Permittivity Of Free Space Research Articles

Theory of Classical Electrodynamics with Topologically Quantized Singularities as Electric Charges

AbstractA theory of classical electrodynamics, where the only admissible electric charges are topological singularities in the electromagnetic field, is formulated. Charge quantization is accounted by the Chern theorem, such that Dirac magnetic monopoles are not needed. The theory allows positive and negative charges of equal magnitude, where the sign of the charge corresponds to the chirality of the topological singularity. Given the trajectory of the singularity, one can calculate electric and magnetic fields identical to those produced by Maxwell's equations for a moving point charge, apart from a multiplicative constant factor related to electron charge and vacuum permittivity. The theory is based on the relativistic Weyl equation in frequency‐wavevector space, with eigenstates comprising the position, velocity, and acceleration of the singularity, and eigenvalues defining the retarded position of the charge. From the eigenstates, one calculates the Berry connection and the Berry curvatures, and identifies the curvatures as electric and magnetic fields.

Understanding the natural units and their hidden role in the laws of physics

The natural units of measure lauded by Max Planck more than 100 years ago are underutilized today. Many physical constants, including the Planck constant, the gravitational constant, the speed of light, vacuum permittivity, and vacuum permeability consist of natural units in their unit dimensions. The natural units are present in all formulas containing these constants. The defining characteristic of the natural units is an alignment of unit values at the Planck scale. This alignment gives a computational basis of proportionality from which the correlated properties and dynamics of elementary particles, including wavelength, period, mass, momentum, and energy, manifest in equal or inversely proportional ratios of the Planck scale. These correlations explain many of the defining equations of quantum mechanics, classical gravity, and electromagnetism.

Space time energy equivalence

Space–time–energy equivalence is the principle that everything that has space and time (in the presence of a constant force with an impact point) has an equivalent amount of energy, and vice versa. This equivalence is widespread in physics and astrophysics. Five examples (Stoney units, Planck units, Newton's law and Interaction of light rays, standard gravitational parameter and Coulomb's law) of the algebraic notation of this principle show its universality. Five examples (repetitions) of the same principle should justify the universality of the new principle and its use in physics and astrophysics. The proposed equivalence reveals the functional relationship between physical constants: Planck's constant, electric charge of an electron, vacuum permittivity and vacuum permeability. The realization of this equivalence will allow, through deepening the understanding of the nature of space–time, to take a fresh look at physics, when describing natural laws and principles.

Non-Maxwellian electron effects on the macroscopic response of a Hall thruster discharge from an axial–radial kinetic model

A 2D axial–radial particle-in-cell (PIC) model of a Hall thruster discharge has been developed to analyze (mainly) the fluid equations satisfied by the azimuthally-averaged slow dynamics of electrons. Their weak collisionality together with a strong interaction with the thruster walls lead to a non-Maxwellian velocity distribution function (VDF). Consequently, the resulting macroscopic response differs from a conventional collisional fluid. First, the gyrotropic (diagonal) part of the pressure tensor is anisotropic. Second, its gyroviscous part, although small, is relevant in the azimuthal momentum balance, where the dominant contributions are orders of magnitude lower than in the axial momentum balance. Third, the heat flux vector does not satisfy simple laws, although convective and conductive behaviors can be identified for the parallel and perpendicular components, respectively. And fourth, the electron wall interaction parameters can differ largely from the classical sheath theory, based on near Maxwellian VDF. Furthermore, these effects behave differently in the near-anode and near-exit regions of the channel. Still, the profiles of basic plasma magnitudes agree well with those of 1D axial fluid models. To facilitate the interpretation of the plasma response, a quasiplanar geometry, a purely-radial magnetic field, and a simple empirical model of cross-field transport were used; but realistic configurations and a more elaborate anomalous diffusion formulation can be incorporated. Computational time was controlled by using an augmented vacuum permittivity and a stationary depletion law for neutrals.

