(Dated: August 28, 2026) We establish a self-consistent 2D hydrothermodynamic analytical model for high-intensity focused ultrasound tumor ablation. Expanding compressible Navier-Stokes equations to second order demonstrates that a stationary cellular matrix suppresses acoustic streaming (v 2 = 0). This constraint forces the absorbed wave momentum flux to convert entirely into localized, time-averaged static pressure gradients (2 = F 2), bridging non-linear hydrodynamics with thermodynamic dissipation. Solving the non-diffusive Pennes bioheat equation under a 1.0 s top-hat pulse reveals that a spherically focusing geometry (∝ 1/ 2) overrides exponential damping past a critical geometric threshold (crit = 2 0), preventing upstream skin overheating. We derive an optimization criterion where the absorption coefficient matches half the inverse target depth (= 1/2 0). Solving the non-isothermal Arrhenius integral yields a sharp lesion boundary radius at = 0.75 0 , where the volume average reaches 72.1 • C while the core peaks at 90.0 • C. Post-pulse 2D free-space Green’s function convolution confirms immediate monotonic thermal decay (/ < 0) outside this boundary. This closed-form framework provides explicit scaling laws for non-invasive wave-matter thermal confinement, bypassing computationally heavy numerical simulations.

In this work, we: 1) extend previous 1-D studies of electromagnetic (EM) wave propagation in an over-dense plasma-metamaterial composite into two spatial dimensions and 2) study blocking of EM waves by the composite 2-D structures (barriers). Such barriers are formed when metamaterial spatially co-exists with a plasma density depletion in the form of a slab or 2-D density rectangular depletions (DRDs). This is analogous to EM wave trapping by preformed density cavities in near-critical density plasmas, studied before. We find that plasma-metamaterial composite allows to block EM waves by both slab and DRD configurations, thus forming a standing wave at the edge of an opaque region. The standing wave subsequently damps which offers applications such as heat deposition or substrate materials (micro) machining depending on EM wave intensity. The established results may find future applications such as more efficient plasma vapor deposition, controlling EM wave propagation (EM wave blocking) in invisibility cloaks and alike. The EM wave-blocking conditions are elucidated by a set of particle-in-cell (PIC) numerical simulations.

We use particle-in-cell, fully electromagnetic, plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin–Helmholtz instability (ESKHI). The results are applicable to collisionless plasmas when, e.g., solar wind interacts with planetary magnetospheres or a magnetic field is generated in AGN jets. We find that as in the case of magnetohydrodynamic (MHD) KHI, in the kinetic regime, the presence of an external magnetic field reduces the growth rate of the instability. In the MHD case, there is a known threshold magnetic field for KHI stabilization, while for ESKHI this is to be analytically determined. Without a kinetic analytical expression, we use several numerical simulation runs to establish an empirical dependence of ESKHI growth rate, Γ(B0)ωpe, on the strength of the applied external magnetic field. We find the best fit is hyperboli

The problem of explaining observed soft X-ray fluxes during solar flares, which invokes acceleration of large fraction of electrons, if the acceleration takes places at the solar coronal loop-top, can potentially be solved by postulating that flare at loop-top creates dispersive Alfven waves (DAWs) which propagate towards the foot-points. As DAWs move in progressively denser parts of the loop (due to gravitational stratification) the large fraction of electrons is no longer needed. Here, we extend our previous results by considering f(-1) frequency spectrum of DAWs and add He++ ions using fully kinetic particle-in-cell (PIC) simulations. We consider cases when transverse density gradient is in the range 4-40c/omega(pe) and DAW driving frequency is 0.3-0.6 omega(cp). We find that (i) The frequency spectrum case does not affect electron acceleration fraction in the like-to-like cases, but few times larger percentage of He++ heating is seen due to ion cyclotron resonance; (ii) In cases when counter propagating DAWs collide multiple-times, much larger electron and ion acceleration fractions are found, but the process is intermittent in time. This is because intensive heating (temperature increase) makes the-above-thermal-fraction smaller; Also more isotropic velocity distributions are seen; (iii) Development of kink oscillations occurs when DAWs collide; (iv) Scaling of the magnetic fluctuations power spectrum steepening in the higher-density regions is seen, due to wave refraction. Our PIC runs produce much steeper slopes than the orginal spectrum, indicating that the electron-scale physics has a notable effect on DAW spectrum evolution.

