The self-similar, non-linear evolution of rotating magnetic flux ropes

1995 ◽  
Vol 13 (8) ◽  
pp. 815-827 ◽  
Author(s):  
C. J. Farrugia ◽  
V. A Osherovich ◽  
L. F. Burlaga
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Small Amplitude ◽  
Symmetry Axis ◽  
Flux Rope ◽  
Magnetic Clouds ◽  
Linear Evolution ◽  
Multiplicative Factor ◽  
Self Similar ◽  
The Magnetic Field

Abstract. We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their symmetry axis. Our force balance consists of inertial terms, which include the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We employ the "separable" class of self-similar magnetic fields, defined recently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillation. We investigate the specific effect rotation has on these two modes of evolution. We focus on critical values of the flux rope parameters and show that rotation can suppress the oscillatory mode. We estimate the critical value of the angular velocity Ωcrit, above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. By setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation ω is inversely proportional to the angular velocity of rotation Ω; the product ωΩbeing proportional to the inverse square of the Alfvén time. The period of large-amplitude oscillations of a rotating flux rope of low beta increases exponentially with the energy of the equivalent 1D oscillator. With respect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This multiplicative factor depends on the ratio of the azimuthal speed to the Alfvén speed. Finally, considering interplanetary magnetic clouds as cylindrical flux ropes, we inquire whether they rotate. We find that at 1 AU only a minority do. We discuss data on two magnetic clouds where we interpret the presence in each of vortical plasma motion about the symmetry axis as a sign of rotation. Our estimates for the angular velocities suggest that the parameters of the two magnetic clouds are below critical values. The two clouds differ in many respects (such as age, bulk flow speed, size, handedness of the magnetic field, etc.), and we find that their rotational parameters reflect some of these differences, particularly the difference in age. In both clouds, a rough estimate of the radial electric field in the rigidly rotating core, calculated in a non-rotating frame, yields values of the order mV m–1.

scholarly journals The expected imprint of flux rope geometry on suprathermal electrons in magnetic clouds

2009 ◽  
Vol 27 (10) ◽  
pp. 4057-4067 ◽  
Author(s):  
M. J. Owens ◽  
N. U. Crooker ◽  
T. S. Horbury
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Pitch Angle ◽  
Flux Rope ◽  
Magnetic Clouds ◽  
Magnetic Field Direction ◽  
Magnetic Flux Rope ◽  
Suprathermal Electron ◽  
Angle Scattering ◽  
The Magnetic Field

Abstract. Magnetic clouds are a subset of interplanetary coronal mass ejections characterized by a smooth rotation in the magnetic field direction, which is interpreted as a signature of a magnetic flux rope. Suprathermal electron observations indicate that one or both ends of a magnetic cloud typically remain connected to the Sun as it moves out through the heliosphere. With distance from the axis of the flux rope, out toward its edge, the magnetic field winds more tightly about the axis and electrons must traverse longer magnetic field lines to reach the same heliocentric distance. This increased time of flight allows greater pitch-angle scattering to occur, meaning suprathermal electron pitch-angle distributions should be systematically broader at the edges of the flux rope than at the axis. We model this effect with an analytical magnetic flux rope model and a numerical scheme for suprathermal electron pitch-angle scattering and find that the signature of a magnetic flux rope should be observable with the typical pitch-angle resolution of suprathermal electron data provided ACE's SWEPAM instrument. Evidence of this signature in the observations, however, is weak, possibly because reconnection of magnetic fields within the flux rope acts to intermix flux tubes.

scholarly journals New Force-Free Models of Magnetic Clouds

2005 ◽  
Vol 13 ◽  
pp. 133-133
Author(s):  
M. Vandas ◽  
E. P. Romashets ◽  
S. Watari
Keyword(s):  
Magnetic Field ◽  
Magnetic Cloud ◽  
Free Field ◽  
Flux Rope ◽  
Field Vector ◽  
Magnetic Clouds ◽  
Field Magnitude ◽  
Flux Ropes ◽  
Magnetic Field Magnitude ◽  
The Magnetic Field

