Surfatron Acceleration Research Articles

Anomalous staged hot-electron acceleration by two-plasmon decay instability in magnetized plasmas.

We present a staged hot-electron acceleration mechanism of the two-plasmon decay (TPD) instability in the transverse magnetic field under the parameters relevant to inertial confinement fusion experiments. After being accelerated by the forward electron plasma wave (FEPW) of TPD, the hot-electrons can be anomalously accelerated again by the backward electron plasma wave (BEPW) of TPD and then obtain higher energy. Moreover, the surfatron acceleration mechanism of TPD in the magnetic field is also confirmed, the electrons trapped by the TPD daughter EPWs are accelerated in the direction along the wave front. Interestingly, the velocity of electrons accelerated by surfing from the FEPW is quite easily close to the BEPW phase velocity, which markedly enhances the efficiency of the staged acceleration. The coexistence of these two acceleration mechanisms leads to a significant increase of energetic electrons generated by TPD in the magnetic field. Meanwhile the EPWs are dissipated, TPD instability is effectively suppressed, and the laser transmission increases.

Surfatron acceleration of the protons to high energy in relativistic jets

This paper describes the acceleration of high-energy protons captured by electrostatic waves in the frame of a jet arising in the area of instability of a relativistic jet, where spiral structures are excited. The wave has a spatially heterogeneous structure of $\mathrm{exp}(i{k}_{\ensuremath{\parallel}}z+i{m}_{\ensuremath{\phi}}\ensuremath{\phi})$. Protons can be captured in potential wells created by spiral waves, and thereby experience acceleration via a mechanism known as surfatron acceleration. Expressions for the maximum energy (${E}_{p}\ensuremath{\simeq}{10}^{19}\text{ }\text{ }\mathrm{eV}$) and energy spectrum from jet parameters are obtained.

Estimation of the Variability of the Combined Electron and Positron Flux of Cosmic Rays

The variability of the combined electron and positron flux (e+ + e–) of cosmic rays (CRs) is numerically estimated using the results obtained in the Fermi-LAT,AMS-02, and DAMPE satellite experiments. The validity of the variability of the (e+ + e–) CR spectra in the energy range of >30 GeV is demonstrated. Correlation between the reliability of the variability for each pair of spectra and the difference of the average monthly sunspot numbers averaged over the time interval of observation is established. The existence of the observed variable component of the (e+ + e–) CR flux on a time scale from ~1 month to ~1 year can be explained using the model of surfatron acceleration of CRs in the close neighborhood of the Solar System (at the periphery of the heliosphere and in the nearby interstellar clouds).

Surfatron acceleration of weakly relativistic electrons by electromagnetic wave packet in space plasma

Resonant interactions between an electromagnetic wave packet and charged particles based on numerical calculations are investigated. The strong surfatron acceleration of weakly relativistic electrons by an electromagnetic wave packet in space plasma is studied. In the central area of the wave packet, the electric field amplitude is above a threshold value and this makes it possible to capture particles in the surfing mode. The work is carried out by exact solving of second order nonlinear, nonstationary equations for the wave packet phase on the particle's trajectory at the carrying frequency. Numerical modeling shows that the trapping of weakly relativistic electrons in strong acceleration mode occurs immediately for a wide enough range of favorable initial wave phase values (80% and more). Furthermore it has been demonstrated that the combination of ranges of the particle's initial parameters corresponding to the capturing in surfatron acceleration is large enough. Temporal dynamics of velocity components for accelerated particles and the particularities of their trajectory, taking into account cyclotron rotation at the initial stage and phase plane structure for numerically solved nonlinear equations, are considered. Simulation results allow us to draw conclusions about the possibility of surfatron acceleration of weakly relativistic charged particles in space plasma by an electromagnetic wave packet.