We use particle-in-cell, fully electromagnetic, plasma kinetic simulation to study the effect of external magnetic field on electron scale Kelvin-Helmholtz instability (ESKHI). The results are applicable to collisionless plasmas when, e.g., solar wind interacts with planetary magnetospheres or a magnetic field is generated in AGN jets. We find that as in the case of magnetohydrodynamic (MHD) KHI, in the kinetic regime, the presence of an external magnetic field reduces the growth rate of the instability. In the MHD case, there is a known threshold magnetic field for KHI stabilization, while for ESKHI this is to be analytically determined. Without a kinetic analytical expression, we use several numerical simulation runs to establish an empirical dependence of ESKHI growth rate, Gamma(B-0)omega(pe), on the strength of the applied external magnetic field. We find the best fit is hyperbolic, Gamma(B-0)omega(pe)=Gamma(0)omega pe/(A+B(Sic) (0)) , where Gamma(0 )is the ESKHI growth rate without an external magnetic field and B(Sic) (0 )=B0/BMHD is the ratio of external and two-fluid MHD stability threshold magnetic field, derived here. An analytical theory to back up this growth rate dependence on the external magnetic field is needed. The results suggest that in astrophysical settings where a strong magnetic field pre-exists, the generation of an additional magnetic field by the ESKHI is suppressed, which implies that nature provides a "safety valve"-natural protection not to "over-generate" magnetic field by the ESKHI mechanism. Remarkably, we find that our two-fluid MHD threshold magnetic field is the same (up to a factor root gamma 0 ) as the DC saturation magnetic field, previously predicted by fully kinetic theory.

In our previous work, we searched for superflares on different types of stars while focusing on G-type dwarfs using entire Kepler data to study statistical properties of the occurrence rate of superflares. Using these new data, as a by-product, we found 14 cases of superflare detection on 13 slowly rotating Sun-like stars with rotation periods of 24.5–44 days. This result supports the earlier conclusion by others that the Sun may possibly undergo a surprise superflare. Moreover, we found 12 and seven new cases of detection of exceptionally large amplitude superflares on six and four main sequence stars of G- and M-type, respectively. No large-amplitude flares were detected in A, F or K main sequence stars. Here we present preliminary analysis of these cases. The superflare detection, i.e., an estimation of flare energy, is based on a more accurate method compared to previous studies. We fit an exponential decay function to flare light curves and study the relation between e-folding decay time, τ , versus flare amplitude and flare energy. We find that for slowly rotating Sun-like stars, large values of τ correspond to small flare energies and small values of τ correspond to high flare energies considered. Similarly, τ is large for small flare amplitudes and τ is small for large amplitudes considered. However, there is no clear relation between these parameters for large amplitude superflares in the main sequence G- and M-type stars, as we could not establish clear functional dependence between the parameters via standard fitting algorithms.

In our previous work, we investigated the occurrence rate of super-flares on various types of stars and their statistical properties, with a particular focus on G-type dwarfs, using entire Kepler data. The said study also considered how the statistics change with stellar rotation period, which in turn, had to be determined. Using such new data, as a by-product, we found 138 Kepler IDs of F- and G-type main sequence stars with rotation periods less than a day ( P rot < 1 day). On one hand, previous studies have revealed short activity cycles in F-type and G-type stars and the question investigated was whether or not short-term activity cycles are a common phenomenon in these stars. On the other hand, extensive studies exist which establish an empirical connection between a star’s activity cycle and rotation periods. In this study, we compile all available Kepler data with P rot < 1 day, and rely on an established empirical relation between P cyc and P rot with the aim to provide predictions for very short 5.09 ≤ P cyc ≤ 38.46 day cases in a tabular form. We propose an observation to measure P cyc using a monitoring program of stellar activity (e.g., activity-related chromospheric emission S-index) or a similar means for the Kepler IDs found in this study in order put the derived empirical relations between P cyc and P rot derived here to the test. We also propose an alternative method for measuring very short P cyc , using flare-detection algorithms applied to future space mission data.

