Phase Space Holes Research Articles

Notes on solution phase space and BTZ black hole

In this paper, we use the solution phase space approach based on the covariant phase space formalism to compute the conserved charges of the BTZ black hole, namely mass, angular momentum, and entropy. Furthermore, we discuss the first law of the BTZ black hole and the Smarr relation. For completeness, outer horizon and inner horizon cases have been all included. Additionally, the results of the three-dimensional Kerr-dS spacetime have also been obtained. Our results are consistent with previous investigations. Considering the simplicity of the circumstances, we have presented the most detailed possible information, with the aim of facilitating rsearch in related fields.

Backward test particle simulation of nonlinear cyclotron wave-particle interactions in the radiation belts

Wave-particle interaction plays a crucial role in the dynamics of the Earth’s radiation belts. Cyclotron resonance between coherent whistler mode electromagnetic waves and energetic electrons of the radiation belts is often called a coherent instability. Coherent instability leads to wave amplification/generation and particle acceleration/scattering. The effect of wave on particle’s distribution function is a key component of the instability. In general, whistler wave amplitude can grow over threshold of quasi-linear (linear) diffusion theory which analytically tracks the time-evolution of a particle distribution. Thus, a numerical approach is required to model the nonlinear wave induced perturbations on particle distribution function. A backward test particle model is used to determine the energetic electrons phase space dynamics as a result of coherent whistler wave instability. The results show the formation of a phase space features with much higher resolution than is available with forward scattering models. In the nonlinear regime the formation of electron phase space holes upstream of a monochromatic wave is observed. The results validate the nonlinear phase trapping mechanism that drives nonlinear whistler mode growth. The key differences in phase-space perturbations between the linear and nonlinear scenarios are also illustrated. For the linearized equations or for low (below threshold) wave amplitudes in the nonlinear case, there is no formation of a phase-space hole and both models show features that can be characterized as linear striations or ripples in phase-space.

Acceleration of ion phase-space holes due to interactions with ion solitons in a wave-guided plasma

Ion phase-space holes are solitary kinetic structures found in the ion phase-space of collision-less plasmas, and are nonlinear solutions to the Vlasov-Poisson equations, identified as Bernstein-Greene-Kruskal (BGK) modes. In this study, interactions between an ion phase-space hole and a travelling ion KdV soliton is presented. This interaction, which is simulated in a fully ionised highly magnetised plasma within a cylindrical wave-guide, exhibits acceleration and deacceleration of the ion hole, depending on its mode of collision with the travelling ion soliton. We present these interactions and discuss the mechanism of this interaction between the two solitary waves.

Topology of charged AdS black hole in restricted phase space* *Supported by the National Natural Science Foundation of China (12075143, 12375050), and the Natural Science Foundation of Shanxi Province, China (202203021221209, 202303021211180)

The local topological properties of black hole systems can be expressed through winding numbers as defects. To date, AdS black hole thermodynamics are often depicted by the dual parameters of in the extended phase space, while there have been several studies on the black hole thermodynamics in the restricted phase space. In this paper, we analyze the topological properties of charged AdS black holes in the restricted phase space under the higher-dimension and higher-order curvature gravity frame. The results show that the topological number of the charged black hole in the same canonical ensembles is a constant and is independent of the concrete dual thermodynamical parameters. However, the topological number in the grand canonical ensemble is different from that in the canonical ensemble for the same black hole system. Furthermore, these results are independent of dimension d and highest order k of the Lanczos-Lovelock densities.

