Open Flux Tubes Research Articles

Propagating kink waves in an open coronal magnetic flux tube with gravitational stratification: Magnetohydrodynamic simulation and forward modelling

Context. In coronal open-field regions, such as coronal holes, there are many transverse waves propagating along magnetic flux tubes, which are generally interpreted as kink waves. Previous studies have highlighted their potential role in coronal heating, solar wind acceleration, and seismological diagnostics of various physical parameters. Aims. This study aims to investigate propagating kink waves, considering both vertical and horizontal density inhomogeneity, using 3D magnetohydrodynamic (MHD) simulations. Methods. We established a 3D MHD model of a gravitationally stratified open flux tube, incorporating a velocity driver at the lower boundary to excite propagating kink waves. Forward modelling was conducted to synthesise observational signatures of the Fe IX 17.1 nm line. Results. Resonant absorption and density stratification both affect the wave amplitude. When diagnosing the relative density profile with velocity amplitude, resonant damping needs to be properly considered to avoid a possible underestimation. In addition, unlike standing modes, propagating waves are believed to be Kelvin-Helmholtz stable. In the presence of vertical stratification, however, the phase mixing of transverse motions around the tube boundary can still induce small-scale structures, partially dissipating wave energy and leading to a temperature increase, especially at higher altitudes. Moreover, we conducted forward modeling to synthesise observational signatures, which revealed the promising potential of future coronal imaging spectrometers such as MUSE in resolving these wave-induced signatures. Also, the synthesised intensity signals exhibit apparent periodic variations, offering a potential method for indirectly observing propagating kink waves with current extreme ultraviolet imagers.

Cutoff of transverse waves through the solar transition region

Context. Transverse oscillations are ubiquitously observed in the solar corona, both in coronal loops and in open magnetic flux tubes. Numerical simulations suggest that their dissipation could heat coronal loops, thus counterbalancing radiative losses. These models rely on a continuous driver at the footpoint of the loops. However, analytical works predict that transverse waves are subject to a cutoff in the transition region. It is thus unclear whether they can reach the corona and indeed heat coronal loops. Aims. Our aims are to determine how the cutoff of kink waves affects their propagation into the corona and to characterize the variation of the cutoff frequency with altitude. Methods. Using 3D magnetohydrodynamic simulations, we modelled the propagation of kink waves in a magnetic flux tube, embedded in a realistic atmosphere with thermal conduction, which starts in the chromosphere and extends into the corona. We drove kink waves at four different frequencies and determined whether they experienced a cutoff. We then calculated the altitude at which the waves were cut off and compared it to the prediction of several analytical models. Results. We show that kink waves indeed experience a cutoff in the transition region, and we identified the analytical model that gives the best predictions. In addition, we show that waves with periods shorter than approximately 500 s can still reach the corona by tunnelling through the transition region with little to no attenuation of their amplitude. This means that such waves can still propagate from the footpoints of loop and result in heating in the corona.

Magnetospheric Plasma Systems Science and Solar Wind Plasma Systems Science: The Plasma-Wave Interactions of Multiple Particle Populations

Building upon the research legacies of Peter Gary and Richard Thorne, this perspective discusses a plasma-system picture wherein multiple ion and electron populations interact with each otherviamultiple types of plasma waves. The two cases discussed are 1) the Earth’s magnetosphere with ion and electron populations trapped in the closed flux tubes of the magnetic dipole and 2) the solar wind with ion and electron populations expanding away from the Sun in open magnetic flux tubes. For the magnetosphere, internal convection drives particle populations into stronger magnetic fields, leading to particle anisotropies; for the solar wind the expansion of the plasma away from the Sun results in the particle populations moving into weaker magnetic fields, leading also to particle anisotropies. In both cases, the anisotropies of the diverse ion and electron populations produce kinetic instabilities resulting in the production of diverse types of plasma waves and wave-particle interactions. Following the extensive research of Richard Thorne, web diagrams of plasma-wave interactions are laid out for the multiple ion and electron populations of the magnetosphere and following the extensive research of Peter Gary web diagrams of plasma-wave interactions are laid out for the multiple ion and electron populations of the solar wind. The advantages of a systems-analysis approach to these two plasma systems is discussed.

