Resistive Magnetohydrodynamics Research Articles

Kinetic-magnetohydrodynamic hybrid simulation of infernal modes in circular tokamak plasmas with effects of kinetic thermal ions

Effects of the kinetic thermal ions (KTIs) on ideal infernal modes and resistive infernal modes have been investigated by using magnetohydrodynamic (MHD) simulation without KTIs and kinetic-MHD hybrid simulation with KTIs. For the ideal infernal modes, the pressure profile is significantly flattened at the saturated state for both the models with and without the KTIs. As the beta value decreases, the ideal infernal modes are stabilized while the resistive infernal modes are still unstable. For the resistive infernal modes, while the saturated pressure profile is significantly flattened in the MHD simulation without KTIs, the pressure profile is not flattened at the saturated state in the kinetic-MHD hybrid simulation with KTIs. The suppression of the saturation level by the effects of the KTIs results from the phase mismatch between the radial velocity and perturbed pressure mode structures. This indicates that KTIs play an essential role for the suppression of pressure profile flattening due to slowly growing resistive MHD instabilities.

Probabilistic locked mode predictor in the presence of a resistive wall and finite island saturation in tokamaks

We present a framework for estimating the probability of locking to an error field in a rotating tokamak plasma. This leverages machine learning methods trained on data from a mode-locking model, including an error field, resistive magnetohydrodynamics modeling of the plasma, a resistive wall, and an external vacuum region, leading to a fifth-order ordinary differential equation (ODE) system. It is an extension of the model without a resistive wall introduced by Akçay et al. [Phys. Plasmas 28, 082106 (2021)]. Tearing mode saturation by a finite island width is also modeled. We vary three pairs of control parameters in our studies: the momentum source plus either the error field, the tearing stability index, or the island saturation term. The order parameters are the time-asymptotic values of the five ODE variables. Normalization of them reduces the system to 2D and facilitates the classification into locked (L) or unlocked (U) states, as illustrated by Akçay et al., [Phys. Plasmas 28, 082106 (2021)]. This classification splits the control space into three regions: L̂, with only L states; Û, with only U states; and a hysteresis (hysteretic) region Ĥ, with both L and U states. In regions L̂ and Û, the cubic equation of torque balance yields one real root. Region Ĥ has three roots, allowing bifurcations between the L and U states. The classification of the ODE solutions into L/U is used to estimate the locking probability, conditional on the pair of the control parameters, using a neural network. We also explore estimating the locking probability for a sparse dataset, using a transfer learning method based on a dense model dataset.

Global solutions of two‐dimensional inviscid and resistive magnetohydrodynamics system near an equilibrium

We investigate the global existence of classical solutions for two‐dimensional incompressible, inviscid, and resistive magnetohydrodynamics (MHD) system. Assuming that the initial magnetic field is close to an equilibrium state of constant magnetic vorticity, the global existence result could be obtained using a time‐weighted energy estimate.

A divergence-free hybrid finite volume / finite element scheme for the incompressible MHD equations based on compatible finite element spaces with a posteriori limiting

We present a novel semi-implicit hybrid finite volume/finite element (FV/FE) method for the equations of viscous and resistive incompressible magnetohydrodynamics (MHD). The scheme preserves the divergence-free property of the magnetic field exactly on the discrete level, is second order accurate in space, and is stable in the limit of vanishing viscosity and resistivity. In particular, the MHD system is first split into a fluid and a magnetic subsystem. The former is then addressed via a semi-implicit hybrid FV/FE method. The latter belongs to a class of generalized advection-diffusion problems, for which we propose a novel semi-implicit scheme based on compatible finite element spaces and interpolation-contraction operators. In the case of vanishing resistivity, the new algorithm avoids the solution of a linear system at each time step, thanks to the framework of physical degrees of freedom, which allow to express the exterior derivative as the incidence matrix of an appropriate refinement of the original mesh. Regarding the timestepping, a local fully-discrete Lax-Wendroff-type evolution is proposed as an alternative to the classical semi-discrete method of lines. In order to suppress spurious oscillations in the presence of discontinuities or steep gradients in the magnetic field, a new simple but efficient a posteriori limiting procedure based on a nonlinear artificial resistivity is introduced. The novel methodology is validated with several test cases in two and three space dimensions using unstructured simplex meshes.

