The purpose of this paper is to explore the dynamical behaviour of hot accretion flow with thermal conduction. The importance of thermal conduction on hot accretion flow is confirmed by observations of the hot gas that surrounds Sgr A$^*$ and a few other nearby galactic nuclei. In this research, the effect of thermal conduction is studied by a saturated form of it, as is appropriate for weakly collisional systems. The angular momentum transport is assumed to be a result of viscous turbulence and the $α$-prescription is used for the kinematic coefficient of viscosity. The equations of accretion flow are solved in a simplified one-dimensional model that neglects the latitudinal dependence of the flow. To solve the integrated equations that govern the dynamical behaviour of the accretion flow, we have used an unsteady self-similar solution. The solution provides some insights into the dynamics of quasi-spherical accretion flow and avoids from limits of the steady self-similar solution. In comparison to accretion flows without thermal conduction, the disc generally becomes cooler and denser. These properties are qualitatively consistent with performed simulations in hot accretion flows. Moreover, the angular velocity increases with the magnitude of conduction, while the radial infall velocity decreases. The mass accretion rate onto the central object is reduced in the presence of thermal conduction. We found that the viscosity and thermal conduction have the opposite effects on the physical variables. Furthermore, the flow represents a transonic point that moves inward with the magnitude of conduction or viscosity.
Steady-state advective accretion flows in the presence of thermal conduction are studied. All three components of velocity in a spherical coordinates are considered and the flow displays both inflowing and outflowing regions according to our similarity solutions. Thermal conductivity provides latitudinal energy transport and so, the flow rotates more slowly and becomes hotter with increasing thermal conductivity coefficient. We also show that opening angle of the outflow region decreases as thermal conduction becomes stronger.
Previous works have clearly shown the existence of winds from black hole hot accretion flow and investigated their detailed properties. In extremely low accretion rate systems, the collisional mean-free path of electrons is large compared with the length-scale of the system, thus thermal conduction is dynamically important. When the magnetic field is present, the thermal conduction is anisotropic and energy transport is along magnetic field lines. In this paper, we study the effects of anisotropic thermal conduction on the wind production in hot accretion flows by performing two-dimensional ma…
We examine the effect of thermal conduction on the observational properties of a super critical hot magnetized flow. We obtained self-similar solution of a magnetized disc when the thermal conduction plays an important role. Follow of our first paper (Ghasemnezhad et al. 2012 (hereafter GKA12)) we have extended our solution on the observational appearance of the disc to show how physical condition such as thermal conduction, viscosity, and advection will change the observed luminosity of the disc, Continuous spectra and surface temperature of such discs was plotted. We apply the present model …
We explore the effects of anisotropic thermal conduction, anisotropic pressure, and magnetic field strength on the hot accretion flows around black holes by solving the axisymmetric, steady-state magnetohydrodynamic equations. The anisotropic pressure is known as a mechanism for transporting angular momentum in weakly collisional plasmas in hot accretion flows with extremely low mass accretion rates. However, anisotropic pressure does not extensively impact the transport of the angular momentum, it leads to shrinkage of the wind region. Our results show that the strength of the magnetic field …
We have explored the structure of hot magnetized accretion flow with thermal conduction. The importance of thermal conduction in hot accretion flows has been confirmed by observations of the hot gas surrounding Sgr $A^*$ and a few other nearby galactic nuclei. For a steady state structure of such accretion flows a set of self similar solutions are presented. In this paper, we have actually tried to re-check the solution presented by Abbassi et al. (2008) using a physical constrain. In this study we find that Eq 29 places a new constrain that limits answers presented by Abbassi et al. 2008. In …
Observations of the hot gas, which is surrounding Sgr A* and a few other nearby galactic nuclei, imply that mean free paths of electron and proton are comparable to gas capture radius. So, hot accretion flows likely proceed under week collision conditions. As a result thermal conduction by ions has a considerable contribution in transfer of the realized heat in accretion mechanisms. We study a 2D advective accretion disk bathed in a poloidal magnetic field of a central accretor in the presence of thermal conduction. We find self-similar solutions for an axisymmetric, rotating, steady, viscose-…
We simulate the evolution of cluster galaxies' hot interstellar medium (ISM) gas due to ram pressure and thermal conduction in the intracluster medium (ICM). At the density and temperature of the ICM, the mean free paths of ICM electrons are comparable to the sizes of galaxies, therefore electrons can efficiently transport heat due to thermal conduction from the hot ICM to the cooler ISM. Galaxies consisting of dark matter halos and hot gas coronae are embedded in an ICM-like `wind tunnel' in our simulations. In this paper, we assume that thermal conduction is isotropic and include the effects…
Since the collisional mean free path of charged particles in hot accretion flows can be significantly larger than the typical length-scale of the accretion flows, the gas pressure is anisotropic to magnetic field lines. For such a large collisional mean free path, the resistive dissipation can also play a key role in hot accretion flows. In this paper, we study the dynamics of resistive hot accretion flows in the presence of anisotropic pressure. We present a set of self-similar solutions where the flow variables are assumed to be a function only of radius. Our results show that the radial and…
The recent image of our galaxy's supermassive black hole Sgr A* derived from the 7 April 2017 data of the Event Horizon Telescope Collaboration shows multiple hot spots in its accretion disk. Using the analytical framework, we demonstrate that the observed hot spots may not be disjoint elements but causally linked components ("petals") of one rotating quasi-stationary macro-structure formed in the thermo-vorticial field within the accretion disk.
