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DOE OSTI2013

ON THE ANISOTROPY IN EXPANSION OF MAGNETIC FLUX TUBES IN THE SOLAR CORONA

Most one-dimensional hydrodynamic models of plasma confined to magnetic flux tubes assume circular tube cross sections. We use potential field models to show that flux tubes in circumstances relevant to the solar corona do not, in general, maintain the same cross-sectional shape through their length and therefore the assumption of a circular cross section is rarely true. We support our hypothesis with mathematical reasoning and numerical experiments. We demonstrate that lifting this assumption in favor of realistic, non-circular loops makes the apparent expansion of magnetic flux tubes consistent with that of observed coronal loops. We propose that in a bundle of ribbon-like loops, those that are viewed along the wide direction would stand out against those that are viewed across the wide direction due to the difference in their column depths. That result would impose a bias toward selecting loops that appear not to be expanding, seen projected in the plane of sky. An implication of this selection bias is that the preferentially selected non-circular loops would appear to have increased pressure scale heights even if they are resolved by current instruments.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2000

Magnetic Flux Compression Concept for Nuclear Pulse Propulsion and Power

The desire for fast, efficient interplanetary transport requires propulsion systems having short acceleration times and very high specific impulse attributes. Unfortunately, most highly efficient propulsion systems which are within the capabilities of present day technologies are either very heavy or yield very low impulse such that the acceleration time to final velocity is too long to be of lasting interest, One exception, the nuclear thermal thruster, could achieve the desired acceleration but it would require inordinately large mass ratios to reach the range of desired final velocities. An alternative approach, among several competing concepts that are beyond our modern technical capabilities, is a pulsed thermonuclear device utilizing microfusion detonations. In this paper, we examine the feasibility of an innovative magnetic flux compression concept for utilizing microfusion detonations, assuming that such low yield nuclear bursts can be realized in practice. In this concept, a magnetic field is compressed between an expanding detonation driven diamagnetic plasma and a stationary structure formed from a high temperature superconductor (HTSC). In general, we are interested in accomplishing two important functions: (1) collimation of a hot diamagnetic plasma for direct thrust production; and (2) pulse power generation for dense plasma ignition. For the purposes of this research, it is assumed that rnicrofusion detonation technology may become available within a few decades, and that this approach could capitalize on recent advances in inertial confinement fusion ICF) technologies including magnetized target concepts and antimatter initiated nuclear detonations. The charged particle expansion velocity in these detonations can be on the order of 10 (exp 6)- 10 (exp 7) meters per second, and, if effectively collimated by a magnetic nozzle, can yield the Isp and the acceleration levels needed for practical interplanetary spaceflight. The ability to ignite pure fusion micro-bursts with reasonable levels of input energy is an equally challenging scientific problem. It remains to be seen, however, whether an effective ignition driver can be developed which meets the requirements for practical spaceflight application (namely high power density, compactness, low weight, and low cost). In this paper, system level performance and design issues are examined including generator performance, magnetic flux compression processes, magnetic diffusion processes, high temperature superconductor (HTSC) material properties, plasmadynamic processes, detonation plasma expansion processes, magnetohydrodynamic instabilities, magnetic nozzle performance, and thrust production performance. Representative generator performance calculations based on a simplified skin layer formulation are presented as well as the results of exploratory small-scale laboratory experiments on magnetic flux diffusion in HTSC materials. In addition, planned follow-on scientific feasibility experiments are described which utilize high explosive detonations and high energy gas discharges to simulate the plasma conditions associated with thermonuclear micro-detonations.

Litchford, Ronald J.↗

NASA NTRS1988

C IV fluxes from the Sun as a star, and the correlation with magnetic flux

A total of 144 C IV wavelength 1548 Solar Maximum Mission (SMM)-UVSP spectroheliograms of solar plages were analyzed, some of which are series of exposures of the same region on the same day. Also analyzed were the C IV wavelength 1551 rasters of plages and C IV wavelength 1548 rasters of the quiet sun. The sample contained data on 17 different plages, observed on 50 different days. The center-to-limb variations of the active regions show that the optical thickness effects in the C IV wavelength 1548 line can be neglected in the conversion from intensity to flux density. As expected for the nearly optically thin situation, the C IV wavelength 1548 line is twice as bright as the C IV 1551 line. The average C IV wavelength 1548 flux density for a quiet region is 2700 ergs/cm/s and, with surprisingly little scatter, 18,000 erg/cm/s for plages. The intensity histograms of rasters obtained at disk center can be separated into characteristic plage and quiet sun contributions with variable relative filling factors. The relationship between the C IV and magnetic flux densities for spatially resolved data is inferred to be almost the same, with only an additional factor of order unity in the constant of proportionality.

