Acceleration Process Research Articles

Direct laser acceleration: A model for the electron injection from the walls of a cylindrical guiding structure.

We use analytical methods and particle-in-cell simulation to investigate the origin of electrons accelerated by the process of direct laser acceleration driven by high-power laser pulses in preformed narrow cylindrical plasma channels. The simulation shows that the majority of accelerated electrons are originally located along the interface between the channel wall and the channel interior. The analytical model based on the electron hydrodynamics illustrates the underlying physical mechanism of the release of electrons from the channel wall when irradiated by an intense laser, the subsequent electron dynamics, and the corresponding evolution of the channel density profile. The quantitative predictions of the total charge of released electrons and the average electron density inside the channel are validated by comparison with the simulation results.

Brain-machine interactive neuromodulation research tool with edge AI computing

Closed-loop neuromodulation with intelligence methods has shown great potentials in providing novel neuro-technology for treating neurological and psychiatric diseases. Development of brain-machine interactive neuromodulation strategies could lead to breakthroughs in precision and personalized electronic medicine. The neuromodulation research tool integrating artificial intelligent computing and performing neural sensing and stimulation in real-time could accelerate the development of closed-loop neuromodulation strategies and translational research into clinical application. In this study, we developed a brain-machine interactive neuromodulation research tool (BMINT), which has capabilities of neurophysiological signals sensing, computing with mainstream machine learning algorithms and delivering electrical stimulation pulse by pulse in real-time. The BMINT research tool achieved system time delay under 3 ms, and computing capabilities in feasible computation cost, efficient deployment of machine learning algorithms and acceleration process. Intelligent computing framework embedded in the BMINT enable real-time closed-loop neuromodulation developed with mainstream AI ecosystem resources. The BMINT could provide timely contribution to accelerate the translational research of intelligent neuromodulation by integrating neural sensing, edge AI computing and stimulation with AI ecosystems.

Dynamic acceleration of energetic protons by an interplanetary collisionless shock

Context. Interplanetary collisionless shocks are known to be capable of accelerating charged particles up to hundreds of MeV. However, the underlying acceleration mechanisms are still under debate. Aims. We present the dynamic behaviors of energetic protons that are accelerated by an interplanetary shock that was observed with unprecedented high-resolution measurements by the Electron-Proton Telescope sensor of the Energetic Particle Detector suite on board the Solar Orbiter spacecraft on 2021 November 3. We constrain the potential acceleration mechanisms and processes. Methods. We first reconstructed the proton pitch-angle distributions (PADs) in the solar wind frame. Then, we examined the temporal flux profile, PAD, and the velocity distribution function of energetic protons close to the shock, and we qualitatively compared the observations with theoretical predictions. Moreover, we applied a velocity dispersion analysis (VDA) to an observed velocity dispersion event and derived the proton path length and release time at the shock. Then, we tested this derivation by comparing it with the shock motion and the magnetic field configuration. Results. We find that ∼1000–4000 keV protons exhibit a rapid-rise, rapid-decay temporal flux profile with a clear velocity dispersion ∼2 min before the shock, similar to impulsive solar energetic particle events. The proton path length based on the VDA of this event is consistent with the length derived from the shock motion and magnetic field configuration. The peak spectrum in this event appears to be steeper than the spectrum at the shock. Furthermore, we find that ∼50–200 keV proton fluxes peak between ∼10 and ∼20 s before the shock, with an inverse velocity dispersion. The velocity dispersion event and the inverse velocity dispersion event are both accompanied by magnetic kinks or switchbacks. In addition, two distinct proton populations appear near the shock. The first population at energies below ∼300 keV is characterized by a power-law spectrum with an index of ∼6–7 and a flux profile that increases before and decreases after the shock. The other population at energies above ∼300 keV shows a long-lasting, anti-sunward-beamed PAD across the shock and a flux profile that remains relatively constant before and increases slightly after the shock. Conclusions. These results suggest that the shock acceleration of energetic protons is highly dynamic due to temporal and/or spatial variations at the shock front. The observation of the velocity dispersion event further suggests that shock acceleration can be impulsive and efficient, which may be due to the interaction between the shock and magnetic kinks or switchbacks. Moreover, these results may support shock-drift acceleration and diffusive shock acceleration as candidate acceleration mechanisms at interplanetary shocks.