Black hole accretion flows can be divided into two broad classes: cold and hot. Cold accretion flows, which consist of cool optically thick gas, are found at relatively high mass accretion rates. Prominent examples are the standard thin disk, which occurs at a fraction of the Eddington mass accretion rate, and the slim disk at super-Eddington rates. These accretion flows are responsible for luminous systems such as active galactic nuclei radiating at or close to the Eddington luminosity and black hole X-ray binaries in the soft state. Hot accretion flows, the topic of this review, are virially…
NGC 3115 is the nearest galaxy hosting a billion solar mass black hole and is also a low-luminosity active galactic nucleus (LLAGN). X-ray observations of this LLAGN are able to spatially resolve the hot gas within the sphere of gravitational influence of the supermassive black hole. These observations make NGC 3115 an important testbed for black hole accretion theory in galactic nuclei since they constrain the outer boundary conditions of the hot accretion flow. We present a compilation of the multiwavelength spectral energy distribution (SED) of the nucleus of NGC 3115 from radio to X-rays. …
Two significant progresses have been made in the past years on our understanding of hot accretion flows. One is that only a small fraction of accretion flow available at the outer boundary can finally falls onto the black hole while most of them is lost in outflow. Another one is that electrons may directly receive a large fraction of the viscously dissipated energy in the accretion flow, i.e, $δ\sim 0.1-0.5$. The radiative efficiency of hot accretion flow when these two progresses are taken into account has not been systematically studied and is the subject of the present paper. We consider t…
Multiwavelength observations of Galactic black hole transients have opened a new path to understanding the physics of the innermost parts of the accretion flows. While the processes giving rise to their X-ray continuum have been studied extensively, the emission in the optical and infrared (OIR) energy bands was less investigated and remains poorly understood. The standard accretion disc, which may contribute to the flux at these wavelengths, is not capable of explaining a number of observables: the infrared excesses, fast OIR variability and a complicated correlation with the X-rays. It was s…
We solve the two-dimensional hydrodynamic equations of hot accretion flow in the presence of the thermal conduction. The flow is assumed to be in steady-state and axisymmetric, and self-similar approximation is adopted in the radial direction. In this hydrodynamic study, we consider the viscous stress tensor to mimic the effects of the magnetorotational instability for driving angular momentum. We impose the physical boundary conditions at both the rotation axis and the equatorial plane and obtain the solutions in the full $ r-θ$ space. We have found that thermal conduction is indispensable te…
A pair of giant gamma-ray bubbles have been revealed by the {\it Fermi} LAT. In this paper we investigate their formation mechanism. Observations have indicated that the activity of the supermassive black hole located at the Galactic center, Sgr A*, was much stronger than the present time. Specifically, one possibility is that while Sgr A* was also in the hot accretion regime, the accretion rate should be $10^3-10^4$ times higher during the past $\sim 10^7$ yr. On the other hand, recent MHD numerical simulations of hot accretion flows have unambiguously shown the existence of strong winds and …
We perform two-dimensional simulations to study how the wind strength changes with accretion rate. We take into account bremsstrahlung, synchrotron radiation and the Comptonization. We find that when the accretion rate is low, radiative cooling is not important, the accretion flow is hot accretion flow. For the hot accretion flow, wind is very strong. The mass flux of wind can be $\sim 50\%$ of the mass inflow rate. When the accretion rate increases to a value at which radiative cooling rate is roughly equal to or slightly larger than viscous heating rate, cold clumps can form around the equat…
We study the effects of accretion environment (gas density, temperature and angular momentum) at large radii ($\sim 10$pc) on luminosity of hot accretion flows. The radiative feedback effects from the accretion flow on the accretion environment are also self-consistently taken into account. We find that the slowly rotating flows at large radii can significantly deviate from Bondi accretion when radiation heating and cooling are considered. We further find that when the temperature of environment gas is low (e.g. $T=2\times 10^7$K), the luminosity of hot accretion flows is high. When the temper…
