Finite Plasma Pressure Research Articles

Self-consistent equilibrium of a helical magnetic flux rope in a finite-pressure plasma

We present an analytical model of the self-consistent equilibrium of a magnetic flux rope, which is obtained in cylindrical geometry. The equilibrium quantities, namely, the azimuthal magnetic field and plasma pressure, are determined in a self-consistent way through the current density, which is derived as a solution of a nonlinear equation. By minimizing the energy functional, it was shown that the constrained equilibrium state is stable. The obtained results are also applicable to the cylindrical tokamak magnetic configurations. It is shown that the analytically predicted radial profiles of equilibrium quantities are in good agreement with the experimental data.

Dispersion and spatial structure of coupled Alfvén and slow magnetosonic modes in the dipole magnetosphere

Numerical analysis of the coupling between the Alfvén and slow azimuthally small scale modes in the dipolar model of the magnetosphere is performed. The field line curvature, inhomogeneity both across the magnetic shells and along the field lines, and finite plasma pressure are taken into account. The field line curvature causes coupling Alfvén and slow modes, while the contribution from the fast mode is neglected due to the assumed small scale of the oscillations in the azimuthal direction. The plasma pressure decreases with distance from the Earth, which is a characteristic for the ring current region. The wave's transverse dispersion, that is, dependence of the radial wave vector kr on the frequency ω, was studied. It was found that the wave can exist in two frequency ranges. Both ranges are bounded by resonant frequency on one side and the cutoff frequency on the other. The higher frequency range corresponds to the Alfvén mode. However, its properties are modified due to the coupling with the slow mode. For example, the divergence of the plasma displacement and the magnetic field compressional component appear. In the slow magnetosonic region, in contrast, the cutoff frequency is always smaller than the resonant one. If the pressure gradient is strong and negative, the slow mode cutoff frequency can disappear, that is, the radial wave vector squared even for the zero frequency. It means that the kr value goes to zero at imaginary frequency. Mode structure along the field line for different plasma pressure values and its pressure gradients was calculated.

Dispersion and spatial structure of the coupled Alfvén and slow magnetosonic oscillations in the Solar corona

Abstract Numerical and analytical analysis of the magnetohydrodynamic (MHD) waves in Solar coronal arcades is performed. A semi-cylinder slab model of arcade is used where the field lines are represented by half-circles intersecting the photosphere, the magnetic shells are represented by nested coaxial semi-cylinders. The finite plasma pressure is taken into account. The “corrugational”perturbations are considered, that is, the perturbations with short wavelength in the direction along the arcade. In this limit, there are two oscillation modes, the Alfvén and slow magnetosonic modes, coupled due to the field line curvature. The transverse dispersion of the modes, that is, the dependence of the radial wave vector’s component kr on the wave frequency ω, is considered. It was found that the wave is concentrated in two regions of mode’s existence, where $k_r^2>0$: the Alfvén and magnetosonic transparent regions. On one side, each of them is bounded by the resonance surface, where $k_r^2 \rightarrow \infty$. On the resonance surface, the wave’s frequency is determined by the Alfvén and slow magnetosonic modes dispersion relations, respectively. On the other side, the transparent regions are bounded by cut-off frequencies where $k_{r}^2 =0$. In both transparent regions, the perturbations have both transverse electric field (characteristic for the Alfvén mode) and field aligned velocity (characteristic for the slow mode). The wave structure along the field line for several models of plasma parameters is calculated.

Single-stage stellarator optimization: combining coils with fixed boundary equilibria

We introduce a novel approach for the simultaneous optimization of plasma physics and coil engineering objectives using fixed-boundary equilibria that is computationally efficient and applicable to a broad range of vacuum and finite plasma pressure scenarios. Our approach treats the plasma boundary and coil shapes as independently optimized variables, penalizing the mismatch between the two using a quadratic flux term in the objective function. Four use cases are presented to demonstrate the effectiveness of the approach, including simple and complex stellarator geometries. As shown here, this method outperforms previous two-stage approaches, achieving smaller plasma objective function values when coils are taken into account.

