Phase Space Holes Research Articles

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

The thermodynamics for Kerr-AdS black hole in four dimensions is revisited using the recently proposed restricted phase space formalism, which includes the central charge C of the dual CFT and the chemical potential mu , but excludes the pressure and the conjugate volume, as thermodynamic variables. The Euler relation holds automatically, and the first order homogeneity of the mass and the zeroth order homogeneity of the intensive variables are made explicit. Thermodynamic processes involving each pair of conjugate variables are studied in some detail, with emphasis on the scaling properties of the equations of states. It turns out that the thermodynamic behavior of the Kerr-AdS black hole is very similar to that of the RN-AdS black hole studied earlier. In particular, it is found that, there is a first order supercritical phase equilibrium in the T-S processes at fixed nonvanishing angular momentum, while at vanishing angular momentum or at fixed angular velocities, there is always a non-equilibrium transition from a small unstable black hole state to a large stable black hole state. Moreover, there is a Hawking–Page phase transition in the mu -C processes. Due to the complicatedness of the Kerr metric, the exact critical point and the Hawking–Page temperature are worked out explicitly only in the slow rotating limit, however the characteristic thermodynamic properties do not rely on the slow rotating approximation.

Spacecraft detect electron phase space holes undergoing strong wave-particle interactions

Magnetospheric Multiscale Mission enables direct millisecond measurements of electron particle flux in space plasma

Electron acceleration by Langmuir turbulence in ionospheric heating

In this study, we investigate the generation of parametric decay instability, Langmuir turbulence formation, and electron acceleration in ionospheric heating via a two-fluid model using the Fokker–Planck equation and Vlasov–Poisson system simulations. The simulation results of both the magnetofluid model and the kinetic model demonstrate the dynamics of electron acceleration. Further, the results of the Vlasov–Poisson simulations suggest the formation of electron holes in phase space at the same spatial scale as the Langmuir wave, which are shown to be related to electron acceleration. In addition, electron acceleration is enhanced through the extension of the wavenumber spectrum caused by strong Langmuir turbulence, leading to more electron holes in phase space.

Millisecond observations of nonlinear wave–electron interaction in electron phase space holes

Electron phase space holes (EHs) associated with electron trapping are commonly observed as bipolar electric field signatures in both space and laboratory plasma. Until recently, it has not been possible to resolve EHs in electron measurements. We report observations of EHs in the plasma sheet boundary layer, here identified as the separatrix region of magnetic reconnection in the magnetotail. The intense EHs are observed together with an electron beam moving toward the X line, showing signs of thermalization. Using the electron drift instrument onboard the satellites of the Magnetospheric Multiscale mission, we make direct millisecond measurements of the electron particle flux associated with individual electron phase space holes. The electron flux is measured at a millisecond cadence in a narrow parallel speed range within that of the trapped electrons. The flux modulations are of order unity and are direct evidence of the strong nonlinear wave–electron interaction that may effectively thermalize beams and contribute to transforming directed drift energy to thermal energy.

Nonlinear Signatures of VLF‐Triggered Emissions: A Simulation Study

AbstractWe conduct a particle‐in‐cell simulation reproducing triggering process of whistler‐mode rising‐tone emissions by injecting a wave with a fixed frequency at the equator. Rising‐tone elements with multiple subpackets with monotonically increasing frequencies are generated from the triggering wave. Generation regions of the subpackets move upstream or downstream depending on the group velocities and resonance velocities for different frequencies. Because of the motion of a source region to the upstream, a long rising‐tone subpacket is generated self‐sustainingly through formation of an electron hole in velocity phase space stretched over the generation region. The long rising‐tone subpacket is modulated with increasing magnitude, splitting into smaller subpackets through propagation. The amplitude modulations in the subpacket arise from two different processes; resonant trapping oscillation of electrons at the equatorial region and enhancement of amplitude variations through propagation in the downstream.

