kinetic-MHD Model Research Articles

Frequency multiplication with toroidal mode number of kink/fishbone modes on a static HL-2A-like tokamak

In the presence of energetic particles (EPs), the long-lived mode (LLM) frequency multiplication with n = 1, 2, 3, or higher is often observed on HL-2A, where n is the toroidal mode number. Hybrid kinetic-MHD model simulations of the energetic particle (EP) driven kink/fishbone modes on a static HL-2A-like tokamak using NIMROD code find that when the background plasma pressure is relatively high, and the EP pressure and the beam energy are relatively low, the mode frequency increases almost linearly with EP pressure, and the frequency is proportional to n (‘frequency multiplication’), even in the absence of any equilibrium plasma rotation. In addition, the frequency multiplication persists as the safety factor at the magnetic axis q 0 varies. In the absence of EPs, the growth rate of the 1/1 mode is the largest; however, as the EP pressure increases, the growth rate of 2/2 modes or 3/3 modes becomes dominant, suggesting that higher-n modes are more vulnerable to EPs. These results may shed light on the understanding of the toroidal mode number dependence of kink/fishbone modes in the advanced scenarios of tokamaks with weak or reversed central magnetic shear.

The Impact of Kinetic Neutrals on the Heliotail

Abstract The shape of the heliosphere is thought to resemble a long, comet tail, however, recently it has been suggested that the heliosphere is tailless with a two-lobe structure. The latter study was done with a three-dimensional (3D) magnetohydrodynamic code, which treats the ionized and neutral hydrogen atoms as fluids. Previous studies that described the neutrals kinetically claim that this removes the two-lobe structure of the heliosphere. In this work, we use the newly developed Solar-wind with Hydrogen Ion Exchange and Large-scale Dynamics (SHIELD) model. SHIELD is a self-consistent kinetic-MHD model of the outer heliosphere that couples the MHD solution for a single plasma fluid from the BATS-R-US MHD code to the kinetic solution for neutral hydrogen atoms solved by the Adaptive Mesh Particle Simulator, a 3D, direct simulation Monte Carlo model that solves the Boltzmann equation. We use the same boundary conditions as our previous simulations using multi-fluid neutrals to test whether the two-lobe structure of the heliotail is removed with a kinetic treatment of the neutrals. Our results show that despite the large difference in the neutral hydrogen solutions, the two-lobe structure remains. These results are contrary to previous kinetic-MHD models. One such model maintains a perfectly ideal heliopause and does not allow for communication between the solar wind and interstellar medium. This indicates that magnetic reconnection or instabilities downtail play a role for the formation of the two-lobe structure.

Heliospheric energetic neutral atoms: Non-stationary modelling and comparison with IBEX-Hi data

ABSTRACT The interstellar boundary explorer (IBEX) has been measuring fluxes of the energetic neutral atoms (ENAs) using the IBEX-Hi (0.3–6 keV) instrument since 2008. We have developed a numerical time-depended code to calculate globally distributed flux (GDF) of hydrogen ENAs employing both (1) 3D kinetic-MHD model of the global heliosphere and (2) reconstruction of atom trajectories from 1 au, where they are observed by IBEX, to the point of their origin in the inner heliosheath (IHS). The key factor in the simulation is a detailed kinetic consideration of the pickup ions (PUIs), the supra-thermal component of protons in the heliosphere, which is ‘parental’ to the ENAs and originates in the region of the supersonic solar wind being picked by the heliospheric magnetic field. As a result of our study, we have concluded that (1) the developed model is able to reproduce the geometry of the multilobe structure seen in the IBEX-Hi GDF maps, (2) the GDF is extremely sensitive to the form of the velocity distribution function of PUIs in the IHS, and the accounting for the existence of an additional energetic population of PUIs is essential to explain the data, (3) despite a relatively good agreement, there are some quantitative differences between the model calculations and IBEX-Hi data. Possible reasons for these differences are discussed.

Ion kinetic effects on linear pressure driven magnetohydrodynamic instabilities in helical plasmas

The linear MHD (magnetohydrodynamic) stability for high beta plasmas in the inward shifted Large Helical Device (LHD) configurations has been investigated for a wide range of magnetic Reynolds numbers $S$ using numerical simulations based on the kinetic MHD model with kinetic thermal ions where the beta is the ratio of the plasma pressure to the magnetic pressure. It is found that the dependence of the linear growth rate of the resistive ballooning modes on the $S$ number changes from $\unicode[STIX]{x1D6FE}\propto S^{-1/3}$ to $\unicode[STIX]{x1D6FE}\propto S^{-1}$ by the kinetic thermal ion effects so that the resistive ballooning modes are significantly suppressed as the $S$ number increases. For a high $S$ number comparable to experimental values, the most unstable modes are interchange modes. The kinetic thermal ion effects change the most unstable interchange mode from the ideal mode to the resistive mode. This transition of the interchange modes by kinetic thermal ion effects is consistent with the shift of the marginal stability boundary for the ideal interchange modes observed in the LHD experiments.

