Three-Dimensional Reconstruction of Two Solar Coronal Mass Ejections Using the STEREO Spacecraft

Based on the multiple-vantage observations of STEREO, SOHO, wind and other spacecraft, the fast and wide coronal mass ejections (CME) during the 24th solar cycle from January 2010 to September 2014 are selected in this paper. Using the outputs of Richardson’s (2014) empirical model of solar energetic particle (SEP) intensity under different conditions, the effects of its associations such as CME, pre-CME, and type II radio bursts, on SEP intensity are analyzed, and the relationship between SEP event and these characteristics is also discussed. The main conclusions are as follows. 1) The presence or absence of pre-CME within 13 h before fast CME significantly improves the model prediction effect and has a significant influence on whether fast CME produces SEP event. Compared with the events without pre-CMEs, the events with pre-CMEs have a low proportion of false alarms (FR: 47.7% <i>vs.</i> 70%). However, the number of pre-CMEs does not improve the model output. 2) CMEs with type-II radio bursts have significantly lower FR to generate SEP events than fast CMEs without type-II radio bursts (42% <i>vs.</i> 68%). And selecting type-II radio bursts as a constraint will filter out some small/weak SEP events, the relationship between model predictions and observations especially for large SEP events (e.g. <i>I</i><sub>p</sub> ≥ 0.01 pfu/MeV) will stand out. Moreover, if the type-II radio enhancement is taken into account, FR can be further reduced to 29.4%, and the proportion of hits can be further increased (HR: 48.5%), and the model prediction is significantly improved. 3) The larger the start frequency of type II radio bursts, the smaller the end frequency is, and FR decreases slightly, but at the same time, a large number of SEP events are excluded by this condition, and the results show that the constraints on the start/end frequency of type-II radio bursts do not improve the model predictions distinctly. 4) If the sub-classification of type-II radio bursts is considered as the model constraint, the CMEs associated with multi-band type-II radio bursts have better model predictions than those with single-band events. For example, m-DH-km type-II radio bursts have lower FR (35.4%) and higher HR (48%), and the accuracy of empirical model is higher. In summary, we find that in addition to the velocity and angular width of CME, the associations of pre-CME, type II radio bursts and their enhancement, and multi-band sub-classification are the favorable conditions for CME to generate SEP events. The SEP intensities obtained by the empirical model have better consistency with the observations, and better predictions can be obtained. This investigation indicates that SEP events are more likely generated by fast and wide CMEs accompanied by pre-CMEs, multi-band type II radio bursts and their enhancements, which seem to serve as discriminative signal for SEP-rich and SEP-poor CMEs.

A series of powerful solar flares and coronal mass ejections (CMEs) occurred between 10 and 14 May 2024. As these eruptions propagated through the corona, they generated multiple solar type II radio bursts, indicating the presence of shock waves. This study characterises a series of type II radio bursts associated with a CME that occurred on 14 May, focusing on the coronal conditions during the event and identifying the likely location of the shocks where the radio bursts are generated. The CME was tracked using a combination of white light and extreme ultraviolet observations of the solar corona taken by three instruments: the Geostationary Operational Environmental Satellite (GOES) Solar Ultraviolet Imager (SUVI) and two coronagraphs of the Solar and Heliospheric Observatory (SOHO) Large Angle and Spectrometric Coronagraph (LASCO), together with ground-based radio observations between 10-240 MHz from the Irish Low-Frequency Array (I-LOFAR). The radial distances of the radio sources were examined using a series of density models, with both potential field source surface and magnetohydrodynamic models used to examine the coronal plasma conditions. Four type II bursts were identified in the I-LOFAR radio dynamic spectrum over ∼15 minutes, exhibiting features such as band splitting, herringbones, and fragmentation. The shocks were found to have speeds ranging between ∼443-2075 km s -1 $, with drift rates of ∼-361 to -78 kHz s^-1. The shocks were found to have a M_A ≈ 3.21-3.57. indicating that they were super-Alfvénic. The first type II burst was triggered $∼18 minutes after the CME launch, with each burst appearing to have been generated at a different height in the corona. Analysis of the derived kinematics and modelling results suggests that the type II bursts were likely produced at the shoulders of the CME near the flanks, where open magnetic field lines and relatively low Alfvén speeds facilitated shock formation. This multi-instrument study shows that multiple type II bursts from a single CME originated at different coronal heights, with modelling indicating their generation near the CME flanks where low Alfvén speeds and open magnetic field lines facilitated shock formation. The findings highlight the role of coronal conditions, particularly the magnetic field configuration and the Alfvén speed distribution, in determining the heights and locations where these bursts originate. Our results reinforce the importance of continuous, multi-wavelength observations for understanding shock dynamics and improving constraints on coronal models.