Solar Origin of Compressive Alfvénic Spikes/Kinks as Observed by Parker Solar Probe

Abstract The solar wind is found by the Parker Solar Probe to be abundant with Alfvénic velocity spikes and magnetic field kinks. Temperature enhancement is another remarkable feature associated with the Alfvénic spikes. How the prototype of these coincident phenomena is generated intermittently in the source region is an important and wide-ranging subject. Here we propose a new model introducing guide-field discontinuity into the interchange magnetic reconnection between open funnels and closed loops with different magnetic helicities. The modified interchange reconnection model not only can accelerate jet flows from the newly opening closed loop but also can excite and launch Alfvénic wave pulses along the newly reconnected and post-reconnected open flux tubes. We find that the modeling results can reproduce the following observational features: (1) Alfvén disturbance is pulsive in time and asymmetric in space; (2) Alfvénic pulse is compressive with temperature enhancement and density variation inside the pulse. We point out that three physical processes co-happening with Alfvén wave propagation can be responsible for the temperature enhancement: (a) convection of heated jet flow plasmas (decrease in density), (b) propagation of compressive slow-mode waves (increase in density), and (c) conduction of heat flux (weak change in density). We also suggest that the radial nonlinear evolution of the Alfvénic pulses should be taken into account to explain the formation of magnetic switchback geometry.

On the Possibility of Heating the Solar Corona by Heat Fluxes from Coronal Magnetic Structures

We estimate the role of heat flux from hot magnetic loops and open flux tubes into the surrounding corona as a possible source of heating of the corona. We show that hot magnetic-flux tubes (Type-II spicules) provide a more efficient source of coronal heating than hot magnetic loops, as the closed magnetic structure of a loop substantially restricts the heat flux into the corona. In order to compensate for radiation and thermal-conduction losses, approximately $10^{4}$ Type-II spicules with a temperature of several million Kelvin are required, which is about 1% of the number of spicules simultaneously observed on the solar disk. Our analysis shows that the principal source of energy that heats the coronal plasma is photospheric convection, which generates electric currents of about $10^{10}$ – $10^{12}$ A in magnetic loops and spicules. Dissipation of the currents increases significantly in the partially ionized plasma, i.e. when ion–atom collisions and the associated Cowling conductivity occur. This results in two important effects: heating of plasma in magnetic structures up to several million Kelvin, and ejection of hot plasma from open magnetic-flux tubes to the corona, replenishing the corona with hot plasma. The ejection of hot plasma results from the heating of the spicule foot-point by electric-current dissipation, which grows with a sporadic increase in the velocity of photospheric convection, for example, due to five-minute oscillations or the Rayleigh–Taylor instability. As a result, the rate of heating the photospheric foot-points of the spicules by ring currents exceeds radiation losses, which leads to a jump in the pressure gradient and the ejection of hot plasma into the corona from the open tips of the magnetic-flux tubes.

On the Relationship between Magnetic Expansion Factor and Observed Speed of the Solar Wind from Coronal Pseudostreamers

Abstract For the past 30+ yr, the magnetic expansion factor (f s ) has been used in empirical relationships to predict solar wind speed (v obs) at 1 au based on an inverse relationship between these two quantities. Coronal unipolar streamers (i.e., pseudostreamers) undergo limited field line expansion, resulting in f s -dependent relationships to predict the fast wind associated with these structures. However, case studies have shown that the in situ observed pseudostreamer solar wind was much slower than that derived with f s . To investigate this further, we conduct a statistical analysis to determine if f s and v obs are inversely correlated for a large sample of periods when pseudostreamer wind was observed at multiple 1 au spacecraft (i.e., ACE, STEREO-A/B). We use the Wang–Sheeley–Arge model driven by Air Force Data Assimilative Photospheric Flux Transport (ADAPT) photospheric field maps to identify 38 periods when spacecraft observe pseudostreamer wind. We compare the expansion factor of the last open field lines on either side of a pseudostreamer cusp with the corresponding in situ measured solar wind speed. We find that only slow wind (v obs < 500 km s−1) is associated with pseudostreamers and that there is not a significant correlation between f s and v obs for these field lines. This suggests that field lines near the open–closed boundary of pseudostreamers are not subject to the steady-state acceleration along continuously open flux tubes assumed in the f s –v obs relationship. In general, dynamics at the boundary between open and closed field lines such as interchange reconnection will invalidate the steady-state assumptions of this relationship.