Numerical model of restrikes in gliding arc discharges

Abstract Direct current (DC) electric arcs are of particular interest because they can produce large volumes of thermal plasmas with controlled energy deposition. When such discharges are applied in a gas flow, convection displaces the top of the arc downstream while the arc roots remain attached to the electrodes, thus increasing the length of the arc over time. However, this growth is limited by a restrike phenomenon, which starts from streamers appearing in high electric field regions and shortcutting the long, stretched electric arc. From a numerical point of view, DC arcs can be efficiently simulated with a resistive magneto-hydrodynamics (MHD) model, with numerical requirements in terms of spatial and temporal discretization that are compatible with classic fluid dynamics and combustion simulations. However, arc restrikes rely on the propagation of streamer discharges that are highly non-neutral phenomena, whereas classical MHD assumes neutrality. To tackle this problem, we propose in this paper a model of restrike that can be used in an MHD approach. After describing the ideas of the model, we perform a parametric study of the input parameters to examine its influence on the discharge dynamics.

Relativistic shocks in conductive media

Context. Relativistic shocks are present in all high-energy astrophysical processes involving relativistic plasma outflows interacting with their ambient medium. While they are well understood in the context of relativistic hydrodynamics and ideal magnetohydrodynamics (MHD), there is a limited understanding of the properties related to their propagation in media characterized by finite electrical conductivity. Aims. This work presents a systematic method for the derivation and solution of the jump conditions for relativistic shocks propagating in MHD media with finite electrical conductivity. This method is applied to the numerical solution of the Riemann problem and the determination of the conditions inside the blastwave that is formed when ultrarelativistic magnetized ejecta interact with the circumburst medium during a gamma-ray burst. Methods. We derived the covariant relations expressing the jump conditions in a frame-independent manner. The resulting algebraic equations expressing the Rankine-Hugoniot conditions in the propagation medium’s frame were then solved numerically. A variable adiabatic index equation of state was used in order to obtain a realistic description of the post-shock fluid’s thermodynamics. This method was then employed for the solution of the Riemann problem for the case of a forward and a reverse shock, both of which form during the interaction of a gamma-ray burst ejecta with the circumburst medium. This allowed us to determine the kinematics of the resulting blastwave and the dynamical conditions in its interior. Results. Our solutions clearly depict the impact of the plasma’s electrical conductivity in the properties of the post-shock medium. Two characteristic regimes are identified with respect to the value of a dimensionless parameter that has a linear dependence on the conductivity. For small values of this parameter, the shock affects only the hydrodynamic properties of the propagation medium and leaves its electromagnetic field unaffected. No current layer forms in the shock front; thus, we refer to this as the current-free regime. For large values of this parameter, the ideal MHD regime has been retrieved. We also show that the assumption of a finite electrical conductivity can lead to higher efficiencies in the conversion of the ejecta energy into thermal energy of the blastwave through the reverse shock. The theory developed in this work can be applied to the construction of Riemann solvers for resistive relativistic MHD (RR4MHD).

On the weak solutions for the MHD systems with controllable total energy and cross helicity

In this paper, we prove the non-uniqueness of three-dimensional magneto-hydrodynamic (MHD) system in C([0,T];L2(T3)) for any initial data in Hβ¯(T3) (β¯>0), by exhibiting that the total energy and the cross helicity can be controlled in a given positive time interval. Our results extend the non-uniqueness results of the ideal MHD system to the viscous and resistive MHD system. Different from the ideal MHD system, the dissipative effect in the viscous and resistive MHD system prevents the nonlinear term from balancing the stress error (R˚q,M˚q) as doing in [4]. We introduce the box flows and construct the perturbation consisting in seven different kinds of flows in convex integral scheme, which ensures that the iteration works and yields the non-uniqueness.