Effect of negative triangularity on tearing mode stability in tokamak plasmas

The influence of negative triangularity (NT) of the plasma shape on the n = 1 (n is the toroidal mode number) tearing mode (TM) stability has been numerically investigated, with results compared to that of the positive triangularity (PT) counterpart. By matching the safety factor profile for a series of toroidal equilibria, several important plasma parameters, including the triangularity, the plasma equilibrium pressure, the plasma resistivity as well as the toroidal rotation, have been varied. The TM localized near the plasma edge is found to be more unstable in the NT plasmas as compared to the PT counterpart. The fundamental reason for this difference is the lack of favorable average curvature stabilization in NT configurations. Direct comparison of the Mercier index corroborates this conclusion. For the core-localized mode, where the difference in the local triangularity between NT and PT becomes small and the curvature stabilization is significantly reduced, larger Shafranov shift in the plasma core associated with the NT configuration results in more stable TM. The plasma toroidal flow generally stabilizes the TM in plasmas with both NTs and PTs. The flow stabilization is however weaker in the case of negative triangularity with finite plasma pressure.

Numerical analysis of the spatial structure of Alfvén waves in a finite pressure plasma in a dipole magnetosphere

We have carried out a numerical analysis of the spatial structure of Alfvén waves in a finite pressure inhomogeneous plasma in a dipole model of the magnetosphere. We have considered three magnetosphere models differing in maximum plasma pressure and pressure gradient. The problem of wave eigenfrequencies was addressed. We have established that the poloidal frequency can be either greater or less than the toroidal frequency, depending on plasma pressure and its gradient. The problem of radial wave vector component eigenvalues was considered. We have found points of Alfvén wave reflection in various magnetosphere models. The wave propagation region in the cold plasma model is shown to be significantly narrower than that in models with finite plasma pressure. We have investigated the structure of the main Alfvén wave harmonic when its polarization changes in three magnetosphere models. A numerical study into the effect of plasma pressure on the structure of behavior of all Alfvén wave electric and magnetic field components has been carried out. We have established that for certain parameters of the magnetosphere model the magnetic field can have three nodes, whereas in the cold plasma model there is only one. Moreover, the longitudinal magnetic field component changes sign twice along the magnetic field line.

Численный анализ пространственной структуры альфвеновских волн в плазме конечного давления в дипольной магнитосфере

We have carried out a numerical analysis of the spatial structure of Alfvén waves in a finite pressure inhomogeneous plasma in a dipole model of the magnetosphere. We have considered three magnetosphere models differing in maximum plasma pressure and pressure gradient. The problem of wave eigenfrequencies was addressed. We have established that the poloidal frequency can be either greater or less than the toroidal frequency, depending on plasma pressure and its gradient. The problem of radial wave vector component eigenvalues was considered. We have found points of Alfvén wave reflection in various magnetosphere models. The wave propagation region in the cold plasma model is shown to be significantly narrower than that in models with finite plasma pressure. We have investigated the structure of the main Alfvén wave harmonic when its polarization changes in three magnetosphere models. A numerical study into the effect of plasma pressure on the structure of behavior of all Alfvén wave electric and magnetic field components has been carried out. We have established that for certain parameters of the magnetosphere model the magnetic field can have three nodes, whereas in the cold plasma model there is only one. Moreover, the longitudinal magnetic field component changes sign twice along the magnetic field line.

Second-order perturbations in Alfvén waves in finite pressure plasma

It is shown first that in finite pressure plasma, just as in cold plasma, Alfvén waves created by an initial perturbation generate plasma flows and decreases in the magnetic field, which propagate along with these waves. Second, at the stage of their interaction, Alfvén waves generate slow magnetosonic (SMS) waves propagating along the magnetic field. These results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves both in the magnetosphere regions with cold plasma and in the magnetosphere regions with finite pressure plasma. They also provide potential possibility for determining the position of a source of Alfvén disturbance from observations of Alfvén waves and their induced SMS waves.