We wrote and used an automated flare detection Python script to search for super-flares on main sequence stars of types A, F, G, K and M in Kepler's long-cadence data from Q0 to Q17. We studied the statistical properties of the occurrence rate of super-flares. For the G-type data set, we compared our results with the previous results of Okamoto et al. by splitting the data set into four rotational bands. We found similar power-law indices for the flare frequency distribution. Hence, we show that inclusion of a high-pass filter, sample biases, gyrochronology and completeness of flare detection is of no significance, as our results are similar to those of Okamoto et al. We estimated that a super-flare on G-type dwarfs with energy of 1035 erg occurs on a star once every 4360 yr. We found 4637 super-flares on 1896 G-type dwarfs. Moreover, we identified 321, 1125, 4538 and 5445 super-flares on 136, 522, 770 and 312 dwarfs of types A, F, K and M, respectively. We ascertained that the occurrence rate (dN/dE) of super-flares versus flare energy, E, shows a power-law distribution with dN/dE proportional to E-alpha, where alpha similar or equal to 2.0 to 2.1 for the spectral types from F-type to M-type stars. In contrast, the obtained alpha similar or equal to 1.3 for A-type stars suggests that the flare conditions differ from those of the other spectral-type stars. We note an increase in flare incidence rate in F-type to M-type stars and a decrease in A-type to F-type stars.

We derive a corrected analytical solution for the propagation and enhanced phase mixing of torsional Alfvén waves, in a potential magnetic field with exponentially divergent field lines, embedded in a stratified solar corona. Further we develop a code named TAWAS which calculates the analytic solution describing torsional Alfvén waves using IDL software language. We then use TAWAS to demonstrate that both our correction to the analytic solution and the inclusion of wave reflection have a significant impact on Alfvén wave damping. We continue to utilise TAWAS by performing a parameter study in order to identify the conditions under which enhanced phase mixing is strongest. We find that phase mixing is the strongest for high frequency Alfvén waves in magnetic fields with highly divergent field lines and without density stratification. We then present a finite difference solver, Wigglewave, which solves the linearised evolution equations for the system directly. Comparing solutions from TAWAS and Wigglewave we see that our analytical solution is accurate within the limits of the WKB approximation but under-reports the wave damping, caused by enhanced phase mixing, beyond the WKB limit. Both TAWAS andWigglewave solve the linearised governing equations and not the complete nonlinear MHD equations. Paper II will consider simulations that solve the full MHD equations including important nonlinear effects.

Alfvén waves have proven to be important in a range of physical systems due to their ability to transport non-thermal energy over long distances in a magnetized plasma. This property is of specific interest in solar physics, where the extreme heating of the atmosphere of the Sun remains unexplained. In an inhomogeneous plasma such as a flux tube in the solar atmosphere, they manifest as incompressible torsional perturbations. However, despite evidence in the upper atmosphere, they have not been directly observed in the photosphere. Here, we report the detection of antiphase incompressible torsional oscillations observed in a magnetic pore in the photosphere by the Interferometric Bidimensional Spectropolarimeter. State-of-the-art numerical simulations suggest that a kink mode is a possible excitation mechanism of these waves. The excitation of torsional waves in photospheric magnetic structures can substantially contribute to the energy transport in the solar atmosphere and the acceleration of the solar wind, especially if such signatures will be ubiquitously detected in even smaller structures with the forthcoming next generation of solar telescopes. Spectropolarimetric observations of a solar pore at high temporal and spatial resolution identify the presence of magnetic field torsional oscillations. Simulations suggest that such oscillations are triggered by a photospheric kink mode, which can contribute substantially to upward energy transport within the solar atmosphere.

2-D particle-in-cell simulations of free charge creation by collisional ionization of C12 and C60 molecules immersed in plasma for the parameters of relevance to plasma gasification are presented. Our main findings are that: 1) in uniform plasmas with smooth walls, two optimal values that emerge for free electron production by collisional ionization (i.e., a most efficient discharge-condition creation) are the C60:C12 fractions of 10:90 and 80:20 and 2) in plasmas with rough walls, modeled by the comb-like electric field at the boundary, the case of tangential electric field creates significant charge localization in the C12+ and C60+ species, again creating the most favorable discharge condition for triboelectrically generated plasma. The numerical simulation results are discussed with reference to recent triboelectric plasma experiments and are corroborated by suitable analytical models.

The ability to predict the occurrence of solar flares in advance is important to humankind due to the potential damage they can cause to Earth's environment and infrastructure. It has been shown in Kusano et al. that a small-scale bipolar region (BR), with its flux reversed relative to the potential component of the overlying field, appearing near the polarity inversion line (PIL) is sufficient to effectively trigger a solar flare. In this study we perform further 3D magnetohydrodynamic simulations to study the effect that the motion of these small-scale BRs has on the effectiveness of flare triggering. The effect of two small-scale BRs colliding is also simulated. The results indicate that the strength of the triggered flare is dependent on how much of the overlying field is disrupted by the BR. Simulations of linear oscillations of the BR showed that oscillations along the PIL increase the flare strength while oscillations across the PIL detract from the flare strength. The flare strength is affected more by larger amplitude oscillations but is relatively insensitive to the frequency of oscillations. In the most extreme case the peak kinetic energy of the flare increased more than threefold compared to a non-oscillating BR. Simulations of torsional oscillations of the BR showed a very small effect on the flare strength. Finally, simulations of colliding BRs showed the generation of much stronger flares as the flares triggered by each individual BR coalesce. These results show that significantly stronger flares can result from motion of the BR along the PIL of a sheared field or from the presence of multiple BRs in the same region.