Kinetic Plasma Turbulence Generated in a 3D Current Sheet With Magnetic Islands

In this article we aim to investigate the kinetic turbulence in a reconnecting current sheet (RCS) with X- and O-nullpoints and to explore its link to the features of accelerated particles. We carry out simulations of magnetic reconnection in a thin current sheet with 3D magnetic field topology affected by tearing instability until the formation of two large magnetic islands using particle-in-cell (PIC) approach. The model utilizes a strong guiding field that leads to the separation of the particles of opposite charges, the generation of a strong polarization electric field across the RCS, and suppression of kink instability in the “out-of-plane” direction. The accelerated particles of the same charge entering an RCS from the opposite edges are shown accelerated to different energies forming the “bump-in-tail” velocity distributions that, in turn, can generate plasma turbulence in different locations. The turbulence-generated waves produced by either electron or proton beams can be identified from the energy spectra of electromagnetic field fluctuations in the phase and frequency domains. From the phase space analysis we gather that the kinetic turbulence may be generated by accelerated particle beams, which are later found to evolve into a phase-space hole indicating the beam breakage. This happens at some distance from the particle entrance into an RCS, e.g. about 7di (ion inertial depth) for the electron beam and 12di for the proton beam. In a wavenumber space the spectral index of the power spectrum of the turbulent magnetic field near the ion inertial length is found to be −2.7 that is consistent with other estimations. The collective turbulence power spectra are consistent with the high-frequency fluctuations of perpendicular electric field, or upper hybrid waves, to occur in a vicinity of X-nullpoints, where the Langmuir (LW) can be generated by accelerated electrons with high growth rates, while further from X-nullponts or on the edges of magnetic islands, where electrons become ejected and start moving across the magnetic field lines, Bernstein waves can be generated. The frequency spectra of high- and low-frequency waves are explored in the kinetic turbulence in the parallel and perpendicular directions to the local magnetic field, showing noticeable lower hybrid turbulence occurring between the electron’s gyro- and plasma frequencies seen also in the wavelet spectra. Fluctuation of the perpendicular electric field component of turbulence can be consistent with the oblique whistler waves generated on the ambient density fluctuations by intense electron beams. This study brings attention to a key role of particle acceleration in generation kinetic turbulence inside current sheets.

Joule–Thomson expansion of the torus-like black hole

In this paper, we study the Joule–Thomson expansion of the torus-like black hole in extended phase space, where the cosmological constant is determined by the pressure. It is noteworthy that the torus-like black hole has a horizon of toroidal topology, rather than a horizon of spherical topology. We study both the inversion and isenthalpic curves of the torus-like black holes in the $$T-P$$ plane and find that their intersection coincides with the inversion point that distinguishes the heat in the cooling process. Compared to the Van der Waals fluid, the inversion curves of torus-like black holes do not end at any point and only lower inversion curves are available. Most importantly, we find that the $$P - V$$ diagram of the torus-like black hole has no inflection point, i.e., the torus-like black hole is always thermally stable. Therefore, the torus-like black hole has no critical point and critical temperature, and there is no ratio between the minimum inversion temperature and the critical temperature. This is completely different from the black hole with the horizon of spherical topology.

Criticality of lower dimensional AdSd black holes

In lower dimensions, charged AdS black holes in an extended phase space, where the cosmological constant is interpreted as the thermodynamic pressure, are typically absent of liquid/gas phase transitions. We investigate the criticality of lower dimensional charged, dilatonic, asymptotically AdS (CDAdS$_d$) black holes generated from consistent truncations of RNAdS$_{d+2}$ black objects. We demonstrate that CDAdS$_{d}$ black holes in $d<4$ can exhibit rich van der Waals behavior and confirm that the associated critical exponents match those expected from mean field theory.

Realistic Electron Diffusion Rates and Lifetimes Due to Scattering by Electron Holes

AbstractPlasma sheet electron precipitation into the diffuse aurora is critical for magnetosphere‐ionosphere coupling. Recent studies have shown that electron phase space holes can pitch‐angle scatter electrons and may produce plasma sheet electron precipitation. These studies have assumed identical electron hole parameters to estimate electron scattering rates (Vasko et al., 2018, https://doi.org/10.1063/1.5039687). In this study, we have re‐evaluated the efficiency of this scattering by incorporating realistic electron hole properties from direct spacecraft observations into computing electron diffusion rates and lifetimes. The most important electron hole properties in this evaluation are their distributions in velocity and spatial scale and electric field root‐mean‐square intensity (). Using direct measurements of electron holes during a plasma injection event observed by the Van Allen Probe at , we find that when 4 mV/m electron lifetimes can drop below 1 h and are mostly within strong diffusion limits at energies below 10 keV. During an injection observed by the THEMIS spacecraft at , electron holes with even typical intensities (1 mV/m) can deplete low‐energy (a few keV) plasma sheet electrons within tens of minutes following injections and convection from the tail. Our results confirm that electron holes are a significant contributor to plasma sheet electron precipitation during injections.

Temporal and spatial chaos in the Kerr-AdS black hole in an extended phase space * *Supported by the National Natural Science Foundation of China (11604121, 11875126)

Based on the Melnikov method, we investigate chaotic behaviors in the extended thermodynamic phase space for a slowly rotating Kerr-AdS black hole under temporal and spatial perturbations. Our results show that the temporal perturbation coming from a thermal quench of the spinodal region in the phase diagram may cause temporal chaos only when the perturbation amplitude is above a critical value, which involves the angular momentum J. Under the spatial perturbation, however, it is found that spatial chaos always occurs, independent of the perturbation amplitude.