Global exact controllability of the viscous and resistive MHD system in a rectangle thanks to the lateral sides and to distributed phantom forces

We consider the 2-D incompressible viscous and resistive magnetohydrodynamics (MHD) system in a rectangle, with controls on the lateral sides. The velocity satisfies Dirichlet boundary conditions, while the magnetic field follows perfectly conducting wall boundary conditions on the remaining, uncontrolled part of the boundary. We extend the small-time global exact null controllability result of Coron et al. in [Ann PDE 5(2):1-49, 2019] from Navier-Stokes equations to MHD equations, with a little help of distributed phantom forces, which can be chosen arbitrarily small in any given Sobolev spaces. Our analysis relies on Coron’s return method, the well-prepared dissipation method, long-time nonlinear Cauchy-Kovalevskaya estimates and Badra’s local exact controllability result.

Resistive instabilities in toroidal anisotropic plasmas

Resistive singular layer equations are developed by applying the magnetohydrodynamic (MHD) model to toroidal anisotropic plasmas. This work extends the previous ideal MHD theory [Shi et al. Phys. Plasmas 23, 082121 (2016)] to the resistive case. These layer equations can be used to investigate resistive localized MHD instabilities, such as tearing instability and resistive interchange instability. Compared to existing resistive theory [Johnson and Hastie, Phys. Fluids 31, 1609 (1988)], our model includes plasma compressibility, allowing for a study of the coupling between parallel motion to perpendicular one, which is known as the apparent mass effect. In addition, these obtained equations are valid for low n modes, where n is the toroidal mode number. The dispersion relation is derived in a reduced model. We find that the anisotropic pressure effect (when p⊥ > p‖) not only increases the stable threshold of the resistive interchange mode but also raises the critical value Δc of the tearing mode stability index Δ′, which represents the logarithmic jump of the radial magnetic field perturbation across the rational surface. This discovery holds significant practical implications for mitigating neoclassical tearing modes in high confinement plasmas, particularly those characterized by a low aspect ratio (such as spherical tokamaks) or low magnetic shear (as designed in ITER hybrid scenarios). However, it enhances the growth rate of the tearing mode in a low growth rate region, where p‖ and p⊥ denote the pressure components parallel and perpendicular to the magnetic fields, respectively.

Effect of the isotope mass on pedestal structure, transport and stability in D, D/T and T plasmas at similar β N and gas rate in JET-ILW type I ELMy H-modes

The work describes the pedestal structure, transport and stability in an effective mass (A eff) scan from pure deuterium to pure tritium plasmas using a type I ELMy H-mode dataset in which key parameters that affect the pedestal behaviour (normalized pressure, ratio of the separatrix density to the pedestal density, pedestal ion Larmor radius, pedestal collisionality and rotation) are kept as constant as possible. Experimental results show a significant increase of the density at the pedestal top with increasing A eff, a modest reduction in the temperature and an increase in the pressure. The variations in the pedestal heights are mainly due to a change in the pedestal gradients while only small differences are observed in the pedestal width. A clear increase in the pedestal density and pressure gradients are observed from deuterium to tritium. The experimental results suggest a reduction of the pedestal inter-edge localized mode (inter-ELM) transport from deuterium to tritium. The reduction is likely in the pedestal inter-ELM particle transport, as suggested by the clear increase of the pedestal density gradients. The experimental results suggest also a possible reduction of the pedestal inter-ELM heat transport, however, the large experimental uncertainties do not allow conclusive claims on the heat diffusivity. The clear experimental reduction of η e (the ratio between density and temperature gradient lengths) in the middle/top of the pedestal with increasing A eff suggests that there may be a link between increasing A eff and the reduction of electron scale turbulent transport. From the modelling point of view, an initial characterization of the behaviour of pedestal microinstabilities shows that the tritium plasma is characterized by growth rates lower than the deuterium plasmas. The pedestal stability of peeling-ballooning modes is assessed with both ideal and resistive magnetohydrodynamics (MHD). No significant effect of the isotope mass on the pedestal stability is observed using ideal MHD. Instead, resistive MHD shows a clear increase of the stability with increasing isotope mass. The resistive MHD results are in reasonable agreement with the experimental results of the normalized pedestal pressure gradient. The experimental and modelling results suggest that the main candidates to explain the change in the pedestal are a reduction in the inter-ELM transport and an improvement of the pedestal stability from deuterium to tritium.