The 3-D particle-in-cell simulations are used for studying proton-driven plasma wake-field acceleration that uses a high-energy proton bunch to drive a plasma wake field for electron beam acceleration. A new parameter regime was found, which generates an essentially constant electric field that is three orders magnitudes larger than that of AWAKE design, i.e., of the order of $2 \times 10^{3}$ GV/m. This is achieved in the extreme blowout regime when the number density of the driving proton bunch exceeds plasma electron number density 100 times.

A program has been designed to generate accurately a potential magnetic field on a staggered grid by extrapolating the magnetic field normal to the photospheric surface. The code first calculates a magnetic potential using the Green’s function method and then uses a finite differencing scheme to calculate the magnetic field from the potential. A new finite differencing formula was derived which accounts for grid staggering; it is shown that this formula gives a numerical approximation that is closest to the real potential field. It is also shown that extending the region over which normal photospheric field is specified can improve the accuracy of the potential field produced. The program is a FORTRAN 90 code that can be used to generate potential magnetic field inputs for Lare3d and other MHD solvers that use a staggered grid for magnetic field components. The program can be parallelised to run quickly over multiple computing cores. The code and supporting description are provided in the appendices.

In some laboratory and most astrophysical situations plasma wakefield acceleration of electrons is one dimensional, i.e. variation transverse to the beam's motion can be ignored. Thus, one dimensional (1D), particle-in-cell (PIC), fully electromagnetic simulations of electron plasma wake field acceleration are conducted in order to study the differences in electron plasma wake field acceleration in MeV versus GeV and linear versus blowout regimes. First, we show that caution needs to be taken when using fluid simulations, as PIC simulations prove that an approximation for an electron bunch not to evolve in time for few hundred plasma periods only applies when it is sufficiently relativistic. Our 1D PIC simulations establish that injecting driving and trailing electron bunches into plasmas with $n_0=5 \times 10^{22}$ m$^{-3}$, results in electric fields of about $- 10^{10}$ V/m, if the bunch density is one third as that of plasma (linear regime), and about $- 10^{11}$ V/m if the driving bunch density is $2.5 n_0$ (blowout regime). We study the differences in the plasma wake created and what is an optimal position of the trailing electron bunch. Starting from initial 36 MeV trailing bunch with $n_b=0.3 n_0$ its acceleration to 85 MeV is readily possible within 200 plasma periods. Beyond this time the approximation for a driving electron bunch not to evolve in time becomes invalid. Starting from initial 20 GeV trailing bunch with $n_b=0.3 n_0$ its acceleration to 21 GeV occurs within 2000 plasma periods. When driving bunch density is increased to $n_b=2.5 n_0$, starting from initial 20 GeV trailing bunch with $n_b=n_0$ its acceleration to 24 GeV occurs within 2000 plasma periods and plasma wake size is much larger. In this case, optimally there should be approximately $(90-100) c/\omega_{pe}$ distance between trailing and driving electron bunches.

We studied the dynamics of all prominence tornadoes detected by the Solar Dynamics Observatory/Atmospheric Imaging Assembly from 2011 January 01 to December 31. In total, 361 events were identified during the whole year, but only 166 tornadoes were traced until the end of their lifetime. Out of 166 tornadoes, 80 (48%) triggered CMEs in hosting prominences, 83 (50%) caused failed coronal mass ejections (CMEs) or strong internal motion in the prominences, and only 3 (2%) finished their lifetimes without any observed activity. Therefore, almost all prominence tornadoes lead to the destabilization of their hosting prominences and half of them trigger CMEs. Consequently, prominence tornadoes may be used as precursors for CMEs and hence for space weather predictions.

Three dimensional, particle-in-cell, fully electromagnetic simulations of electron plasma wake field acceleration applicable to the solar atmosphere are presented. It is established that injecting driving and trailing electron bunches into solar coronal and chromospheric plasmas results in electric fields (−(20−5)×106 V/m), leading to acceleration of the trailing bunch up to 52 MeV, starting from initial 36 MeV. The results provide one of the potentially important mechanisms for the extremely energetic solar flare electrons, invoking plasma wake field acceleration.