Detailed Imaging of Coronal Rays with the Parker Solar Probe

Abstract The Wide-field Imager for Solar PRobe (WISPR) obtained the first high-resolution images of coronal rays at heights below 15 R ⊙ when the Parker Solar Probe (PSP) was located inside 0.25 au during the first encounter. We exploit these remarkable images to reveal the structure of coronal rays at scales that are not easily discernible in images taken from near 1 au. To analyze and interpret WISPR observations, which evolve rapidly both radially and longitudinally, we construct a latitude versus time map using the full WISPR data set from the first encounter. From the exploitation of this map and also from sequential WISPR images. we show the presence of multiple substructures inside streamers and pseudostreamers. WISPR unveils the fine-scale structure of the densest part of streamer rays that we identify as the solar origin of the heliospheric plasma sheet typically measured in situ in the solar wind. We exploit 3D magnetohydrodynamic models, and we construct synthetic white-light images to study the origin of the coronal structures observed by WISPR. Overall, including the effect of the spacecraft relative motion toward the individual coronal structures, we can interpret several observed features by WISPR. Moreover, we relate some coronal rays to folds in the heliospheric current sheet that are unresolved from 1 au. Other rays appear to form as a result of the inherently inhomogeneous distribution of open magnetic flux tubes.

Magnetic Reconnection of Solar Flux Tubes and Coronal Reconnection Signatures in the Solar Wind at 1 AU

AbstractThe origin of interplanetary magnetic field that is frozen‐in to the solar wind plasma flow is clearly magnetic flux from the Sun's corona. However, the filamented structure of magnetic fields observed in the solar wind cannot be accounted for quite so simply. Given the 2 days or more for solar wind to travel from the Sun to 1 AU, some argue that many current sheets are present due to turbulence and other in‐transit effects in the dynamic plasma outflow. Alternatively, it is postulated that a “flux tube texture” of the solar wind exists as fossil structure of the corona. In this paper we examine the possible influence of magnetic reconnection occurring close to the Sun or in the solar wind on the character of current sheets observed by Magnetospheric Multiscale at 1 AU. Photospheric convection is used to perturb a magnetic carpet‐like configuration, which has well‐segmented open flux tubes defined by topological elements of the magnetic field. Flux tube boundaries in the model are defined by magnetic sepratrix surfaces which are a preferential location for strong currents and magnetic reconnection. Reconnection is associated with signatures in the magnetic field and plasma that may advect with the solar wind all the way to 1 AU. Aided by three‐dimensional coronal modeling and two‐dimensional simulation examples of reconnection layers, we examine properties of current sheets observed by Magnetospheric Multiscale and how these solar wind boundaries may relate to reconnection operating earlier in the solar wind or corona.

Modelling 3D magnetic networks in a realistic solar atmosphere

ABSTRACT The magnetic network extending from the photosphere (solar radius ≃ R⊙) to the lower corona ($\mathrm{ R}_\odot +10\, {\rm Mm}$) plays an important role in the heating mechanisms of the solar atmosphere. Here we develop further the models of the authors with realistic open magnetic flux tubes, in order to model more complicated configurations. Closed magnetic loops and combinations of closed and open magnetic flux tubes are modelled. These are embedded within a stratified atmosphere, derived from observationally motivated semi-empirical and data-driven models subject to solar gravity and capable of spanning from the photosphere up into the chromosphere and lower corona. Constructing a magnetic field comprising self-similar magnetic flux tubes, an analytic solution for the kinetic pressure and plasma density is derived. Combining flux tubes of opposite polarity, it is possible to create a steady background magnetic field configuration, modelling a solar atmosphere exhibiting realistic stratification. The result can be applied to the Solar and Heliospheric Observatory Michelson Doppler Imager (SOHO/MDI), Solar Dynamics Observatory Helioseismic and Magnetic Imager (SDO/HMI) and other magnetograms from the solar surface, for which photospheric motions can be simulated to explore the mechanism of energy transport. We demonstrate this powerful and versatile method with an application to HMI data.

Alfvén Wave-driven Wind from RGB and AGB Stars

Abstract We develop a magnetohydrodynamical model of Alfvén wave-driven wind in open magnetic flux tubes piercing the stellar surface of red giant branch (RGB) and asymptotic giant branch (AGB) stars, and investigate the physical properties of the winds. The model simulations are carried out along the evolutionary tracks of stars with initial mass in the range of 1.5–3.0 M ⊙ and initial metallicity Z ini = 0.02. Setting the surface magnetic field strength to 1 G, we find that the wind during the evolution of the star can be classified into the following four types: the first is wind with velocity higher than 80 km s−1 in the RGB and early AGB (E-AGB) phases, the second is wind with outflow velocity less than 10 km s−1 seen around the tip of the RGB or in the E-AGB phase, the third is the unstable wind in the E-AGB and thermally pulsing AGB (TP-AGB) phases, and the fourth is the stable massive and slow wind with mass-loss rate higher than 10−7 M ⊙ yr−1 and outflow velocity lower than 20 km s−1 in the TP-AGB phase. The mass-loss rates in the first and second types of wind are two or three orders of magnitude lower than the values evaluated by an empirical formula. The presence of a massive and slow wind of the fourth type suggests the possibility that the massive outflow observed in TP-AGB stars could be attributed to Alfvén wave-driven wind.