Using 3D high-resolution hydrodynamic simulations, tracking both electrons and ions, we study the effects of turbulence and conduction in the hot intracluster medium. We show how the power spectrum of the gas density perturbations can accurately constrain both processes. The characteristic amplitude of density perturbations is linearly related to the strength of turbulence, i.e. the 3D Mach number, as A(k)_max = 0.25 M. The slope of A(k) in turn reflects the level of conduction. In a non-conductive medium, subsonic stirring motions advect density with a similar nearly Kolmogorov cascade. Incre…
We study slowly rotating accretion flow at parsec and sub-parsec scale irradiated by a low luminosity active galactic nuclei. We take into account the Compton heating, photoionization heating by the central X-rays. The bremsstrahlung cooling, recombination and line cooling are also included. We find that due to the Compton heating, wind can be thermally driven. The power of wind is in the range $(10^{-6}-10^{-3}) L_{\rm Edd}$, with $L_{\rm Edd}$ being the Eddington luminosity. The mass flux of wind is in the range $(0.01-1) \dot M_{\rm Edd}$ ($\dot M_{\rm Edd}= L_{\rm Edd}/0.1c^2$ is the Eddin…
We simulate anisotropic thermal conduction between the intracluster medium (ICM) and the hot coronal interstellar medium (ISM) gas in cluster galaxies. In the earlier Paper I (Vijayaraghavan & Sarazin 2017a), we simulated the evaporation of the hot ISM due to isotropic (possibly saturated) conduction between the ISM and ICM. We found that hot coronae evaporate on $\sim 10^2$ Myr timescales, significantly shorter than the $\sim 10^3$ Myr gas loss times due to ram pressure stripping. No tails of stripped gas are formed. This is in tension with the observed ubiquity and implied longevity of compa…
Can Isotropic Thermal Conduction Heat One of the Hottest Cool Cores?
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research（国际理论科学中心，塔塔基础研究所）；Department of Theoretical Physics and Astrophysics, Faculty of Science, Masaryk University（马萨里克大学理学院理论与天体物理学系）
For most of their lifetime, super-massive black holes (SMBHs) commonly found in galactic nuclei obtain mass from the ambient at a rate well below the Eddington limit, which is mediated by a radiatively inefficient, hot accretion flow. Both theory and numerical simulations predict that a strong wind must exist in such hot accretion flows. The wind is of special interest not only because it is an indispensable ingredient of accretion, but perhaps more importantly, it is believed to play a crucial role in the evolution of the host galaxy via the so-called kinetic mode AGN feedback. Observational …
We propose a two-temperature radial inflow-outflow model near Sgr A* with self-consistent feeding and conduction. Stellar winds from individual stars are considered to find the rates of mass injection and energy injection. These source terms help to partially eliminate the boundary conditions on the inflow. Electron thermal conduction is crucial for inhibiting the accretion. Energy diffuses out from several gravitational radii, unbinding more gas at several arcseconds and limiting the accretion rate to <1% of Bondi rate. We successfully fit the X-Ray surface brightness profile found from the e…
We propose a 2-temperature radial dynamical model of plasma flow near Sgr A* and fit the bremsstrahlung emission to extensive quiescent X-Ray Chandra data. The model extends from several arcseconds to black hole (BH) gravitational radius, describing the outer accretion flow together with the infalling region. The model incorporates electron heat conduction, relativistic heat capacity of particles and feeding by stellar winds. Stellar winds from each star are considered separately as sources of mass, momentum and energy. Self-consistent search for the stagnation and sonic points is performed. M…
We investigate state transitions in black hole X-ray binaries through different parameters by using two-dimensional axisymmetric hydrodynamical simulation method. For radiative cooling in hot accretion flow, we take into account the bremsstrahlung, synchrotron and synchrotron-self Comptonization self-consistently in the dynamics. Our main result is that the state transitions occur when the accretion rate reaches a critical value $\dot M \sim 3α \dot M_{\rm Edd}$, above which cold and dense clumpy/filamentary structures are formed, embedded within the hot gas. We argued this mode likely corresp…