Optical flow is a powerful image processing tool for measuring motion in digital images. The optical flow algorithm provides an estimate of the velocity vector at every pixel from a pair of successive images. Here we present an application of this method to images of coronal mass ejections (CMEs). The technique is first tested and validated on a simulated CME. It is then applied to several CMEs observed with the LASCO C2 coronagraph to derive their velocity fields. The resulting velocity measurements allow us to visualize the evolution of the CME plasma and to separate the bulk velocity from the expansion velocity of a given CME. To our knowledge, this is the first time that such information has been extracted from CME observations. We discuss the limitations and accuracy of our optical flow method and propose further improvements.

<p>Previous studies of Coronal Mass Ejections (CMEs) have shown the importance of understanding their geometrical structure and internal magnetic field configuration for improving forecasting at Earth. The precise prediction of the CME shock and the magnetic cloud arrival time, their magnetic field strength and the orientation upon impact at Earth is still challenging and relies on solar wind and CME evolution models and precise input parameters. In order to understand the propagation of CMEs in the interplanetary medium, we need to understand their interaction with the complex features in the magnetized background solar wind which deforms, deflects and erodes the CMEs and determines their geo-effectiveness. Hence, it is important to model the internal magnetic flux-rope structure in the CMEs as they interact with CIRs/SIRs, other CMEs and solar transients in the heliosphere. The spheromak model (Verbeke et al. 2019) in the heliospheric wind and CME evolution simulation EUHFORIA (Pomoell and Poedts, 2018), fits well with the data near the CME nose close to its axis but fails to predict the magnetic field in CME legs when these impact Earth (Scolini et al. 2019). Therefore, we implemented the FRi3D stretched flux-rope CME model (Isavnin, 2016) in EUHFORIA to model a more realistic CME geometry. Fri3D captures the three-dimensional magnetic field structure with parameters like skewing, pancaking and flattening that quantify deformations experienced by an interplanetary CME. We perform test runs of real CME events and validate the ability of FRi3D coupled with EUHFORIA in predicting the CME geo-effectiveness. We have modeled two real events with FRi3D. First, a CME event on 12 July 2012 which was a head-on encounter at Earth. Second, the flank CME encounter of 14 June 2012 which did not leave any magnetic field signature at Earth when modeled with Spheromak. We compare our results with the results from non-magnetized cone simulations and magnetized simulations employing the spheromak flux-rope model. We further discuss how constraining observational parameters using the stretched flux rope CME geometry in FRi3D affects the prediction of the magnetic field strength in our simulations, highlighting improvements and discussing future perspective.</p><p><em>This research has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 870405 (EUHFORIA 2.0)</em></p>

The interaction of interplanetary coronal mass ejections (ICME) with each other and with co-rotating interaction regions (CIR) changes their configuration, dynamics, magnetic field and plasma characteristics and can make space weather forecasting difficult. During the period of March 20–25, 2011, the Solar Terrestrial Relation Observatory (STEREO B) encountered a compound stream containing several interacting structures. Our analysis suggests that the stream consists of two ICMEs followed by an embedded ICME/CIR. The sudden appearance of the third ICME within the fast wind side of the CIR causes the proton temperature(T_{p} ) to drop suddenly to its lowest level in about 1.2 hours, from 3.89 times 10^{5} K to 1.07 times 10^{4} K (by a factor of ≈36). The fast wind which follows the CIR influences not only the third ICME’s temperature but also its proton beta (upbeta_{mathrm{p}}). In addition, the third ICME impacts the CIR through expansion and deceleration. A forward pressure wave penetrates ICME1. It’s source is either the second ICME, the merged third ICME and CIR, or it may be a remnant shock. The compression causes an increase of the T_{p} and upbeta_{mathrm{p}} of the second and part of the first ICME. Despite the signatures of four large-scale interacting structures within the compound stream, it is difficult to reconcile the in-situ sequence with other remote sensing observations of ejecta close to the Sun because of the large system of coronal expanding loops above the active region. Compound streams therefore remain difficult to interpret, and further understanding of the subject will depend on the future study of similar events.