MMS Observations of Broadband Electrostatic Waves in Electron Diffusion Region of Magnetotail Reconnection

AbstractIn this study, the broadband electrostatic waves are observed in electron diffusion region (EDR). Detailed analysis has shown that the parallel electric field of these waves have a bipolar or continuous steepening waveform. The bipolar structures of the parallel electric field are usually accompanied by electron holes (EHs) in phase space. The parallel spatial scales of EHs are ∼3–5 ( is the Debye length), and the perpendicular spatial scales are larger than ∼18.6 . Therefore, the length ratios are larger than ∼3.7–6.2, which means that the EHs have oblate shapes. Associated with these plasma waves, electron beams propagating away from the X‐line have been observed. By performing a one‐dimensional (1‐D) electrostatic particle‐in‐cell simulation of the bump‐on‐tail instability, we reproduce two types of waveforms similar to those observed in the EDR during the different evolution stage of the instability, which implies that these electrostatic waves are generated by the bump‐on‐tail instabilities.

Analytic phase structures and thermodynamic curvature for the charged AdS black hole in alternative phase space

In this paper, we visit the thermodynamic criticality and thermodynamic curvature of the charged AdS black hole in a new phase space. It is shown that when the square of the total charge of the charged black hole is considered as a thermodynamic quantity, the charged AdS black hole also admits an van der Waals-type critical behavior without the help of thermodynamic pressure and thermodynamic volume. Based on this, we study the fine phase structures of the charged AdS black hole with fixed AdS background in the new framework. On the one hand, we give the phase diagram structures of the charged AdS black hole accurately and analytically, which fills up the gap in dealing with the phase transition of the charged AdS black holes by taking the square of the charge as a thermodynamic quantity. On the other hand, we analyse the thermodynamic curvature of the black hole in two coordinate spaces. The thermodynamic curvatures obtained in two different coordinate spaces are equivalent to each other and are also positive. Based on an empirical conclusion under the framework of thermodynamic geometry, we speculate that when the square of charge is treated as an independent thermodynamic quantity, the charged AdS black hole is likely to present a repulsive between its molecules. More importantly, based on the thermodynamic curvature, we obtain an universal exponent at the critical point of phase transition.

Non-monotonic double layers and electron two-stream instabilities resulting from intermittent ion acoustic wave growth

Transient characteristics of a current-carrying plasma subjected to ion acoustic instability are studied via Vlasov–Poisson simulations. After saturation of the ion acoustic instability, when a sufficient range of long-wavelength ion acoustic modes is considered, ion acoustic wave packets form and give rise to ion phase space holes. These ion holes grow in magnitude until asymmetric electron reflection, due to the current carrying plasma, results in a potential gradient across the hole known as a non-monotonic double layer. Downstream of the double layer, an electron two-stream instability is generated due to a depletion of forward-streaming electrons by reflection. This secondary instability initiates a plasma wave whose phase velocity is determined by the magnitude of the double layer potential. While the double layer potential depends on the ion mass for a given domain length, the phase velocity of the secondary wave is consistently observed to be greater than the ion acoustic speed. Implications for the presence of these transient phenomena are discussed in the context of experimental plume measurements of hollow cathode devices.

Nonlinear dynamics of the fishbone-induced alpha transport on ITER

The fishbone-induced transport of alpha particles is computed for the ITER 15 MA baseline scenario (ITER Physics Expert Group on Energy Drive 1999 Nucl. Fusion 39 2471) using the non-linear hybrid Kinetic-MHD code XTOR-K. Two limit cases have been studied, in order to analyse the characteristic regimes of the fishbone instability: the weak kinetic drive limit (Berk et al 1999 Phys. Plasmas 6 3102) and the strong kinetic drive limit (Zonca et al 2015 New J. Phys. 17 013052). In both those regimes, characteristic features of the n = m = 1 fishbone instability are recovered, such as a strong up/down-chirping of the mode frequency, associated with a resonant transport of trapped and passing alpha particles. The effects of the n = m = 0 sheared poloidal and toroidal plasma rotation are taken into account in the simulations. The shear is not negligible, which implies that the fishbone mode frequency has a radial dependency, impacting the wave-particle resonance condition. Phase space hole and clump structures are observed in both non-linear regimes, centered around the precessional and passing resonances. These structures remains attached to the resonances as the different mode frequencies chirp up and down. In the non-linear phase, the transport of individual resonant trapped particles is identified to be linked to mode-particle synchronization. On this basis, a partial mechanism for the non-linear coupling between particle transport and mode dominant down-chirping is proposed. The overall transport of alpha particles through the q = 1 surface is of order 2–5\\% of the initial population between the simulations. The loss of alpha power is found to be directly equal to the loss of alpha particles.

