Non-thermal Tail Research Articles

Universal Nonthermal Power-law Distribution Functions from the Self-consistent Evolution of Collisionless Electrostatic Plasmas

Collisionless systems often exhibit nonthermal power-law tails in their distribution functions. Interestingly, collisionless plasmas in various physical scenarios (e.g., the ion population of the solar wind) feature a v −5 tail in their velocity (v) distribution, whose origin has been a long-standing puzzle. We show this power-law tail to be a natural outcome of the collisionless relaxation of driven electrostatic plasmas. Using a quasi-linear analysis of the perturbed Vlasov–Poisson equations, we show that the coarse-grained mean distribution function (DF), f 0, follows a quasi-linear diffusion equation with a diffusion coefficient D(v) that depends on v through the plasma dielectric constant. If the plasma is isotropically forced on scales larger than the Debye length with a white-noise-like electric field, D(v) ∼ v 4 for σ < v < ω P/k, with σ the thermal velocity, ω P the plasma frequency, and k the characteristic wavenumber of the perturbation; the corresponding quasi-steady-state f 0 develops a v −(d + 2) tail in d dimensions (v −5 tail in 3D), while the energy (E) distribution develops an E −2 tail independent of dimensionality. Any redness of the noise only alters the scaling in the high v end. Nonresonant particles moving slower than the phase velocity of the plasma waves (ω P/k) experience a Debye-screened electric field, and significantly less (power-law suppressed) acceleration than the near-resonant particles. Thus, a Maxwellian DF develops a power-law tail, while its core (v < σ) eventually also heats up but over a much longer timescale. We definitively show that self-consistency (ignored in test-particle treatments) is crucial for the emergence of the universal v −5 tail.

Electron Acceleration at Quasi-parallel Nonrelativistic Shocks: A 1D Kinetic Survey

We present a survey of 1D kinetic particle-in-cell simulations of quasi-parallel nonrelativistic shocks to identify the environments favorable for electron acceleration. We explore an unprecedented range of shock speeds v sh ≈ 0.067–0.267c, Alfvén Mach numbers MA=5–40 , sonic Mach numbers Ms=5–160 , as well as the proton-to-electron mass ratios m i/m e = 16–1836. We find that high Alfvén Mach number shocks can channel a large fraction of their kinetic energy into nonthermal particles, self-sustaining magnetic turbulence and acceleration to larger and larger energies. The fraction of injected particles is ≲0.5% for electrons and ≈1% for protons, and the corresponding energy efficiencies are ≲2% and ≈10%, respectively. The extent of the nonthermal tail is sensitive to the Alfvén Mach number; when MA≲10 , the nonthermal electron distribution exhibits minimal growth beyond the average momentum of the downstream thermal protons, independently of the proton-to-electron mass ratio. Acceleration is slow for shocks with low sonic Mach numbers, yet nonthermal electrons still achieve momenta exceeding the downstream thermal proton momentum when the shock Alfvén Mach number is large enough. We provide simulation-based parameterizations of the transition from thermal to nonthermal distribution in the downstream (found at a momentum around pi,e/mivsh≈3mi,e/mi ), as well as the ratio of nonthermal electron to proton number density. The results are applicable to many different environments and are important for modeling shock-powered nonthermal radiation.

Applications of Fast Magnetic Reconnection Models to the Atmospheres of the Sun and Protoplanetary Disks

Partially ionized plasmas consist of charged and neutral particles whose mutual collisions modify magnetic reconnection compared with the fully ionized case. The collisions alter the rate and locations of the magnetic dissipation heating and the distribution of energies among the particles accelerated into the nonthermal tail. We examine the collisional regimes for the onset of fast reconnection in two environments: the partially ionized layers of the solar atmosphere, and the protoplanetary disks that are the birthplaces for planets around young stars. In both these environments, magnetic nulls readily develop into resistive current sheets in the regime where the charged and neutral particles are fully coupled by collisions, but the current sheets quickly break down under the ideal tearing instability. The current sheets collapse repeatedly, forming magnetic islands at successively smaller scales, until they enter a collisionally decoupled regime where the magnetic energy is rapidly turned into heat and charged-particle kinetic energy. Small-scale, decoupled fast reconnection in the solar atmosphere may lead to preferential heating and energization of ions and electrons that escape into the corona. In protoplanetary disks such reconnection causes localized heating in the atmospheric layers that produce much of the infrared atomic and molecular line emission observed with the Spitzer and James Webb Space Telescopes.