AbstractMagnetic clouds are thought to be large flux ropes propagating through the heliosphere. Their twisted magnetic fields are mostly modeled by a constant-alpha force-free field in a circular cylindrical flux rope (the Lundquist solution). However, the interplanetary flux ropes are three dimensional objects. In reality they possibly have a curved shape and an oblate cross section. Recently we have found two force-free models of flux ropes which takes into account the mentioned features. These are (i) a constant-alpha force-free configuration in an elliptic flux rope (Vandas & Romashets 2003, A&A, 398, 801), and (ii) a non-constant-alpha force-free field in a toroid with arbitrary aspect ratio (Romashets & Vandas 2003, AIP Conf Ser. 679, 180). Two magnetic cloud observations were analyzed. The magnetic cloud of October 18-19, 1995 has been fitted by Lepping et al. (1997, JGR, 102, 14049) with use of the Lundquist solution. The cloud has a very flat magnetic field magnitude profile. We fitted it by the elliptic solution (i). The magnetic cloud of November 17-18, 1975 has been fitted by Marubashi (1997) with use of a toroidally adjusted Lundquist solution. The cloud has a large magnetic field vector rotation and a large magnetic field magnitude increase over the background level. We fitted it by the toroidal solution (ii). The both fits match the rotation of the magnetic field vector in a comparable quality to the former fits, but the description of the magnetic field magnitude profiles is remarkable better. It is possible to incorporate temporal effects (expansion) of magnetic clouds into the new solutions through a time-dependent alpha parameter as in Shimazu & Vandas (2002, EP&S, 54, 783).

The evolution of magnetic flux ropes in sheared plasma flows

2000 ◽  
Vol 64 (1) ◽  
pp. 41-55 ◽  
Author(s):  
J. M. SCHMIDT ◽  
P. J. CARGILL
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Shear Layer ◽  
Cross Section ◽  
Circular Cross Section ◽  
Flux Rope ◽  
Plasma Pressure ◽  
Magnetic Flux Ropes ◽  
Flux Ropes ◽  
The Magnetic Field

The evolution of magnetic flux ropes in a sheared plasma flow is investigated. When the magnetic field outside the flux rope lies parallel to the axis of the flux rope, a flux rope of circular cross-section, whose centre is located at the midpoint of the shear layer, has its shape distorted, but remains in the shear layer. Small displacements of the flux-rope centre above or below the midpoint of the shear layer lead to the flux-rope being expelled from the shear layer. This motion arises because small asymmetries in the plasma pressure around the flux-rope boundary leads to a force that forces the flux rope into a region of uniform flow. When the magnetic field outside the flux rope lies in a plane perpendicular to the flux-rope axis, the flux rope and external magnetic field reconnect with each other, leading to the destruction of the flux rope.

scholarly journals Long-duration magnetic clouds: a comparison of analyses using torus- and cylinder-shaped flux rope models

2007 ◽  
Vol 25 (11) ◽  
pp. 2453-2477 ◽  
Author(s):  
K. Marubashi ◽  
R. P. Lepping
Keyword(s):  
Magnetic Field ◽  
Model Fitting ◽  
Flux Rope ◽  
Magnetic Clouds ◽  
Heat Flows ◽  
Spacecraft Trajectory ◽  
Long Duration ◽  
The Difference ◽  
Magnetic Field Variations ◽  
The Magnetic Field

Abstract. We identified 17 magnetic clouds (MCs) with durations longer than 30 h, surveying the solar wind data obtained by the WIND and ACE spacecraft during 10 years from 1995 through 2004. Then, the magnetic field structures of these 17 MCs were analyzed by the technique of the least-squares fitting to force-free flux rope models. The analysis was made with both the cylinder and torus models when possible, and the results from the two models are compared. The torus model was used in order to approximate the curved portion of the MCs near the flanks of the MC loops. As a result, we classified the 17 MCs into 4 groups. They are (1) 5 MC events exhibiting magnetic field rotations through angles substantially larger than 180° which can be interpreted only by the torus model; (2) 3 other MC events that can be interpreted only by the torus model as well, though the rotation angles of magnetic fields are less than 180°; (3) 3 MC events for which similar geometries are obtained from both the torus and cylinder models; and (4) 6 MC events for which the resultant geometries obtained from both models are substantially different from each other, even though the observed magnetic field variations can be interpreted by either of the torus model or the cylinder model. It is concluded that the MC events in the first and second groups correspond to those cases where the spacecraft traversed the MCs near the flanks of the MC loops, the difference between the two being attributed to the difference in distance between the torus axis and the spacecraft trajectory. The MC events in the third group are interpreted as the cases where the spacecraft traversed near the apexes of the MC loops. For the MC events in the fourth group, the real geometry cannot be determined from the model fitting technique alone. Though an attempt was made to determine which model is more plausible for each of the MCs in this group by comparing the characteristics of associated bidirectional electron heat flows, the results were not very definitive. It was also found that the radii of the flux ropes obtained from the torus fitting tend to be generally smaller than those obtained from the cylinder fitting. This result raises a possible problem in estimating the magnetic flux and helicity carried away from the Sun by the MCs.

scholarly journals Coronal Magnetic Field Measurements along a Partially Erupting Filament in a Solar Flare