Zero-Point Energy Density at the Origin of the Vacuum Permittivity and Photon Propagation Time Fluctuation

We give a vacuum description with zero-point density for virtual fluctuations. One of the goals is to explain the origin of the vacuum permittivity and permeability and to calculate their values. In particular, we improve on existing calculations by avoiding assumptions on the volume occupied by virtual fluctuations. We propose testing of the models that assume a finite lifetime of virtual fluctuation. If during its propagation, the photon is stochastically trapped and released by virtual pairs, the propagation velocity may fluctuate. The propagation time fluctuation is estimated for several existing models. The obtained values are measurable with available technologies involving ultra-short laser pulses, and some of the models are already in conflict with the existing astronomical observations. The phase velocity is not affected significantly, which is consistent with the interferometric measurements.

Electron extraction mechanism of magnet array microwave discharge neutralizer

Microwave discharge neutralizer is an important part of microwave discharge ion thruster system, which plays a vital role in maintaining potential balance between spacecraft and neutralizing ion beam. Its electron extraction property directly affects the operation condition of ion thruster system. In order to break through the power limit of miniature microwave discharge ion thruster, a magnet array microwave discharge ion thruster system is designed and tested. In the experiment on finalizing magnetic field structure of magnet array microwave discharge neutralizer, an interesting phenomenon is found that the <i>I</i>-<i>V</i> curves of electron current, after rotating the magnetic array orientation, are very different. Defining forward direction of magnet array can normally extract electrons, then backward direction of magnet array can hardly extract electrons. Because the diameter of discharge chamber is only 10 mm, it is too small to perform Langmuir probe diagnosis. And thus, an integrative particle-in-cell method is used to simulate the neutralizer operation processes of two different magnetic field structures, and for the sake of accuracy, real vacuum permittivity is used. The simulation results show good consistence with experimental phenomenon. In the initial discharge process, it is found that the magnetic field gradient leads to different plasma distributions; in electron extraction process, it is found that the potential distribution near the orifice determines the electron extraction property of the neutralizer. Through comparing the plasma parameter distributions under different magnetic field structures and operating voltages, an assumption that the ion is an important factor in electron extraction process is proposed. Then, a simulation that ions disappear artificially outside the orifice is conducted, and the simulation results show that electrons cannot be effectively extracted without ions near the orifice. According to the simulation and experiment results, two necessary conditions are summarized for electron extraction of the neutralizer. The first condition is magnetic field structure: the magnetic field gradient should point towards the orifice to guide plasma migration towards the orifice, the second one is potential distribution: there should be enough ions to lift the potential near the orifice for reducing or breaking the potential well. These two conditions can help understand the electron extraction mechanism of microwave discharge neutralizer and provide theoretical reference for optimizing the performance of neutralizer in future.

Nonlinear inverse bremsstrahlung absorption in magnetized laser-fusion plasma

The nonlinear inverse bremsstrahlung absorption (NLIBA) in magnetized plasma has been investigated within the framework of relativistic kinetic theory. Collisions are described by an improved Krook collision term that accounts for relativistic effects and the Landau microscopic collision form. The non-linearity considered in this paper arises from the anisotropy in electron momentum space in the plasma that is heated by an intense laser pulse. The absorption is explicitly expressed, under reasonable approximations, as a function of the plasma, laser pulse, and magnetic field parameters. Numerical treatment of the model equations shows that absorption increases with laser intensity but decreases with plasma temperature and laser wavelength. It has been shown that the polarization of the laser wave has a significant influence on absorption for high-intense magnetic fields used in magneto-inertial fusion (MIF) experiments. Nonlinear effects clearly reduce absorption for laser intensities comparable to the characteristic intensity, I0=me2c3ε0ωL2/e2, where me is the electron mass, c is the speed of light in vacuum, ɛ0 is the electric permittivity of free space, ωL is the laser wave frequency, and e is the elementary electric charge. Within the intensity I ≪ I0 and laser wavelength in the micro-meter range (λ ∼ μm), relativistic effects appear in the third order of absorption. These findings allow for the optimization of laser pulse parameters to achieve efficient absorption in MIF experiments.

Physical Mechanisms Underpinning the Vacuum Permittivity

The debate about the emptiness of space goes back to the prehistory of science and is epitomized by the Aristotelian ‘horror vacui’, which can be seen as the precursor of the ether, whose modern version is the dynamical quantum vacuum. In this paper, we suggest to change a common view to ‘gaudium vacui’ and discuss how the vacuum fluctuations fix the value of the permittivity, ε0, and permeability, μ0, by modelling their dynamical response by three-dimensional harmonic oscillators.