Evidence for Super-Alfvénic Oscillations in Solar Type III Radio Burst Sources

Abstract At the site of their origin, solar meter-wave radio bursts contain pristine information about the local coronal magnetic field and plasma parameters. On its way through the turbulent corona, this radiation gets substantially modified due to propagation effects. Effectively disentangling the intrinsic variations in emission from propagation effects has remained a challenge. We demonstrate a way to achieve this using a snapshot spectroscopic imaging study of weak type III bursts using data from the Murchison Widefield Array. Using this study, we present the first observational evidence for second-scale quasi-periodic oscillations (QPOs) in burst source sizes and orientation with simultaneous QPOs in intensity. The observed oscillations in source sizes are so fast and large that they require two orders of magnitude larger Alfvén speed than the typical local value of 0.5 Mm s−1 at the burst generation heights, if interpreted within an MHD framework. These observations imply the presence of a quasi-periodic regulation mechanism operating at the particle injection site, modulating the geometry of energetic electron beams that generate type III bursts. In addition, we introduce a method to characterize plasma turbulence in the mid-coronal ranges. We also detect evidence for a systematic drift in the location of the burst sources superposed on the random jitter induced by scattering. We interpret this as the motion of the open flux tube within which the energetic electron beams travel.

Generation of Inverted Heliospheric Magnetic Flux by Coronal Loop Opening and Slow Solar Wind Release

Abstract In situ spacecraft observations provide much-needed constraints on theories of solar wind formation and release, particularly the highly variable slow solar wind, which dominates near-Earth space. Previous studies have shown an association between local inversions in the heliospheric magnetic field (HMF) and solar wind released from the vicinity of magnetically closed coronal structures. We here show that in situ properties of inverted HMF are consistent with the same hot coronal source regions as the slow solar wind. We propose that inverted HMF is produced by solar wind speed shear, which results from interchange reconnection between a coronal loop and open flux tube, and introduces a pattern of fast–slow–fast wind along a given HMF flux tube. This same loop-opening process is thought to be central to slow solar wind formation. The upcoming Parker Solar Probe and Solar Orbiter missions provide a unique opportunity to directly observe these processes and thus determine the origin of the slow solar wind.

Spectrum of the open QCD flux tube and its effective string description I: 3d static potential in SU(N = 2, 3)

We perform a high precision measurement of the static qoverline{q} potential in three-dimensional SU(N) gauge theory with N = 2, 3 and compare the results to the potential obtained from the effective string theory. In particular, we show that the exponent of the leading order correction in 1/R is 4, as predicted, and obtain accurate results for the continuum limits of the string tension and the non-universal boundary coefficient {overline{b}}_2 , including an extensive analysis of all types of systematic uncertainties. We find that the magnitude of {overline{b}}_2 decreases with increasing N, leading to the possibility of a vanishing {overline{b}}_2 in the large N limit. In the standard form of the effective string theory possible massive modes and the presence of a rigidity term are usually not considered, even though they might give a contribution to the energy levels. To investigate the effect of these terms, we perform a second analysis, including these contributions. We find that the associated expression for the potential also provides a good description of the data. The resulting continuum values for {overline{b}}_2 are about a factor of 2 smaller than in the standard analysis, due to contaminations from an additional 1/R4 term. However, {overline{b}}_2 shows a similar decrease in magnitude with increasing N. In the course of this extended analysis we also obtain continuum results for the masses appearing in the additional terms and we find that they are around twice as large as the square root of the string tension in the continuum and compatible between SU(2) and SU(3) gauge theory. In the follow up papers we will extend our investigations to the large N limit and excited states of the open flux tube.