Schrijver, C. J.↗

NASA NTRS2023

The Eruption of a Magnetic Flux Rope Observed By Solar Orbiter and Parker Solar Probe

Magnetic flux ropes are a key component of coronal mass ejections, forming the core of these eruptive phenomena. However, determining whether a flux rope is present prior to eruption onset and, if so, the rope’s handedness and the number of turns that any helical field lines make is difficult without magnetic field modelling or in-situ detection of the flux rope. We present two distinct observations of plasma flows along a filament channel on 4 and 5 September 2022 made using the Solar Orbiter spacecraft. Each plasma flow exhibited helical motions in a right-handed sense as the plasma moved from the source active region across the solar disk to the quiet Sun, suggesting that the magnetic configuration of the filament channel contains a flux rope with positive chirality and at least one turn. The length and velocity of the plasma flow increased from the first to the second observation, suggesting evolution of the flux rope, with the flux rope subsequently erupting within ∼5 hours of the second plasma flow. The erupting flux rope then passed over the Parker Solar Probe spacecraft during its Encounter 13, enabling in-situ diagnostics of the structure. Although complex and consistent with the flux rope erupting from underneath the heliospheric current sheet, the in-situ measurements support the inference of a right-handed flux rope from remote-sensing observations. These observations provide a unique insight into the eruption and evolution of a magnetic flux rope near the Sun.

Dynamics↗

NASA NTRS1984

Numerical simulation of reconnection in an emerging magnetic flux region

Numerical solutions in two dimensions are presented for the resistive MHD equations of an initial boundary value problem, simulating reconnection between an emerging magnetic flux region and an overlying coronal magnetic field. This numerical model displays four main phases, which are interpreted in terms of (1) a slowly evolving quasi-steady phase during which most of the magnetic flux emerges, with approximate equilibrium between magnetic and pressure forces; (2) an impulsive phase in which either the reconnection or continuing emergence of the first phase comes to disrupt the equilibrium, and extensive acceleration occurs as the high pressure region within the emerging region drives the fluid upwards and outwards; (3) a second quasi-steady phase; and (4) a potential-static phase in which continuing reconnection, ohmic dissipation, and fluid transport through boundaries depletes the system of all currents and flows.

Forbes, T. G.↗

NASA NTRS2001

Coronal Heating and the Magnetic Flux Content of the Network

Previously, from analysis of SOHO coronal images in combination with Kitt Peak magnetograms, we found that the quiet corona is the sum of two components: the large-scale corona and the coronal network. The large-scale corona consists of all coronal-temperature (T approximately 10(exp 6) K) structures larger than supergranules (greater than approximately 30,000 kilometers). The coronal network (1) consists of all coronal-temperature structures smaller than supergranules, (2) is rooted in and loosely traces the photospheric magnetic network, (3) has its brightest features seated on polarity dividing lines (neutral lines) in the network magnetic flux, and (4) produces only about 5% of the total coronal emission in quiet regions. The heating of the coronal network is apparently magnetic in origin. Here, from analysis of EIT coronal images of quiet regions in combination with magnetograms of the same quiet regions from SOHO/MDI and from Kitt Peak, we examine the other 95% of the quiet corona and its relation to the underlying magnetic network. We find: (1) Dividing the large-scale corona into its bright and dim halves divides the area into bright "continents" and dark "oceans" having spans of 2-4 supergranules. (2) These patterns are also present in the photospheric magnetograms: the network is stronger under the bright half and weaker under the dim half. (3) The radiation from the large-scale corona increases roughly as the cube root of the magnetic flux content of the underlying magnetic network. In contrast, the coronal radiation from an active region increases roughly linearly with the magnetic flux content of the active region. We assume, as is widely held, that nearly all of the large-scale corona is magnetically rooted in the network. Our results suggest that either the coronal heating in quiet regions has a large non-magnetic component, or, if the heating is predominantly produced via the magnetic field, the mechanism is significantly different than in active regions.