Возмущения второго порядка в альфвеновских волнах в плазме с давлением

It is shown first that in finite pressure plasma, just as in cold plasma, Alfvén waves created by an initial perturbation generate plasma flows and decreases in the magnetic field, which propagate along with these waves. Second, at the stage of their interaction, Alfvén waves generate slow magnetosonic (SMS) waves propagating along the magnetic field. These results suggest that at least some of the fast plasma flows observed in the magnetotail can be one of the manifestations of propagating Alfvén waves both in the magnetosphere regions with cold plasma and in the magnetosphere regions with finite pressure plasma. They also provide potential possibility for determining the position of a source of Alfvén disturbance from observations of Alfvén waves and their induced SMS waves.

Plasma Flow Generation due to the Nonlinear Alfvén Wave Propagation around a 3D Magnetic Null Point

Abstract The behavior of current density accumulation around the sharp gradient of magnetic field structure or a 3D magnetic null point and with the presence of finite plasma pressure is investigated. It has to be stated that in this setup, the fan plane locates at the xy plane and the spine axis aligns along the z-axis. Current density generation in presence of the plasma pressure that acts as a barrier for developing current density is less well understood. The shock-capturing Godunov-type PLUTO code is used to solve the magnetohydrodynamic set of equations in the context of wave-plasma energy transfer. It is shown that propagation of Alfvén waves in the vicinity of a 3D magnetic null point leads to current density excitations along the spine axis and also around the magnetic null point. Besides, it is pointed out the x component of current density has oscillatory behavior while the y and z components do not show this property. It is plausible that it happens because the fan plane encompasses separating unique topological regions, while the spine axis does not have this characteristic and is just a line without separate topological regions. Besides, current density generation results in plasma flow. It is found that the y component of the current density defines the x component of the plasma flow behavior, and the x component of the current density prescribes the behavior of the y component of the plasma flow.

Assessment of potential heat flux overload of target and first wall components in Wendelstein 7-X finite-beta magnetic configurations and choice of locations for temperature monitoring

Abstract Within the framework of R&D activities on the Wendelstein 7-X (W7-X) stellarator machine, the assessment of heat loads onto the plasma facing components (PFCs) is an important aspect. So far, W7-X was operated in short pulses without water cooling of the PFCs. Presently, the device is being prepared for future operation phases with water cooling. The target plates, which receive the highest heat loads, are monitored by a thermography system. The rest of the first wall (heat shield) is not designed to receive convective particle loads, and it is in part poorly monitored by the infrared cameras. Recent studies have shown that for many plasma configurations there are locations on the heat shield which do receive significant convective heat flux. This is in particular true for the heat shields adjacent to the target plates (called baffles) and for configurations with finite plasma pressure, where the magnetic configuration is modified by plasma currents. On the other side, the heat flux limit to the baffle tiles had to be reduced from 0.50 to 0.25 MW/m2. In this work an evaluation of the heat flux to targets and baffles in plasma configurations with finite plasma pressure is presented. To this end, Field Line Diffusion (FLD) calculations have been performed to obtain the heat load pattern distributions for the considered magnetic configurations. The results have been assessed statistically to achieve a measure of certainty in the prediction of an overload in a certain location. The possibility of overloads onto the baffles due to plasma radiation has also been investigated. The results of the entire analysis show that local temperature monitoring by thermocouples in a rather limited number of locations will be sufficient to avoid heat flux overloads of the baffles and heat shields in all magnetic configurations considered.

SPATIAL STRUCTURE OF AZIMUTHALLY SMALL-SCALE MHD WAVES IN ONE-DIMENSIONALLY INHOMOGENEOUS FINITE PRESSURE PLASMA WITH CURVED FIELD LINES

We have studied propagation of hydromagnetic (MHD) waves in one-dimensionally inhomogeneous finite pressure plasma with curved field lines. Magnetic surfaces are considered to be concentric cylinders, where the cylinder’s radius models the radial coordinate in Earth’s magnetosphere. The waves are supposed to be azimuthally small-scale. In this approximation there are only two MHD modes — Alfvén and slow magnetosonic (SMS). We have derived an ordinary differential equation for the spatial structure of the wave field in this model. We have examined the character of the singularity on the surface of Alfvén and SMS resonances and the influence of field line curvature on them. We have determined wave transparent regions. The SMS transparent region was found to essentially broaden as compared to the straight field line case. The very existence of the Alfvén transparent region is caused by the field line curvature and finite plasma pressure; otherwise, the wave structure is represented by a localized resonance.