A nuclear-reaction-based method for probing the nonthermal ion energy spectrum in high energy density laboratory plasmas

The nuclear reactions in a plasma system with particle distributions deviated from the Maxwellian are proved to have some unique characteristics, in particular, in their reaction product energy spectra. Based on this, a new nuclear-reaction-based method for probing the nonthermal ion energy spectrum in high-energy-density (HED) laboratory plasmas is proposed, where the energy spectrum of the nonthermal ion high-energy tails can be accurately evaluated through analysis from the spread and peak of the product energy spectrum. The principle of this diagnostic method is theoretically derived and verified by two-dimensional particle-in-cell simulations that self-consistently includes the nuclear reaction calculations. As an example, our simulations demonstrate clearly how this method is applied for probing the nonthermal high-energy protons produced in the HED magnetic reconnection experiment, where a small ratio of boron element is dopped in the laser-ablated hydrocarbon target and the proton-boron (pB) reaction is chosen as the referenced nuclear reaction. The simulations also show that the pB reaction rate is increased by four orders of magnitude and the peak of the energy spectrum of the generated alpha particles shift significantly towards the high-energy range due to the nonthermal protons accelerated from the reconnections.

Fast Particle Acceleration in 3D Hybrid Simulations of Quasiperpendicular Shocks.

Understanding the conditions conducive to particle acceleration at collisionless, nonrelativistic shocks is important for the origin of cosmic rays. We use hybrid (kinetic ions-fluid electrons) kinetic simulations to investigate particle acceleration and magnetic field amplification at nonrelativistic, weakly magnetized, quasiperpendicular shocks. So far, no self-consistent kinetic simulation has reported nonthermal tails at quasiperpendicular shocks. Unlike 2D simulations, 3D runs show that protons develop a nonthermal tail spontaneously (i.e., from the thermal bath and without preexisting magnetic turbulence). They are rapidly accelerated via shock drift acceleration up to a maximum energy determined by their escape upstream. We discuss the implications of our results for the phenomenology of heliospheric shocks, supernova remnants, and radio supernovae.

Bi-Kappa Proton Mirror and Cyclotron Instabilities in the Solar Wind

The charged particles in the solar wind are often observed to possess a nonthermal tail in the velocity distribution function, a feature that can be fitted with the Kappa model. The anisotropic, or bi-Kappa, model of protons, electrons, and other charged particles is thus adopted in the literature for interpreting the data as well as in the context of the analysis of wave–particle interactions. The present paper develops an approximate but efficient theory of the mirror and cyclotron instabilities excited by the bi-Kappa protons in the solar wind. A velocity moment-based quasi-linear theory of these instabilities is also formulated in order to investigate the saturation behavior. Applications of the formalism are made for instabilities close to the marginally unstable state, which is typical of the solar wind near 1 au.

The 2022 High-energy Outburst and Radio Disappearing Act of the Magnetar 1E 1547.0–5408

We report the radio and high-energy properties of a new outburst from the radio-loud magnetar 1E 1547.0−5408. Following the detection of a short burst from the source with Swift-BAT on 2022 April 7, observations by NICER detected an increased flux peaking at (6.0 ± 0.4) × 10−11 erg s−1 cm−2 in the soft X-ray band, falling to a baseline level of 1.7 × 10−11 erg s−1 cm−2 over a 17 day period. Joint spectroscopic measurements by NICER and NuSTAR indicated no change in the hard nonthermal tail despite the prominent increase in soft X-rays. Observations at radio wavelengths with Murriyang, the 64 m Parkes radio telescope, revealed that the persistent radio emission from the magnetar disappeared at least 22 days prior to the initial Swift-BAT detection and was redetected two weeks later. Such behavior is unprecedented in a radio-loud magnetar, and may point to an unnoticed slow rise in the high-energy activity prior to the detected short bursts. Finally, our combined radio and X-ray timing revealed the outburst coincided with a spin-up glitch, where the spin frequency and spin-down rate increased by 0.2 ± 0.1 μHz and (−2.4 ± 0.1) × 10−12 s−2, respectively. A linear increase in the spin-down rate of (−2.0 ± 0.1) × 10−19 s−3 was also observed over 147 days of postoutburst timing. Our results suggest that the outburst may have been associated with a reconfiguration of the quasi-polar field lines, likely signaling a changing twist, accompanied by spatially broader heating of the surface and a brief quenching of the radio signal, yet without any measurable impact on the hard X-ray properties.