Falconer, D. A.↗

NASA NTRS2001

Coronal Heating and the Magnetic Flux Content of the Network

Previously, from analysis of SOHO/EIT coronal images in combination with Kitt Peak magnetograms (Falconer et al 1998, ApJ, 501, 386-396), we found that the quiet corona is the sum of two components: the e-scale corona and the coronal network. The large-scale corona consists of all coronal-temperature (T approx. 10(exp 6) K) structures larger than supergranules (>approx.30,000 km). The coronal network (1) consists of all coronal-temperature structures smaller than supergranules, (2) is rooted in and loosely traces the photospheric magnetic network, (3) has its brightest features seated on polarity dividing fines (neutral lines) in the network magnetic flux, and (4) produces only about 5% of the total coronal emission in quiet regions. The heating of the coronal network is apparently magnetic in origin. Here, from analysis of EIT coronal images of quiet regions in combination with magnetograms of the same quiet regions from SOHO/MDI and from Kitt Peak, we examine the other 95% of the quiet corona and its relation to the underlying magnetic network. We find: (1) Dividing the large-scale corona into its bright and dim halves divides the area into bright "continents" and dark "oceans" having spans of 2-4 supergranules. (2) These patterns are also present in the photospheric magnetograms: the network is stronger under the bright half and weaker under the dim half. (3) The radiation from the large-scale corona increases roughly as the cube root of the magnetic flux content of the underlying magnetic network. In contrast, Fisher et A (1998, ApJ, 508, 985-998) found that the coronal radiation from an active region increases roughly linearly with the magnetic flux content of the active region. We assume, as is widely held, that nearly all of the large-scale corona is magnetically rooted in the network. Our results, together with the result of Fisher et al (1999), suggest that either the coronal heating in quiet regions has a large non-magnetic component, or, if the heating is predominantly produced via the magnetic field, the mechanism is significantly different than in active regions. This work is funded by NASA's Office of Space Science through the Solar Physics Supporting Research and Technology Program and the Sun-Earth Connection Guest Investigator Program.

Falconer, D. A.↗

DOE OSTI2017

A Solar Blowout Jet Caused by the Eruption of a Magnetic Flux Rope

We investigate the three-dimensional (3D) magnetic structure of a blowout jet originating in the western edge of NOAA active region (AR) 11513 on 2012 July 2 by means of recently developed forced field extrapolation model. The results show that the blowout jet was caused by the eruption of the magnetic flux rope (MFR) consisting of twisted field lines. We further calculate the twist number T{sub w} and squashing factor Q of the reconstructed magnetic field and find that (1) the MFR corresponds well with the high T{sub w} region, and (2) the MFR outer boundary corresponds well with the high Q region, probably interpreting the bright structure at the base of the jet. The twist number of the MFR is estimated to be T{sub w}=−1.54±0.67. Thus, the kink instability is regarded as the initiation mechanism of the blowout jet as T{sub w} reaches or even exceeds the threshold value of the kink instability. Our results also indicate that the bright point at the decaying phase is actually composed of some small loops that are heated by the reconnection occurring above. In summary, the blowout jet is mostly consistent with the scenario proposed by Moore et al., except that the kink instability is found to be a possible trigger.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1984

The turbulent twisted magnetic flux tube gas

The kinematic behavior of a dilute, two-dimensional 'gas' of parallel twisted magnetic flux tubes in a highly conducting fluid is considered. Collisions between flux tubes with the same sense of twist are inelastic due to the reconnection of their oppositely directed azimuthal magnetic field components at impact. In some collisions, the tension in the reconnected magnetic flux is sufficient to bind the two flux tubes together. Collisions between flux tubes with the opposite sense of twist are elastic. It is shown that a tenuous gas of individual twisted flux tubes condenses into two large-scale regions of magnetic field with opposite twists. This calculation illustrates the results of Montgomery and co-workers on the migration of magnetic energy towards small wavenumbers in two-dimensional magnetohydrodynamic (MHD) turbulence. In particular, this problem illustrates the dynamical nonequilibrium of the relaxation phase in turbulent MHD systems.

Bogdan, T. J.↗

DOE OSTI2014

Design of set-point weighting PI{sup λ} + D{sup μ} controller for vertical magnetic flux controller in Damavand tokamak

In this paper, a simple method is presented for tuning weighted PI{sup λ} + D{sup μ} controller parameters based on the pole placement controller of pseudo-second-order fractional systems. One of the advantages of this controller is capability of reducing the disturbance effects and improving response to input, simultaneously. In the following sections, the performance of this controller is evaluated experimentally to control the vertical magnetic flux in Damavand tokamak. For this work, at first a fractional order model is identified using output-error technique in time domain. For various practical experiments, having desired time responses for magnetic flux in Damavand tokamak, is vital. To approach this, at first the desired closed loop reference models are obtained based on generalized characteristic ratio assignment method in fractional order systems. After that, for the identified model, a set-point weighting PI{sup λ} + D{sup μ} controller is designed and simulated. Finally, this controller is implemented on digital signal processor control system of the plant to fast/slow control of magnetic flux. The practical results show appropriate performance of this controller.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRSDate not supplied

