N. S. Erokhin

Surfatron acceleration of protons by an electromagnetic wave at the heliosphere periphery

The trapping and subsequent efficient surfatron acceleration of weakly relativistic protons by an electromagnetic wave propagating across an external magnetic field in plasma at the heliosphere periphery is considered. The problem is reduced to analysis of a second-order time-dependent nonlinear equation for the wave phase on the particle trajectory. The conditions of proton trapping by the wave, the dynamics of the components of the particle momentum and velocity, the structure of the phase plane, the particle trajectories, and the dependence of the acceleration rate on initial parameters of the problem are analyzed. The asymptotic behavior of the characteristics of accelerated particles for the heliosphere parameters is investigated. The optimum conditions for surfatron acceleration of protons by an electromagnetic wave are discussed. It is demonstrated that the experimentally observed deviation of the spectra of cosmic-ray protons from standard power-law dependences can be caused by the surfatron mechanism. It is shown that protons with initial energies of several GeV can be additionally accelerated in the heliosphere (the region located between the shock front of the solar wind and the heliopause at distances of about 100 astronomical units (a.u.) from the Sun) up to energies on the order of several thousands of GeV. In order to explain the proton spectra in the energy range of ∼20–500 GeV, a two-component phenomenological model is proposed. The first component corresponds to the constant (in this energy range) galactic contribution, while the second (variable) component corresponds to the heliospheric contribution, which appears due to the additional acceleration of soft cosmic-ray protons at the heliosphere periphery. Variations in the proton spectra measured on different time scales between 1992 and 2008 in the energy range from several tens to several hundred GeV, as well as the dependence of these spectra on the heliospheric weather, can be explained by surfatron acceleration of protons in the heliosphere.

Trapping of high-energy electrons into regime of surfatron acceleration by electromagnetic waves in space plasma

The phenomenon of trapping of weakly relativistic charged particles (with kinetic energies on the order of mc2) into a regime of surfatron acceleration by an electromagnetic wave that propagates in plasma across a weak external magnetic field has been studied using nonlinear numerical calculations based on a solution of the relativistic equations of motion. Analysis showed that, for the wave amplitude above a certain threshold value and the initial wave phase outside the interval favorable for the surfing regime, the trajectory of a charged particle initially corresponds to its cyclotron rotation in the external magnetic field. For the initial particle energies studied, the period of this rotation is relatively short. After a certain number (from several dozen to several thousand and above) of periods of rotation, the wave phase takes a value that is favorable for trapping of the charged particle on its trajectory by the electromagnetic wave, provided the Cherenkov resonance conditions are satisfied. As a result, the wave traps the charged particle and imparts it an ultrarelativistic acceleration. In momentum space, the region of trapping into the regime of surfing on an electromagnetic wave turns out to be rather large.

Exactly solvable model of resonance tunneling of an electromagnetic wave in plasma containing short-scale inhomogeneities

Different variants of resonance tunneling of a transverse electromagnetic wave through a plasma layer containing short-scale (subwavelength) inhomogeneities, including evanescence regions to which approximate methods are inapplicable, are analyzed in the framework of an exactly solvable one-dimensional model. Complex plasma density profiles described by a number of free parameters determining the permittivity modulation depth, the characteristic scale lengths of plasma structures, their number, and the thickness of the inhomogeneous plasma layer are considered. It is demonstrated that reflection-free propagation of the wave incident on the layer from vacuum (the effect of wave-barrier transillumination) can be achieved for various sets of such structures, including plasma density profiles containing a stochastic component. Taking into account cubic nonlinearity, it is also possible to obtain an exact solution to the one-dimensional problem on the nonlinear transillumination of nonuniform plasma. In this case, the thicknesses of the evanescence regions decrease appreciably. The problem of resonance tunneling of electromagnetic waves through such barriers is of interest for a number of practical applications.