Guiding-centre theory for kinetic-magnetohydrodynamic modes in strongly flowing plasmas

A kinetic-magnetohydrodynamic model with kinetic pressure closure is derived from a consistent guiding-centre framework. Higher-order (gyroviscous) corrections to the pressure tensor are derived in complex geometry from a reduced kinetic equation. The proposed model allows for flows of the order of the thermal ion velocity, taking into account important centrifugal effects due to the E × B flow, as well as the effects of diamagnetic flows associated with finite Larmor radius corrections to both ion fluid inertia and long mean-free path contributions. Wave–particle interactions, such as toroidal drift-resonance, are retained. Furthermore, the linearised model includes a quasi-neutrality equation, allowing the effects of a parallel electric field to be studied in fast rotating tokamak plasmas.

Investigation of ion fishbone stability on HL-2A using NIMROD

Numerical calculations of resistive internal kink mode with effects of energetic particles (EPs) on HL-2A have been performed using the hybrid kinetic-MHD model inplemented in the NIMROD code. The m/n = 1/1 resistive internal kink mode is unstable in MHD limit. However, with kinetic effects of energetic ions, a fishbone mode is excited with mode frequency around 10 kHz. We calculate the impact of resistivity on the growth rate and frequency of ion fishbone mode, and the results are in good agreement with the analytic solutions, which are obtained by solving the fishbone dispertion relation including resistivity effect. The effects of βfrac and cut off velocity of EP on fishbone mode are calculated in detail, where βfrac is the ratio of EP pressure to background plasma pressure. This work presents a clear explanation of the stabilizing effect of ECRH on ion fishbone, which is first observed on HL-2A.

Global structure of the heliosphere: 3D kinetic-MHD model and the interpretation of spacecraft data

This paper is a brief overview of research into the interaction between the solar wind and local interstellar medium. This interaction determines the global structure of the heliosphere (the region occupied by the solar wind) and has a complex multicomponent character. We describe the three-dimensional kinetic-magnetohydrodynamic model of the interaction, which includes plasma and neutral components of the interstellar medium and solar wind, the heliospheric and interstellar magnetic fields, and the latitudinal and temporal variations of solar wind parameters. In describing the results, magnetic-field-related effects are given special attention, in particular, the magnetic-field-driven plasma depletion in the vicinity of the heliopause. The model explains a sufficiently large body of data from Voyager-1 and Voyager-2, the Interstellar Boundary Explorer (IBEX), the Solar and Heliospheric Observatory (SOHO), the Hubble Space Telescope (HST), and other spacecraft. Based on the experimental data and using the model, the parameters of the interstellar medium and of the interstellar magnetic field are determined. It is shown, however, that a single model using a single set of boundary conditions cannot self-consistently explain all the data available. The Voyager-1 data on the scattered solar Lyman-alpha radiation is taken as an example to illustrate the difficulties that arise.

NIMROD calculations of energetic particle driven toroidal Alfvén eigenmodes

Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in the absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings, such as electron and ion Landau damping, and collisional and radiative damping. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity group, is studied in this work. The numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a δf particle-in-cell representation of EPs with the 3D MHD representation of the bulk plasma through moment closure for the momentum conservation equation. Both the excitation of TAEs and their transition to energetic particle modes (EPMs) have been observed. The influence of EP density, temperature, density gradient, and position of the maximum relative density gradient, on the frequency and the growth rate of TAEs are obtained, which are consistent with those from the eigen-analysis calculations, kinetic-MHD, and gyrokinetic simulations for an initial Maxwellian distribution of EPs. The relative pressure gradient of EP at the radial location of the TAE gap, which represents the drive strength of EPs, can strongly affect the growth rate of TAEs. It is demonstrated that the mode transition due to EP drive variation leads to not only the change of frequency but also the change of the mode structure. This mechanism can be helpful in understanding the nonlinear physics of TAE/EPM, such as frequency chirping.

