Low-beta Plasma Research Articles

Geoeffectiveness of CMEs in the Solar Wind

The main drivers of strong geomagnetic activity at the Earth are interplanetary manifestations of coronal mass ejections. A magnetic storm can be caused by compressed sheath fields before the CME, by the CME ejecta or by the combination of these two structures. The most geoeffective subset of CMEs are magnetic clouds. When observed near 1 AU magnetic clouds are characterized by monotonous rotation of magnetic field direction through a large angle, high magnetic field magnitude, low temperature and low plasma beta. We have investigated the magnetic structure and the geomagnetic consequences of magnetic clouds identified from WIND and ACE data for the years 1997-2003. The geomagnetic response of a certain magnetic cloud depends greatly on its magnetic structure and orientation of sheath fields. We have investigated drivers of intense magnetic storms (Dst ¡ −100 nT) during the interval of 1997-2002, i.e. rising, maximum and early declining phases of solar cycle 23. Sheath regions and post-shock streams caused nearly half of all intense storms. Importance of sheath regions as storm drivers even increased as the level of the storm increased. In 2003 two most intense geomagnetic storms of the solar cycle 23 took place. Both of these were driven by southward fields embedded in a magnetic cloud that had axis highly inclined to the ecliptic plane. Though sheath regions alone efficiently drive intense Dst storms (¡ −100 nT) the largest storms (Dst ¡ −300 nT) require exceptionally long-time and intense southward magnetic fields that presumably only magnetic clouds can provide. High solar wind dynamic pressure seems to be important in generating extremely intense Dst storms. As an example we show solar wind condition during Nov 19-20, 2003 magnetic cloud that caused the largest storm of the solar cycle 23.Magnetic clouds have smoothly changing magnetic field direction combined with low solar wind dynamic pressure. Sheath regions typically have rapidly varying magnetic field direction and high dynamic pressure. Thus, these two solar wind drivers put magnetosphere under different type of driving. We also studied the responses of the Dst index that aims to measure the strength of the equatorial ring current and the Kp index that records more global and higher latitude activity than Dst to different storm drivers. We found that in general sheath regions generate higher Kp activity when compared to the level of the the Dst disturbance than magnetic clouds. In some cases rapidly fluctuating magnetic field in the sheath region caused very strong high-latitude activity (Kp 8-9) though the Dst index was significantly less enhanced. This suggest that magnetospheric current systems have different responses to different solar wind drivers.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Contour dynamics method for solving the Grad–Shafranov equation with applications to high beta equilibria

Numerous methods exist to solve the Grad–Shafranov equation, describing the equilibrium of a plasma confined by an axisymmetric magnetic field. Nevertheless, they are limited to low beta or small plasma pressure. Combining a nonconservative variational principle with a contour dynamics approach, the approach presented in this paper converges for extreme high beta configurations. By reducing the dimension of the problem from two to one, a compact and efficient numerical algorithm can be developed, and a wide range of boundary shapes can be utilized. Furthermore, the iterative nature of this technique greatly facilitates convergence at high beta while minimizing computation times.

Impact of magnetic clouds on the middle atmosphere and geomagnetic disturbances

Magnetic clouds, characterized by high magnetic field magnitude, low proton temperature and plasma beta, and a smooth rotation in the magnetic field direction, cause strong geomagnetic disturbances. In the present paper we study the impact of magnetic clouds on the middle atmosphere and geomagnetic disturbances. We find that the effects of magnetic clouds depend on both the phase of the quasibiennial oscillations of equatorial stratospheric winds, and on the handedness, or direction of rotation, of the magnetic field in the cloud. Strongest influence on the stratosphere both in the Northern and Southern hemispheres has left-handed magnetic clouds in QBO Easterly phase. Effects of magnetic clouds are seen in the mesopause region as well, and their effects on the neutral winds and geomagnetic disturbances also depend on QBO phase and the handedness of the clouds, being strongest again for left-handed clouds in QBO Easterly phase.