Magnetically threaded accretion disks in resistive magnetohydrodynamic simulations and asymptotic expansion

Aims. A realistic model of magnetic linkage between a central object and its accretion disk is a prerequisite for understanding the spin history of stars and stellar remnants. To this end, we aim to provide an analytic model in agreement with magnetohydrodynamic (MHD) simulations. Methods. For the first time, we wrote a full set of stationary asymptotic expansion equations of a thin magnetic accretion disk, including the induction and energy equations. We also performed a resistive MHD simulation of an accretion disk around a star endowed with a magnetic dipole, using the publicly available code PLUTO. We compared the analytical results with the numerical solutions, and discussed the results in the context of previous solutions of the induction equation describing the star-disk magnetospheric interaction. Results. We found that the magnetic field threading the disk is suppressed by orders of magnitude inside thin disks, so the presence of the stellar magnetic field does not strongly affect the velocity field, nor the density profile inside the disk. Density and velocity fields found in the MHD simulations match the radial and vertical profiles of the analytic solution. Qualitatively, the MHD simulations result in an internal magnetic field similar to the solutions previously obtained by solving the induction equation in the disk alone. However, the magnetic field configuration is quantitatively affected by magnetic field inflation outside the disk; this is reflected in the net torque. The torque on the star is an order of magnitude larger in the magnetic than in the non-magnetic case. Spin-up of the star occurs on a timescale comparable to the accretion timescale in the MHD case, and is an order of magnitude slower in the absence of a stellar magnetic field.

A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume / finite element scheme for the incompressible MHD equations

We present a new exactly divergence-free and well-balanced hybrid finite volume/finite element scheme for the numerical solution of the incompressible viscous and resistive magnetohydrodynamics (MHD) equations on staggered unstructured mixed-element meshes in two and three space dimensions. The equations are split into several subsystems, each of which is then discretized with a particular scheme that allows to preserve some fundamental structural features of the underlying governing PDE system also at the discrete level. The pressure is defined on the vertices of the primary mesh, while the velocity field and the normal components of the magnetic field are defined on an edge-based/face-based dual mesh in two and three space dimensions, respectively. This allows to account for the divergence-free conditions of the velocity field and of the magnetic field in a rather natural manner. The non-linear convective and the viscous terms in the momentum equation are solved at the aid of an explicit finite volume scheme, while the magnetic field is evolved in an exactly divergence-free manner via an explicit finite volume method based on a discrete form of the Stokes law in the edges/faces of each primary element. The latter method is stabilized by the proper choice of the numerical resistivity in the computation of the electric field in the vertices/edges of the 2D/3D elements. To achieve higher order of accuracy, a piecewise linear polynomial is reconstructed for the magnetic field, which is guaranteed to be exactly divergence-free via a constrained L2 projection. Finally, the pressure subsystem is solved implicitly at the aid of a classical continuous finite element method in the vertices of the primary mesh and making use of the staggered arrangement of the velocity, which is typical for incompressible Navier-Stokes solvers. In order to maintain non-trivial stationary equilibrium solutions of the governing PDE system exactly, which are assumed to be known a priori, each step of the new algorithm takes the known equilibrium solution explicitly into account so that the method becomes exactly well-balanced. We show numerous test cases in two and three space dimensions in order to validate our new method carefully against known exact and numerical reference solutions. In particular, this paper includes a very thorough study of the lid-driven MHD cavity problem in the presence of different magnetic fields and the obtained numerical solutions are provided as free supplementary electronic material to allow other research groups to reproduce our results and to compare with our data. We finally present long-time simulations of Soloviev equilibrium solutions in several simplified 3D tokamak configurations, showing that the new well-balanced scheme introduced in this paper is able to maintain stationary equilibria exactly over very long integration times even on very coarse unstructured meshes that, in general, do not need to be aligned with the magnetic field.