Exploring critical behavior of thermodynamic variables of the Kerr-Newman-AdS black hole in the restricted phase space

The present work investigates the thermodynamic properties of the four-dimensional Kerr-Newmann-AdS black hole, utilizing the recently proposed framework of restricted phase space thermodynamics. This approach introduces a novel set of paired thermodynamic variables; the central charge (C) of the corresponding dual conformal field theory and the chemical potential (μ). Through rigorous analysis, we establish fundamental relationships, including the Euler relation, Gibbs-Duhem relation, and the zeroth-order homogeneity of intensive variables. Furthermore, numerical techniques are employed to explore thermodynamic processes between the conjugate variables in canonical and grand canonical ensembles. Our investigation reveals first-order and second-order phase transitions across various macroscopic processes. Despite the absence of complete analytical expressions, our findings unveil striking similarities in behavior between Reissner-Nordström-Anti-de Sitter and Kerr-anti–de Sitter, underscoring the presence of underlying universality within the restricted phase space thermodynamics formalism. Published by the American Physical Society 2024

Resonant Electron Signatures in the Formation of Chorus Wave Subpackets

AbstractA 2‐D GCPIC simulation in a dipole field system has been conducted to explore the excitation of oblique whistler mode chorus waves driven by energetic electrons with temperature anisotropy. The rising tone chorus waves are initially generated near the magnetic equator, consisting of a series of subpackets, and become oblique during their propagation. It is found that electron holes in the wave phase space, which are formed due to the nonlinear cyclotron resonance, oscillate in size with time during subpacket formation. The associated inhomogeneity factor varies accordingly, giving rise to various frequency chirping in different phases of subpackets. Distinct nongyrotropic electron distributions are detected in both wave gyrophase and stationary gyrophase. Landau resonance is found to coexist with cyclotron resonance. This study provides multidimensional electron distributions involved in subpacket formation, enabling us to comprehensively understand the nonlinear physics in chorus wave evolution.

Intermittency, bursty turbulence, and ion and electron phase-space holes formation in collisionless current-carrying plasmas

In the previous studies of nonlinear saturation of the Buneman instability caused by high electron drift velocity relative to ions, the phase-space holes and the plateau on the electron velocity distribution function were identified as features of the saturation stage of instability [notably in the paper by Omura et al., J. Geophys. Res. 108, 1197 (2003)]. We have performed a much longer simulation of the Buneman instability and observed a secondary instability. This secondary instability generates fast electron-acoustic waves. By analyzing the phase-space plot of ions and electrons, we show that the fast electron heating and the formation of the plateau of electron velocity distribution function are not due to the quasi-linear diffusion but due to the nonlinear interaction of ion- and electron-acoustic solitary waves (phase-space holes) by exchange of trapped electrons in each wave. We also report the details on the intermittent and bursty nature of turbulence driven by this instability.

Magnetic Black Hole Thermodynamics in an Extended Phase Space with Nonlinear Electrodynamics.

We study Einstein's gravity coupled to nonlinear electrodynamics with two parameters in anti-de Sitter spacetime. Magnetically charged black holes in an extended phase space are investigated. We obtain the mass and metric functions and the asymptotic and corrections to the Reissner-Nordström metric function when the cosmological constant vanishes. The first law of black hole thermodynamics in an extended phase space is formulated and the magnetic potential and the thermodynamic conjugate to the coupling are obtained. We prove the generalized Smarr relation. The heat capacity and the Gibbs free energy are computed and the phase transitions are studied. It is shown that the electric fields of charged objects at the origin and the electrostatic self-energy are finite within the nonlinear electrodynamics proposed.

3D cylindrical BGK model of electron phase-space holes with finite velocity and polarization drift

Nonlinear kinetic structures, called electron phase-space holes (EHs), are regularly observed in space and experimental magnetized plasmas. The existence of EHs is conditioned and varies according to the ambient magnetic field and the parameters of the electron beam(s) that may generate them. The objective of this paper is to extend the 3D Bernstein–Greene–Kruskal model with cylindrical geometry developed by L.-J. Chen et al. [“Bernstein–Greene–Kruskal solitary waves in three-dimensional magnetized plasma,” Phys. Rev. E 69, 055401 (2004)] and L.-J. Chen et al., [“On the width-amplitude inequality of electron phase space holes,” J. Geophys. Res. 110, A09211 (2005)] to include simultaneously finite effects due to (i) the strength of the ambient magnetic field B0, by modifying the Poisson equation with a term derived from the electron polarization current, and (ii) the drift velocity ue of the background plasma electrons with respect to the EH, by considering velocity-shifted Maxwellian distributions for the boundary conditions. This allows us to more realistically determine the distributions of trapped and passing particles forming the EHs, as well as the width-amplitude relationships for their existence.