Based on our previous works regarding solar eruptions, we focus on the relationships among different eruptive phenomena, such as solar flares, eruptive prominences and coronal mass ejections (CMEs). The three processes show clear correlations under certain circumstances. The correlation between a CME and solar flare depends the energy that stored in the relevant magnetic structure, which is available to drive the eruption: the more energy that is stored, the better the correlation is; otherwise, the correlation is poor. The correlation between a CME and eruptive prominence, on the other hand, depends on the plasma mass concentration in the configuration prior to the eruption: if the mass concentration is significant, a CME starts with an eruptive prominence, otherwise, a CME develops an without an apparent associated eruptive prominence. These results confirm that solar flares, eruptive prominences and CMEs are different significances of a single physical process that is related to the energy release in a disrupted coronal magnetic field. The impact of gravity on CME propagation and the above correlations is also investigated. Our calculations indicate that the effect of gravity is not significant unless the strength of the background field in the disrupted magnetic configuration becomes weak, say weaker than 30 G.

Interplanetary coronal mass ejections (ICMEs) are the heliospheric counterparts of solar coronal mass ejections, and their comprehensive cataloging near Earth has enabled significant advances across space science disciplines. As a part of the Project Space Life by Eco Astronomy Inc, this review presents a synthesis of the Near-Earth ICME since 1996” dataset compiled by I. G. Richardson and H. V. Cane, highlighting its historical development, methodology, key findings, and broad applications. The dataset encompasses approximately 600 ICMEs observed at 1 AU from 1996 through early 2024, spanning solar cycles 23, 24, and the rise of 25. We discuss how ICMEs are identified using in-situ plasma, magnetic field, composition, and energetic particle signatures, and how this approach has evolved with improved data (e.g. ACE spacecraft measurements). The ICME catalogs reveals clear solar-cycle trends, ICME occurrence rises by an order of magnitude from solar minimum to maximum with the yearly counts peaking in 2000 (51 events) and dipping to only a few events at recent minima. It also captures intriguing temporal patterns such as a quasi-periodicity of ~150 days in ICME occurrence (Cane & Richardson, January 1, 2003). We synthesize the typical ICME properties (duration, speed, magnetic field strength) and how they vary between cycles: e.g. cycle 23 produced more frequent and faster ICMEs than the weaker cycle 24. The dataset’s extensive annotations (footnotes) link each ICME to associated phenomena like geomagnetic sudden commencements, storm indices, and cosmic ray depressions, allowing analysis of ICME impacts. We review how ~90% of major geomagnetic storms (Dst ≤ –100 nT) in 1996–2005 were caused by ICMEs or their driven shocks (Richardson & Cane, 2007), underlining their geo effectiveness. We summarize statistical correlations between ICME parameters (speed, magnetic field, size) and geomagnetic storm intensity and discuss notable events. Beyond geomagnetism, ICMEs are shown to modulate galactic cosmic rays, causing short-term intensity drops (Forbush decreases) in ~80% of cases (I & H, 2011) and contributing to long-term cosmic-ray modulation over the solar cycle. The rich Richardson-Cane ICME database has fostered multidisciplinary benefits: improving space weather forecasts (by providing empirical event data for CME arrival and storm predictions), informing heliospheric physics (e.g. ICME propagation and solar-cycle variability), elucidating cosmic ray transport (through ICME-caused particle decreases), and aiding studies of impacts on technological systems (satellites, power grids, GPS) and Earth’s atmosphere. We conclude by emphasizing the value of this continually updated ICME catalogs for future research and cross-disciplinary applications, and we include a comprehensive appendix of ICME analysis figures derived from the dataset.