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. The formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

Accretion disc backflow in resistive MHD simulations

ABSTRACT We investigate accretion onto a central star, with the size, rotation rate, and magnetic dipole of a young stellar object, to study the flow pattern (velocity and density) of the fluid within and outside of the disc. We perform resistive magnetohydrodynamic (MHD) simulations of thin discs, varying the parameters such as the stellar rotation rate and (anomalous) coefficients of viscosity and resistivity in the disc. To provide a benchmark for the results and to compare them with known analytic results, we also perform purely hydrodynamic (HD) simulations for the same problem. Although obtained for different situations with differing inner boundary condition, the disc structure in the HD simulations closely follows the analytic solution of Kluzniak and Kita – in particular, a region of ‘mid-plane’ backflow exists in the right range of radii, depending on the viscosity parameter. In the MHD solutions, whenever the magnetic Prandtl number does not exceed a certain critical value, the mid-plane backflow exists throughout the accretion disc, extending all the way down to the foot point of the accretion funnel flow where the disc transitions to a magnetic funnel flow. For values of the magnetic Prandtl number close to the critical value the backflow and the inner disc undergo a quasi-periodic radial oscillation, otherwise the backflow is steady, as is the disc solution. From our results, supplemented by our reading of the literature, we suggest that mid-plane backflow is a real, physical, and not only numerical feature of at least some accretion discs.

On the frequency bifurcations of the MHD startup modes in NSTX

The observed bifurcations of the low frequency (<50 kHz) and low toroidal periodicity (n < 5) magnetohydrodynamic (MHD) activity often present in the initial part of the National Spherical Tokamak Experiment (NSTX) discharges can be explained by the evolution of the radial profile of the safety factor (q=rBϕ/RBθ) crossing multiple rational surfaces in the core. Important performance limiting instability mechanisms in the NSTX spherical tokamak are often linked to low frequency and low-n MHD activity. They are quite common in long-pulse NSTX plasmas. They can be present at the beginning of the plasma current flat-top, at the end of the discharge or during the whole duration, and they have been observed to deleteriously impact performance over a wide range of q95. An interesting feature observed in some NSTX discharges is the presence of a bifurcation in the frequency of the low n modes, as low as n = 1, that have frequencies comparable to the plasma core rotation divided by n. Equilibrium reconstructions constrained by magnetic diagnostics data and motional stark effect pitch angle radial profiles suggest that the observed bifurcations are linked to a fast evolving minimum value of q. 3D non-linear resistive MHD simulations show that these modes are ideal and exist as non-resonant before the correspondent rational surface enters the plasma.

Extending the Spectral Difference Method with Divergence Cleaning (SDDC) to the Hall MHD Equations

The Hall Magnetohydrodynamic (MHD) equations are an extension of the standard MHD equations that include the “Hall” term from the general Ohm’s law. The Hall term decouples ion and electron motion physically on the ion inertial length scales. Implementing the Hall MHD equations in a numerical solver allows more physical simulations for plasma dynamics on length scales less than the ion inertial scale length but greater than the electron inertial length. The present effort is an important step towards producing physically correct results to important problems, such as the Geospace Environmental Modeling (GEM) Magnetic Reconnection problem. The solver that is being modified is currently capable of solving the resistive MHD equations on unstructured grids using the spectral difference scheme which is an arbitrarily high-order method that is relatively simple to parallelize. The GEM Magnetic Reconnection problem is used to evaluate whether the Hall MHD equations have been correctly implemented in the solver using the spectral difference method with divergence cleaning (SDDC) algorithm by comparing against the reconnection rates reported in the literature.

Data-driven assessment of magnetic charged particle confinement parameter scaling in magnetized liner inertial fusion experiments on Z

In magneto-inertial fusion, the ratio of the characteristic fuel length perpendicular to the applied magnetic field R to the α-particle Larmor radius ϱα is a critical parameter setting the scale of electron thermal-conduction loss and charged burn-product confinement. Using a previously developed deep-learning-based Bayesian inference tool, we obtain the magnetic-field fuel-radius product BR∝R/ϱα from an ensemble of 16 magnetized liner inertial fusion (MagLIF) experiments. Observations of the trends in BR are consistent with relative trade-offs between compression and flux loss as well as the impact of mix from 1D resistive radiation magneto-hydrodynamics simulations in all but two experiments, for which 3D effects are hypothesized to play a significant role. Finally, we explain the relationship between BR and the generalized Lawson parameter χ. Our results indicate the ability to improve performance in MagLIF through careful tuning of experimental inputs, while also highlighting key risks from mix and 3D effects that must be mitigated in scaling MagLIF to higher currents with a next-generation driver.