Characterization of stability of dynamic particle ensemble systems using topological data analysis.

Holes are ubiquitous structures in phase space, and their time evolution could indicate an instability in the dynamics of the system. However, the properties of these holes are difficult to study directly due to their theoretical complexity and lack of computational tools. This study proposes the use of persistent homology (PH), a technique from topological data analysis, as a computational tool for analyzing the properties of these phase-space holes, or more formally the H1 homology class according to PH. Initially, by using a toy data set, it is shown that the time evolution and the growth rate of a H1 class in phase space could be obtained by PH. For further validation, PH is applied to particle ensemble systems, such as the Hamiltonian flow and the two-stream instability (TSI). Both the stable case, where no H1 forms, and the unstable case, where H1 forms, were analyzed. It was shown that PH can distinguish between the stable and unstable cases purely from the phase-space time evolution plots. In unstable TSI, the PH also distinguished the transition of the H1 class from linear to non-linear growth. The growth rate, thus, obtained is in excellent agreement with the growth rate of the particle energy in the TSI system.

Thermodynamics of 4D-EGB black holes in the quintessential phase space

In this paper, we examine the 4D-EGB black holes in the quintessential phase space, where the quintessence dark energy surrounds the 4D-EGB black hole. We study the effect of quintessence dark energy on thermodynamic behavior of 4D-EGB black holes i.e. the phase transition and critical phenomena. For a specific condition, we recover the Van der Waals equation of state as the Gauss–Bonnet coupling plays the role of an effective charge. Furthermore, we study the effect of black hole on dark energy that resides near their event horizon in different process. We find that the quintessence dark energy accretes near the horizon of the black hole and we observe that the dark energy pressure sign changes from negative to positive. This behavior is analogous to the “stretched water” (Altabet et al., 2017) phenomenon in thermodynamics of ordinary materials. We call this process quintessence dark energy/stretched quintessence phase transition.

Thermodynamics of Kerr-Sen-AdS black holes in the restricted phase space

Thermodynamics of Kerr-Sen-AdS black holes in the restricted phase space

Contact and metric structures in black hole chemistry

We review recent studies of contact and thermodynamic geometry for black holes in AdS spacetimes in the extended thermodynamics framework. The cosmological constant gives rise to the notion of pressure P = −Λ/8π and, subsequently a conjugate volume V, thereby leading to a close analogy with hydrostatic thermodynamic systems. To begin with, we review the contact geometry approach to thermodynamics in general and then consider thermodynamic metrics constructed as the Hessians of various thermodynamic potentials. We then study their correspondence to statistical ensembles for systems with two-dimensional spaces of equilibrium states. From the zeroes and divergences of the curvature scalar obtained from the metric, we carefully analyze the issue of ensemble non-equivalence and show certain complimentary behaviors in the description of a thermodynamic system. Following a thorough analysis of the familiar van der Waals system, we turn our attention to black holes in extended phase space. Considering the example of charged AdS black holes, we discuss the generic features of their thermodynamic geometry in detail. The relationship of the thermodynamic curvature(s) with critical points as well as microscopic interactions in black holes is also briefly explored. We finally set up the thermodynamic geometry for finite temperature gauge theories dual to black holes in AdS via holographic correspondence and comment on recent progress.