An important parameter in the theory of hot accretion flows around black holes is $δ$, which describes the fraction of ``viscously'' dissipated energy in the accretion flow that goes directly into heating electrons. For a given mass accretion rate, the radiative efficiency of a hot accretion flow is determined by $δ$. Unfortunately, the value of $δ$ is hard to determine from first principles. The recent Event Horizon Telescope Collaboration (EHTC) results on M87* and Sgr A* provide us with a different way of constraining $δ$. By combining the mass accretion rates in M87* and Sgr A* estimated b…
We investigate the dependency of the inflow-wind structure of the hot accretion flow on the kinematic viscosity coefficient. In this regard, we propose a model for the kinematic viscosity coefficient to mimic the behavior of the magnetorotational instability and would be maximal at the rotation axis. Then, we compare our model with two other prescriptions from numerical simulations of the accretion flow. We solve two-dimensional hydrodynamic equations of hot accretion flows in the presence of the thermal conduction. The self-similar approach is also adopted in the radial direction. We calculat…
The temperature of hot accretion flows around black holes is sufficiently high for the ignition of nuclear reactions. This is potentially an important nucleosynthesis mechanism in the universe. As the first step in studying this problem, we need to measure physical quantities such as density and temperature of the accretion flow. In usual studies of the hot accretion flow, viscous dissipation is considered to be the only heating mechanism, while the heating caused by nuclear reactions is not considered. In this paper, we investigate whether the energy generation rate of nuclear reaction is imp…
Context. Many low-redshift active galactic nuclei harbor a supermassive black hole accreting matter at low or medium rates. At such rates, the accretion flow usually consists of a cold optically thick disk, plus a hot, low density, collisionless corona. In the latter component, charged particles can be accelerated to high energies by various mechanisms. Aims. We aim to investigate, in detail, nonthermal processes in hot accretion flows onto supermassive black holes, covering a wide range of accretion rates and luminosities. Methods. We developed a model consisting of a thin Shakura-Sunyaev dis…
We have studied the effects of thermal conduction on the structure of viscous and resistive advection-dominated accretion flows (ADAFs). The importance of thermal conduction on hot accretion flow is confirmed by observations of hot gas that surrounds Sgr A$^*$ and a few other nearby galactic nuclei. In this research, thermal conduction is studied by a saturated form of it, as is appropriated for weakly-collisional systems. It is assumed the viscosity and the magnetic diffusivity are due to turbulence and dissipation in the flow. The viscosity also is due to angular momentum transport. Here, th…
We present global radiation GRMHD simulations of strongly magnetized accretion onto a spinning, stellar mass black hole at sub-Eddington rates. Using a frequency-dependent Monte Carlo procedure for Compton scattering, we self-consistently evolve a two-temperature description of the ion-electron fluid and its radiation field. For an Eddington ratio $L/L_{\rm Edd} \gtrsim 10^{-3}$, the emergent spectrum forms an apparent power law shape from thermal Comptonization up to a cutoff at $\simeq 100$ keV, characteristic of that seen in the hard spectral states of black hole X-ray binary systems. At th…
Radiatively inefficient, hot accretion flows are widely considered as a relevant accretion mode in low-luminosity AGNs. We study spectral formation in such flows using a refined model with a fully general relativistic description of both the radiative (leptonic and hadronic) and hydrodynamic processes, as well as with an exact treatment of global Comptonization. We find that the X-ray spectral index--Eddington ratio anticorrelation as well as the cut-off energy measured in the best-studied objects favor accretion flows with rather strong magnetic field and with a weak direct heating of electro…
How many fraction of gas available at the outer boundary can finally fall onto the black hole is an important question. It determines the observational appearance of accretion flows, and is also related with the evolution of black hole mass and spin. Previous two-dimensional hydrodynamical simulations of hot accretion flows find that the flow is convectively unstable because of its inward increase of entropy. As a result, the mass accretion rate decreases inward, i.e., only a small fraction of accretion gas can fall onto the black hole, while the rest circulates in the convective eddies or los…
Numerical simulations of cold clumps in the hot accretion flows around black holes
Xiamen University（厦门大学）；Shanghai Astronomical Observatory, Chinese Academy of Sciences（中国科学院上海天文台）；Shanghai Normal University（上海师范大学）；Chongqing University（重庆大学）