Numerical analysis of the transient characteristics of internal flow in the acceleration process of variable speed regulation of a centrifugal pump

Abstract In this study, a method of combining Flowmaster and ANSYS CFX software was adopted. Based on the consistency between the numerical calculation results of the hydraulic performance of a centrifugal pump and the test results, an operating model of a centrifugal pump system is established, variation law of the external characteristic parameters in the transient process is obtained, and different acceleration times and modes are set. The change law of the transient external characteristics and the evolution mechanism of the internal flow field during the variable speed regulation and acceleration of the centrifugal pump are disclosed. By introducing a control system evaluation index, the effects of acceleration time and mode on performance and internal flow field of variable speed control process of the centrifugal pump are analysed in detail. The results show that the turbulent kinetic energy in the pump changes violently, and the high turbulent kinetic energy and high vorticity are widely distributed, which has an obvious transient effect. An exponential acceleration method can effectively reduce the peak value and overshoot of external characteristic parameters while reducing the speed regulation time.

Single-Shot Diagnosis of Electron Energy Evolution via Streaked Betatron X Rays in a Curved Laser Wakefield Accelerator.

We report on an experimental observation of the streaking of betatron x rays in a curved laser wakefield accelerator. The streaking of the betatron x rays was realized by launching a laser pulse into a plasma with a transverse density gradient. By controlling the plasma density and the density gradient, we realized the steering of the laser driver, electron beam, and betatron x rays simultaneously. Moreover, we observed an energy-angle correlation of the streaked betatron x rays and utilized it in diagnosing the electron acceleration process in a single-shot mode. Our work could also find applications in advanced control of laser beam and particle propagation. More importantly, the angular streaked betatron x ray has an intrinsic spatiotemporal correlation, which makes it a promising tool for single-shot pump-probe applications.

Cannibals in PARADISE: The Effect of Merging Interplanetary Shocks on Solar Energetic Particle Events

Gradual solar energetic particle (SEP) events are associated with shocks driven by coronal mass ejections (CMEs). The merging of two CMEs (so-called cannibalistic CMEs) and the interaction of their associated shocks has been linked to some of the most powerful solar storms ever recorded. Multiple studies have focused on the observational aspects of these SEP events, yet only a handful have focused on modeling similar CME–CME interactions in the heliosphere using advanced magnetohydrodynamic (MHD) models. This work presents, to our knowledge, the first modeling results of a fully time-dependent 3D simulation that captures both the interaction of two CMEs and its effect on the acceleration and transport of SEPs. This is achieved by using an MHD model for the solar wind and CME propagation together with an integrated SEP model. We perform different simulations and compare the behavior of the energetic protons in three different solar wind environments, where a combination of two SEP-accelerating CMEs are modeled. We find that particle acceleration is significantly affected by the presence of both CMEs in the simulation. Initially, less efficient acceleration results in lower-energy particles. However, as the CMEs converge and their shocks eventually merge, particle acceleration is significantly enhanced through multiple acceleration processes between CME-driven shocks, resulting in higher particle intensities and energy levels.

Three-stage Acceleration of Solar Energetic Particles Detected by Parker Solar Probe

Coronal mass ejections (CMEs) drive powerful shocks and thereby accelerate solar energetic particles (SEPs) as they propagate from the corona into interplanetary space. Here we present the processes of three-stage particle acceleration by a CME-driven shock detected by the in situ spacecraft—Parker Solar Probe (PSP) on 2022 August 27. The onset of SEPs is produced by a fast CME with a speed of 1284 km s−1 when it propagates to ∼2.85 R ⊙. The second stage of particle acceleration occurs when the fast CME catches up and interacts with a preceding slow one in interplanetary space at ∼40 R ⊙ (∼0.19 au). The CME interaction is accompanied by an intense interplanetary type II radio enhancement. Such direct measurement of particle acceleration during interplanetary CME interaction/radio enhancement is rarely recorded in previous studies. The third stage of energetic storm particles is associated with the CME-driven shock passage of the PSP at ∼0.38 au. Obviously, harder particle spectra are found in the latter two stages than the first one, which can arise from a stronger shock produced by the CME interaction and the enriched seed particles inside the preceding CME.

