Ultrarelativistic Acceleration Research Articles

Acceleration mechanism of radiation belt electrons through interaction with multi-subpacket chorus waves

We conduct test particle simulations to examine the acceleration mechanism of relativistic electrons through interaction with multi-subpacket chorus waves. As the analysis of recent observations reveals, amplitude of a rising tone element of chorus wave consists of many short wave packets. We call this single rising tone chorus element with the collective structure of multiple short wave packets as a multi-subpacket chorus wave. In this simulation, we develop the wave model with rapidly fluctuating amplitude and phase discontinuities across each subpacket, in order to examine how these features of multi-subpacket chorus wave influence the nonlinear trapping processes in efficient acceleration of relativistic electrons such as relativistic turning acceleration (RTA) and ultra-relativistic acceleration (URA). To conduct comprehensive examinations, we test more than nine million particles with various initial conditions covering the energy range from 100 to 6 MeV, and the equatorial pitch angles from 10° to 89°. The test particles interact with a single rising tone element of multi-subpacket chorus wave set up with the maximum amplitude of about 2 nT and the frequency rise from about 1.3 kHz to 3.8 kHz over 0.25 s. Relativistic electrons are accelerated by about 160 keV under preferable conditions. The energy increase verifies the high efficiency of acceleration by the wave–particle interactions, based on the fact that it is achieved by a short time interaction less than 1 s with a single element of chorus wave. By analyzing the detailed behavior of the accelerated electrons, we find successive trapping of the resonant electrons resulting in the efficient accelerations from the consecutive multiple subpackets of a chorus wave element.

On the reason for the kink in the rigidity spectra of cosmic-ray protons and helium nuclei near 230 GV

A three-component phenomenological model describing the specific features of the spectrum of cosmic-ray protons and helium nuclei in the rigidity range of 30–2×105 GV is proposed. The first component corresponds to the constant background; the second, to the variable “soft” (30–500 GV) heliospheric source; and the third, to the variable “hard” (0.5–200 TV) source located inside a local bubble. The existence and variability of both sources are provided by the corresponding “surfatron accelerators,” whose operation requires the presence of an extended region with an almost uniform (in both magnitude and direction) magnetic field, orthogonally (or obliquely) to which electromagnetic waves propagate. The maximum energy to which cosmic rays can be accelerated is determined by the source size. The soft source with a size of ∼100 AU is located at the periphery of the heliosphere, behind the front of the solar wind shock wave. The hard source with a size of >0.1 pc is located near the boundary of an interstellar cloud at a distance of ∼0.01 pc from the Sun. The presence of a kink in the rigidity spectra of p and He near 230 GV is related to the variability of the physical conditions in the acceleration region and depends on the relation between the amplitudes and power-law exponents in the dependences of the background, soft heliospheric source, and hard near galactic source. The ultrarelativistic acceleration of p and He by an electromagnetic wave propagating in space plasma across the external magnetic field is numerically analyzed. Conditions for particle trapping by the wave and the dynamics of the particle velocity and momentum components are considered. The calculations show that, in contrast to electrons and positrons (e+), the trapped protons relatively rapidly escape from the effective potential well and cease to accelerate. Due to this effect, the p and He spectra are softer than that of e+. The possibility that the spectra of accelerated protons deviate from standard power-law dependences due to the surfatron mechanism is discussed.

Formation process of relativistic electron flux through interaction with chorus emissions in the Earth's inner magnetosphere

AbstractWe perform test particle simulations of energetic electrons interacting with whistler mode chorus emissions. We compute trajectories of a large number of electrons forming a delta function with the same energy and equatorial pitch angle. The electrons are launched at different locations along the magnetic field line and different timings with respect to a pair of chorus emissions generated at the magnetic equator. We follow the evolution of the delta function and obtain a distribution function in energy and equatorial pitch angle, which is a numerical Green's function for one cycle of chorus wave‐particle interaction. We obtain the Green's functions for the energy range 10 keV–6 MeV and all pitch angles greater than the loss cone angle. By taking the convolution integral of the Green's functions with the distribution function of the injected electrons repeatedly, we follow a long‐time evolution of the distribution function. We find that the energetic electrons are accelerated effectively by relativistic turning acceleration and ultrarelativistic acceleration through nonlinear trapping by chorus emissions. Further, these processes result in the rapid formation of a dumbbell distribution of highly relativistic electrons within a few minutes after the onset of the continuous injection of 10–30 keV electrons.