Variable Physical Constants and Beyond

We previously revealed that the speed of light in vacuum c, the gravitational constant G, the vacuum permittivity ε, and the vacuum permeability μ can be defined by the temperature T (or the expected average frequency f) of cosmic microwave background (CMB) radiation. Given that CMB is continuously cooling, that is, T is continuously decreasing, we proposed that the above “constants” are variable and their values at some space-time with CMB temperature T (cT, GT, εT, and μT) can be described using their values (c0, G0, ε0, and μ0) and the temperature (T0) of CMB at present space-time. Based on the above observation, a number of physical equations related with these constants are re-described in this study, including relativity equation, mass-energy equation, and Maxwell’s equations, etc.

The Number of Elementary Fermions and the Electromagnetic Coupling

Electric charges and masses of elementary fermions of the Standard Model and fundamental physical constants (speed of light in vacuum, Planck constant, gravitational constant, vacuum permittivity, electron charge) are related through a simple equation. This new relation links 10 of the free parameters of the Standard Model—the masses of the three charged leptons and six quarks, and the electromagnetic coupling—in a compact formula, leaving strong constraints for allowing further elementary charged fermions beyond the Standard Model’s physics. The formula is not derived by theoretical calculations, but it is based on the empirically measured values of the electric charges and proper masses of the known elementary fermions.

Calibration-Free Time-Domain Free-Space Permittivity Extraction Technique

A time-domain free-space technique has been proposed to extract relative permittivity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{r}$ </tex-math></inline-formula> ) and effective conductivity ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{e}$ </tex-math></inline-formula> ) of low-loss dielectric samples using their metal- and air-backed calibration-free reflected powers. Numerical computations and 3-D electromagnetic simulations were performed to validate the method. A sensitivity analysis was carried out to examine its accuracy. Calibration-free time-domain free-space measurements over 1–12 GHz were conducted by VNA to extract <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{r}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\sigma _{e}$ </tex-math></inline-formula> of polyethylene and polypropylene low-loss samples.

Fine-Structure Constant Connects Electronic Polarizability and Geometric van-der-Waals Radius of Atoms.

The fine-structure constant (FSC) measures the coupling strength between photons and charged particles and is more strongly associated with quantum electrodynamics than with atomic and molecular physics. Here we present an elementary derivation that accurately predicts the electronic polarizability of atoms from their geometric van-der-Waals (vdW) radius RvdW and the FSC α through the compact formula = (4πε0/a04) × α4/3RvdW7, where ε0 is the permittivity of free space and a0 is the Bohr radius. The validity of this formula is empirically confirmed by estimating the value of α from nonrelativistic quantum calculations of atomic polarizabilities and atomic vdW radii obtained from both theory and experiment. Our heuristic derivation based on empirical data extends the influence of FSC from quantum electrodynamics and specific materials properties such as the visual transparency of graphene to atomic electronic properties throughout the periodic table of elements.

Fast Computation by MLFMM-FFT with NURBS in Large Volumetric Dielectric Structures

A refinement for the computation of the rigorous part of the multi-level fast multipole method (MLFMM) of analyzing volumetric objects is presented. A scheme based on the fast Fourier technique (FFT) is proposed with the objective of reducing the computational resources required to accurately analyze large homogeneous and non-homogeneous dielectric volumes. In order to reduce the memory requirements, the storage of the near-field terms of the method of moments (MoM) matrix is performed only for the positions corresponding to a parallelepiped with the size of the level 1 block of the MLFMM, computed with the vacuum permittivity, taking advantage of the Toeplitz symmetry present in regular hexahedral meshes. The FFT avoids applying the near-field MoM matrix in the iterative solution process. The application of this approach results in huge improvements in terms of memory usage, but also a speeds up the iterative solution process because the use of three-dimensional (3D) FFTs is very efficient for computing convolutions when the number of unknowns of the problems becomes very large as happens in volumetric problems. We also propose a new approach for the numerical treatment of the transition of the dielectric permittivity between different dielectrics or between a dielectric and a free space. To validate the computation technique, the radar cross section (RCS) of several dielectric bodies is computed using the classical MLFMM approach and it is compared with the presented FFT-based-MLFMM solution. The results demonstrate that the efficient memory and computation time usage of the proposed approach.