Filamentary plasma eruptions and the heating and acceleration of electrons

We present test-particle simulations of electrons during a nonlinear magnetohydrodynamic (MHD) simulation of a type-I edge localized mode to explore the effect of an eruptive plasma filament on the kinetic level. The electrons are moderately heated and accelerated during the filamentary eruption on a fast timescale of the order of 0.5 ms. A clearly non-thermal tail is formed in the distribution of the kinetic energy that is of power-law shape and reaches 90 keV for some particles. The acceleration is exclusively observed in the direction parallel to the magnetic field, i.e., with a clear preference in countercurrent direction, and we show that the parallel electric field is the cause of the observed acceleration. Most particles that escape from the system leave at one distinct strike-line in the outer divertor leg at some time during their energization. The escaping high-energy electrons in the tail of the energy distribution are not affected by collisions; thus, they show characteristics of runaway electrons. The mean square displacement indicates that transport in energy space clearly is superdiffusive, and interpreting the acceleration process as a random walk, we find that the distributions of energy-increments exhibit exponential tails, and transport in energy space is equally important of convective (systematic) and diffusive (stochastic) nature. By analyzing the MHD simulations per se, it turns out that the histograms of the parallel electric field in the edge region exhibit power-law shapes, and this clearly non-Gaussian statistics is ultimately one of the reasons for the moderately anomalous phenomena of particle transport that we find in energy space.

Comptonization by reconnection plasmoids in black hole coronae II: Electron-ion plasma

ABSTRACT We perform 2D particle-in-cell simulations of magnetic reconnection in electron-ion plasmas subject to strong Compton cooling and calculate the X-ray spectra produced by this process. The simulations are performed for trans-relativistic reconnection with magnetization 1 ≤ σ ≤ 3 (defined as the ratio of magnetic tension to plasma rest-mass energy density), which is expected in the coronae of accretion discs around black holes. We find that magnetic dissipation proceeds with inefficient energy exchange between the heated ions and the Compton-cooled electrons. As a result, most electrons are kept at a low temperature in Compton equilibrium with radiation, and so thermal Comptonization cannot reach photon energies $\sim 100\,$ keV observed from accreting black holes. Nevertheless, magnetic reconnection efficiently generates $\sim 100\,$ keV photons because of mildly relativistic bulk motions of the plasmoid chain formed in the reconnection layer. Comptonization by the plasmoid motions dominates the radiative output and controls the peak of the radiation spectrum Epk. We find Epk ∼ 40 keV for σ = 1 and Epk ∼ 100 keV for σ = 3. In addition to the X-ray peak around 100 keV, the simulations show a non-thermal MeV tail emitted by a non-thermal electron population generated near X-points of the reconnection layer. The results are consistent with the typical hard state of accreting black holes. In particular, we find that the spectrum of Cygnus X-1 is well explained by electron-ion reconnection with σ ∼ 3.

Microphysics of Relativistic Collisionless Electron-ion-positron Shocks

We perform particle-in-cell simulations to elucidate the microphysics of relativistic weakly magnetized shocks loaded with electron-positron pairs. Various external magnetizations σ ≲ 10−4 and pair-loading factors Z ± ≲ 10 are studied, where Z ± is the number of loaded electrons and positrons per ion. We find the following: (1) The shock becomes mediated by the ion Larmor gyration in the mean field when σ exceeds a critical value σ L that decreases with Z ±. At σ ≲ σ L the shock is mediated by particle scattering in the self-generated microturbulent fields, the strength and scale of which decrease with Z ±, leading to lower σ L. (2) The energy fraction carried by the post-shock pairs is robustly in the range between 20% and 50% of the upstream ion energy. The mean energy per post-shock electron scales as . (3) Pair loading suppresses nonthermal ion acceleration at magnetizations as low as σ ≈ 5 × 10−6. The ions then become essentially thermal with mean energy , while electrons form a nonthermal tail, extending from to . When σ = 0, particle acceleration is enhanced by the formation of intense magnetic cavities that populate the precursor during the late stages of shock evolution. Here, the maximum energy of the nonthermal ions and electrons keeps growing over the duration of the simulation. Alongside the simulations, we develop theoretical estimates consistent with the numerical results. Our findings have important implications for models of early gamma-ray burst afterglows.