On the cause of variability of the cosmic ray spectrum in the knee region

Cosmic ray (CR) energy spectra for H, He, Si, and Fe nuclei with energy-to-charge number ratios ℰ/Z in the range from 10 to 5 × 107 GeV are studied using observational data obtained at different times in different energy ranges: AMS-02, CREAM, Tibet ASγ, Tibet (hybrid), GRAPES-3, KASCADE, and KASCADE-Grande. Comparison of the H and He CR fluxes according to the KASCADE and KASCADE-Grande data (for different models of deconvolving CR spectra) with the Tibet ASγ and Tibet (hybrid) data obtained at another time in the range of ℰ/Z ∼ 3 × 106 GeV demonstrates space weather-caused variability of the CR flux. This feature of CR energy spectra in the Tibet ASγ data is most clearly observed in the spectra of heavier nuclei (Si and Fe) according to the KASCADE-Grande and GRAPES-3 data. The variability in the energy spectra of all CRs in the vicinity of the “knee” is shown in the data of Yakutsk EAS, CASA-BLANCA, and Tibet-III experiments. The variability of the CR flux on a time scale on the order of several years exists only if the source corresponding to the peak in the energy spectrum is situated at a distance of no more than 1 pc from the Sun. Rapid surfatron acceleration of CRs may result from colliding interstellar clouds nearest to the Sun (LIC and G). This acceleration mechanism allows one to explain the variability of the CR spectrum in the range 103 GeV < ℰ/Z < 108 GeV. Conditions for the trapping of strongly relativistic Fe nuclei by an electromagnetic wave, the dynamics of the components of the particle velocity and momentum, and the dependence of the particle acceleration rate on the initial parameters of the problem are analyzed using numerical calculations. The structure of the phase plane of the accelerated Fe nuclei is examined. Optimal conditions for the implementation of ultrarelativistic surfatron acceleration of Fe nuclei by an electromagnetic wave are formulated.

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 E СН/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 E СL/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 E CL ~ 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.

Analysis of the dependence of surfatron acceleration of electrons by an electromagnetic wave in space plasma on the particle momentum along the wave front

Based on the numerical solution of the nonlinear nonstationary second-order equation for the wave phase on the particle trajectory, the dynamics of surfatron acceleration of electrons by an electromagnetic wave propagating across the external magnetic field in space plasma is analyzed as a function of the electron momentum along the wave front. Numerical calculations show that, for strongly relativistic initial values of the electron momentum component along the wave front gy(0) (the other parameters of the problem being the same), electrons are trapped into the regime of ultrarelativistic surfatron acceleration within a certain interval of the initial wave phase Ψ(0) on the particle trajectory. It is assumed in the calculations that |Ψ(0)| ≤ π. For strongly relativistic values of gy(0), electrons are immediately trapped by the wave for 19% of the initial values of the phase Ψ(0) (favorable phases). For the rest of the values of Ψ(0), trapping does not occur even at long times. This circumstance substantially simplifies estimations of the wave damping due to particle acceleration in subsequent calculations. The dynamics of the relativistic factor and the components of the electron velocity and momentum under surfatron acceleration is also analyzed. The obtained results are of interest for the development of modern concepts of possible mechanisms of generation of ultrarelativistic particle fluxes in relatively calm space plasma, as well as for correct interpretation of observational data on the fluxes of such particles and explanation of possible reasons for the deviation of ultrarelativistic particle spectra detected in the heliosphere from the standard power-law scalings and the relation of these variations to space weather and large-scale atmospheric processes similar to tropical cyclones.