Off/on switchable smart electromagnetic interference shielding aerogel

Summary Smart electromagnetic interference (EMI) shielding materials with tunable EM wave response characteristics are attractive for future EM devices. Here, we report an off/on switchable EMI shielding material that can be tuned from EM wave transmission to shielding and vice versa by mechanical compression and decompression. This smart material is prepared by filling conductive carbon nanoparticles into wood-derived lamellar carbon aerogel, showing reversible compressibility and strain-sensitive conductivity. The original aerogel has good impedance matching and low dielectric loss, allowing the EM wave to pass through. Mechanical compression enables the carbon nanoparticles to establish highly conductive pathways in the aerogel, which significantly increases the conductivity of aerogel and thus activates its EMI shielding performance. This function switch is reversible by repeatedly compressing and decompressing the aerogel. The availability of such a never-before-realized off/on switchable EMI shielding material provides an opportunity for the development of advanced smart EM devices.

Large gyro-orbit model of ion velocity distribution in plasma near a wall in a grazing-angle magnetic field

A model is presented for the ion distribution function in a plasma at a solid target with a magnetic field $\boldsymbol {B}$ inclined at a small angle, $\alpha \ll 1$ (in radians), to the target. Adiabatic electrons are assumed, requiring $\alpha \gg \sqrt {Zm_{e}/m_{i}}$ , where $m_{e}$ and $m_{i}$ are the electron and ion mass, respectively, and $Z$ is the charge state of the ion. An electric field $\boldsymbol {E}$ is present to repel electrons, and so the characteristic size of the electrostatic potential $\phi$ is set by the electron temperature $T_{e}$ , $e\phi \sim T_{e}$ , where $e$ is the proton charge. An asymptotic scale separation between the Debye length $\lambda _{D} = \sqrt {\epsilon _0 T_{{e}} / e^{2} n_{{e}} }$ , the ion sound gyro-radius $\rho _{s} = \sqrt { m_{i} ( ZT_{e} + T_{i} ) } / (ZeB)$ and the size of the collisional region $d_{c} = \alpha \lambda _{\textrm {mfp}}$ is assumed, $\lambda _{D} \ll \rho _{s} \ll d_{c}$ . Here $\epsilon _0$ is the permittivity of free space, $n_{e}$ is the electron density, $T_{i}$ is the ion temperature, $B= |\boldsymbol {B}|$ and $\lambda _{\textrm {mfp}}$ is the collisional mean free path of an ion. The form of the ion distribution function is assumed at distances $x$ from the wall such that $\rho _{s} \ll x \ll d_{c}$ , that is, collisions are not treated. A self-consistent solution of the electrostatic potential for $x \sim \rho _{s}$ is required to solve for the quasi-periodic ion trajectories and for the ion distribution function at the target. The large gyro-orbit model presented here allows to bypass the numerical solution of $\phi (x)$ and results in an analytical expression for the ion distribution function at the target. It assumes that $\tau =T_{i}/(ZT_{e})\gg 1$ , and ignores the electric force on the quasi-periodic ion trajectory until close to the target. For $\tau \gtrsim 1$ , the model provides an extremely fast approximation to energy–angle distributions of ions at the target. These can be used to make sputtering predictions.