Energetic particle activity in AD Leo: Detection of a solar-like type-IV burst

Context. AD Leo is a young and active M dwarf with high flaring rates across the X-ray-to-radio bands. Flares accelerate particles in the outer coronal layers and often impact exo-space weather. Wide-band radio dynamic spectra let us explore the evolution of particle acceleration activity across the corona. Identifying the emission features and modelling the mechanisms can provide insights into the possible physical scenarios driving the particle acceleration processes.Aims. We performed an 8 h monitoring of AD Leo across the 550-850 MHz band using upgraded-Giant Metrewave Radio Telescope (uGMRT). The possible flare and post-flare emission mechanisms are explored based on the evolution of flux density and polarisation.Methods. The python-based module, Visibility Averaged Dynamic spectrum (VISAD), was developed to obtain the visibility-averaged wide-band dynamic spectra. Direct imaging was also performed with different frequency-time averaging. Based on existing observational results on AD Leo and on solar active region models, radial profiles of electron density and magnetic fields were derived. Applying these models, we explored the possible emission mechanisms and magnetic field profile of the flaring active region.Results. The star displayed a high brightness temperature (TB≈ 1010−1011K) throughout the observation. The emission was also nearly 100% left circularly polarised during bursts. The post-flare phase was characterised by a highly polarised (60–80%) solar-like type IV burst confined above 700 MHz.Conclusions. The flare emission favours a Z-mode or a higher harmonic X-mode electron cyclotron maser emission mechanism. The >700 MHz post-flare activity is consistent with a type-IV radio burst from flare-accelerated particles trapped in magnetic loops, which could be a coronal mass ejection (CME) signature. This is the first solar-like type-IV burst reported on a young active M dwarf belonging to a different age-related activity population (‘C’ branch) compared to the Sun (‘I’ branch). We also find that a multipole expansion model of the active region magnetic field better accounts for the observed radio emission than a solar-like active region profile.

Topography and accumulation rate as controls of asynchronous surging behaviour in the eastern and western branches of the Western Kunlun Glacier, Northwestern Tibetan Plateau

ABSTRACT The western Kunlun main peak region is among the areas in High Mountain Asia where surge-type glaciers are highly concentrated. Here, we analyse the surging characteristics of the eastern and western branches of the Western Kunlun Glacier and the factors controlling the asynchronous behaviour of their surges. The eastern branch entered an unstable state in 1999 and remained so until the culmination of its surge in the summer of 2019, spanning 21 years. Conversely, the surge of the western branch commenced in the summer of 2020. The surge duration for this glacier was four years, characterized by a rapid acceleration and deceleration process. Based on the glacier surge characteristics, we posit that western branch of Western Kunlun Glacier was influenced by hydrological mechanisms, while eastern branch was affected by subglacial thermal processes. These process intensifies crevasse formation on the glacial surface, providing conduits for surface meltwater to reach the glacier bed, thus elevating subglacial water pressure. The difference of subglacial hydrology and thermal processes caused by different subglacial topography and mass accumulation rates was the main factor of the asynchronous behaviour of the west and east branches of the West Kunlun glacier.

Optical probing of ultrafast laser-induced solid-to-overdense-plasma transitions

Understanding the solid target dynamics resulting from the interaction with an ultrashort laser pulse is a challenging fundamental multi-physics problem involving atomic and solid-state physics, plasma physics, and laser physics. Knowledge of the initial interplay of the underlying processes is essential to many applications ranging from low-power laser regimes like laser-induced ablation to high-power laser regimes like laser-driven ion acceleration. Accessing the properties of the so-called pre-plasma formed as the laser pulse’s rising edge ionizes the target is complicated from the theoretical and experimental point of view, and many aspects of this laser-induced transition from solid to overdense plasma over picosecond timescales are still open questions. On the one hand, laser-driven ion acceleration requires precise control of the pre-plasma because the efficiency of the acceleration process crucially depends on the target properties at the arrival of the relativistic intensity peak of the pulse. On the other hand, efficient laser ablation requires, for example, preventing the so-called “plasma shielding”. By capturing the dynamics of the initial stage of the interaction, we report on a detailed visualization of the pre-plasma formation and evolution. Nanometer-thin diamond-like carbon foils are shown to transition from solid to plasma during the laser rising edge with intensities < 1016 W/cm². Single-shot near-infrared probe transmission measurements evidence sub-picosecond dynamics of an expanding plasma with densities above 1023 cm−3 (about 100 times the critical plasma density). The complementarity of a solid-state interaction model and kinetic plasma description provides deep insight into the interplay of initial ionization, collisions, and expansion.