Secondary Interstellar Oxygen in the Heliosphere: Numerical Modeling and Comparison with IBEX-Lo Data

Abstract Quantitative analysis of the interstellar heavy (oxygen and neon) atom fluxes obtained by the Interstellar Boundary Explorer (IBEX) suggests the existence of the secondary interstellar oxygen component. This component is formed near the heliopause due to charge exchange of interstellar oxygen ions with hydrogen atoms, as was predicted theoretically. A detailed quantitative analysis of the fluxes of interstellar heavy atoms is only possible with a model that takes into account both the filtration of primary and the production of secondary interstellar oxygen in the boundary region of the heliosphere as well as a detailed simulation of the motion of interstellar atoms inside the heliosphere. This simulation must take into account photoionization, charge exchange with the protons of the solar wind and solar gravitational attraction. This paper presents the results of modeling interstellar oxygen and neon atoms through the heliospheric interface and inside the heliosphere based on a three-dimensional kinetic-MHD model of the solar wind interaction with the local interstellar medium and a comparison of these results with the data obtained on the IBEX spacecraft.

Impact of hot particles on resistive wall mode stability in rotating high-beta plasmas

We investigate kinetic effects of hot particles and rotating bulk plasmas on resistive wall mode (RWM) stability. To this end, we invoke the hybrid kinetic-magnetohydrodynamic (MHD) model, extended to include self-consistent rotation effects. The extended model needs macroscopic ‘rotation’ due to collective motion of hot and bulk particles. In this paper, we point out that the rotation of hot particles is arbitrary in the hybrid kinetic-MHD formalism, due to the assumption of small hot particle density. To remove this arbitrariness, by considering an equilibrium distribution function of hot particles interacting with rotating bulk particles, we compute the ‘rotation’ of hot particles. By applying the extended hybrid kinetic-MHD model to bulk and hot particles, we have carried out numerical analysis of RWM stability. By varying parameters for neutral beam injection (injection energy and injection pitch angle), we find that new stable regions arise due to additional energy exchange between RWMs and hot particles, induced by the hot particles’ rotation.

Глобальная структура гелиосферы: трёхмерная кинетико-магнитогидродинамическая модель и анализ данных космических аппаратов

Глобальная структура гелиосферы: трёхмерная кинетико-магнитогидродинамическая модель и анализ данных космических аппаратов

Kinetic modelling of primary and secondary interstellar oxygen atom fluxes in the heliosphere

The interstellar neutral (ISN) oxygen atoms penetrate into the heliosphere from the Local Interstellar Medium (LISM). Oxygen atoms that directly penetrate into the heliosphere are called primary, while secondary oxygen population is formed near the heliopause due to the process of charge exchange of interstellar oxygen ions with hydrogen atoms and its existence in the heliosphere was previously predicted theoretically (Izmodenov et al., 1997, 1999, 2004). In this work we study the distribution of both primary and secondary oxygen atoms in the heliosphere and its fluxes at 1 AU.The analysis of the distribution of ISN O atoms in the heliosphere is only possible in the frame of a model that takes into account both filtration of the primary and origin of the secondary interstellar oxygen in the region of interaction of the solar wind (SW) with the LISM, as well as a detailed simulation of the motion of interstellar atoms inside the heliosphere. This simulation should take into account the temporal and heliolatitudinal dependences of ionization, the process of charge exchange with SW protons and the effect of the solar gravitational attraction. This paper presents the results of modelling ISN O atoms inside the heliosphere based on a new three-dimensional kinetic-MHD model of the SW interaction with the LISM (Izmodenov and Alexashov, 2015). Oxygen atoms are of a particular interest because they are strongly coupled with the protons through the charge exchange process and due to the fact that the fluxes of interstellar oxygen are directly measured by the Interstellar Boundary Explorer (IBEX). The first quantitative measurements of the interstellar heavy neutral atoms (O and Ne) obtained on the IBEX spacecraft were presented in (Park et al., ApJS, 2015). Qualitative analysis of these data shows that the secondary component of the interstellar oxygen atoms was also measured along with the primary interstellar atoms.

Neutron spectra from beam-target reactions in dense Z-pinches

The energy spectrum of neutrons emitted by a range of deuterium and deuterium-tritium Z-pinch devices is investigated computationally using a hybrid kinetic-MHD model. 3D MHD simulations are used to model the implosion, stagnation, and break-up of dense plasma focus devices at currents of 70 kA, 500 kA, and 2 MA and also a 15 MA gas puff. Instabilities in the MHD simulations generate large electric and magnetic fields, which accelerate ions during the stagnation and break-up phases. A kinetic model is used to calculate the trajectories of these ions and the neutron spectra produced due to the interaction of these ions with the background plasma. It is found that these beam-target neutron spectra are sensitive to the electric and magnetic fields at stagnation resulting in significant differences in the spectra emitted by each device. Most notably, magnetization of the accelerated ions causes the beam-target spectra to be isotropic for the gas puff simulations. It is also shown that beam-target spectra can have a peak intensity located at a lower energy than the peak intensity of a thermonuclear spectrum. A number of other differences in the shapes of beam-target and thermonuclear spectra are also observed for each device. Finally, significant differences between the shapes of beam-target DD and DT neutron spectra, due to differences in the reaction cross-sections, are illustrated.