The luminosity of X-ray pulsars powered by accretion onto magnetized neutron stars covers a wide range over a few orders of magnitude. The brightest X-ray pulsars recently discovered as pulsating ultraluminous X-ray sources reach accretion luminosity above $10^{40}\,{\rm erg\,s^{-1}}$ which exceeds the Eddington value more than by a factor of ten. Most of the energy is released within small regions in the vicinity of magnetic poles of accreting neutron star - in accretion columns. Because of the extreme energy release within a small volume accretion columns of bright X-ray pulsars are ones of …
We present a magneto-hydrodynamic model developed for investigations of advective non-stationary, asymmetric Keplerian accretion disks in the normal magnetic field. The introduced model allows us to trace the evolution in different fixed moments and to get detailed description of the self-structuring of the disk. We have introduced "meeting coefficients" that define the feedback. It determines the impact from nonlinear effects have over the structure of the flow. We have obtained solutions for the radial structure of the disk for two crucial moments of its evolution.
Observations of black hole X-ray binaries and active galactic nuclei indicate that the accretion flows around black holes are composed of hot and cold gas, which have been theoretically described in terms of either a hot geometrically thick corona lying above and below a cold geometrically thin disk or an inner advection dominated accretion flow connected to an outer thin disk. This article reviews the accretion flows around black holes, with an emphasis on the physics that determines the configuration of hot and cold accreting gas, and how the configuration varies with the accretion rate and …
We investigate acceleration and propagation processes of high-energy particles inside hot accretion flows. The magnetorotational instability (MRI) creates turbulence inside accretion flows, which triggers magnetic reconnection and may produce non-thermal particles. They can be further accelerated stochastically by the turbulence. To probe the properties of such relativistic particles, we perform magnetohydrodynamic simulations to obtain the turbulent fields generated by the MRI, and calculate orbits of the high-energy particles using snapshot data of the MRI turbulence. We find that the partic…
Hydrodynamics and magnetohydrodynamic simulations of hot accretion flow have indicated that there is an inward decreasing of mass accretion rate with decreasing radius. Consequently, we have a flatter density profile ($ρ\propto r^{-p}$ with $p\propto 1.5-s$ in the case of $\dot{M}\propto r^{s}$, $0 \leq s<1$) compared to the case of a constant accretion rate (($ρ\propto r^{-\frac{3}{2}}$). In order to describe this behavior two models have been proposed: inflow-outflow solution and convection-dominated accretion flows. We have studied the properties of a hot accretion flow in the presence of c…
Previous numerical simulations have shown that strong winds can be produced in the hot accretion flows around black holes. Most of those studies focus only on the region close to the central black hole, therefore it is unclear whether the wind production stops at large radii around Bondi radius. Bu et al. 2016 studied the hot accretion flow around the Bondi radius in the presence of nuclear star gravity. They find that when the nuclear stars gravity is important/comparable to the black hole gravity, winds can not be produced around the Bondi radius. However, for some galaxies, the nuclear star…
We study the high energy emission of two active galactic nuclei (AGN), NGC 4258 and NGC 7213. We directly apply the general-relativistic (GR) hot flow model, kerrflow, to the archival BeppoSAX, NuSTAR and Suzaku observations of these objects. Most of these data sets indicate that about 10-20 per cent of the accretion power is used for the direct heating of electrons, however, we find also indications for significant changes of the electron heating efficiency in some cases. Furthermore, all these X-ray data sets indicate rather strongly magnetized flows, with the magnetic field close to the equ…
3D MHD simulation of accretion onto neutron stars have shown in the last few years that the footprint (hotspot) of the accretion flow changes with time. Two different kinds of accretion, namely the funnel flow and the equatorial accretion produced by instabilities at the inner disk, produce different kinds of motion of the hotspot. The funnel flow produces hotspots that move around the magnetic pole, while instabilities produce other hotspots that appear randomly and move along the equator or slightly above. The angular velocities of the two hotspots are different, the equatorial one being hig…