Observation of Energetic Electron Near the Electron Diffusion Region of Magnetic Reconnection

AbstractMagnetic reconnection can effectively convert magnetic energy into plasma energy, and accelerate electrons. In this article, the electrons with energies up to 150 keV are observed in the separatrix region and near the electron diffusion region (EDR) detected by the Magnetospheric Multiscale mission in the magnetotail. Combined with the electron pitch‐angle distribution, the electrons in these two regions have a striking behavior: the low‐energy electrons (&lt;∼10 keV) move mainly toward the X‐line, while the energetic electrons (69–139 keV) move mainly away from the X‐line. In the EDR, the energy of electrons can reach up to 10 keV and there is a notable enhancement in the flux of electrons in the direction perpendicular to the magnetic field, which implies the presence of acceleration processes occurring in the EDR, leading to the energization of electrons. Furthermore, the energy spectrum of non‐thermal electron with energies above 6 keV shows a power law distribution in this event, suggesting the occurrence of multiple acceleration processes rather than a single energization mechanism. These findings underscore the EDR's role as a crucial region for electron acceleration during magnetic reconnection. The study provides essential clues about the mechanisms driving electron acceleration, contributing to our understanding of space weather phenomena and the broader dynamics of plasma physics in space environments.

A novel configuration capable of enhancing flame acceleration and detonation

This study proposes a novel design concept that leverages the geometric effects of channels with varying diameters and bends to boost flame acceleration and detonation in microchannels. A quasi-direct numerical simulation with detailed chemical kinetics is used to evaluate the processes of flame acceleration and detonation. A comparative study on the impact of equidistant spiral and converging spiral shapes of detonation channels on flame acceleration is conducted and discussed. The results indicate that in the low-speed and high-speed stages of flame propagation, Fermat's spiral channel exhibits a more significant promoting effect on flame acceleration compared to the Archimedes spiral channel. Fermat's spiral channel has significant advantages in terms of combustion efficiency and can save about 30% of fuel during the detonation process. This study helps to further reduce the scale of the detonation system.

Dynamic analysis of composite flywheel energy storage rotor

Dynamic analysis is a key problem of flywheel energy storage system (FESS). In this paper, a one-dimensional finite element model of anisotropic composite flywheel energy storage rotor is established for the composite FESS, and the dynamic characteristics such as natural frequency and critical speed are calculated. Through the analysis of acceleration transient response, it is found that the flywheel rotor have two critical speeds during acceleration or deceleration process, which are prone to resonance and damage the bearing. Therefore, in order to avoid resonance or reduce resonance peak, the influence of bearing support stiffness, damping and speed-up rate on the critical speed and resonance peak is studied. The calculation results show that the first two order critical speed are affected by the support stiffness. When the stiffness increases, the critical speed of the flywheel rotor increases, but the growth rate decreases. When the damping increases, the critical speed is basically not affected, and the vibration amplitude decreases rapidly. In addition, the resonance peak value of transient response can be effectively reduced by increasing the speed-up rate.

A Joint Microwave and Hard X-Ray Study toward Understanding the Transport of Accelerated Electrons During an Eruptive Solar Flare

The standard flare model, despite its success, is limited in comprehensively explaining the various processes involving nonthermal particles. One such missing ingredient is a detailed understanding of the various processes involved during the transport of accelerated electrons from their site of acceleration to different parts of the flare region. Here we use simultaneous radio and X-ray observations from the Expanded Owens Valley Solar Array and the Spectrometer/Telescope for Imaging X-rays on board the Solar Orbiter, respectively, from two distinct viewing perspectives, to study the electron transport processes. Through detailed spectral modeling of the coronal source using radio data and footpoint sources using X-ray spectra, we compare the nonthermal electron distribution at the coronal and footpoint sources. We find that the flux of the nonthermal electrons precipitated at the footpoint is an order of magnitude greater than that trapped in the looptop, consistent with earlier works that primarily used X-ray for their studies. In addition, we find that the electron spectral indices obtained from X-ray footpoints are significantly softer than the spectral hardness of the nonthermal electron distribution in the corona. We interpret these differences based on transport effects and the difference in sensitivity of microwave and X-ray observations to different regimes of electron energies. Such an understanding is crucial for leveraging different diagnostic methods of nonthermal electrons simultaneously to achieve a more comprehensive understanding of the electron acceleration and transport processes of solar flares.