The current progression toward solar maximum provides a unique opportunity to use multi-perspective spacecraft observations together with numerical models to better understand the evolution and propagation of coronal mass ejections (CMEs). Of interest to both the scientific and forecasting communities are the Earth-directed “halo” CMEs, since they typically produce the most geoeffective events. However, determining the actual initial geometries of halo CMEs is a challenge due to the plane-of-sky projection effects. Thus the recent 15 February 2011 halo CME event has been selected for this study. During this event the Solar TErrestrial RElations Observatory (STEREO) A and B spacecraft were fortuitously located ∼ 90° away from the Sun–Earth line such that the CME was viewed as a limb event from these two spacecraft, thereby providing a more reliable constraint on the initial CME geometry. These multi-perspective observations were utilized to provide a simple geometrical description that assumes a cone shape for a CME to calculate its angular width and central position. The event was simulated using the coupled Wang–Sheeley–Arge (WSA)-Enlil 3D numerical solar corona-solar wind model. Daily updated global photospheric magnetic field maps were used to drive the background solar wind. To improve our modeling techniques, the sensitivity of the modeled CME arrival times to the initial input CME geometry was assessed by creating an ensemble of numerical simulations based on multiple sets of cone parameters for this event. It was found that the accuracy of the modeled arrival times not only depends on the initial input CME geometry, but also on the accuracy of the modeled solar wind background, which is driven by the input maps of the photospheric field. To improve the modeling of the background solar wind, the recently developed data-assimilated magnetic field synoptic maps produced by the Air Force Data Assimilative Photospheric flux Transport (ADAPT) model were used. The ADAPT maps provide a more instantaneous snapshot of the global photospheric field distribution than that provided by traditional daily updated synoptic maps. Using ADAPT to drive the background solar wind, an ensemble set of eight different CME arrival times was generated, where the spread in the predictions was ∼ 13 hours and was nearly centered on the observed CME shock arrival time.

The problem of forecasting southward pointing magnetic fields in coronal mass ejections (CMEs) is closely tied to our ability to measure their magnetic field configuration between the Sun and 1 AU. I will review some of the ideas that have been developed to tackle this problem, from using solar proxies, heliospheric images, Faraday rotation and measuring the in situ magnetic field near the Sun Earth-line. Another way to make progress is to use the L1 data as boundary conditions for fast ensemble simulations, focusing on the flux rope parts inside CMEs. However, for any type of modeling and forecasting we need to better understand the global magnetic structure and shape of CME flux ropes from multi-spacecraft observations, now delivered by spacecraft such as Parker Solar Probe, Solar Orbiter, BepiColombo, STEREO-Ahead and Wind, ACE or DSCOVR. In the future, the PUNCH mission will allow for the first time to extract 3D information from heliospheric images, forming another trailblazer towards developing models for ESA's Vigil mission, and setting the stage for possible interplanetary fleets of small spacecraft.

Hostile space weather is one of the principal threats to modern human technology because of the dependency of our lives on satellites. Solar coronal mass ejections, solar flares, and high‐speed solar wind streams often cause some sequences of damaging disturbances within the Earth's magnetosphere, in the atmosphere, and even on the Earth's surface. The time‐varying Sun, as the main source of space weather causes geomagnetic storms and substorms in many ways with coronal mass ejections (CME) being possibly the most harmful among them. CMEs cause transient magnetized plasma flows as interplanetary consequences, which drive the geomagnetic storms and substorms in the Earth's magnetosphere. It is shown that the cyclic solar activity has chaotic characteristics. It seems that the chaotic modeling of solar and geomagnetic activity indices is an important approach for analysis and prediction of the solar extreme events. This is particularly useful for engineers and designers interested in space weather prediction and its applications. One of the most important tools for eliciting the chaotic trends is the “Lyapunov exponents,” which is a useful measure of the stability of a dynamic system. This paper analyzes the variation of Lyapunov exponents (LE) for three solar and geomagnetic activity indices during CMEs: the sunspot number, disturbance storm time, and proton temperature. The analysis has been carried out using the technique of adaptive LE estimation adopted from previous works; the suitable window for which has been determined via trial and error. It is shown that the LE of these solar and geomagnetic activity indices varies rapidly during CMEs. The variation in LEs creates a pattern as a precursor for the forthcoming CME. This precursor, which is an oscillation in the values of Les, begins several steps sooner than the CME's occurrence. Then, during the CME, the LEs decrease to a small positive or a negative value, which demonstrates that during an anomaly such as a CME the chaotic characteristics of solar and geomagnetic activity indices decrease and solar and geomagnetic activity indices follow more regular dynamics.