Compact Optical Spectroscopy for Identification of Colloidal Metals

Optical spectroscopy has provided new capabilities and opportunities in materials science, structural engineering, chemistry, biology, and medicine. The expense of spectroscopic instrumentation can be prohibitive—often in the range of tens of thousands of dollars. It would be useful to have a compact, practical alternative that is more cost-effective in specific cases. One example is the case of detecting colloidal metals in solution, in which the metal is in nanoparticle or microparticle form; normally suspended in a dielectric material or fluid, such as water.In this project, we provide a practical, low-cost alternative to more traditional spectroscopic techniques for identifying metals in colloidal form. The basis for the method is the interaction of light with materials, as described by the plasma frequency and band gaps in metals. Metals reflect electromagnetic radiation whose frequency is below the plasma frequency. A glance at the plasma-frequency expression, ωp = √((Ne q 2)/(m* ε 0)), provides an explanation of why the plasma frequency can be a useful tool for identifying a given metal. In this expression, ωp is the plasma frequency in radians per second; Ne is the number of electrons per unit volume (numerical volume density); q is the charge of an electron; m* is the effective mass of an electron; and ε 0 is the permittivity of free space. Now, the quantity Ne can be found in reference tables, or it can be readily calculated for a particular metal. As a consequence, a prominent spectral output band can be a clear indicator of a metal’s “identity.”When a metal sample is in bulk form, it will have a plasma frequency in the ultraviolet range. As a result, a strong spectral response will be observed at the wavelength corresponding to that frequency (referred to as the plasma wavelength). Now, the plasma frequency does not change when a material is in colloidal form—but, due to interband transitions within the metal, the response wavelength will be at a lower value than the plasma wavelength. This wavelength may be in the visible or near infrared (NIR) region of the spectrum. This is the case with many metals, such as gold, silver, copper, lead, and magnesium. The presence of the response wavelength in the optical region is the basis for the method we are proposing.In the compact system we have developed, dual-convex lenses are used to collimate a white-light LED source, and then focus this light onto a sample. The sample is a glass slide populated with silver, copper, or magnesium particles of micrometer radius. Upon passing through the metal sample, the white light interacts with the sample, causing a variation in the intensities of the white light’s constituent components. This amounts to a variation in intensity as a function of wavelength, which is based on that particular metal’s plasma frequency and interband transitions. In our work, we have focused on the intensities of the red, green, and blue light that emerge from the sample—all three of which can be measured easily, after they have been spatially separated by a diffraction grating. To measure the intensities, we used low-cost optical sensors (photodiode arrays) which provided real-time measurements of the intensities of the red, green, and blue light. We were able to experimentally differentiate among silver, copper, magnesium, and iron using this method. Figure 1

Size Effect in Nanostructured SnO2/TiO2 Gas Sensors

Introduction Size effect in resistive-type responses to gases has been demonstrated for the first time in the case of SnO2 polycrystalline sensors [1]. Since then it is believed that the smallest the grain size, the higher change in the electrical resistivity of metal oxide nanomaterials can be expected upon interaction with oxidizing or reducing gases. This belief is based on the argument that the surface-to-volume ration increases with a decrease in the grain diameter and as a gas adsorption is a surface process this in consequence leads to an increased density of active sites available for gas-solid interaction [2-3].Therefore, the size reduction has been considered as a fundamental strategy for nanosensors, justifying an enormous effort towards application of nanotechnology in gas sensing devices.A closer look at this issue reveals that such simplified reasoning is not always true. Geometrical decrease in the grain size below 10 nm for SnO2 does not necessarily mean to be a good solution for other oxides such as TiO2. In fact, the most important is a comparison between the grain diameter d and the Debye length λD defined as: λD={(ε ε0φS)/(eND)}1/2 where ε and ε0 denote relative permittivity of the material and vacuum permittivity, respectively, φ S is the surface potential, e represents electron charge and ND stands for donor concentration.When the condition d << λD is fulfilled, the size effect should play a substantial role in gas sensing. Therefore, the aim of this work is to investigate the size effect in the electrical resistivity of SnO2/TiO2 upon interaction with oxidizing/reducing gases by intentional modification of λD by influencing: the electrical properties through donor concentration ND the structural properties through anatase to rutile ratio thus affecting relative permittivity, εmorphology through its impact on the surface potential, φ S Technology TiO2/SnO2 bi-layer nanoheterostructures have been synthesized in a two-step process: (i) magnetron sputtering, MS, followed by (ii) Langmuir-Blodgett, LB technique [4]. Mixed TiO2/SnO2 composites have been obtained by means of Flame Spray Synthesis, FSS [5], sol-gel [6] and by mechanical mixing of commercial Sigma-Aldrich nanopowders [7]. Experimental Methods Crystallographic structure of the nanocomposites was studied by X-ray diffraction in Bragg-Brentano geometry while that of thin films was determined by X-ray diffraction in grazing incidence GID geometry using Philips X’pert Pro diffractometer. Scanning electron microscopy SEM investigations were carried out with the use of FEI Nova Nano SEM 200 microscope. Transmission electron microscopy TEM was employed to study the morphology of the nanopowders. FEI Tecnai TF 20 X-TWIN microscope was used. Gas sensing properties were established by measuring resistive-type responses to hydrogen, and NO2 vs. time, within a temperature range of 200-400oC both in dc and ac mode. The experimental setup for sensor characterization was already described in [8]. Sensitivity of the sensors to the reducing gas was defined as R0/R while that to the oxidizing as R/R0, where R0 is the baseline resistance in the reference gas, i.e. in air. Results and Conclusions Nanopowders of TiO2 with different crystallite size, grown by FSS, demonstrate a size effect in the electrical conductivity (Fig.1a) which can be attributed to the activation energy decreasing with the particle size. No grain size effect in hydrogen sensing has been observed.Bi-layered heterostructures synthesized on special gas sensor substrates with precisely defined interdigital electrodes were tested towards NO2 detection over the low concentration range from 200 ppb to 20 ppm.High response to low concentration of NO2 (Fig. 1b) could be accounted for by two factors: particular morphology of SnO2 base layer with small, well-dispersed grains indicating possibility of a grain size effectwell-developed, rough surface of TiO2 overlayer grown by the LB technique. Acknowledgement National Science Center NCN, Poland project no. 2016/23/B/ST7/00894 is acknowledged.