Writhed Analytical Magnetic Flux Rope Model

We summarise our findings from a recently published paper “Writhed Analytical Magnetic Flux Rope Model”, JGR Space Physics. In this publication we present a novel method to describe and characterize writhed flux ropes. By describing the flux rope axis in terms of a general space curve we can arbitrarily vary the curvature and torsion. We derive expressions for the magnetic field components under the assumption of a circular cross-section and invariant axial magnetic flux. We expect that our approach can also be extended to more complicated non-axisymmetric cross-sections in the future.

A J Weiss↗

DOE OSTI2025

Statistical Survey of Magnetic Flux Integral Quantities in Saturn's Magnetosphere

Magnetic flux integral quantities (e.g., flux tube entropy, flux tube content) are conserved quantities under the frozen-in assumption. The change of these quantities often indicates the violation of the frozen-in condition (e.g., interchange instability). In this study, we combine the Cassini CAPS and CHEMS moments data with a steady-state magnetic field model (i.e., the Caudal model) to estimate the flux tube mass and flux tube entropy in Saturn's magnetosphere. Our statistical survey found that the flux tube mass rapidly decreases with radial distance away from Saturn in the inner magnetosphere and roughly levels out in the middle magnetosphere. This indicates that the radial transport processes could occur via a double-reconnection process in the inner magnetosphere, while the radial transport processes appear to be more advective in the middle magnetosphere. Notice that Saturn's magnetosphere is stabilized by a radially increasing profile of flux tube entropy and destabilized by a radially decreasing profile of flux tube content. In this study, we also estimate the expected penetration location by using the flux tube interchange stability formalism developed by Southwood and Kivelson (1987, https://doi.org/10.1029/ja092ia01p00109). The results show that flux tube entropy can play a crucial role in braking the injections, while the flux tube content has a relatively smaller influence on the injected flux tube, being consistent with our previous case study by Wing et al. (2022, https://doi.org/10.3847/1538-4357/ac85b2).

Ma, Xuanye [Embry-Riddle Aeronautical University, ↗

NASA NTRS2023

The Eruption of A Magnetic Flux Rope Observed By Solar Orbiter and Parker Solar Probe

Magnetic flux ropes are a key component of coronal mass ejections, forming the core of these eruptive phenomena. However, determining whether a flux rope is present prior to eruption onset and, if so, the rope's handedness and the number of turns that any helical field lines make is difficult without magnetic field modeling or in situ detection of the flux rope. We present two distinct observations of plasma flows along a filament channel on 2022 September 4 and 5 made using the Solar Orbiter spacecraft. Each plasma flow exhibited helical motions in a right-handed sense as the plasma moved from the source active region across the solar disk to the quiet Sun, suggesting that the magnetic configuration of the filament channel contains a flux rope with positive chirality and at least one turn. The length and velocity of the plasma flow increased from the first to the second observation, suggesting evolution of the flux rope, with the flux rope subsequently erupting within ∼5 hr of the second plasma flow. The erupting flux rope then passed over the Parker Solar Probe spacecraft during its encounter (13), enabling in situ diagnostics of the structure. Although complex and consistent with the flux rope erupting from underneath the heliospheric current sheet, the in situ measurements support the inference of a right-handed flux rope from remote-sensing observations. These observations provide a unique insight into the eruption and evolution of a magnetic flux rope near the Sun.

David M. Long↗

DOE OSTI2016

Quasi-static and dynamic magnetic tension forces in arched, line-tied magnetic flux ropes

Solar eruptions are often driven by magnetohydrodynamic instabilities such as the torus and kink instabilities that act on line-tied magnetic flux ropes. We designed our recent laboratory experiments to study these eruptive instabilities which have demonstrated the key role of both dynamic (Myers et al 2015 Nature 528 526) and quasi-static (Myers et al 2016 Phys. Plasmas 23 112102) magnetic tension forces in contributing to the equilibrium and stability of line-tied magnetic flux ropes. In our paper, we synthesize these laboratory results and explore the relationship between the dynamic and quasi-static tension forces. And while the quasi-static tension force is found to contribute to the flux rope equilibrium in a number of regimes, the dynamic tension force is substantial mostly in the so-called failed torus regime where magnetic self-organization events prevent the flux rope from erupting.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Gauge-invariant perturbation expansion in powers of electric charge for the density-of-states of a network model for charged-particle motion in a uniform background magnetic flux density