Kinetic-Gasdynamic Modeling of the Heliospheric Interface

Heliospheric energetic neutral atoms (ENAs) that will be measured by the Interstellar Boundary Explorer (IBEX) originate from the heliosheath. The heliosheath is formed as a result of the interaction of the solar wind (SW) with the circum-heliospheric interstellar medium (CHISM). The expected fluxes of ENAs are strongly dependent on the nature of this interaction. In turn, the interaction of the solar wind with the local interstellar cloud has a complex and multi-component nature. Detailed theoretical modeling of the interaction between the SW and the local interstellar medium is required to understand the physics of the heliosheath and to predict and explain the heliospheric ENAs. This paper summarizes current state-of-art kinetic-gasdynamic models of the SW/CHISM interaction. We shall restrict our discussion to the kinetic-gasdynamic and kinetic-magnetohydrodynamic (MHD) models developed by the Moscow group. This paper summarizes briefly the main results of the first self-consistent, two-component, kinetic-gasdynamic model by Baranov and Malama (J. Geophys. Res. 98:15157–15163, 1993), presents new results obtained from the 3D kinetic-MHD model by Izmodenov et al. (Astron. Astrophys. 437:L35–L38, 2005a), describes the basic formulation and results of the model by Malama et al. (Astron. Astrophys. 445:693–701, 2006) as well as reports current developments in the model. This self-consistent model considers pickup protons as a separate non-equilibrium component. Then we discuss a stochastic acceleration model for pickup protons in the supersonic solar wind and in the heliosheath. We also present the expected heliospheric ENA fluxes obtained in the framework of the models.

Preliminary Simulations of FLR Effects on RFP Tearing Modes

Preliminary simulations of finite Larmor radius (FLR) effects on m = 1 tearing instabilities in a reverse field pinch (RFP) plasma are presented. δ f particle-in-cell (PIC) simulations were performed by extending a hybrid drift kinetic-MHD model to include the full Lorentz equations of motion to take into account finite Larmor radius (FLR) effects. The simulations show that for an idealized phase space distribution, sufficiently energetic ions stabilize the tearing mode. These simulations show good agreement with analytic theory and demonstrate the FLR physics capability of the hybrid kinetic-MHD model.

Direction of the interstellar H atom inflow in the heliosphere: Role of the interstellar magnetic field

Recently Lallement et al. (2005, Science, 307, 1447) reported that the direction of the flow of interstellar neutral hydrogen in the heliosphere is deflected by ~4° from the direction of the pristine local interstellar gas flow. The most probable physical phenomenon responsible for such a deviation is the interstellar magnetic field inclined to the direction of the interstellar gas flow. In this case the flow of the interstellar charged component is asymmetric and distorted in the region of the solar wind interaction with the local interstellar medium, which is called the heliospheric interface. The interstellar H atoms pass through the heliospheric interface and interact with the plasma component by charge exchange. Some imprints of the asymmetry of the heliospheric plasma interface should be seen in the distribution of the interstellar H atom component. In this letter we explore this scenario quantitatively and demonstrate that our new self-consistent 3D kinetic-MHD model of the solar wind interaction with the magnetized interstellar plasma is able to produce the measured deviation in the case of a rather strong interstellar magnetic field of ~2.5 μ G inclined by ~45° to the direction of interstellar flow.

Hybrid kinetic-MHD simulations in general geometry

We present a hybrid kinetic-MHD model consisting of 3 species, the bulk fluid ions and electrons, and a kinetic minority hot particle species. The 3 species equations are derived from moments of the Vlasov Equation and then reduced using the usual hot particle assumption of n h ⪡ n 0, β h ∼ β 0 to formulate the hybrid kinetic MHD model. The 3 species equations reproduce the usual MHD equations with the addition of a hot particle pressure in the momentum equation. In the limit n h →0, the MHD equations are recovered. These model equations are implemented and examined in the NIMROD code [C.R. Sovinec, et al., Nonline magnetohydrodynamic simulations using higher-order finite elements, JCP submitted for publication] which solves three dimensional magnetohydrodynamic initial-value problems using the finite element method (FEM). The finite elements allow the representation of highly shaped geometries, but the particle-in-cell (PIC) method is complicated by the irregular grid. The associated complications are a nontrivial shape function, a more complex search algorithm, parallelization. We present our implementation of PIC in a FEM simulation and some preliminary results and performance measurements.