The first nova eruption in a novalike variable: YZ Ret as seen in X-rays and γ-rays

ABSTRACT Peaking at 3.7 mag on 2020 July 11, YZ Ret was the second-brightest nova of the decade. The nova’s moderate proximity (2.7 kpc, from Gaia) provided an opportunity to explore its multiwavelength properties in great detail. Here, we report on YZ Ret as part of a long-term project to identify the physical mechanisms responsible for high-energy emission in classical novae. We use simultaneous Fermi/LAT and NuSTAR observations complemented by XMM–Newton X-ray grating spectroscopy to probe the physical parameters of the shocked ejecta and the nova-hosting white dwarf. The XMM–Newton observations revealed a supersoft X-ray emission which is dominated by emission lines of C v, C vi, N vi, N vii, and O viii rather than a blackbody-like continuum, suggesting CO-composition of the white dwarf in a high-inclination binary system. Fermi/LAT-detected YZ Ret for 15 d with the γ-ray spectrum best described by a power law with an exponential cut-off at 1.9 ± 0.6 GeV. In stark contrast with theoretical predictions and in keeping with previous NuSTAR observations of Fermi-detected classical novae (V5855 Sgr and V906 Car), the 3.5–78-keV X-ray emission is found to be two orders of magnitude fainter than the GeV emission. The X-ray emission observed by NuSTAR is consistent with a single-temperature thermal plasma model. We do not detect a non-thermal tail of the GeV emission expected to extend down to the NuSTAR band. NuSTAR observations continue to challenge theories of high-energy emission from shocks in novae.

Kinetic simulation of electron, proton and helium acceleration in a non-relativistic quasi-parallel shock

ABSTRACT In addition to accelerating electrons and protons, non-relativistic quasi-parallel shocks are expected to possess the ability to accelerate heavy ions. The shocks in supernova remnants are generally supposed to be accelerators of Galactic cosmic rays, which consist of many species of particles. We investigate the diffusive shock acceleration of electrons, protons and helium ions in a non-relativistic quasi-parallel shock through a 1D particle-in-cell simulation with a helium-to-proton number density ratio of 0.1, which is relevant for Galactic cosmic rays. The simulation indicates that waves can be excited by the flow of energetic protons and helium ions upstream of a non-relativistic quasi-parallel shock with a sonic Mach number of 14 and an Alfvén Mach number of 19.5 in the shock rest frame, and that the charged particles are scattered by the self-generated waves and accelerated gradually. Moreover, the spectra of the charged particles downstream of the shock are thermal with a non-thermal tail, and the acceleration is efficient, with about $7{{\ \rm per\ cent}}$ and $5.4{{\ \rm per\ cent}}$ of the bulk kinetic energy transferred into the non-thermal protons and helium ions, respectively, in the near downstream region by the end of the simulation.

Turbulence and Particle Acceleration in a Relativistic Plasma

Abstract In a collisionless plasma, the energy distribution function of plasma particles can be strongly affected by turbulence. In particular, it can develop a nonthermal power-law tail at high energies. We argue that turbulence with initially relativistically strong magnetic perturbations (magnetization parameter σ ≫ 1) quickly evolves into a state with ultrarelativistic plasma temperature but mildly relativistic turbulent fluctuations. We present a phenomenological and numerical study suggesting that in this case, the exponent α in the power-law particle-energy distribution function, f(γ)d γ ∝ γ −α d γ, depends on magnetic compressibility of turbulence. Our analytic prediction for the scaling exponent α is in good agreement with the numerical results.