An explicitly gauge-invariant expansion in powers of e/$\hbar$ times the magnetic flux density is formally obtained for the density of states [as characterized by the trace of the resolvent $\hat{G}$ = (ω-$\hat{ℎ}$)-1] of a charged particle moving on a Hermitian quantum network that is embedded in a Euclidean background that supports a uniform magnetic flux density. The explicit expressions, given here up to third order in the flux density, are also valid for the “local trace” (the trace of $\hat{P}_i\hat{G}$ , where $\hat{P}_i$ is the projector on a network node) and do not appear to have been previously given.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

Formation of magnetic flux ropes during confined flaring well before the onset of a pair of major coronal mass ejections

NOAA active region (AR) 11429 was the source of twin super-fast coronal mass ejections (CMEs). The CMEs took place within an hour from each other, with the onset of the first taking place in the beginning of 2012 March 7. This AR fulfills all the requirements for a “super active region”; namely, Hale's law incompatibility and a δ-spot magnetic configuration. One of the biggest storms of Solar Cycle 24 to date (D{sub st}=−143 nT) was associated with one of these events. Magnetic flux ropes (MFRs) are twisted magnetic structures in the corona, best seen in ∼10 MK hot plasma emission and are often considered the core of erupting structures. However, their “dormant” existence in the solar atmosphere (i.e., prior to eruptions), is an open question. Aided by multi-wavelength observations by the Solar Dynamics Observatory (SDO) and by the Solar Terrestrial Relations Observatory (STEREO) and a nonlinear force-free model for the coronal magnetic field, our work uncovers two separate, weakly twisted magnetic flux systems which suggest the existence of pre-eruption MFRs that eventually became the seeds of the two CMEs. The MFRs could have been formed during confined (i.e., not leading to major CMEs) flaring and sub-flaring events which took place the day before the two CMEs in the host AR 11429.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1977

Solar cycle variation of magnetic flux emergence

The number of X-ray bright points (XBP) has been measured from solar X-ray images obtained during two rocket flights in 1976. When compared with the data obtained during the Skylab mission (1973), the number is found to be higher by a factor of 2. As the probability of obtaining the result by chance is less than 1 in 5 million, it is concluded that the number of XBP has increased in the three year interval. As all other indicators of activity have decreased between 1973 and 1976, the cyclical variation of the short-lifetime end of the magnetic-flux-emergence spectrum is out of phase with the solar cycle as defined by active regions or sunspots. Since XBP in 1973 contributed more to the emerging magnetic flux than did active regions, the possibility exists that the total amount of emerging magnetic flux may be maximized at a sunspot minimum.

Davis, J. M.↗

NASA NTRS1989

Siphon flows in isolated magnetic flux tubes. 3: The equilibrium path of the flux tube arch

The arched equilibrium path of a thin magnetic flux tube in a plane-stratified, nonmagnetic atmosphere is calculated for cases in which the flux tube contains a steady siphon flow. The large scale mechanical equilibrium of the flux tube involves a balance among the magnetic buoyancy force, the net magnetic tension force due to the curvature of the flux tube axis, and the inertial (centrifugal) force due to the siphon flow along curved streamlines. The ends of the flux tube are assumed to be pinned down by some other external force. Both isothermal and adiabatic siphon flows are considered for flux tubes in an isothermal external atmosphere. For the isothermal case, in the absence of a siphon flow the equilibrium path reduces to the static arch calculated by Parker (1975, 1979). The presence of a siphon flow causes the flux tube arch to bend more sharply, so that magnetic tension can overcome the additional straightening effect of the inertial force, and reduces the maximum width of the arch. The curvature of the arch increases as the siphon flow speed increases. For a critical siphon flow, with supercritical flow in the downstream leg, the arch is asymmetric, with greater curvature in the downstream leg of the arch. Adiabatic flow have qualitatively similar effects, except that adiabatic cooling reduces the buoyancy of the flux tube and thus leads to significantly wider arches. In some cases the cooling is strong enough to create negative buoyancy along sections of the flux tube, requiring upward curvature of the flux tube path along these sections and sometimes leading to unusual equilibrium paths of periodic, sinusoidal form.

Thomas, John H.↗