~1460 cm-1. The obtained results indicate the high potential of Raman spectroscopy for studying the electron-vibrational interaction in organic semiconductors. The revealed contribution of various vibrational modes to the electron-vibrational interaction allowed us to suggest the ways for suppression of the electron-phonon interaction in TPCOs. Our conclusions are important for rational design of organic semiconductors for efficient optoelectronic devices.

Show Abstract## Research the influence of the magnetic field on phase transition in antiferromagnetic films by computer modeling

## Research the influence of the magnetic field on phase transition in antiferromagnetic films by computer modeling

### S. V. Belim, I. B. Larionov

In article the influence of external magnetic field on phase transition temperature for antiferromagnetic thin films is investigated. The computer modeling method for the antiferromagnetic Ising model with a thin film geometry is used. Films with thickness from 4 to 16 layers are investigated. It is shown that temperature of antiferromagnetic phase transition decreases according to the square law with increase in an external magnetic field. Speed of decrease the phase transition temperature depends on the film's thickness and the relation of exchange coupling on surface and bulk of a system. For each system there is the limiting value of a magnetic intensity above which antiferromagnetic phase transition is absent. Dependence of the magnetic intensity limiting value on the relation of exchange coupling also has square law.

Show Abstract## Substantiation of experimentally observed self-accommodation complexes of martensitic crystals in alloys with shape memory effects.

## Substantiation of experimentally observed self-accommodation complexes of martensitic crystals in alloys with shape memory effects.

### A. G. Khundjua$^1$, E. A. Brovkina$^1$, A. G. Ptitsin$^1$, M. M. Melnikov$^1$, B. A. Volodin$^2$

The paper presents algorithm for analysis of the possibility of self-accommodation complexes formation of martensitic crystals in alloys with shape memory effects, taking into account the twinning and minimizing the average for the corresponding set of deformation domains. It is shown that complete self-accommodation is possible only in complexes containing simultaneously all variants of the orientation relationship. The carried out calculation for the case of rhombohedral martensite (4 possible orientation relations) showed that the average deformation of the form in four domains is absent. The resulting four-domain complex includes all possible variants of the orientation relationship and is therefore self-accommodative. These complexes have been repeatedly observed in titanium Nickel alloys. Analysis of monoclinic 18R-martensite shows that complete self-accommodation can be achieved only in a complex of 12 different domains. The observed experimentally complexes of four domains in Cu-Al-Ni and Cu-Al-Mn alloys can be explained by partial self-accommodation, which takes into account the martensite crystal exit to the outer surface of the crystal.

Show Abstract## X-ray transmission through infinite dielectric wedge-shaped objects

## X-ray transmission through infinite dielectric wedge-shaped objects

### A. P. Oreshko

The problem of transmission and reflection of X-rays 0.1 Å < λ < 10 Å) from an infinite amorphous homogeneous dielectric wedge-shaped plate was solved analytically. The solution obtained is a “zero” step in solving the problem of X-ray diffraction on a semi-infinite amorphous homogeneous dielectric wedge within the framework of the heuristic geometric theory of diffraction.

Show Abstract## Spectrophotometric study of near Earth asteroids and Main belt ones

## Spectrophotometric study of near Earth asteroids and Main belt ones

### M. P. Shcherbina$^1$, V. V. Busarev$^3$, S. I. Barabanov$^2$

We have carried out observation, calculation and analysis of reectance spectra in the range of 0.35-0.92 µm of 5 near-Earth asteroids and Mars-crossers, and 5 asteroids of Main Belt. Observations of the asteroids were performed in 2013-2017 using 2-m telescope with a CCD-spectrograph of INASAN Terskol Observatory to estimate their taxonomic types and compositions. The results show that some of studied asteroids have a heterogeneous composition of matter, according to variations of their reflectance spectra within close taxonomic classes. Interestingly, some of the asteroids are double. The obtained reectance spectra and their interpretation are given in our paper