Reconstruction of the magnetic perturbation in a toroidal reversed field pinch

A new method to obtain the radial profile of the magnetic perturbation in a toroidal force-free plasma having a circular cross section is developed. The toroidal geometry produces poloidal harmonics in the equilibrium quantities (at the leading order m = ±1, n=0), which act as mediators between perturbations with the same toroidal number and different poloidal numbers. The approach proposed here, based on the contravariant representation of the magnetic field in flux co-ordinates, is formally simple and rigorous and maintains a nice similarity with the cylindrical treatment. The method is quite general and can be applied to any circular low-beta plasma. In this work we describe its application to the Reversed Field eXperiment (RFX) plasma. It is customary in reversed field pinches to approach the analysis of MHD instabilities by using a cylindrical geometry. Nonetheless, the effect of a more realistic toroidal geometry can play an important role, and indeed we found that the toroidal effects on the magnetic perturbations are not negligible.

A new solar flare scenario: - High-beta plasma disruption -

The solar corona is believed to be generally low beta. In a low-beta plasma, energy is mainly stored as magnetic energy or current. To dissipate the stored magnetic energy in the highly conductive corona, anomalous resistivity is needed. Activities of outer layers of X-ray loops in solar flares have been interpreted as the result of reconnection of magnetic field due to anomalous resistivity in a current sheet located above the flaring loop.However, recent high-cadence EUV observations show many flares without opening up of magnetic field. This means that existence of current sheets above flaring loops is not a necessary element for flares. It is also found for many flares that low temperature prominence plasma are heated in the very early phase of lifting. These observational facts require a new solar flare scenario different from reconnection.Recent multi-wavelength high-spatial and -temporal resolution observations show that flares originate in the lower atmosphere. We can expect high beta plasma and small curvature magnetic loops in the lower atmosphere. It is also observed high-velocity flows along magnetic loops associated with flares. Bounded motions of charged particles (both thermal motion and flow) along the magnetic lines of force create the centrifugal force. They exceed gravity force under certain conditions (small curvature and high velocity). They can even exceed magnetic tension force depending on beta values of the plasma in the loop.In the case of the upward acceleration (centrifugal - gravity ) plasma in a loop, whose ends are anchored at the photosphere, is unstable against the localized interchange (BALLOONING) mode. It can develop into non-linear phase and explosive phenomena are expected. This is called HIGH-BETA DISRUPTION. The high-beta disruption has many common characteristics to solar flares. Various phenomena related to solar flares such as, high-energy particle acceleration, plasma turbulence, plasma ejections, plasma heating, are interpred as the result of high-beta disruption. High spatial and temporal resolution observations of flares at various wavelengths are used to see the actual instability process. Shibasaki (2001)To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

MHD instabilities and their effects on plasma confinement in Large Helical Device plasmas

Characteristics of MHD instabilities and their impacts on plasma confinement are studied in current free plasmas of the Large Helical Device. Spontaneous L–H transition is often observed in high beta plasmas close to 2% at low toroidal fields (Bt ⩽ 0.75 T). The stored energy starts to rise rapidly just after the transition accompanying the clear rise in the electron density but quickly saturates due to the growth of the m = 2/n = 3 mode (m and n: poloidal and toroidal mode numbers), the rational surface of which is located in the edge barrier region, and edge localized mode (ELM) like activities having fairly small amplitude but high repetition frequency. Even in low beta plasmas without L–H transitions, ELM-like activities are sometimes induced in high performance plasmas with a steep edge pressure gradient and transiently reduce the stored energy up to 10%. Energetic ion driven MHD modes such as Alfvén eigenmodes (AEs) are studied in a very wide range of characteristic parameters (the averaged beta of energetic ions, ⟨βb∥⟩, and the ratio of energetic ion velocity to the Alfvén velocity, Vb∥/VA), of which range includes all tokamak data. In addition to the observation of toroidicity induced AEs (TAEs), coherent magnetic fluctuations of helicity induced AEs (HAEs) have been detected for the first time in NBI heated plasmas. The transition of a core-localized TAE to a global AE (GAE) is also observed in a discharge with temporal evolution of the rotational transform profile, having a similarity to the phenomenon observed in a reversed shear tokamak. At low magnetic fields, bursting TAEs transiently induce a significant loss of energetic ions, up to 40% of injected beams, but on the other hand play an important role in triggering the formation of transport barriers in the core and edge regions.