In previous simulations of collisionless 2D magnetic reconnection it was consistently found that the term in the generalised Ohm's law that breaks the frozen-in condition is the divergence of the electron pressure tensor's non-gyrotropic components. A fully relativistic particle-in-cell (PIC) code was used to model $X$-point collapse with a guide-field in two and three spatial dimensions. We show that in a 2D $X$-point collapse with a guide-field close to the strength of the in-plane field, the increased induced shear flows along the diffusion region lead to a new reconnection regime in which electron inertial terms play a dominant role at the $X$-point. This transition is marked by the emergence of a magnetic island - and hence a second reconnection site - as well as electron flow vortices moving along the current sheet. The reconnection electric field at the $X$-point is shown to exceed all lower guide-field cases for a brief period, indicating a strong burst in reconnection. By extending the simulation to three spatial dimensions it is shown that the locations of vortices along the current sheet (visualised by their $Q$-value) vary in the out-of-plane direction, producing tilted vortex tubes. The vortex tubes on opposite sides of the diffusion region are tilted in opposite directions, similarly to bifurcated current sheets in oblique tearing-mode reconnection. The tilt angles of vortex tubes were compared to a theoretical estimation and were found to be a good match. Particle velocity distribution functions for different guide-field runs, for 2.5D and 3D simulations, are analysed and compared.

In the previous works harmonic, phase-mixed, Alfven wave dynamics was considered both in the kinetic and magnetohydrodynamic (MHD) regimes. Up till today, only the magnetohydrodynamic, phase-mixed, Gaussian Alfven pulses were investigated. In the present work, we extend this into the kinetic regime. Here phase-mixed, Gaussian Alfven pulses are studied, which are more appropriate for solar flares, than harmonic waves, as the flares are impulsive in nature. Collisionless, phase-mixed, dispersive, Gaussian Alfven pulse in transversely inhomogeneous plasma is investigated by particle-in-cell (PIC) simulations and by an analytical model. The pulse is in inertial regime with the plasma beta less than electron-to-ion mass ratio and has a spatial width of 12 ion inertial length. The linear analytical model predicts that the pulse amplitude decrease is described by the linear Korteweg de Vries (KdV) equation. The numerical and the analytical solution of the linear KdV equation produces the pulse amplitude decrease in time as t–1. The latter scaling law is corroborated by full PIC simulations. It is shown that the pulse amplitude decrease is due to dispersive effects, while the electron acceleration is due to Landau damping of the phase-mixed waves. The established amplitude decrease in time as t–1 is different from the MHD scaling of t−3∕2. This can be attributed to the dispersive effects resulting in the different scaling compared to MHD, where the resistive effects cause the damping, in turn, enhanced by the inhomogeneity. Reducing the background plasma temperature and increase in ion mass yields more efficient particle acceleration.

Three dimensional, particle-in-cell, fully electromagnetic simulations of electron plasma wake field acceleration in the blow out regime are presented. Earlier results are extended by (i) studying the effect of longitudinal density gradient; (ii) avoiding use of co-moving simulation box; (iii) inclusion of ion motion; and (iv) studying fully electromagnetic plasma wake fields. It is established that injecting driving and trailing electron bunches into a positive density gradient of ten-fold increasing density over 10 cm long Lithium vapor plasma, results in spatially more compact and three times larger, compared to the uniform density case, electric fields ($-6.4 \times 10^{10}$ V/m), leading to acceleration of the trailing bunch up to 24.4 GeV (starting from initial 20.4 GeV), with an energy transfer efficiencies from leading to trailing bunch of 75 percent. In the uniform density case $-2.5 \times 10^{10}$ V/m wake is created leading to acceleration of the trailing bunch up to 22.4 GeV, with an energy transfer efficiencies of 65 percent. It is also established that injecting the electron bunches into a negative density gradient of ten-fold decreasing density over 10 cm long plasma, results in spatially more spread and two-and-half smaller electric fields ($-1.0 \times 10^{10}$ V/m), leading to a weaker acceleration of the trailing bunch up to 21.4 GeV, with an energy transfer efficiencies of 45 percent. Inclusion of ion motions into consideration shows that in the plasma wake ion number density can increase over few times the background value. It is also shown that transverse electromagnetic fields in plasma wake are of the same order as the longitudinal (electrostatic) ones.