Computations on fall of the leaning tower with considering air resistance

The free fall of a sphere was studied by considering air buoyancy and resistance. After selecting the reasonable drag coefficient formula recommended by the literature, partial differential formulas on the motion of balls falling in the Leaning Tower of Pisa are solved. The variation process of acceleration, velocity and displacement over time during the falling process of two spheres is obtained. The research results indicate that the kinematics of free fall considering air resistance is different from that neglecting air resistance. Air Resistance must be considered in the free fall of the solid ball after 0.3005 seconds. In the free fall of the leaning tower, air resistance makes the solid ball land at 0.4418 seconds which is earlier than the hollow. The variation of the acceleration of a solid ball with time can be described by a second-order function a=-0.115t2 -0.022t+9.801. Velocity does not satisfy the product of acceleration and time but can be described as a polynomial function of the velocity variation with time v = c1t2 + c2t + c3 . About the relationship between displacement and time, for a solid sphere, displacement is proportional to 1.9526 power of time h=5.4945t1.9526 , while for a hollow sphere, it cannot be expressed by a function. The relationship between air resistance and velocity during the falling process of an iron ball satisfies a polynomial function Fd =c1v2 -c2v+c3 rather than a simple relationship where air resistance is directly proportional to the first or second power of speed, which was used in many papers as a reasonable assumption.

Properties of Electrons Accelerated by the Ganymede‐Magnetosphere Interaction: Survey of Juno High‐Latitude Observations

AbstractThe encounter between the Jovian co‐rotating plasma and Ganymede gives rise to electromagnetic waves that propagate along the magnetic field lines and accelerate particles by resonant or non‐resonant wave‐particle interaction. They ultimately precipitate into Jupiter's atmosphere and trigger auroral emissions. In this study, we use Juno/JADE, Juno/UVS data, and magnetic field line tracing to characterize the properties of electrons accelerated by the Ganymede‐magnetosphere interaction in the far‐field region. We show that the precipitating energy flux exhibits an exponential decay as a function of downtail distance from the moon, with an e‐folding value of 29°, consistent with previous UV observations from the Hubble Space Telescope (HST). We characterize the electron energy distributions and show that two distributions exist. Electrons creating the Main Alfvén Wing (MAW) spot and the auroral tail always have broadband distribution and a mean characteristic energy of 2.2 keV while in the region connected to the Transhemispheric Electron Beam (TEB) spot the electrons are distributed non‐monotonically, with a higher characteristic energy above 10 keV. Based on the observation of bidirectional electron beams, we suggest that Juno was located within the acceleration region during the 11 observations reported. We thus estimate that the acceleration region is extended, at least, between an altitude of 0.5 and 1.3 Jupiter radius above the 1‐bar surface. Finally, we estimate the size of the interaction region in the Ganymede orbital plane using far‐field measurements. These observations provide important insights for the study of particle acceleration processes involved in moon‐magnetosphere interactions.

Radio surface fluctuations in radio relics

Recent observations have revealed detailed structures of radio relics across a wide range of frequencies. In this work, we performed three-dimensional magnetohydrodynamical (3D MHD) simulations of merger shocks propagating through a turbulent magnetized intracluster medium. We then employed on-the-fly Lagrangian particles to explore the physical processes behind the origination of radio substructures and their appearance in high and low-frequency observations. We employed two cosmic-ray (CR) electron acceleration models, with a fresh injection of electrons from the thermal pool and the re-acceleration of mildly relativistic electrons. We used the relative surface brightness fluctuations, δSν, to define a “degree of patchiness.” First, we found that patchiness is produced if the shock’s surface has a distribution of Mach numbers, rather than a single Mach number. Second, radio relics appear patchier if the Mach number distribution consists of a large percentage of low Mach numbers (ℳ ≲ 2.5). Furthermore, as the frequency increases, the patchiness also becomes larger. Nevertheless, if radio relics are patchy at high frequencies (e.g., 18.6 GHz), they necessarily will also be patchy at low frequencies (e.g., 150 MHz). Then, to produce noticeable differences in the patchiness at low and high frequencies, the shock front should have a Mach number spread of σℳ ≳ 0.3 − 0.4. Finally, the extent of the patchiness depends on the Mach number distribution as well as the CR acceleration model. We propose δSν as a potential tool for extracting merger shock properties and information on particle acceleration processes at shocks in radio observations.