Hawking radiation from a Reissner-Nordstrom-AdS black hole with integral monopoles in extended phase space

In recent years, thermodynamics and phase transitions of black holes in extended phase space have been extensively studied. The results show that the original first law of thermodynamics needs revising and new phase transitions will appear. However, so far, Hawking tunneling radiation has not been widely studied in the extended phase space. In particular, whether the tunneling radiation probability changes at this time is still uncertain. This work focuses on this topic, that is, to calculate the specific value of the tunneling probability in the extended phase space and ascertains whether the results obtained in the normal phase space are consistent with those in the extended phase space. The methods used herein are described below. Taking Reissner-Nordstrom-AdS black holes with global monopole for example, the cosmological parameters are regarded as dynamic variables, which is different from previous treatment methods that regard them as constants and ignore their contributions to the tunneling probability. In particular, cosmological parameters are introduced and regarded as thermodynamic pressure when the tunneling probability is calculated, and their contribution to the tunneling probability is considered. In the work the tunneling process of mass particles is mainly studied. The outgoing particles are viewed as spherical de Broglie waves, and then the relative phase velocity and group velocity are calculated. The geodesic equation is obtained according to the relationship between the two velocities, and the tunneling probability is calculated from the geodesic equation. It is concluded that the results show that the tunneling probability of the ingoing particles is proportional to the difference in the Bekenstein-Hawking entropy of the black hole before and after the particles tunnel, and the radiation spectrum deviates from the pure thermal spectrum, which is exactly the same as the case that the cosmological parameters are treated as constants. This means that the tunneling probability of particles can be obtained in the extended phase space, and the tunneling process does not depend on thermodynamic parameters. In addition, it is found that although the global monopole affects the dynamical behavior and thermodynamic quantity of the particle, it does not affect the entropy change or tunneling rate. In other words, the conclusion that the tunneling probability in extended phase space is exactly the same as that in normal phase space does not depend on the space-time topology.

Banded chorus generation by an electron shell distribution in an inhomogeneous magnetic field: 1D PIC simulations

Although many theoretical models have been proposed over several decades, the origin of banded chorus with a gap in intensity at Ωe/2 (Ωe being the angular electron cyclotron frequency) is still debated. In one of those models, the chorus gap formation is attributed to two anisotropic electron populations separated by an isotropized population (called the parallel plateau) at energy resonant with waves of frequency ∼Ωe/2. Here, we simplify the plateau population as an electron shell distribution in velocity space and investigate its role in the gap formation using a particle-in-cell code in a non-uniform magnetic field. The base plasma is configured to generate rising chorus elements spanning in frequency from below to above Ωe/2. Then, multiple simulations are run with an additional shell distribution with different density values to investigate the gap formation. The simulation results show that even a relatively small fraction of shell is quite effective in arresting the frequency chirping of lower-band chorus at ∼Ωe/2, resulting in a power gap there. Phase space analysis indicates that the resonant current contributed by the phase-trapped shell electrons (forming a phase space hill) can counteract nonlinear chorus growth driven by the phase space hole of energetic, anisotropic electrons. This process occurs in combination with the linear cyclotron damping suggested in earlier studies, and the resulting nonlinear damping may exceed the latter effect.

Thermodynamics of black holes in the quintessential phase space* *This work is supported by the National Natural Science Foundation of China (Grant No. 11903025) and the Natural Science Foundation of Sichuan Province, China (Grant No. 2022NSFSC1833).

Considering that the negative pressure of the accelerated expansion of the universe results from the cosmological constant or the dark energy quintessence, we use the dark energy quintessence to construct the "quintessential" phase space. In contrast to the previous discussion in which the cosmological constant is considered as the black hole (BH) phase transition pressure, in this analysis, we believe that the pressure results from quintessence. The characteristics of critical behavior, Gibbs free energy, and temperature behavior in quintessential phase space are investigated. We observe that the phase transition belongs to van der Waals phase transition within. If is within (–2/3, –1/3), the phase transition loses the large BH phase transition characteristics, which is caused by the later stage of the phase transition being completely dominated by quintessence dark energy with negative pressure. These results suggest that the quintessential phase space can be constructed with the pressure from the thermal quintessence, and it can be used as a new probe to explore the thermodynamics of BHs.