2021 ◽  
Vol 923 (2) ◽  
pp. 213
Author(s):  
Yuqian Wei ◽  
Bin Chen ◽  
Sijie Yu ◽  
Haimin Wang ◽  
Ju Jing ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Flare ◽  
Magnetic Flux ◽  
Extreme Ultraviolet ◽  
Flux Rope ◽  
Solar Array ◽  
Owens Valley ◽  
Microwave Source ◽  
Flux Ropes ◽  
The Magnetic Field

Abstract Magnetic flux ropes are the centerpiece of solar eruptions. Direct measurements for the magnetic field of flux ropes are crucial for understanding the triggering and energy release processes, yet they remain heretofore elusive. Here we report microwave imaging spectroscopy observations of an M1.4-class solar flare that occurred on 2017 September 6, using data obtained by the Expanded Owens Valley Solar Array. This flare event is associated with a partial eruption of a twisted filament observed in Hα by the Goode Solar Telescope at the Big Bear Solar Observatory. The extreme ultraviolet (EUV) and X-ray signatures of the event are generally consistent with the standard scenario of eruptive flares, with the presence of double flare ribbons connected by a bright flare arcade. Intriguingly, this partial eruption event features a microwave counterpart, whose spatial and temporal evolution closely follow the filament seen in Hα and EUV. The spectral properties of the microwave source are consistent with nonthermal gyrosynchrotron radiation. Using spatially resolved microwave spectral analysis, we derive the magnetic field strength along the filament spine, which ranges from 600 to 1400 Gauss from its apex to the legs. The results agree well with the nonlinear force-free magnetic model extrapolated from the preflare photospheric magnetogram. We conclude that the microwave counterpart of the erupting filament is likely due to flare-accelerated electrons injected into the filament-hosting magnetic flux rope cavity following the newly reconnected magnetic field lines.

scholarly journals A Theoretical Model for the Convection of Magnetic Flux in and near Sunspots

1974 ◽  
Vol 56 ◽  
pp. 235-237
Author(s):  
F. Meyer ◽  
H. U. Schmidt ◽  
N. O. Weiss ◽  
P. R. Wilson
Keyword(s):  
Magnetic Field ◽  
Theoretical Model ◽  
Magnetic Flux ◽  
Rapid Growth ◽  
Initial Phase ◽  
Convection Zone ◽  
Deep Convection ◽  
Flux Rope ◽  
Physical Processes ◽  
The Magnetic Field

In this paper we investigate the physical processes that lead to the growth and decay of magnetic flux in and near sunspots.An initial phase of rapid growth is characterized by the emergence of magnetic flux from the deep convection zone. As the flux rope rises through the surface the magnetic field is swept to the junctions of the supergranular network where sunspots are formed. These flux concentrations follow the footpoints of the emergent flux rope as they rapidly move apart.

scholarly journals Toroidal models of magnetic field with twisted structure

2019 ◽  
Vol 5 (2) ◽  
pp. 69-75 ◽  
Author(s):  
Анастасия Петухова ◽  
Anastasia Petukhova ◽  
Станислав Петухов ◽  
Stanislav Petukhov
Keyword(s):  
Magnetic Field ◽  
Flux Rope ◽  
Forbush Decrease ◽  
Magnetic Clouds ◽  
Integral Model ◽  
Model Parameters ◽  
Magnetic Field Region ◽  
Transport Effects ◽  
Mass Ejection ◽  
The Magnetic Field

We present and discuss properties of the following magnetic field models in a magnetic cloud: Miller and Turner solution, modified Miller–Turner solution, Romashets–Vandas toroidal and integral models, and Krittinatham–Ruffolo model. Helicity of the magnetic field in all the models is the main feature of magnetic clouds. The first three models describe the magnetic field inside an ideal torus. In the integral model, parameters of a generating torus ambiguously determine the volume and form of the magnetic field region. In the Krittinatham–Ruffolo model, the cross-section radius of the torus is variable, thereby it corresponds more closely to the real form of magnetic clouds in the inner heliosphere. These models can be used to interpret in-situ observations of the magnetic flux rope, to study a Forbush decrease in magnetic clouds and transport effects of solar energetic particles injected into a coronal mass ejection.

scholarly journals Toroidal models of magnetic field with twisted structure

2019 ◽  
Vol 5 (2) ◽  
pp. 74-81
Author(s):  
Анастасия Петухова ◽  
Anastasia Petukhova ◽  
Станислав Петухов ◽  
Stanislav Petukhov
Keyword(s):  
Magnetic Field ◽  
Flux Rope ◽  
Forbush Decrease ◽  
Magnetic Clouds ◽  
Integral Model ◽  
Model Parameters ◽  
Magnetic Field Region ◽  
Transport Effects ◽  
Mass Ejection ◽  
The Magnetic Field