Smoothed particle hydrodynamics method for pinch plasma simulation with non-ideal MHD model

When plasma is compressed by magnetic forces, a pinch phenomenon is observed. Pinch plasma has received significant attention as an efficient source of radiation and a way for high-density plasma physics analysis. In this study, a non-ideal magnetohydrodynamics (MHD) model is applied to a smoothed particle hydrodynamics (SPH) framework to analyze pinch plasmas whose local resistivity varies with temperature and pressure. The proposed SPH model incorporates several numerical treatments, such as a correction term to satisfy the ∇·B constraint and some artificial dissipation terms to govern the shock wave. Moreover, it includes the evaluation of a novel SPH discretization for non-ideal MHD terms, including current density calculations. Furthermore, the proposed model is validated with three benchmark cases: (1) Brio and Wu shock tube (ideal MHD), (2) resistive MHD shock simulation, and (3) magnetized Noh Z-pinch problem. The simulation results are compared with the results of some reference Eulerian MHD simulations and analytical solutions. The simulations agree well with the reference data, and the introduced numerical treatments are effective. Finally, X-pinch simulations are performed using the proposed model. The simulations well produce the micro Z-pinch and jet shapes, which are important X-pinch features. Overall, the proposed SPH model has extensive potential for studying the complex pinch plasma phenomena.

Self-consistent integrated modeling of combined hybrid discharge-laser produced plasma devices for extreme ultraviolet metrology

Discharge- and laser-produced plasma (DLPP) devices are being used as light sources for extreme ultraviolet (EUV) generation. A key challenge for both, DPP and LPP, is achieving sufficient brightness to support the throughput requirements of nanometrology tools. To simulate the environment of a hybrid DLPP device and optimize the EUV output, we have developed an integrated HEIGHTS-DLPP computer simulation package. The package integrates simulation of two evolving plasmas (DPP and LPP) and includes modeling of a set of integrated self-consistent processes: external power source and plasma energy balance, plasma resistive magnetohydrodynamics, plasma heat conduction, detailed radiation transport (RT), and laser absorption and refraction. We simulated and optimized DLPP devices using Xe gas as a target material. We synchronized the external circuit parameters, chamber gas parameters, and laser beam temporal and spatial profiles to achieve maximum EUV output. The full 3D Monte Carlo scheme was integrated for detailed RT and EUV output calculations in Xe using more than 3600 spectral groups. The modeling results are in good agreement with Julich Forschungszentrum experimental data. Theoretical models, developed and integrated into the HEIGHTS package, showed wide capabilities and flexibility. The models and package can be used for optimization of the experimental parameters and settings, investigation of DLPP devices with complex design, analyzing the impact of integrated spatial effects and working timeline arrangement on the final EUV output, and EUV source size, shape, and angular distribution.

Dark photon superradiance: Electrodynamics and multimessenger signals

We study the electrodynamics of a kinetically mixed dark photon cloud that forms through superradiance around a spinning black hole, and design strategies to search for the resulting multimessenger signals. A dark photon superradiance cloud sources a rotating dark electromagnetic field which, through kinetic mixing, induces a rotating visible electromagnetic field. Standard model charged particles entering this field initiate a transient phase of particle production that populates a plasma inside the cloud and leads to a system which shares qualitative features with a pulsar magnetosphere. We study the electrodynamics of the dark photon cloud with resistive magnetohydrodynamics methods applicable to highly magnetized plasma, adapting techniques from simulations of pulsar magnetospheres. We identify turbulent magnetic field reconnection as the main source of dissipation and electromagnetic emission, and compute the peak luminosity from clouds around solar-mass black holes to be as large as $10^{43}$ erg/s for open dark photon parameter space. The emission is expected to have a significant X-ray component and is potentially periodic, with period set by the dark photon mass. The luminosity is comparable to the brightest X-ray sources in the Universe, allowing for searches at distances of up to hundreds of Mpc with existing telescopes. We discuss observational strategies, including targeted electromagnetic follow-ups of solar-mass black hole mergers and targeted continuous gravitational wave searches of anomalous pulsars.