NED-AdS black holes, extended phase space thermodynamics and Joule–Thomson expansion

We study and discuss the critical behaviour of charged by nonlinear electrodynamics (NED) AdS black holes in an extended phase space. The negative cosmological constant is treated as a thermodynamic pressure and the black hole mass is considered as the chemical enthalpy. We show the analogy of thermodynamics and phase transitions studied with the Van der Walls liquid–gas system. We introduce new thermodynamic quantities conjugated to the NED coupling and a magnetic charge. It was demonstrated that the first law of black hole thermodynamics and the Smarr relation hold. We have calculated the Joule–Thomson thermodynamic coefficient and inversion temperature, and the Joule–Thomson adiabatic expansion is investigated.

Observations of Electron Vorticity and Phase Space Holes in the Magnetopause Reconnection Separatrix

AbstractWe report Magnetospheric Multiscale (MMS) observations of two electron vortices with a roughly 10 km or 2–3 electron skin depths cross‐section across the magnetospheric separatrix of a dayside magnetopause reconnection structure. The enhanced electron vorticity, which is caused by a significant velocity shear in the electron flows streaming in opposite directions along northward‐directed magnetic field lines, leads to perturbations perpendicular to the reconnecting magnetic field on the order of 1–2 nT. The high electron vorticity periods are also associated with electron phase space holes having the largest bipolar parallel electric field amplitudes ∼25 mV/m observed across this exhaust. Less intense ∼10 mV/m electron phase space holes propagate along a northward magnetic field away from the X‐line within a northward reconnection exhaust. The electron phase space holes with the largest bipolar parallel electric fields are observed to propagate toward the X‐line within discrete channels of southward and super‐Alfvénic 1,500 km/s electron flows in the magnetospheric separatrix layer.

Nonlinear triggering process of whistler-mode emissions in a homogeneous magnetic field

We perform an electromagnetic particle simulation of triggered emissions in a uniform magnetic field for understanding of nonlinear wave–particle interaction in the vicinity of the magnetic equator. A finite length of a whistler-mode triggering wave packet with a constant frequency is injected by oscillating an external current at the equator. We find that the first subpacket of triggered emissions is generated in the homogeneous magnetic field. By analyzing resonant currents and resonant electron dynamics in the simulation, we find that the formation of an electron hole in a velocity phase space results in resonant currents, and the currents cause wave amplification and frequency increase. We obtain the interaction time of counter-streaming resonant electrons in a triggering wave packet with a finite width. By changing the duration time of the triggering pulse, we evaluate the interaction time necessary for formation of an electron hole. We conduct 4 runs with different duration times of the triggering pulse, 980, 230, 105, 40 Omega _e^{-1}, which correspond to cases with interaction times, 370%, 86%, 39%, and 15% of the nonlinear trapping period, respectively. We find generation of triggered emissions in the three cases of 370%, 86%, and 39%, which agrees with the conventional nonlinear model that the nonlinear transition time, which is necessary for formation of resonant currents, is about a quarter of the nonlinear trapping period.Graphic

Nonlinearly charged AdS black holes, extended phase space thermodynamics and Joule–Thomson expansion

We study thermodynamics and phase transitions of magnetically charged by nonlinear electrodynamics (NED) Anti-de Sitter (AdS) black holes in an extended phase space. The cosmological constant is treated as a thermodynamic pressure whereas the black hole mass is considered such as the chemical enthalpy. The horizon thermodynamics of black holes shows an analogy with the Van der Walls liquid–gas system. We define a quantities which are conjugated to the parameter of NED and a magnetic charge. It is shown that the first law of thermodynamics and the generalized Smarr relation hold. The critical exponents are the same as in the Van der Waals system. The Joule–Thomson adiabatic expansion of NED-AdS black holes is investigated because of thermodynamic behavior of black holes. The Joule–Thomson coefficient, the inversion and isenthalpic curves are discussed. The minimum of inversion temperature and the corresponding event horizon radius are obtained.