Dayside and nightside magnetic field responses at 780 km altitude to dayside reconnection

AbstractDuring southward interplanetary magnetic field, dayside reconnection will drive the Dungey cycle in the magnetosphere, which is manifested as a two‐cell convection pattern in the ionosphere. We address the response of the ionospheric convection to changes in the dayside reconnection rate by examining magnetic field perturbations at 780 km altitude. The Active Magnetosphere and Planetary Electrodynamics Response Experiment data products derived from the Iridium constellation provide global maps of the magnetic field perturbations. Cluster data just upstream of the Earth's bow shock have been used to estimate the dayside reconnection rate. By using a statistical model where the magnetic field can respond on several time scales, we confirm previous reports of an almost immediate response both near noon and near midnight combined with a 10–20 min reconfiguration time of the two‐cell convection pattern. The response of the ionospheric convection has been associated with the expansion of the polar cap boundary in the Cowley‐Lockwood paradigm. In the original formulation of this paradigm the expansion spreads from noon to midnight in 15–20 min. However, also an immediate global response has been shown to be consistent with the paradigm when the previous dayside reconnection history is considered. In this paper we present a new explanation for how the immediate response can be accommodated in the Cowley‐Lockwood paradigm. The new explanation is based on how MHD waves propagate in the magnetospheric lobes when newly reconnected open flux tubes are added to the lobes, and the magnetopause flaring angle increases.

High‐latitude circulation in giant planet magnetospheres

AbstractWe follow‐up the proposal by Cowley et al. (2004) that the plasma circulation in the magnetospheres of the giant planets is a combination of two cycles or circulation systems. The Vasyliunas cycle transports heavy material ionized deep within the magnetosphere eventually to loss in the magnetotail. The second cycle is driven by magnetic reconnection between the planetary and the solar wind magnetic fields (the Dungey cycle) and is found on flux tubes poleward of those of the Vasyliunas cycle. We examine features of the Dungey system, particularly what occurs out of the equatorial plane. The Dungey cycle requires reconnection on the dayside, and we suggest that at the giant planets the dayside reconnection occurs preferentially in the morning sector. Second, we suggest that most of the solar wind material that enters through reconnection on to open flux tubes on the dayside never gets trapped on closed field lines but makes less than one circuit of the planet and exits down tail. In its passage to the nightside, the streaming ex‐solar wind material is accelerated centrifugally by the planetary rotation primarily along the field; thus, in the tail it will appear very like a planetary wind. The escaping wind will be found on the edges of the tail plasma sheet, and reports of light ion streams in the tail are likely due to this source. The paper concludes with a discussion of high‐latitude circulation in the absence of reconnection between the solar wind and planetary field.

TIME-DEPENDENT TURBULENT HEATING OF OPEN FLUX TUBES IN THE CHROMOSPHERE, CORONA, AND SOLAR WIND

We investigate several key questions of plasma heating in open-field regions of the corona that connect to the solar wind. We present results for a model of Alfven-wave-driven turbulence for three typical open magnetic field structures: a polar coronal hole, an open flux tube neighboring an equatorial streamer, and an open flux tube near a strong-field active region. We compare time-steady, one-dimensional turbulent heating models (Cranmer et al., 2007) against fully time-dependent three-dimensional reduced-magnetohydrodynamics modeling of BRAID (van Ballegooijen et al., 2011). We find that the time-steady results agree well with time-averaged results from BRAID. The time-dependence allows us to investigate the variability of the magnetic fluctuations and of the heating in the corona. The high-frequency tail of the power spectrum of fluctuations forms a power law whose exponent varies with height, and we discuss the possible physical explanation for this behavior. The variability in the heating rate is bursty and nanoflare-like in nature, and we analyze the amount of energy lost via dissipative heating in transient events throughout the simulation. The average energy in these events is 10^21.91 erg, within the "picoflare" range, and many events reach classical "nanoflare" energies. We also estimated the multithermal distribution of temperatures that would result from the heating-rate variability, and found good agreement with observed widths of coronal differential emission measure (DEM) distributions. The results of the modeling presented in this paper provide compelling evidence that turbulent heating in the solar atmosphere by Alfven waves accelerates the solar wind in open flux tubes.