Stochastic Electron Acceleration by Temperature Anisotropy Instabilities under Solar Flare Plasma Conditions

Abstract Using 2D particle-in-cell plasma simulations, we study electron acceleration by temperature anisotropy instabilities, assuming conditions typical of above-the-loop-top sources in solar flares. We focus on the long-term effect of T e,⊥ &gt; T e,∥ instabilities by driving the anisotropy growth during the entire simulation time through imposing a shearing or a compressing plasma velocity (T e,⊥ and T e,∥ are the temperatures perpendicular and parallel to the magnetic field). This magnetic growth makes T e,⊥/T e,∥ grow due to electron magnetic moment conservation, and amplifies the ratio ω ce/ω pe from ∼0.53 to ∼2 (ω ce and ω pe are the electron cyclotron and plasma frequencies, respectively). In the regime ω ce/ω pe ≲ 1.2–1.7, the instability is dominated by oblique, quasi-electrostatic modes, and the acceleration is inefficient. When ω ce/ω pe has grown to ω ce/ω pe ≳ 1.2–1.7, electrons are efficiently accelerated by the inelastic scattering provided by unstable parallel, electromagnetic z modes. After ω ce/ω pe reaches ∼2, the electron energy spectra show nonthermal tails that differ between the shearing and compressing cases. In the shearing case, the tail resembles a power law of index α s ∼ 2.9 plus a high-energy bump reaching ∼300 keV. In the compressing runs, α s ∼ 3.7 with a spectral break above ∼500 keV. This difference can be explained by the different temperature evolutions in these two types of simulations, suggesting that a critical role is played by the type of anisotropy driving, ω ce/ω pe, and the electron temperature in the efficiency of the acceleration.

Ion Acceleration and the Development of a Power-law Energy Spectrum in Magnetic Reconnection

Abstract How charged particles are accelerated efficiently and form a power-law energy spectrum in magnetic reconnection is a problem that is not well understood. In a previous paper, it was shown that the electron Kelvin–Helmholtz instability (EKHI) in force-free magnetic reconnection generates fast-expanding vortices that can accelerate electrons in a few tens of ion gyroperiods (less than 1 ms in the solar corona) to form a power-law energy distribution. In this paper, we present a particle-in-cell (PIC) simulation study of ion acceleration in force-free magnetic reconnection in the presence of the EKHI-induced turbulence. We find that ions are not significantly accelerated by the EKHI-induced stochastic electric field until the magnetic vortices expand to sizes comparable to the ion gyroradius. The Alfvén waves generated by the EKHI couple with the magnetic vortices, leading to resonance between the ions inside the magnetic vortices and Alfvén waves and enhanced ion heating. The induced Alfvén wave resonance results in a broken power-law energy spectrum with a breakpoint at ∼ m i v A 2 , where v A is the Alfvén velocity. We show that the process that forms the nonthermal tail is a second-order Fermi mechanism and the mean spectral index is α = (1 + 4a 2 D/R)/2, where D is the spatial scale of the inductive electric field, R is that of vortices, and a = B g /B 0, with ratio of guide field B g and asymptotic B 0.

NICER Detection of Thermal X-Ray Pulsations from the Massive Millisecond Pulsars PSR J0740+6620 and PSR J1614–2230

Abstract We report the detection of X-ray pulsations from the rotation-powered millisecond-period pulsars PSR J0740+6620 and PSR J1614−2230, two of the most massive neutron stars known, using observations with the Neutron Star Interior Composition Explorer (NICER). We also analyze X-ray Multi-Mirror Mission (XMM-Newton) data for both pulsars to obtain their time-averaged fluxes and study their respective X-ray fields. PSR J0740+6620 exhibits a broad double-peaked profile with a separation of ∼0.4 in phase. PSR J1614−2230, on the other hand, has a broad single-peak profile. We show the NICER detections of X-ray pulsations for both pulsars and also discuss the phase relationship to their radio pulsations. The XMM-Newton X-ray spectra of both pulsars shows they are thermally dominated but in the case of PSR J1614−2230 a weak nonthermal high energy tail appears to be present in the spectrum. The thermally dominated spectra along with broad modulations for both pulsars are indicative of thermal radiation from one or more small regions of the stellar surface. For PSR J0740+6620, this paper documents the data reduction performed to obtain the pulsation detection and prepare for pulse light curve modeling analysis.