Nonlinear Dynamics of Phase Space Structures Arising from Counterinjection of Overlimiting Relativistic Electron Beams into a Long Equipotential Cavity

Dynamics of phase space structures arising from counterinjection of O-LREBs into a long equipotential cavity is studied using PIC simulation. It is found that alternating regions of the squeezed state and the two-stream state (phase space holes) are formed in the phase portraits. It is shown that phase space holes tend to diverge from the middle of the cavity to its edges, where they are absorbed. Oscillations superimpose on the directed motion of the phase space holes. Evolution ends up with disappearance of all phase space holes and establishment of the squeezed state over the almost entire length of the cavity.

On the Nature and Origin of Bipolar Electrostatic Structures in the Earth's Bow Shock

We present a statistical analysis of large-amplitude bipolar electrostatic structures measured by the Magnetospheric Multiscale spacecraft in the Earth's bow shock. The analysis is based on 371 large-amplitude bipolar structures collected in nine supercritical quasi-perpendicular Earth's bow shock crossings. We have found that 361 of the bipolar structures have negative electrostatic potentials, and only 10 structures (> 1, a parameter range typical of collisionless shocks in the heliosphere and various astrophysical environments. This analysis indicates that the original mechanism of electron surfing acceleration involving electron phase space holes is not likely to be efficient in realistic collisionless shocks.

Electrostatic Turbulence and Debye-scale Structures in Collisionless Shocks

Abstract We present analysis of more than 100 large-amplitude bipolar electrostatic structures in a quasi-perpendicular supercritical Earth’s bow shock crossing, measured by the Magnetospheric Multiscale spacecraft. The occurrence of the bipolar structures is shown to be tightly correlated with magnetic field gradients in the shock transition region. The bipolar structures have negative electrostatic potentials and spatial scales of a few Debye lengths. The bipolar structures propagate highly oblique to the shock normal with velocities (in the plasma rest frame) of the order of the ion-acoustic velocity. We argue that the bipolar structures are ion phase space holes produced by the two-stream instability between incoming and reflected ions. This is the first identification of the ion two-stream instability in collisionless shocks.

Tricritical point and solid/liquid/gas phase transition of higher dimensional AdS black hole in massive gravity

By considering the fifth order graviton term in massive gravity theory, we study the P–V critical behaviors of AdS black hole in d≥7 dimensional space–time, and find the solid/liquid/gas phase transition with the “common” tricritical point, which does not exist in absence of higher graviton terms. Moreover, we also find the number of positive real roots of critical radius equation plays a key role in classifying different kinds of phase transitions. If there is only one positive root of equation, the first order Van der Waals-like phase transition emerges. For two roots, the system could experience a zero-order reentrant phase transition. Notably, for three roots, the solid/liquid/gas phase transition can occur. In addition, because the critical radius equation is a (n−2)-order polynomial equation associated with the graviton terms, the critical phenomena of black holes in extended phase space depend crucially on the number n of the graviton terms in high dimensional massive gravity.

Chaos in Born–Infeld–AdS black hole within extended phase space

Born-Infeld-AdS black holes in extended phase space may possess phase structures resembling that of van der Waals fluid in four-dimensional spacetime. We study dynamics of its state, which is in the unstable spinodal region initially on phase space, under time-periodic thermal perturbations. By applying the Melnikov method, it is found that there exists a critical amplitude $\gamma_c$ of the perturbations, which depends on the Born-Infeld parameter $b$ and the black hole charge $Q$, such that chaos occurs for $\gamma > \gamma_c$. We found that larger $b$ or $Q$ makes the onset of chaos easier. Space-periodic thermal perturbations on its equilibrium state are also studied and there is always chaos for whatever the perturbation amplitude is.

Thermodynamics and weak cosmic censorship conjecture of BTZ black holes in extended phase space * *Supported by National Natural Science Foundation of China (11875095) and Basic Research Project of Science and Technology Committee of Chongqing (cstc2018jcyjA2480, cstc2019jcyjA2091)

As a charged fermion drops into a BTZ black hole, the laws of thermodynamics and the weak cosmic censorship conjecture are investigated in both the normal and extended phase space, where the cosmological parameter and renormalization length are regarded as extensive quantities. In the normal phase space, the first and second law of thermodynamics, and the weak cosmic censorship are found to be valid. In the extended phase space, although the first law and weak cosmic censorship conjecture remain valid, the second law is dependent on the variation of the renormalization energy dK. Moreover, in the extended phase space, the configurations of extremal and near-extremal black holes are not changed, as they are stable, while in the normal phase space, the extremal and near-extremal black holes evolve into non-extremal black holes.