Analysis of a pressure disturbance in a homogeneous magnetic field

It is well known that in contrast to the Alfvén wave, which is propagating strictly along the direction of the magnetic field, a slow mode wave shows a deviation from the ambient magnetic field. This deviation is determined by the dispersion equation for the slow mode wave. With the help of this dispersion equation we present a theoretical study of the spatial and temporal evolution of an initial pressure disturbance in a homogeneous and constant background magnetic field. The main factor determining the amount of the deviation is the so-called plasma beta, i.e., the ratio of magnetic to thermal energy, which is investigated quantitatively. We obtain that for a low beta plasma, the disturbance propagates more or less strictly along the magnetic field. However, for increasing beta the disturbances across the magnetic field gets stronger. These results can be applied to magnetospheric phenomena, where slow shocks may play a role as a kind of energy carrier as in the case of the Io–Jupiter interaction or magnetic field line reconnection.

Computing nonlinear force free coronal magnetic fields

Abstract. Knowledge of the structure of the coronal magnetic field is important for our understanding of many solar activity phenomena, e.g. flares and CMEs. However, the direct measurement of coronal magnetic fields is not possible with present methods, and therefore the coronal field has to be extrapolated from photospheric measurements. Due to the low plasma beta the coronal magnetic field can usually be assumed to be approximately force free, with electric currents flowing along the magnetic field lines. There are both observational and theoretical reasons which suggest that at least prior to an eruption the coronal magnetic field is in a nonlinear force free state. Unfortunately the computation of nonlinear force free fields is way more difficult than potential or linear force free fields and analytic solutions are not generally available. We discuss several methods which have been proposed to compute nonlinear force free fields and focus particularly on an optimization method which has been suggested recently. We compare the numerical performance of a newly developed numerical code based on the optimization method with the performance of another code based on an MHD relaxation method if both codes are applied to the reconstruction of a semi-analytic nonlinear force-free solution. The optimization method has also been tested for cases where we add random noise to the perfect boundary conditions of the analytic solution, in this way mimicking the more realistic case where the boundary conditions are given by vector magnetogram data. We find that the convergence properties of the optimization method are affected by adding noise to the boundary data and we discuss possibilities to overcome this difficulty.

Confinement and compression of magnetic flux by plasma shells

Confinement and compression of magnetic flux by plasma shells is of interest for a variety of applications associated with keV x-ray production in pulsed-power driven Z-pinch plasma radiation sources (PRS). Confinement of a Bz field with a Bθ field of the pinch current can help stabilize the implosion of a shell from a large initial radius. Compression of the azimuthal magnetic flux in the PRS (secondary) circuit with a plasma shell driven by Bθ field of the primary circuit may represent a new opportunity for using a low-cost, relatively slow pulsed power to generate large amounts of keV x rays. The magnetic field has to be compressed and/or confined by low-mass plasma shells emitting soft x-ray radiation that limits the temperature and conductivity of the shell plasma. The thickness of a plasma shell is established self-consistently during the implosion, and it is not obvious whether or not the shell becomes thick enough to confine or compress the magnetic flux. The results of analytical theory and numerical simulations demonstrate that the flux-compressing capability of a low-beta plasma shell is surprisingly good because the shell is shown to dynamically adjust its thickness so that it always remains of the order of its skin depth. The self-similar profiles of confined magnetic field predicted by the theory are consistently reproduced in the simulations.

Coronal Plume Heating and Kinetic Dissipation of Kinetic Alfven Waves

Coronal plumes are steady-state (for periods of at least 24 hr) bright rays that extend nearly radially from the photosphere to approximately 12 R-circle dot in coronal holes and are believed to be denser than the surrounding media. In a low-beta plasma such as coronal holes, kinetic dissipation of Alfven waves due to the wave-particle resonant interaction can directly lead to electron heating. On the basis of an empirical model of coronal plumes, we investigate the kinetic dissipation of Alfven waves in a plume embedded in the coronal hole. The results show that in the main body of the dense plume, which is embedded in a nearly uniformly magnetized coronal hole, the dissipation of the wave energy can provide an additional local electron heating that is enough to balance the extra radiative loss of the dense bright plume.