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.

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.

Ultra-relativistic ion acceleration in the laser-plasma interactions

An analytical relativistic model is proposed to describe the relativistic ion acceleration in the interaction of ultra-intense laser pulses with thin-foil plasmas. It is found that there is a critical value of the ion momentum to make sure that the ions are trapped by the light sail and accelerated in the radiation pressure acceleration (RPA) region. If the initial ion momentum is smaller than the critical value, that is in the classical case of RPA, the potential has a deep well and traps the ions to be accelerated, as the same described before by simulation results [Eliasson et al., New J. Phys. 11, 073006 (2009)]. There is a new ion acceleration region different from RPA, called ultra-relativistic acceleration, if the ion momentum exceeds the critical value. In this case, ions will experience a potential downhill. The dependence of the ion momentum and the self-similar variable at the ion front on the acceleration time has been obtained. In the ultra-relativistic limit, the ion momentum at the ion front is proportional to t4/5, where t is the acceleration time. In our analytical hydrodynamical model, it is naturally predicted that the ion distribution from RPA is not monoenergetic, although the phase-stable acceleration mechanism is effective. The critical conditions of the laser and plasma parameters which identify the two acceleration modes have been achieved.

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.

Effect of Magnetic-Field Gradient on Positron Acceleration along the Magnetic Field in an Oblique Shock Wave

Ultrarelativistic positron acceleration along the magnetic field due to shock waves in an electron-positron-ion plasma is studied with use of one-dimension (one space coordinate and three velocities), fully kinetic, fully electromagnetic, particle simulations. First, ultrarelativistic acceleration to γ ∼ 104 in a uniform external magnetic field B0 is demonstrated with a simulation with the shock speed vsh close to c cos θ, where c is the speed of light and θ is the angle between the external magnetic field and the wave normal. Then, the effect of non-uniformity of B0 is investigated; comparisons are made of two different cases: 1) the strength of the external magnetic field increases as a shock wave propagates (∇B0 is parallel to the wave normal), and 2) it decreases (∇B0 is unti-parallel to the wave normal). It is found that positron acceleration in the latter tends to be stronger than in the former.

Rapid energization of radiation belt electrons by nonlinear wave trapping

Abstract. We show that nonlinear wave trapping plays a significant role in both the generation of whistler-mode chorus emissions and the acceleration of radiation belt electrons to relativistic energies. We have performed particle simulations that successfully reproduce the generation of chorus emissions with rising tones. During this generation process we find that a fraction of resonant electrons are energized very efficiently by special forms of nonlinear wave trapping called relativistic turning acceleration (RTA) and ultra-relativistic acceleration (URA). Particle energization by nonlinear wave trapping is a universal acceleration mechanism that can be effective in space and cosmic plasmas that contain a magnetic mirror geometry.

Ultra‐relativistic acceleration of electrons in planetary magnetospheres

We present a new particle acceleration mechanism called ultra‐relativistic acceleration (URA). URA comprises electron energization due to a special form of nonlinear phase trapping by a coherent whistler‐mode wave for electrons with an initial Lorentz factor γ0 satisfying γ0 &gt; ΩEQ/ω; ω is the wave frequency and ΩEQ is the electron cyclotron frequency at the equator of an assumed dipole magnetic field. Radiation belt electrons that encounter a combination of relativistic turning acceleration (RTA) followed by multiple URA interactions can undergo significant energy increase. Under ideal conditions, at Earth (L = 4) several‐hundred‐keV electrons can be energized to several MeV within a few seconds, while at Jupiter (L = 8), several‐hundred‐keV electrons can be energized by tens of MeV in a few tens of seconds. URA can play a prominent role in generating the several‐MeV electrons observed in Earth's outer zone and the tens‐of‐MeV electrons observed in Jupiter's magnetosphere. More generally, we expect URA to be an effective electron energization mechanism in cosmic plasma environments that contain a magnetic mirror geometry and electromagnetic whistler‐mode emissions.