ДИНАМИКА ЗАХВАТА И ПОСЛЕДУЮЩЕГО СЕРФОТРОННОГО УСКОРЕНИЯ ЭЛЕКТРОНОВ ЭЛЕКТРОМАГНИТНЫМИ ВОЛНАМИ В КОСМИЧЕСКОЙ ПЛАЗМЕ

The research of dynamics of the capture and subsequent surfatron acceleration of electrons by electromagnetic waves, propagating perpendicular to the magnetic field in cosmic plasma is conducted on the basis of nonlinear numerical calculations. The optimal conditions for the realization of ultra-relativistic electron acceleration by wave packets in cosmic plasma including favorable initial phase of the wave on the particle trajectory, the sign of electron initial impulse in the direction of the wave front, the magnitude of the phase velocity of the wave are formulated. The asymptotic behavior of the electron characteristics under hard acceleration (relativistic factor, the impulse components and the captured particle velocity, position of the bottom of the effective potential well, etc.) is obtained. It is shown that the trajectories have the form of a spiral on the phase plane for trapped electrons and gradually approach the singular point of the type of stable focus. The bottom position of effective non-stationary potential well for the trapped electrons is different because it depends on the charge sign of the accelerated particle. For trapped electrons the wave phase graphics on the particle trajectory correspond to oscillations with an increasing period and decreasing amplitude with the increase of energy of the particle. The bottom of an effective non-stationary potential well is achieved by trapped particle asymptotically. Thus, the trapped electrons with different initial wave phases in their trajectory are gradually condensed on the bottom of the effective non-stationary potential well. It is important to emphasize that the packets of electromagnetic waves in the vicinity of relatively quiet stars (like the Sun) can be local sources of additional acceleration of the spectrum of cosmic rays with initial energies of the order of GeV up to the energies of hundreds of GeV and a dozen of TeV, which provides the observed variation of the spectrum of cosmic rays in this area depending on the space weather. Much more additional acceleration of cosmic rays can be in the plasma of local interstellar clouds at distances from the Sun of about parsecs. The analysis of surfatron generation mechanism of relativistic particles charged with electromagnetic waves in the relatively tranquil cosmic plasma is important for understanding the causes of the observed variability of the energy spectra of cosmic rays and the appearance of various features in their energy spectrum. This allows giving a correct interpretation of the experimental data. It is important to note that the flows of cosmic rays can significantly affect the vertical profiles of atmospheric temperature, precipitation, and the dynamics of large-scale tropical cyclogenesis

Trajectories of electrons with large longitudinal momenta in the phase plane during surfatron acceleration by an electromagnetic wave

The trajectories of electrons with large longitudinal momenta in the phase plane in the course of their surfatron acceleration by an electromagnetic wave propagating in space plasma across the external magnetic field are analyzed. Electrons with large longitudinal momenta are trapped immediately if the initial wave phase Ψ(0) on the particle trajectory is positive. For negative values of Ψ(0), no electrons trapping by the wave is observed over the available computational times. According to numerical calculations, the trajectories of trapped particles in the phase plane have a singular point of the stable focus type and the behavior of the trajectory corresponds to the motion in a complex nonstationary effective potential well. For some initial phases, electrons are confined in the region of the accelerating electric field for relatively short time, the energy gain being about 50–130% and more.

Angular distribution of energetic argon ions emitted by a 90 kJ Filippov-type plasma focus

Characteristics of the energetic argon ions emitted by a 90 kJ Filippov-type plasma focus are studied by employing an array of Faraday cups. The Faraday cups are designed to minimize the secondary electron emission effects on their response. Angular distribution of the ions is measured, and the results indicate a highly anisotropic emission with a dip at the device axis and a local maximum at the angle of 7° with respect to the axis. It has been argued that this kind of anisotropic emission may be related to the surfatron acceleration mechanism and shown that this behavior is independent of the working gas pressure. It has been also demonstrated that this mechanism is responsible for the generation of MeV ions. Measuring the total ion number at different working gas pressures gives an optimum pressure of 0.3 Torr. In addition, the energy spectrum of ions is measured by taking into account of the ambient gas effects on the energy and charge of the ions. The current neutralization effect of electrons trapped in the ion beam as well as the effect of conducting boundaries surrounding the beam, on the detected signals are investigated.

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.

Stability of relativistic surfatron acceleration.

In this paper we consider the surfatron acceleration of relativistic charged particles by a strong electrostatic wave propagating in a transverse direction relative to the background magnetic field. We investigate how high-frequency fluctuations of the background magnetic field affect the process of the resonant acceleration. We show that the presence of fluctuations leads to particle escape from the surfatron resonance and illustrate that fluctuations of different components of the magnetic field have quite a distinct effect on the energy gained by particles. In the case of the same power density, the strongest effect corresponds to fluctuations of the component directed along the background magnetic field, while the effect of the component along the wave front is substantially weaker. This is more important for particles with a large velocity component along the background magnetic field. We demonstrate that the dynamics of particles can statistically be described in terms of the adiabatic invariant diffusion. We derive the corresponding diffusion equation and compare solutions of that equation with results obtained by the explicit particle tracing.