Effect of the longitudinal momentum of electrons on their surfatron acceleration by an electromagnetic wave in space plasma

By numerically calculating the second-order nonlinear time-dependent equation for the wave phase on a particle trajectory, the effect of the longitudinal (with respect to the external magnetic field) momentum of electrons on the dynamics of their surfatron acceleration by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed. It is shown that, for strongly relativistic initial values of the longitudinal component of the electron momentum (the other parameters of the problem being fixed), the electrons are trapped into the ultrarelativistic regime of surfatron acceleration within a definite interval of the initial wave phase Ψ(0) on the particle trajectory. It was assumed in the calculations that Ψ(0) ≤ π. For the initial wave phases lying within the interval of 0 < Ψ(0) ≤ π, the electrons are immediately trapped by the wave, whereas at π ≤ Ψ(0) ≤ 0, no electron trapping is observed even at long computation times. This result substantially simplifies estimates of the wave damping caused by particle acceleration. The dynamics of the velocity components, momentum, and relativistic factor of electrons in the course of their ultrarelativistic acceleration are considered. The obtained results present interest for the development of modern concepts of the mechanisms for the generation of ultrarelativistic particles in space plasma, correct interpretation of experimental data on the flows of such particles, explanation of possible reasons for the deviation of the fast particle spectra observed in the heliosphere from the standard power-law scaling, and analysis of the relation between such deviations and the space weather.

Reflectionless passage of an electromagnetic wave through an inhomogeneous plasma layer

An exactly solvable model is used as a basis to study the reflectionless passage of a transverse electromagnetic wave through an inhomogeneous plasma containing large-amplitude, small-scale (subwave-length) structures (in particular, opaque regions) that cannot be correctly described by approximate methods. It is shown that, during the reflectionless passage of an electromagnetic wave, strong wave field splashes can occur in certain plasma sublayers. The nonuniform spatial plasma density profile is characterized by a number of free parameters describing the modulation depth of the dielectric function, the characteristic sizes of the structures and their number, the thickness of the inhomogeneous plasma region, and so on. Such plasma density structures are shown to be very diverse when, e.g., a wave that is incident from vacuum propagates without reflection through a plasma layer (wave barrier transillumination). With the cubic nonlinearity taken into account, a one-dimensional problem of the nonlinear transillumination of an inhomogeneous plasma can be solved exactly.

On the origin of a kink in the hardness spectra of cosmic-ray protons and helium nuclei in the vicinity of 230 GV

A three-component phenomenological model for the description of specific features of spectra of cosmic-ray protons and helium nuclei in the hardness range from 30 to 2 × 105 GV is proposed. The first component corresponds to the constant background; the second component, to a variable “soft” (30–500 GV) heliospheric source; and the third component, to a variable “hard” (0.5–200 TV) galactic source inside a local bubble. The corresponding “surfatron accelerators” are responsible for the existence and variability of both sources. In order for such accelerators to operate, there should be an extended area with a nearly uniform and constant (in both the magnitude and direction) magnetic field and electromagnetic waves propagating perpendicular (or obliquely) to it. The dimensions of each source determine the maximum energy to which cosmic rays can be accelerated. The soft source with a size of ~100 au lies at the periphery of the heliosphere, beyond the terminal shock, while the hard source with a size of >0.1 pc is located near the boundary of a local interstellar cloud at a distance of ~0.01 pc from the Sun. A kink in the hardness spectra of p and He (near the hardness of about 230 GV) is caused by the variability of physical conditions in the acceleration region and depends on the relation between the amplitudes and power-law indices of the background, the soft heliospheric source, and the nearby hard galactic source. Ultrarelativistic acceleration of p and He in space plasma by an electromagnetic wave propagating perpendicular to the external magnetic field is investigated using numerical calculations. The conditions for particle trapping by the wave, as well as the dynamics of the velocity and momentum components, are analyzed. The calculations show that, in contrast to electrons and positrons (e+), a trapped proton can escape from the effective potential well after a relatively short time, thereby terminating to accelerate. Such an effect gives rise to softer spectra of p and He sources as compared to those of e+. The possibility of deviation of the spectra of accelerated protons from standard power-law dependences due to the surfatron mechanism is discussed.