Пространственная структура азимутально-мелкомасштабных МГД-волн в одномерно-неоднородной плазме конечного давления с кривыми силовыми линиями

We have studied propagation of hydromagnetic (MHD) waves in one-dimensionally inhomogeneous finite pressure plasma with curved field lines. Magnetic surfaces are considered to be concentric cylinders, where the cylinder’s radius models the radial coordinate in Earth’s magnetosphere. The waves are supposed to be azimuthally small-scale. In this approximation there are only two MHD modes — Alfvén and slow magnetosonic (SMS). We have derived an ordinary differential equation for the spatial structure of the wave field in this model. We have examined the character of the singularity on the surface of Alfvén and SMS resonances and the influence of field line curvature on them. We have determined wave transparent regions. The SMS transparent region was found to essentially broaden as compared to the straight field line case. The very existence of the Alfvén transparent region is caused by the field line curvature and finite plasma pressure; otherwise, the wave structure is represented by a localized resonance.

Do Current and Magnetic Helicities Have the Same Sign?

Abstract Current helicity, H c , and magnetic helicity, H m , are two main quantities used to characterize magnetic fields. For example, such quantities have been widely used to characterize solar active regions and their ejecta (magnetic clouds). It is commonly assumed that H c and H m have the same sign, but this has not been rigorously addressed beyond the simple case of linear force-free fields. We aim to answer whether H m H c ≥ 0 in general, and whether it is true over some useful set of magnetic fields. This question is addressed analytically and with numerical examples. The main focus is on cylindrically symmetric straight flux tubes, referred to as flux ropes (FRs), using the relative magnetic helicity with respect to a straight (untwisted) reference field. Counterexamples with H m H c < 0 have been found for cylindrically symmetric FRs with finite plasma pressure, and for force-free cylindrically symmetric FRs in which the poloidal field component changes direction. Our main result is a proof that H m H c ≥ 0 is true for force-free cylindrically symmetric FRs where the toroidal field and poloidal field components are each of a single sign, and the poloidal component does not exceed the toroidal component. We conclude that the conjecture that current and magnetic helicities have the same sign is not true in general, but it is true for a set of FRs of importance to coronal and heliospheric physics.

Two-dimensional self-similar plasma equilibria

Force-free plasma equilibria are expected to form in the solar corona, while in-situ spacecraft observations have shown that force-free equilibria are formed in the planetary magnetotails. In this paper, we develop fluid models of two-dimensional axially symmetric force-free equilibria and discuss similar slab equilibria. The group theory approach is used to find the symmetry groups and reduce the Grad-Shafranov equation with exponential and power law nonlinearities to ordinary differential equations for the self-similar (automodel) solutions that we analyze analytically and numerically. Force-free equilibria of the developed class have a magnetotail-type configuration with magnetic field lines stretched in the radial direction and represent nonlinear force-free equilibria, because rot B=α(r) B with α(r)≠const. Making use of the same symmetry groups, we generalize the developed force-free equilibria by including a finite plasma pressure gradient and compare different equilibria of the developed class. These models can be useful for describing the structure and stability of current sheets observed in planetary magnetotails and formed in the solar atmosphere.

Stability of ideal and non-ideal edge localized infernal mode

Stability of a special class of the infernal mode, i.e., the one which is localized near the plasma edge, is numerically investigated for a toroidal plasma, using the single fluid code MARS-F [Liu et al., Phys. Plasmas 7, 3681 (2000)] and magneto-hydrodynamic-kinetic hybrid code MARS-K [Liu et al., Phys. Plasmas 15, 112503 (2008)]. Unlike the peeling-ballooning instabilities, which are thought to be responsible for the onset of type-I edge localized modes, the edge localized infernal mode may be responsible for accessing certain quiescent H-mode regimes in tokamak discharges. The finite plasma pressure near the plasma edge drives this instability. The local flattening of the safety factor near a rational surface at the plasma edge region, due to the large bootstrap current contribution in H-mode plasmas, is a necessary condition for the mode instability. It is found that the plasma toroidal flow shear in the pedestal region, as well as the plasma resistivity, further destabilizes the edge localized infernal mode. The drift kinetic effects from thermal particles, on the other hand, partially stabilize the mode. The flow shear and the drift kinetic effects also modify the symmetry of the mode spectrum, by enlarging the unstable domain towards higher local qmin value. No substantial modification of the mode eigen-structure is observed by the plasma flow, resistivity, or the kinetic effects. These results can be relevant to understanding physics of certain quiescent H-mode regimes.