Abstract. The apparent contradiction between small-scale source regions of, and large-scale coronal response to, coronal mass ejections (CMEs) has been a long-standing puzzle. For some, CMEs are considered to be inherently large-scale events – eruptions in which a number of flux systems participate in an unspecified manner, while others consider magnetic reconnection in special global topologies to be responsible for the large-scale response of the lower corona to CME events. Some of these ideas may indeed be correct in specific cases. However, what is the key element which makes CMEs large-scale? Observations show that the extent of the coronal disturbance matches the angular width of the CME – an important clue, which does not feature strongly in any of the above suggestions. We review observational evidence for the large-scale nature of CME source regions and find them lacking. Then we compare different ideas regarding how CMEs evolve to become large-scale. The large-scale magnetic topology plays an important role in this process. There is amounting evidence, however, that the key process is magnetic reconnection between the CME and other magnetic structures. We outline a CME evolution model, which is able to account for all the key observational signatures of large-scale CMEs and presents a clear picture how large portions of the Sun become constituents of the CME. In this model reconnection is driven by the expansion of the CME core resulting from an over-pressure relative to the pressure in the CME's surroundings. This implies that the extent of the lower coronal signatures match the final angular width of the CME.

The principal scientific objective of the Solar-Terrestrial Relations Observatory (STEREO) is to understand the origin and consequences of coronal mass ejections (CMEs). CMEs are the most energetic eruptions on the Sun. They are responsible for essentially all of the largest solar energetic particle events and are the primary cause of major geomagnetic storms. They may be a critical element in the solar dynamo because they remove the dynamo-generated magnetic flux from the Sun. Two spacecraft at 1 AU from the Sun, one drifting ahead of Earth and one behind, will image CMEs. They will also map the distribution of magnetic fields and plasmas in the heliosphere and accomplish a variety of science goals described in the 1997 report of the NASA Science Definition Team for the STEREO Mission. Current plans call for the two STEREO launches in early 2003. Simultaneous image pairs will be obtained by the STEREO telescopes at gradually increasing spacecraft separations in the course of the mission. Additionally, in-situ measurements will provide accurate information about the state of the ambient solar wind and energetic particle populations ahead of and behind CMEs. These measurements will allow definitive tests of CME and interplanetary shock models. The mission will include a beacon mode to warn of either coronal or interplanetary conditions indicative of impending disturbances at Earth.

The period between late October and early November of 2003 included a series of large solar events that resulted in some of the most extreme space weather of the current solar cycle. Space weather has been defined as the conditions on the sun and in the solar wind, magnetosphere, ionosphere, and thermosphere that can influence the performance and reliability of space-borne and ground-based technological systems. Adverse conditions in the space environment can cause disruption of satellite operations, communications, navigation, and electric power distribution grids, leading to a variety of socioeconomic losses (National Science Foundation 2000). The space weather events of October–November 2003 were initiated by three very large sunspot clusters that became visible on the Sun over a period of approximately 7 days beginning on 18 October, 2003. One of these clusters, region 486, became the largest sunspot group of the current solar cycle and the largest seen since 1991. This sudden increase in sunspots induced a series of solar flares and coronal mass ejections (CMEs), (Department of Commerce 2004). Solar flares are explosions on the surface of the Sun that produce a quick directed high-speed blast of charged particles and electromagnetic energy. One of the largest solar flares ever seen on the Sun occurred on 28 October. It was the third largest detected since regular monitoring began approximately 30 years ago and the largest since April 2001 (US Department of Commerce 2004). This activity was accompanied by a CME. CME’s are huge bubbles of plasma ejected from the Sun that speed into space. They disrupt the flow of the solar wind and produce disturbances that can strike the Earth with sometimes-catastrophic results (http://science.nasa.gov/ssl/pad/solar/ cmes.htm). This particular CME was one of the fastest on record in that it left the sun with a speed of 2,500 km/s, five times the average speed (Murtagh 2004). Figure 1 illustrates the observed active regions on 27 October together with the images of the solar flare and CME recorded on 28 October as observed by the SOHO spacecraft (http://sohowww.nascom.nasa.gov/). These events resulted in a severe geomagnetic storm in the Earth’s environment at 06:00 UT on 29 October. The disturbance levels on the Sun remained high for several days with a second powerful CME occurring at approximately 21:00 UT on 29 October. Figure 2 illustrates the planetary 3-h Kp indices for the period of 29 October 2003 to 1 November 2003. The Kp index is derived from 13 global magnetic observatories. It is a measure of the disturbance level of the geomagnetic field by auroral ionospheric currents. Kp values greater than 4 represent disturbed conditions. As the Kp values increase, the severity of the storm increases. Kp values of 9 represent the most extreme disturbed conditions and occur only a few times during the course of each 11-year solar cycle (http://www.sec.noaa.gov/NOAAscales). Note that Kp values of 9 were reached multiple times during 29–30 October in response to the CME activity.