Propagation of non-linear circularly polarised Alfvén waves in a homogeneous medium

We study the evolution of non-linear circularly polarised Alfven waves by solving numerically the time-dependent equations of magnetohydrodynamics (MHD) in one dimension. We examine the behaviour of the waves and find that different physical mechanisms are relevant in different ranges of beta. In a low beta plasma the wave may undergo a parametric decay. This is because the wave excites a density enhancement that travels slower than the wave itself and thus interacts with the wave. When beta is greater or equal to one the density enhancement does not interact with the wave and no decay takes place, instead the Alfven wave is reflected against the density enhancement. The reflection zone propagates with the speed 1/n of the Alfven speed. Because of that the magnetic flux is conserved which results in an amplification of the oscillating magnetic field by a factor 1/n. We find that n depends on beta, and that in particular it is less or equal to one for values of beta ~ 1 and is greater or equal to one for beta >> 1. We discuss the relevance of these mechanisms to the acceleration of the solar wind, and the triggering of MHD turbulence in the polar wind region. In particular these simulations can explain the presence of inward propagating Alfven waves in the solar corona.

Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications

We present numerical simulations and explore scalings and anisotropy of compressible magnetohydrodynamic (MHD) turbulence. Our study covers both gas pressure dominated (high beta) and magnetically dominated (low beta) plasmas at different Mach numbers. In addition, we present results for superAlfvenic turbulence and discuss in what way it is similar to the subAlfvenic turbulence. We describe a technique of separating different magnetohydrodynamic (MHD) modes (slow, fast and Alfven) and apply it to our simulations. We show that, for both high and low beta cases, Alfven and slow modes reveal the Kolmogorov spectrum (index=-5/3) and scale-dependent Goldreich-Sridhar anisotropy, while fast modes exhibit spectrum with index=-3/2 and isotropy. We discuss the statistics of density fluctuations arising from MHD turbulence at different regimes. Our findings entail numerous astrophysical implications ranging from cosmic ray propagation to gamma ray bursts and star formation. In particular, we show that the rapid decay of turbulence reported by earlier researchers is not related to compressibility and mode coupling in MHD turbulence. In addition, we show that magnetic field enhancements and density enhancements are marginally correlated. Addressing the density structure of partially ionized interstellar gas on AU scales, we show that the new regime of MHD turbulence that we earlier reported for incompressible flows persists for compressible turbulence and therefore may provide an explanation for those mysterious structures.

Interaction and Dynamics of the Photospheric Network Magnetic Elements

Small-scale magnetic elements in the quiet photospheric network are believed to play a key role in the energy flow from the solar surface to upper layers of atmosphere. Their intense hydro-magnetic activity includes merging and fragmentation of same polarity fluxes, `total' or partial cancellation of neighboring flux elements of opposite polarity, dynamic appearance and disappearance of compact bipoles, etc. We study the general features of these processes, and show that non-collinearity of flux tubes, sharp stratification of low atmosphere and finite plasma beta lead to several specific effects in the interacting flux tubes that may explain the morphological properties of network magnetic field and also provide a mechanism for the energy build up and release in the nearby chromosphere and transition region. We show that during the collision of flux tubes in the photosphere reconnection occurs regardless of whether the flux tubes are of opposite or of the same polarity. But the dynamics of reconnection products are significantly different and lead to different macroscopic effects that can be observed.

Detailed measurements of the electron cyclotron current drive efficiency on DIII-D

Electron cyclotron current drive (ECCD) experiments on the DIII-D tokamak are solidifying the physics basis for localized, off-axis current drive, the goal being to validate a predictive model for ECCD. The ECCD profiles are determined from the magnetic field pitch angles measured by motional Stark effect polarimetry. The measured ECCD switches from the co- to the counter-direction as the toroidal injection angle is varied with a profile width that is in accordance with ray tracing calculations. Tests of electron trapping in low beta plasmas show that the ECCD efficiency decreases rapidly as the deposition is moved off-axis and towards the outboard side of the plasma, but the detrimental effects of electron trapping on the current drive are greatly reduced in high beta plasmas. Overall, the measured ECCD is in good agreement with theoretical calculations using a quasilinear Fokker–Planck code over a wide range of injection angles and plasma parameters.