The role of thermal conduction in tearing mode theory

The role of anisotropic thermal diffusivity in tearing mode stability is analysed in general toroidal geometry following similar techniques to Glasser et al (1975 Phys. Fluids 18 875), although a stronger ordering of the plasma compressibility is required. Resistive layer equations are obtained for a resistive magnetohydrodynamic (MHD) model with anisotropic transport of pressure. A dispersion relation linking the growth rate to the tearing mode stability parameter, Δ′, characterising the external ideal MHD region, is derived. By using a resistive MHD code modified to include such thermal transport to calculate tearing mode growth rates, this dispersion relation is employed to determine Δ′ in situations with finite plasma pressure that are stabilised by favourable average curvature when using a simple resistive MHD code. We also demonstrate that the same code can be used to obtain the basis-functions (Ham et al 2012 Plasma Phys. Control. Fusion 54 105014) needed for an alternative approach to calculating Δ′.

Properties of dispersive Alfven waves: 4. Hydrodynamics (finite and high-pressure plasmas)

The behavior of dispersive Alfven waves (DAWs) in astrophysical plasmas of finite and high pressure, which have not been considered thus far, is studied in the hydrodynamic approximation. The results are analyzed and compared with those obtained in the kinetic approach. It is shown that one general solution for DAWs in plasmas of finite and high pressure can be obtained using the hydrodynamic approach in contrast to the kinetic one. Kinetic and hydrodynamic solutions correspond to each other very well in a domain with weakly damped DAWs; however, solutions may differ appreciably in some parameter domains, especially in high-pressure plasma. The effect of parameters of the astrophysical medium on the DAW behavior and properties is analyzed. All the main wave characteristics were determined: dispersion, damping, polarization, density perturbations, and charge density perturbations. Since finite-pressure plasma is one of the most frequently encountered states of astrophysical plasma, it is very important to take into account specific features in behavior of these waves for their detecting and a more correct understanding of their behavior and the role they play in different astrophysical processes that occur in space environment.

Longitudinal structure of ballooning MHD disturbances in a model magnetosphere

Large-scale toroidal Pc5 pulsations are commonly treated as Alfven oscillations of a magnetic field line. According to observations, their longitudinal structure is described well by theory. At the same time, the longitudinal structure of azimuthal small-scale poloidal Pc5 pulsations is virtually unknown. These pulsations are associated with ballooning disturbances described by a system of coupled equations for Alfvenic and slow magnetosonic (SMS) modes. In this work, the Voigt model is used to describe the equilibrium finite-pressure plasma configuration in an inhomogeneous magnetosphere plasma in a curved magnetic field. Spectral characteristics and the spatial structure of natural ballooning modes are calculated for this model. The model calculations demonstrate the possibility of different longitudinal scales for transverse and longitudinal magnetic components of oscillations near the top of the field line.

Dipole magnetic-field disturbance and generation of current systems by asymmetric plasma pressure

Nonlinear disturbance of the dipole field by nonaxisymmetric plasma pressure distribution was analyzed under the assumption of magnetostatic equilibrium for finite values of the plasma parameter at the pressure maximum area. The distributions of isolines of the constant value of magnetic-field component BZ and the volume of magnetic flux tube in the equatorial plane were obtained. At a finite plasma pressure, local minima and maxima of the magnetic field are formed. The formation of these local maxima and minima leads to the formation of contours (not surrounding the Earth) Bmin = const, where Bmin is the minimum magnetic field on the magnetic field line. This changes the direction of the gradient of the volume of the magnetic flux tube. The configuration of appearing field-aligned currents was determined. The results obtained are discussed in terms of their use in explaining a number of effects observed in the Earth’s magnetosphere.