Relativistic surfatron process for Landau resonant electrons in radiation belts

Abstract. Recent theoretical studies of the nonlinear wave-particle interactions for relativistic particles have shown that Landau resonant orbits could be efficiently accelerated along the mean background magnetic field for propagation angles θ in close proximity to a critical propagation θc associated with a Hopf–Hopf bifurcation condition. In this report, we extend previous studies to reach greater modeling capacities for the study of electrons in radiation belts by including longitudinal wave effects and inhomogeneous magnetic fields. We find that even though both effects can limit the surfatron acceleration of electrons in radiation belts, gains in energy of the order of 100 keV, taking place on one tenth of a millisecond, are sufficiently strong for the mechanism to be relevant to radiation belt dynamics.

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.

Numerical investigation of the surfatron acceleration efficiency of charged particles by wave packets in space plasma

A theoretical study of the efficiency of the relativistic acceleration of charged particles by a finite amplitude electromagnetic wave packet in space plasma is presented. The effect of surfatron mechanism particle acceleration is investigated by numerical analysis of the second-order, non-stationary, nonlinear equation for the wave packet phase at the particle trajectory. The influence of the phase and group velocities of the wave packet at the wave packet carrying frequency on the acceleration efficiency is studied. The optimal conditions for weakly relativistic particles captured by electromagnetic wave packets with the following highly relativistic charge acceleration are determined. The particle energy growth rate for the regime of surfatron relativistic acceleration is determined. The temporal dynamics of particle acceleration are investigated. The conclusion about the possibilities of ultrarelativistic surfatron acceleration of charges by a wave packet with a smooth amplitude envelope is given.

Dynamical-systems approach to relativistic nonlinear wave-particle interaction in collisionless plasmas

In this report, we present a dynamical systems approach to study the exact nonlinear wave-particle interaction in relativistic regime. We give particular attention to the effect of wave obliquity on the dynamics of the orbits by studying the specific cases of parallel (θ = 0) and perpendicular (θ = -π/2) propagations in comparison to the general case of oblique propagation θ =]-π/2,0[. We found that the fixed points of the system correspond to Landau resonance and that the dynamics can evolve from trapping to surfatron acceleration for propagation angles obeying a Hopf bifurcations condition. Cyclotron-resonant particles are also studied by the construction of a pseudo-potential structure in the Lorentz factor γ. We derived a condition for which Arnold diffusion results in relativistic stochastic acceleration. Hence, two general conclusions are drawn: (1) The propagation angle θ can significantly alter the dynamics of the orbits at both Landau and cyclotron-resonances. (2) Considering the short-time scales upon which the particles are accelerated, these two mechanisms for Landau and cyclotron resonant orbits could become potential candidates for problems of particle energization in collisionless space and cosmic plasmas.

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.

Resonant acceleration of charged particles in the presence of random fluctuations

We present a quantitative theory of the nonlinear dynamics and surfatron resonant acceleration of charged particles in the presence of random fluctuations of magnetic field. We demonstrate that the surfatron mechanism of acceleration is sufficiently stable versus the influence of fluctuations and particle accelerate even in the presence of a random noise. We estimate the maximum energy which particles could gain in the course of the surfatron acceleration.

Adiabatic description of capture into resonance and surfatron acceleration of charged particles by electromagnetic waves

We present an analytical and numerical study of the surfatron acceleration of nonrelativistic charged particles by electromagnetic waves. The acceleration is caused by capture of particles into resonance with one of the waves. We investigate capture for systems with one or two waves and provide conditions under which the obtained results can be applied to systems with more than two waves. In the case of a single wave, the once captured particles never leave the resonance and their velocity grows linearly with time. However, if there are two waves in the system, the upper bound of the energy gain may exist and we find the analytical value of that bound. We discuss several generalizations including the relativistic limit, different wave amplitudes, and a wide range of the waves' wavenumbers. The obtained results are used for qualitative description of some phenomena observed in the Earth's magnetosphere.

Surfatron acceleration in electromagnetic waves with a low phase velocity

The possibility of unlimited surfatron acceleration of nonrelativistic charged particles by slow electromagnetic waves has been revealed. The capture into such an acceleration regime has been described. The region of the parameters in which the effect of the capture and acceleration exists has been considered. The contribution of this mechanism to an increase in the energy of charged particles in the Earth’s magnetosphere has been estimated.