On drift instabilities in magnetized target fusion devices

Some versions of magnetized target fusion (MTF) devices will be using a high beta plasma, with local beta exceeding 1. Drift instabilities in such a plasma are electromagnetic and are quite different from the analogous instabilities in a low beta plasma. In a collisionless limit they have been analyzed by El Nadi and Rosenbluth [Phys. Fluids 16, 2036 (1973)] who have shown that the cross-field transport coefficients in such a plasma may exceed a Bohm value. On the other hand, high-density plasma in MTF systems is usually strongly collisional in the sense that the drift frequency for the most dangerous large-scale perturbations is smaller than the ion–ion collision frequency, and the particle mean free path is shorter than the parallel wavelength. This regime is studied in the present paper. It is shown that transport coefficients in the MTF plasma are usually smaller than the Bohm diffusion coefficient.

Coronal Magnetic Field Relaxation by Null‐Point Reconnection

We derive the minimum energy state resulting from complete magnetic reconnection in a translationally or axisymmetric MHD system, in the limit of a low plasma beta and high magnetic Reynolds number—conditions appropriate to the solar corona. The results are necessary for determining the amount of energy that can be liberated by reconnection and, hence, are important for understanding coronal heating and other forms of solar activity. The key difference between our approach and previous work is that because of line tying at the high-beta photosphere, reconnection is limited to occur only at magnetic null points initially present in the system. We find that under these circumstances the minimum energy state is not the usual linear force-free field but a state in which the nonpotential component of the field is distributed uniformly on equal flux surfaces. We discuss the implications of our results for the Sun's corona and for laboratory plasmas.

Measurements of anomalous particle and energy fluxes in a magnetized plasma.

Electrostatic probe measurements of low frequency plasma fluctuations and anomalous particle and energy flux densities in a magnetized plasma are presented. A method allowing the simultaneous recording of instantaneous electric field, electron density, and temperature is invoked. The method is applied to flux density measurements in a weakly ionized, low beta plasma created in a toroidal device without magnetic rotational transform. It is also used to identify modes belonging to different dispersion branches and to obtain the dispersion relations for these modes. For the plasma states studied, the phase velocities and the cross phase between the electron density and electric field agree with those predicted from a local, linear stability analysis for electrostatic flute modes and drift waves. The instability threshold, however, is one order of magnitude higher than predicted by theory for unsheared flow. The fluxes measured are consistent with the estimated ionization rate.

Compressible sub-Alfvénic MHD turbulence in low-beta plasmas.

We present a model for compressible sub-Alfvénic isothermal magnetohydrodynamic (MHD) turbulence in low- beta plasmas and numerically test it. We separate MHD fluctuations into three distinct families: Alfvén, slow, and fast modes. We find that production of slow and fast modes by Alfvénic turbulence is suppressed. As a result, Alfvén modes in compressible regime exhibit scalings and anisotropy similar to those in incompressible regime. Slow modes passively mimic Alfvén modes. However, fast modes show isotropy and a scaling similar to acoustic turbulence.

Effects of MHD slow shocks propagating along magnetic flux tubes in a dipole magnetic field

Abstract. Variations of the plasma pressure in a magnetic flux tube can produce MHD waves evolving into shocks. In the case of a low plasma beta, plasma pressure pulses in the magnetic flux tube generate MHD slow shocks propagating along the tube. For converging magnetic field lines, such as in a dipole magnetic field, the cross section of the magnetic flux tube decreases enormously with increasing magnetic field strength. In such a case, the propagation of MHD waves along magnetic flux tubes is rather different from that in the case of uniform magnetic fields. In this paper, the propagation of MHD slow shocks is studied numerically using the ideal MHD equations in an approximation suitable for a thin magnetic flux tube with a low plasma beta. The results obtained in the numerical study show that the jumps in the plasma parameters at the MHD slow shock increase greatly while the shock is propagating in the narrowing magnetic flux tube. The results are applied to the case of the interaction between Jupiter and its satellite Io, the latter being considered as a source of plasma pressure pulses.

Explosive energy release in magnetic shocks.

We show that a magnetic shock whose initial density and/or magnetic perturbation exceeds the Hugoniot limit may lead to substantial and rapid energy release in low beta plasmas (such as occur in the magnetospheres of neutron stars). We illustrate this effect for a fast Magnetohydrodynamic perturbation, as well as for large density perturbations which can be naturally created in low beta plasmas. Using the Riemann solution and simulations, we show that slow modes of finite magnitudes and Alfvénic perturbations can generate strong density perturbations. These perturbations develop into shocks, resulting in efficient energy release.