Multi-spacecraft observations are used to study the in-situ effects of a large coronal mass ejection (CME) erupting from the farside of the Sun on 3 November 2011, with particular emphasis on the associated solar energetic particle (SEP) event. At that time both Solar Terrestrial Relations Observatory (STEREO) spacecraft were located more than 90 degrees from Earth and could observe the CME eruption directly, with the CME visible on-disk from STEREO-B and off the limb from STEREO-A. Signatures of pressure variations in the corona such as deflected streamers were seen, indicating the presence of a coronal shock associated with this CME eruption. The evolution of the CME and an associated extreme-ultraviolet (EUV) wave were studied using EUV and coronagraph images. It was found that the lateral expansion of the CME low in the corona closely tracked the propagation of the EUV wave, with measured velocities of 240±19 km s−1 and 221±15 km s−1 for the CME and wave, respectively. Solar energetic particles were observed to arrive first at STEREO-A, followed by electrons at the Wind spacecraft at L1, then STEREO-B, and finally protons arrived simultaneously at Wind and STEREO-B. By carrying out a velocity-dispersion analysis on the particles arriving at each location, it was found that energetic particles arriving at STEREO-A were released first and that the release of particles arriving at STEREO-B was delayed by about 50 minutes. Analysis of the expansion of the CME to a wider longitude range indicates that this delay is a result of the time taken for the CME edge to reach the footpoints of the magnetic-field lines connected to STEREO-B. The CME expansion is not seen to reach the magnetic footpoint of Wind at the time of solar-particle release for the particles detected here, suggesting that these particles may not be associated with this CME.

Aims. We introduce a new model for coronal mass ejections (CMEs) that has been implemented in the magnetohydrodynamics (MHD) inner heliosphere model EUHFORIA. Utilising a linear force-free spheromak (LFFS) solution, the model provides an intrinsic magnetic field structure for the CME. As a result, the new model has the potential to predict the magnetic components of CMEs at Earth. In this paper, we present the implementation of the new model and show the capability of the new model. Methods. We present initial validation runs for the new magnetised CME model by considering the same set of events as used in the initial validation run of EUHFORIA that employed the Cone model. In particular, we have focused on modelling the CME that was responsible for creating the largest geomagnetic disturbance (Dst index). Two scenarios are discussed: one where a single magnetised CME is launched and another in which we launch all five Earth-directed CMEs that were observed during the considered time period. Four out of the five CMEs were modelled using the Cone model. Results. In the first run, where the propagation of a single magnetized CME is considered, we find that the magnetic field components at Earth are well reproduced as compared to in-situ spacecraft data. Considering a virtual spacecraft that is separated approximately seven heliographic degrees from the position of Earth, we note that the centre of the magnetic cloud is missing Earth and a considerably larger magnetic field strength can be found when shifting to that location. For the second run, launching four Cone CMEs and one LFFS CME, we notice that the simulated magnetised CME is arriving at the same time as in the corresponding full Cone model run. We find that to achieve this, the speed of the CME needs to be reduced in order to compensate for the expansion of the CME due to the addition of the magnetic field inside the CME. The reduced initial speed of the CME and the added magnetic field structure give rise to a very similar propagation of the CME with approximately the same arrival time at 1 au. In contrast to the Cone model, however, the magnetised CME is able to predict the magnetic field components at Earth. However, due to the interaction between the Cone model CMEs and the magnetised CME, the magnetic field amplitude is significantly lower than for the run using a single magnetised CME. Conclusions. We have presented the LFFS model that is able to simulate and predict the magnetic field components and the propagation of magnetised CMEs in the inner heliosphere and at Earth. We note that shifting towards a virtual spacecraft in the neighbourhood of Earth can give rise to much stronger magnetic field components. This gives the option of adding a grid of virtual spacecrafts to give a range of values for the magnetic field components.