Show Abstract## Operating experience of the automatic system for estimation of tsunami hazard of an earthquake «Tsunami Observer»

## Operating experience of the automatic system for estimation of tsunami hazard of an earthquake «Tsunami Observer»

### S. V. Kolesov$^2$, M. A. Nosov$^1$

An automated system for estimation of tsunami hazard of an earthquake "Tsunami Observer" has been in operation since January 2018. In this report we analyze the results of the system over the past year and a half, comparison of the estimates made by the system and in-situ observations data is performed. The issue of focal mechanism latency, which is critical to fast tsunami hazards assessment, is discussed.

Show Abstract## Passive acoustic method for detection and estimation of shallow-water bubble gas fluxes

## Passive acoustic method for detection and estimation of shallow-water bubble gas fluxes

### A. A. Budnikov$^1$, T. V. Malakhova$^2$, I. N. Ivanova$^1$, E. V. Linchenko

A passive acoustic method for estimating the flow of underwater bubble gas emissions for shallow water areas is proposed and tested. The method is based on the connection between the frequency of the audio signal produced by the gas bubble when separated from the output underwater channel and the size of the bubble. In the conducted laboratory experiments, the frequencies of audio signals in the range from 2.7 to 0.4 kHz were recorded during the generation of bubbles from 2 to 15 mm in the liquid thickness. In the analysis of acoustic recordings made near the existing shallow-water spines in Laspi Bay, a series of short audio signals produced by the released methane bubbles of 0.5-2 s duration, grouped into packages containing about ten pulses, was identified. Frequency peaks with maxima of 1 and 1.4 kHz were recorded in the frequency spectrum of the records for the two investigated MIPS. According to the theoretical estimate of the diameter of the bubbles generating such a signal is 7 mm and 5 mm, respectively. Taking into account the intensity of bubble discharge, the calculated gas flow was 40 and 6 l/day, respectively.

Show Abstract## The stability of titanomagnetite basalt of the red sea during the heatings in air and argon.

## The stability of titanomagnetite basalt of the red sea during the heatings in air and argon.

### V. I. Maksimochkin, R. A. Grachev

In order to optimize the conditions of heating during the Thellier procedure and improve reliability of paleofield determination thermal stability experiments of titanomagnetite and titanomaghemite were conducted. The experiments were performed on basalts P72/2 and P72/4 of the zone of the red sea, that contain titanomagnetite with a concentration of magnetite component equal to (44.73.9) % and (465)%, respectively. Annealing titanomagnetite for 10 hours at temperature range 290 – 410 °C in air leads single-phase oxidation process. The increase of annealing temperature up to 460-535 °C leads to the fact that single-phase oxidation is replaced by oxiexsolution. The temperature range of thermal stability of single-phase oxidized titanomagnetite increases with the degree of oxidation. In particular, at an oxidation state close to 0.9, titanomaghemite is stable up to temperatures of 410 - 460°C. The use of the Thellier technique to study the properties of the chemical remanement magnetization of single-phase oxidized titanomagnetite with an oxidation state above z0.6 is limited to approximately 20% of it’s value. To stabilize the single-phase oxidized state of titanomagnetite at temperatures above 460°C and thereby improve the quality of CRM research by Thellier method is possible by selecting the value of the partial oxygen pressure. Keyword. Titanomagnetite, titanomaghemite, chemical magnetization, thermal stability, single-phase oxidation, Thellier method.

Show Abstract## ERRATUM: Improved Generation of Higher Harmonics and Suppression of the Lowest Harmonics in an X-Ray FEL with a Two-Frequency Undulator

## ERRATUM: Improved Generation of Higher Harmonics and Suppression of the Lowest Harmonics in an X-Ray FEL with a Two-Frequency Undulator

### K. V. Zhukovsky

Erratum to the article: Moscow University Physics Bulletin, 2018, Vol. 73, No. 5, pp. 462–469

Show Abstract