The effects of numerical acceleration techniques on PIC-MCC simulations of ion thrusters

The particle-in-cell-Monte Carlo collision method has been widely used in simulation studies of ion thrusters. Due to the huge computational demand of such simulations, numerical acceleration techniques are required. However, the effects of such numerical acceleration techniques on the simulation results are not clear. In this study, the effects of three numerical acceleration techniques are investigated using a series of simulations that implement different numerical acceleration factors. The resulting plasma potentials, plasma density distributions, and plasma currents in the discharge chamber are compared for simulations accelerated by increasing the vacuum permittivity, reducing the mass of heavy particles, and making use of self-similarity. The results demonstrate that increasing the permittivity thickens the sheath. When the sheath expands enough to extend to the cusps, the distributions of the potentials and the plasma densities are affected, influencing the current parameters. Reducing the masses of heavy particles greatly influences ion properties, especially the plasma density. Thus, it causes significant errors in the potential and current parameters. Errors in the beam current can be significantly decreased by correcting the beam current using an exponent relationship between the mass scaling factor and the plasma density. The use of self-similarity simultaneously thickens the sheath and decreases the particle number density and may slightly reduce the plasma current values. A number of suggestions for employing these techniques are also provided.

Polarization of Vacuum Fluctuations: Source of the Vacuum Permittivity and Speed of Light

There are two types of fluctuations in the quantum vacuum: type 1 vacuum fluctuations are on shell and can interact with matter in specific, limited ways that have observable consequences; type 2 vacuum fluctuations are off shell and cannot interact with matter. A photon will polarize a type 1, bound, charged lepton–antilepton vacuum fluctuation in much the same manner that it would polarize a dielectric, suggesting the method used here for calculating the permittivity epsilon _{0} of the vacuum. In a model that retains only leading terms, epsilon _{0} cong (6mu _{0}/pi )(8e^{2}/hbar )^{2}= 9.10times 10^{-12} C/(Vm). The calculated value for epsilon _{0} is 2.7% more than the accepted value. The permittivity of the vacuum, in turn, determines the speed c of light in the vacuum. Since the vacuum is at rest with respect to every inertial frame of reference, c is the same in every inertial reference frame.

Computer Simulation of the O2- Superoxide Ion Stability in a Continuous Dielectric Medium

In this paper, computer modeling is carried out, and stability parameters (total energy, binding energy, ionization and electron affinity, vibrational frequencies) at the ground states of the O2 (X 3Zg-) molecule and the superoxide ion O2- (X 2Пg) in dielectric media are calculated. Chemical particles have been placed in the topological cavity of the continuum medium. The CPCM model takes into account cavitation energy, electrostatic and dispersion interactions with a continuous polarized solvent medium. Calculations are performed using the algorithms of the ORCA package by the method of the hybrid density functional B3LYP in the basic set 6-31+G (d). The calculated data for effective media with a dielectric constant of vacuum, benzene, and water are obtained. It is shown that an increase in the dielectric constant of the solvent significantly increases the stability of the O2- superoxide ion with respect to oxidation and transition to an inactivated state of an oxygen molecule with a calculated electron affinity of 0.495 eV, 2.723 eV, 3.803 eV for vacuum, benzene, and water, respectively.