The magnitude of the viscosity and magnetic field parameters in hot accretion flows is investigated in low luminosity active galactic nuclei (LLAGNs). Theoretical studies show that a geometrically thin, optically thick disk is truncated at mass accretion rates less than a critical value by mass evaporated vertically from the disk to the corona, with the truncated region replaced by an advection dominated accretion flow (ADAF). The critical accretion rate for such a truncation is a function of the viscosity and magnetic field. Observations of X-ray photon indices and spectral fits of a number o…
Optically thin accretion plasmas can reach ion temperatures $T_{\rm i} \geq 10^{10}$K and thus trigger nuclear reactions. Using a large nuclear interactions network, we studied the radial evolution of the chemical composition of the accretion flow toward the black hole and computed the emissivity in nuclear $γ$-ray lines. In the advection dominated accretion flow (ADAF) regime, CNO and heavier nuclei are destroyed before reaching the last stable orbit. The overall luminosity in the de-excitation lines for a solar composition of plasma can be as high as few times $10^{-5}$ the accretion luminos…
Both analytical and numerical works show that magnetic reconnection must occur in hot accretion flows. This process will effectively heat and accelerate electrons. In this paper we use the numerical hybrid simulation of magnetic reconnection plus test-electron method to investigate the electron acceleration and heating due to magnetic reconnection in hot accretion flows. We consider fiducial values of density, temperature, and magnetic parameter $β_e$ (defined as the ratio of the electron pressure to the magnetic pressure) of the accretion flow as $n_{0} \sim 10^{6} {\rm cm^{-3}}$, $T_{e}^0\si…
Observations indicate that wind can be generated in hot accretion flow. By performing numerical simulations, Yuan et al. studied the detailed properties of wind generated from weakly magnetized accretion flow. However, properties of wind generated from strongly magnetized hot accretion flow have not been studied. In this paper, we study the properties of wind generated from both weakly and strongly magnetized accretion flow. We focus on how the magnetic field strength affects the wind properties. We solve time-steady two-dimensional magnetohydrodynamic (MHD) equations of black hole accretion i…
Numerical simulations of hot accretion flow have shown that the mass accretion rate decreases with decreasing radius; consequently the density profile of accretion flow becomes flatter compared to the case of a constant accretion rate. This result has important theoretical and observational implications. However, because of technical difficulties, the radial dynamic range in almost all previous simulations usually spans at most two orders of magnitude. This small dynamical range, combined with the effects of boundary conditions, makes the simulation results suspectable. Especially, the radial …
How many fraction of gas available at the outer boundary can finally fall onto the black hole is an important question. It determines the observational appearance of accretion flows, and is also related with the evolution of black hole mass and spin. Previous two-dimensional hydrodynamical simulations of hot accretion flows find that the flow is convectively unstable because of its inward increase of entropy. As a result, the mass accretion rate decreases inward, i.e., only a small fraction of accretion gas can fall onto the black hole, while the rest circulates in the convective eddies or los…
We present a coherent timing analysis of the 2003 outburst of the accreting millisecond pulsar XTE J1807-294. We find an upper limit for the spin frequency derivative of 5E-14 Hz/s. The sinusoidal fractional amplitudes of the pulsations are the highest observed among the accreting millisecond pulsars and can reach values of up to 27% (2.5-30 keV). The pulse arrival time residuals of the fundamental follow a linear anti-correlation with the fractional amplitudes that suggests hot spot motion over the surface of the neutron star both in longitude and latitude. An anti-correlation between residua…
We have developed an improved model of X-ray emission from optically thin, two-temperature accretion flows, \texttt{kerrflow}, using an exact Monte Carlo treatment of global Comptonization as well as with a fully general relativistic description of both the radiative and hydrodynamic processes. It also includes pion-decay electrons, whose synchrotron emission dominates the seed photons yield at high accretion rates in flows around supermassive black holes. We consider in detail the dependence of the model spectra on the black hole spin, the electron heating efficiency, the plasma magnetization…