Electron flux scattering in strongly turbulent ionospheric plasma regions

Abstract The results of analysis of low energy electron flux decreases recorded by a high time-resolution counter system on the satellite Cosmos-1809 crossing strongly turbulent plasma regions are discussed. The near-satellite plasma turbulization is induced by the HF radiation pulses of the powerful onboard sounder transmitter. The energy spectrum dip near the energy ∼120 eV is the electron flux perturbation interpreted in terms of the charged particles scattering/deceleration.

Broadband Wide-Angle Second Harmonic Generation in Magnetized Plasma: Double Resonant Effect

Conditions for the phase synchronism between high-frequency electromagnetic waves with frequencies ω and 2ω propagating in magnetized plasma are investigated. The variety of the values of the plasma density and magnetic field, as well as of wave polarizations, obeying the synchronism conditions are shown to provide resonant broadband wide-angle nonlinear generation of the second harmonic of the pumping wave. Special attention is given to oblique propagation of interacting waves. The coupling strengths for the resonant mode conversion in magnetized collisional plasma are obtained. The double resonance ensuring efficient nonlinear generation of extraordinary mode in the vicinity of the electron cyclotron resonance (ω(2k) = ωce) is considered. Examples illustrating these nonlinear phenomena for some plasma and radiation parameters are presented.

Surfatron accelerator in the local interstellar cloud

Taking into account results of numerous experiments, the variability of the energy spectra of cosmic rays (protons and helium nuclei) in the energy range of 10 GeV to ~107 GeV is explained on the basis of a hypothesis of the existence of two variable sources close to the Sun. The first (soft) surfatron source (with a size of ~100 AU) is located at the periphery of the heliosphere. The second (hard) surfatron source (with a size of ~1 pc) is situated in the Local Interstellar Cloud (LIC) at a distance of <1 pc. The constant background is described by a power-law spectrum with a slope of ~2.75. The variable heliospheric surfatron source is described by a power-law spectrum with a variable amplitude, slope, and cutoff energy, the maximum cutoff energy being in the range of EСН/Z < 1000 GeV. The variable surfatron source in the LIC is described by a power-law spectrum with a variable amplitude, slope, and cut-off energy, the maximum cut-off energy being EСL/Z ≤ 3 × 106 GeV. The proposed model is used to approximate data from several experiments performed at close times. The energy of each cosmic-ray component is calculated. The possibility of surfatron acceleration of Fe nuclei (Z = 26) in the LIC up to an energy of ECL ~ 1017 eV and electron and positrons to the “knee” in the energy spectrum is predicted. By numerically solving a system of nonlinear equations describing the interaction between an electromagnetic wave and a charged particle with an energy of up to E/Z ~ 3 × 106 GeV, the possibility of trapping, confinement, and acceleration of charged cosmic-ray particles by a quasi-longitudinal plasma wave is demonstrated.

Peculiarities of charged particle dynamics under cyclotron resonance conditions

Peculiarities of the dynamics of charged particles interacting with electromagnetic radiation under nearly autoresonance conditions are analyzed. In particular, analysis of nonlinear cyclotron resonances shows that their widths increase when the autoresonance conditions are approached. In this case, however, the distance between nonlinear resonances increases even faster, due to which nonlinear resonances do not overlap and, accordingly, regimes with dynamic chaos do not occur. According to calculations, the dynamics of charged particles under the autoresonance conditions is very sensitive to fluctuations, the effect of which can be anomalously large and lead to superdiffusion. It is shown that, under the autoresonance conditions, particle dynamics on small time intervals can differ significantly from that on large time intervals. This effect is most pronounced in the presence of fluctuations in the system.