Response of Solar Wind on Extreme Solar Activity

We investigate how the mass loss by the solar wind depends on the solar activity levels, particularly focusing on the solar wind during extremely high activity. We perform forward-type magnetohydrodynamical (MHD) numerical experiments for Alfvén wave-driven solar winds with a wide range of the input Poynting flux from the photosphere. Increasing the magnetic field strength and the turbulent velocity at the solar photosphere from the current solar level, the mass loss rate rapidly increases at first owing to the suppression of the reflection of the Alfvén waves. The surface materials are lifted up by the magnetic pressure associated with the Alfvén waves, and the cool dense chromosphere is extended to ∼ 10% of the stellar radius. The dense atmospheres enhance the radiative losses and eventually most of the input Poynting energy from the surface escapes by the radiation. As a result, there is no more sufficient energy remained for the kinetic energy of the wind; the solar wind saturates for the extreme activity level, as observed in Wood et al. The saturation level is positively correlated with the average magnetic field strength contributed from open flux tubes. If the field strength is a few times larger than the present level, the mass loss rate could be as high as 1000 times.

Alfvén instability of steady state flux tubes

Context. MHD instabilities play an important role in the dynamics and energetics of the solar atmosphere. Aims. An open vertical magnetic flux tube is permeated by an upflow in a stratified atmosphere with variable temperature. The stability of the tube is investigated with respect to small-amplitude torsional perturbations generated at the footpoint by random convective motions. Methods. A steady state equilibrium incorporating the effects of a vertical body force, heating, and losses is derived analytically. The governing equations for torsional motions are integrated with a fourth-order Runge-Kutta method and matched with the analytical solutions in the upper regions to obtain a numerical dispersion relation. The dependence of the eigenmode frequencies on different parameters is analysed. Unstable modes are found for a range of Alfven and flow speeds in the photosphere, as well as expansion factors of the flux tubes. Both supersonic and subsonic flows are considered. Results. It is shown that torsional perturbations are exponentially amplified in time if a section of the tube exists where the upflowing plasma decelerates and the tube expands. The flow speeds required for the instability are sub-Alfvenic. Conclusions. The instability may be important for understanding the abundance of Alfven waves seen in recent observations and the associated heating in magnetic regions of the solar atmosphere.

The role of magnetic flux tube deformation and magnetosheath plasma beta in the saturation of the Region 1 field‐aligned current system

AbstractThe phenomena of cross polar cap potential (CPCP) and ionospheric field‐aligned current (FAC) saturation remain largely unexplained. In the present study, we expand upon the Alfvén wing model of CPCP saturation by investigating its impact on the magnetosphere‐ionosphere current system, particularly the Region 1 FAC input into the polar cap. Our hypothesis is that the ability of open flux tubes to deform in response to applied fluid stress from the magnetosheath is governed by the magnetosheath plasma beta, which in turn governs the Maxwell stress imposed on ionospheric plasma from the magnetosphere. We performed 32 MHD simulations with varying solar wind density and interplanetary magnetic field strength and show that the plasma beta does govern the deformation of open field lines, as well as the nonlinear response of the Region 1 FAC system to increasingly southward interplanetary magnetic field. Further, we show that the current‐voltage relationship in the ionosphere also shows a dependence on the plasma beta in the magnetosheath, with the ionosphere becoming more resistive at lower beta.

MAGNETOHYDROSTATIC EQUILIBRIUM. II. THREE-DIMENSIONAL MULTIPLE OPEN MAGNETIC FLUX TUBES IN THE STRATIFIED SOLAR ATMOSPHERE

A system of multiple open magnetic flux tubes spanning the solar photosphere and lower corona is modelled analytically, within a realistic stratified atmosphere subject to solar gravity. This extends results for a single magnetic flux tube in magnetohydrostatic equilibrium, described in Gent et al. (MNRAS, 435, 689, 2013). Self-similar magnetic flux tubes are combined to form magnetic structures, which are consistent with high-resolution observations. The observational evidence supports the existence of strands of open flux tubes and loops persisting in a relatively steady state. Self-similar magnetic flux tubes, for which an analytic solution to the plasma density and pressure distribution is possible, are combined. We calculate the appropriate balancing forces, applying to the equations of momentum and energy conservation to preserve equilibrium. Multiplex flux tube configurations are observed to remain relatively stable for up to a day or more, and it is our aim to apply our model as the background condition for numerical studies of energy transport mechanisms from the solar surface to the corona. We apply magnetic field strength, plasma density, pressure and temperature distributions consistent with observational and theoretical estimates for the lower solar atmosphere. Although each flux tube is identical in construction apart from the location of the radial axis, combinations can be applied to generate a non-axisymmetric magnetic field with multiple non-uniform flux tubes. This is a considerable step forward in modelling the realistic magnetized three-dimensional equilibria of the solar atmosphere.