Secondary Energization in Compressing Plasmoids during Magnetic Reconnection

Abstract Plasmoids—magnetized quasi-circular structures formed self-consistently in reconnecting current sheets—were previously considered to be the graveyards of energetic particles. In this paper, we demonstrate the important role of plasmoids in shaping the particle energy spectrum in relativistic reconnection (i.e., with upstream magnetization σ up ≫ 1). Using 2D particle-in-cell simulations in pair plasmas with σ up = 10 and 100, we study a secondary particle energization process that takes place inside compressing plasmoids. We demonstrate that plasmoids grow in time, while their interiors compress, amplifying the internal magnetic field. The magnetic field felt by particles injected in an isolated plasmoid increases linearly with time, which leads to particle energization as a result of magnetic moment conservation. For particles injected with a power-law distribution function, this energization process acts in such a way that the shape of the injected power law is conserved, while producing an additional nonthermal tail f(E) ∝ E −3 at higher energies, followed by an exponential cutoff. The cutoff energy, which increases with time as , can greatly exceed σ up m e c 2. We analytically predict the secondary acceleration timescale and the shape of the emerging particle energy spectrum, which can be of major importance in certain astrophysical systems, such as blazar jets.

First-principles Demonstration of Diffusive-advective Particle Acceleration in Kinetic Simulations of Relativistic Plasma Turbulence

Abstract Nonthermal relativistic plasmas are ubiquitous in astrophysical systems like pulsar wind nebulae and active galactic nuclei, as inferred from their emission spectra. The underlying nonthermal particle acceleration (NTPA) processes have traditionally been modeled with a Fokker–Planck (FP) diffusion-advection equation in momentum space. In this Letter, we directly test the FP framework in ab initio kinetic simulations of driven magnetized turbulence in relativistic pair plasma. By statistically analyzing the motion of tracked particles, we demonstrate the diffusive nature of NTPA and measure the FP energy diffusion (D) and advection (A) coefficients as functions of particle energy . We find that scales as in the high-energy nonthermal tail, in line with second-order Fermi acceleration theory, but has a much weaker scaling at lower energies. We also find that A is not negligible and reduces NTPA by tending to pull particles toward the peak of the particle energy distribution. This study provides strong support for the FP picture of turbulent NTPA, thereby enhancing our understanding of space and astrophysical plasmas.

Stochastic Ion Acceleration by the Ion-cyclotron Instability in a Growing Magnetic Field

Abstract Using 1D and 2D particle-in-cell simulations of a plasma with a growing magnetic field , we show that ions can be stochastically accelerated by the ion-cyclotron (IC) instability. As grows, an ion pressure anisotropy arises due to the adiabatic invariance of the ion magnetic moment ( and p ⊥,i are the ion pressures parallel and perpendicular to ). When initially β i = 0.5 ( , where p i is the ion isotropic pressure), the pressure anisotropy is limited mainly by inelastic pitch-angle scattering provided by the IC instability, which in turn produces a nonthermal tail in the ion energy spectrum. After is amplified by a factor of ∼2.7, this tail can be approximated as a power law of index ∼3.4 plus two nonthermal bumps and accounts for 2%–3% of the ions and ∼18% of their kinetic energy. On the contrary, when initially β i = 2, the ion scattering is dominated by the mirror instability, and the acceleration is suppressed. This implies that efficient ion acceleration requires that initially, β i ≲ 1. Although we focus on cases where is amplified by plasma shear, we check that the acceleration occurs similarly if grows due to plasma compression. Our results are valid in a subrelativistic regime where the ion thermal energy is ∼10% of the ion rest-mass energy. This acceleration process can thus be relevant in the inner region of low-luminosity accretion flows around black holes.

Nonthermal ion acceleration by the kink instability in nonrelativistic jets

We investigate the self-consistent particle acceleration physics associated with the development of the kink instability (KI) in nonrelativistic, electron-ion plasma jets. Using 3D fully kinetic particle-in-cell simulations, we show that the KI efficiently converts the initial toroidal magnetic field energy into energetic ions. The accelerated ions form a nonthermal power-law tail in the energy spectrum, containing ≃10% of the initial magnetic field energy, with the maximum ion energy extending to the confinement energy of the jet. We find that the ions are efficiently accelerated by the concerted action of the motional electric field and the highly tangled magnetic field that develop in the nonlinear phase of the KI: fast curvature drift motions of ions across magnetic field lines enable their acceleration along the electric field. We further investigate the role of Coulomb collisions in the ion acceleration efficiency and identify the collisional threshold above which nonthermal ion acceleration is suppressed. Our results reveal how energetic ions may result from unstable nonrelativistic plasma jets in space and astrophysics and provide constraints on the plasma conditions required to reproduce this acceleration mechanism in laboratory experiments.