Numerical investigation on cavitation and induced noise reduction mechanisms of a three-dimensional hydrofoil with leading-edge protuberances

In this work, a National Advisory Committee for Aeronautics 66 hydrofoil with leading-edge protuberances is designed. The large eddy simulation combined with the Schnerr–Sauer cavitation model is used to obtain a satisfactory result as compared with the experimental measurement, integrating the permeable Ffowcs Williams–Hawkings equation for cavitation-induced noise analysis. It is found that the special leading-edge geometric structure deflects the incoming flow, creating two counter-rotating streamwise vortices at the peak shoulders. These lead to upwash and downwash effects and alter the pressure distribution on the suction side. The low pressure localized in the trough facilitates the advancement of the leading-edge cavitation while severely limiting the spanwise development of the cloud cavity, shortening the cavitation evolution by about 20% and reducing the maximum cavitation volume by about 35%. Analysis using the vorticity transport equation indicates that different vorticity transport equation splitting terms play dominant roles at different stages of cavitation evolution. Although the cavitation induces disturbances in the primary vortex, the effect is limited. Acoustic simulation shows that the bionic structure can reduce the total sound pressure level by 7.8–8.3 dB. The spherical noise reduction is not as effective as expected due to the similar cavitation volume acceleration processes of the two hydrofoils. However, the pressure fluctuation caused by the collapse of the cloud cavity is reduced by cavitation suppression, which reduces the linear noise. In addition, the protuberances suppress the generation of large-scale vortex systems and transform them into smaller ones, resulting in reduced spanwise correlation and coherence of the shedding vortices. This is a critical factor in noise reduction. Finally, we hypothesize that the unstable noise reduction is related to the streamwise vortices in the trough regions. These vortices increase the momentum exchange within the boundary layer, affecting its stability and weakening the acoustic feedback loop.

A Study of Particle Acceleration in Blazar Jets

The particle acceleration of blazar jets is crucial to high-energy astrophysics, yet the acceleration mechanism division in blazar subclasses and the underlying nature of these mechanisms remain elusive. In this work, we utilized the synchrotron spectral information (synchrotron peak frequency, logνsy , and corresponding curvature, b sy) of 2705 blazars from the literature and studied the subject of particle acceleration in blazar jets by analyzing the correlation between logνsy and 1/b sy. Our results suggested that the entire sample follows an energy-dependent probability acceleration (EDPA). Specifically, the low inverse Compton peak sources (LCPs) follow the mechanism of fluctuations of fractional gain acceleration (FFGA), while the high inverse Compton peak sources (HCPs) follow an acceleration mechanism of EDPA. Our results indicated that the separation between LCPs and HCPs results from the electron peak Lorentz factor (γ p), and the differentiation should originate from different acceleration mechanisms. Moreover, our study revealed a transition in the acceleration mechanism from FFGA to EDPA around logνsy∼15 through a detailed analysis of binned- logνsy . The mechanism of FFGA dominates the particle acceleration in LCP jets because of stronger jets and the EDPA dominates the particle energy gain in the HCPs due to a more efficient acceleration process.

Revealing the Variation Mechanism of ON 231 via the Two-component Shock-in-jet Model

The variation mechanism of blazars is a long-standing unresolved problem. In this work, we present a scenario to explain diverse variation phenomena for ON 231, where the jet emissions are composed of the flaring and the less variable components (most probably from the post-flaring blobs), and the variation is dominated by shock-in-jet instead of the Doppler effect. We perform correlation analysis for the multiwavelength light curves and find no significant correlations. For the optical band, ON 231 exhibits a harder when brighter (HWB) trend, and the trend seems to shift at different periods. Correspondingly, the correlation between the degree of polarization and flux exhibits a V-shaped behavior, and a similar translation relation during different periods is also found. These phenomena could be understood via the superposition of the flaring component and slowly varying background component. We also find that the slopes of the HWB trend become smaller at higher flux levels, which indicates the energy-dependent acceleration processes of the radiative particles. For the X-ray band, we discover a trend transition from HWB to softer when brighter (SWB) to HWB. We consider that the X-ray emission is composed of both the synchrotron tail and the synchrotron self-Compton components, which could be described by two log-parabolic functions. By varying the peak frequency, we reproduce the observed trend transition in a quantitative manner. For the γ-ray band, we find the SWB trend, which could be explained naturally if a very-high-energy γ-ray background component exists. Our study elucidates the variation mechanism of intermediate synchrotron-peaked BL Lac objects.