We present and discuss properties of the following magnetic field models in a magnetic cloud: Miller and Turner solution, modified Miller–Turner solution, Romashets–Vandas toroidal and integral models, and Krittinatham–Ruffolo model. Helicity of the magnetic field in all the models is the main feature of magnetic clouds. The first three models describe the magnetic field inside an ideal torus. In the integral model, parameters of a generating torus ambiguously determine the volume and form of the magnetic field region. In the Krittinatham–Ruffolo model, the cross-section radius of the torus is variable, thereby it corresponds more closely to the real form of magnetic clouds in the inner heliosphere. These models can be used to interpret in-situ observations of the magnetic flux rope, to study a Forbush decrease in magnetic clouds and transport effects of solar energetic particles injected into a coronal mass ejection.

Emergence of Twisted Magnetic Flux Related Sigmoidal Brightening

2000 ◽  
Vol 179 ◽  
pp. 263-264
Author(s):  
K. Sundara Raman ◽  
K. B. Ramesh ◽  
R. Selvendran ◽  
P. S. M. Aleem ◽  
K. M. Hiremath
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Magnetic Flux ◽  
Ultra Violet ◽  
Active Regions ◽  
Morphological Properties ◽  
Energy Storage And Conversion ◽  
The Sun ◽  
X Rays ◽  
The Magnetic Field

Extended AbstractWe have examined the morphological properties of a sigmoid associated with an SXR (soft X-ray) flare. The sigmoid is cospatial with the EUV (extreme ultra violet) images and in the optical part lies along an S-shaped Hαfilament. The photoheliogram shows flux emergence within an existingδtype sunspot which has caused the rotation of the umbrae giving rise to the sigmoidal brightening.It is now widely accepted that flares derive their energy from the magnetic fields of the active regions and coronal levels are considered to be the flare sites. But still a satisfactory understanding of the flare processes has not been achieved because of the difficulties encountered to predict and estimate the probability of flare eruptions. The convection flows and vortices below the photosphere transport and concentrate magnetic field, which subsequently appear as active regions in the photosphere (Rust & Kumar 1994 and the references therein). Successive emergence of magnetic flux, twist the field, creating flare productive magnetic shear and has been studied by many authors (Sundara Ramanet al.1998 and the references therein). Hence, it is considered that the flare is powered by the energy stored in the twisted magnetic flux tubes (Kurokawa 1996 and the references therein). Rust & Kumar (1996) named the S-shaped bright coronal loops that appear in soft X-rays as ‘Sigmoids’ and concluded that this S-shaped distortion is due to the twist developed in the magnetic field lines. These transient sigmoidal features tell a great deal about unstable coronal magnetic fields, as these regions are more likely to be eruptive (Canfieldet al.1999). As the magnetic fields of the active regions are deep rooted in the Sun, the twist developed in the subphotospheric flux tube penetrates the photosphere and extends in to the corona. Thus, it is essentially favourable for the subphotospheric twist to unwind the twist and transmit it through the photosphere to the corona. Therefore, it becomes essential to make complete observational descriptions of a flare from the magnetic field changes that are taking place in different atmospheric levels of the Sun, to pin down the energy storage and conversion process that trigger the flare phenomena.

scholarly journals Design of a New 1D Halbach Magnet Array with Good Sinusoidal Magnetic Field by Analyzing the Curved Surface

Sensors ◽  
2021 ◽  
Vol 21 (7) ◽  
pp. 2522
Author(s):  
Guangdou Liu ◽  
Shiqin Hou ◽  
Xingping Xu ◽  
Wensheng Xiao
Keyword(s):  
Magnetic Field ◽  
Magnetic Flux ◽  
Permanent Magnet ◽  
Flux Density ◽  
Permanent Magnets ◽  
Air Gap ◽  
Curved Surface ◽  
Magnetic Flux Density ◽  
Sinusoidal Magnetic Field ◽  
The Magnetic Field

In the linear and planar motors, the 1D Halbach magnet array is extensively used. The sinusoidal property of the magnetic field deteriorates by analyzing the magnetic field at a small air gap. Therefore, a new 1D Halbach magnet array is proposed, in which the permanent magnet with a curved surface is applied. Based on the superposition of principle and Fourier series, the magnetic flux density distribution is derived. The optimized curved surface is obtained and fitted by a polynomial. The sinusoidal magnetic field is verified by comparing it with the magnetic flux density of the finite element model. Through the analysis of different dimensions of the permanent magnet array, the optimization result has good applicability. The force ripple can be significantly reduced by the new magnet array. The effect on the mass and air gap is investigated compared with a conventional magnet array with rectangular permanent magnets. In conclusion, the new magnet array design has the scalability to be extended to various sizes of motor and is especially suitable for small air gap applications.

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