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Register a new userElectron and Proton Heating in Transrelativistic Guide Field Reconnection
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Michael E. Rowan n Harvard
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The plasma in low-luminosity accretion flows, such as the one around the black hole at the center of M87 or Sgr A* at our Galactic Center, is expected to be collisioness and two-temperature, with protons hotter than electrons. Here, particle heating is expected to be controlled by magnetic reconnection in the transrelativistic regime $sigma_{w}sim 0.1$-$1$, where the magnetization $sigma_{w}$ is the ratio of magnetic energy density to plasma enthalpy density. By means of large-scale 2D particle-in-cell simulations, we explore for a fiducial $sigma_w=0.1$ how the dissipated magnetic energy gets partitioned between electrons and protons, as a function of $beta_{rm i}$ (the ratio of proton thermal pressure to magnetic pressure) and of the strength of a guide field $B_{rm g}$ perpendicular to the reversing field $B_0$. At low $beta_{rm i};(lesssim 0.1)$, we find that the fraction of initial magnetic energy per particle converted into electron irreversible heat is nearly independent of $B_{rm g}/B_0$, whereas protons get heated much less with increasing $B_{rm g}/B_0$. As a result, for large $B_{rm g} /B_{0}$, electrons receive the overwhelming majority of irreversible particle heating (${sim}93%$ for $B_{rm g} /B_{0}=6$). This is significantly different than the antiparallel case $B_{rm g}/B_0=0$, in which electron irreversible heating accounts for only ${sim}18%$ of the total particle heating. At $beta_{rm i} sim 2$, when both species start already relativistically hot (for our fiducial $sigma_w=0.1$), electrons and protons each receive ${sim}50%$ of the irreversible particle heating, regardless of the guide field strength. Our results provide important insights into the plasma physics of electron and proton heating in hot accretion flows around supermassive black holes.
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Hot collisionless accretion flows, such as the one in Sgr A$^{*}$ at our Galactic center, provide a unique setting for the investigation of magnetic reconnection. Here, protons are non-relativistic while electrons can be ultra-relativistic. By means of two-dimensional particle-in-cell simulations, we investigate electron and proton heating in the outflows of trans-relativistic reconnection (i.e., $sigma_wsim 0.1-1$, where the magnetization $sigma_w$ is the ratio of magnetic energy density to enthalpy density). For both electrons and protons, we find that heating at high $beta_{rm i}$ (here, $beta_{rm i}$ is the ratio of proton thermal pressure to magnetic pressure) is dominated by adiabatic compression (adiabatic heating), while at low $beta_{rm i}$ it is accompanied by a genuine increase in entropy (irreversible heating). For our fiducial $sigma_w=0.1$, the irreversible heating efficiency at $beta_{rm i}lesssim 1$ is nearly independent of the electron-to-proton temperature ratio $T_{rm e}/T_{rm i}$ (which we vary from $0.1$ up to $1$), and it asymptotes to $sim 2%$ of the inflowing magnetic energy in the low-$beta_{rm i}$ limit. Protons are heated more efficiently than electrons at low and moderate $beta_{rm i}$ (by a factor of $sim7$), whereas the electron and proton heating efficiencies become comparable at $beta_{rm i}sim 2$ if $T_{rm e}/T_{rm i}=1$, when both species start already relativistically hot. We find comparable heating efficiencies between the two species also in the limit of relativistic reconnection ($sigma_wgtrsim 1$). Our results have important implications for the two-temperature nature of collisionless accretion flows, and may provide the sub-grid physics needed in general relativistic MHD simulations.
We report electrostatic Debye-scale turbulence developing within the diffusion region of asymmetric magnetopause reconnection with moderate guide field using observations by the Magnetospheric Multiscale (MMS) mission. We show that Buneman waves and beam modes cause efficient and fast thermalization of the reconnection electron jet by irreversible phase mixing, during which the jet kinetic energy is transferred into thermal energy. Our results show that the reconnection diffusion region in the presence of a moderate guide field is highly turbulent, and that electrostatic turbulence plays an important role in electron heating.
We analyze the development and influence of turbulence in three-dimensional particle-in-cell simulations of guide-field magnetic reconnection at the magnetopause with parameters based on observations of an electron diffusion region by the Magnetospheric Multiscale (MMS) mission. Along the separatrices the turbulence is a variant of the lower hybrid drift instability (LHDI) that produces electric field fluctuations with amplitudes much greater than the reconnection electric field. The turbulence controls the scale length of the density and current profiles while enabling significant transport across the magnetopause despite the electrons remaining frozen-in to the magnetic field. Near the X-line the electrons are not frozen-in and the turbulence, which differs from the LHDI, makes a significant net contribution to the generalized Ohms law through an anomalous viscosity. The characteristics of the turbulence and associated particle transport are consistent with fluctuation amplitudes in the MMS observations. However, for this event the simulations suggest that the MMS spacecraft were not close enough to the core of the electron diffusion region to identify the region where anomalous viscosity is important.
Particle-in-Cell simulations of collisionless magnetic reconnection with a guide field reveal for the first time the three dimensional features of the low density regions along the magnetic reconnection separatrices, the so-called cavities. It is found that structures with further lower density develop within the cavities. Because their appearance is similar to the rib shape, these formations are here called low density ribs. Their location remains approximately fixed in time and their density progressively decreases, as electron currents along the cavities evacuate them. They develop along the magnetic field lines and are supported by a strong perpendicular electric field that oscillates in space. In addition, bipolar parallel electric field structures form as isolated spheres between the cavities and the outflow plasma, along the direction of the low density ribs and of magnetic field lines.
Works of D. Tsiklauri, T. Haruki, Phys. of Plasmas, 15, 102902 (2008) and D. Tsiklauri and T. Haruki, Phys. of Plasmas, 14, 112905, (2007) are extended by inclusion of the out-of-plane magnetic (guide) field. In particular, magnetic reconnection during collisionless, stressed $X$-point collapse for varying out-of-plane guide-fields is studied using a kinetic, 2.5D, fully electromagnetic, relativistic particle-in-cell numerical code. Cases for both open and closed boundary conditions are investigated, where magnetic flux and particles are lost and conserved respectively. It is found that reconnection rates and out-of-plane currents in the $X$-point increase more rapidly and peak sooner in the closed boundary case, but higher values are reached in the open boundary case. The normalized reconnection rate is fast: 0.10-0.25. In the open boundary case an increase of guide-field yields later onsets in the reconnection peak rates, while in the closed boundary case initial peak rates occur sooner but are suppressed. The reconnection current increases for low guide-fields but then decreases similarly. In the open boundary case, for guide-fields of the order of the in-plane magnetic field, the generation of electron vortices occurs. Possible causes of the vortex generation, based on the flow of particles in the diffusion region and localized plasma heating, are discussed. Before peak reconnection onset, oscillations in the out-of-plane electric field at the $X$-point are found, ranging in frequency from approximately 1 to 2 $omega_{pe}$ and coinciding with oscillatory reconnection. These oscillations are found to be part of a larger wave pattern. Mapping the out-of-plane electric field over time and applying 2D Fourier transforms reveals that the waves predominantly correspond to the ordinary mode and may correspond to observable radio waves such as solar radio burst fine structure spikes.
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