Multispacecraft measurements and the perceived need for them generally followed the study of SEPs on or near Earth. The SEP events observed first (Forbush, 1946) were rare, large, energetic “ground-level enhancements” (GLEs), where GeV protons produce a nuclear cascade through the atmosphere to the ground level that enhances the continuous signal produced similarly by the galactic cosmic rays (GCRs). Since solar flares were found to accompany these early SEP events, flares were considered a possible source. However, the spatial span of these flares, stretching from the east on the Sun to behind the western limb, raised a significant problem: how could the SEPs cross magnetic field lines radiating out from the Sun to find their way to Earth?

Meanwhile, solar radio astronomers, also using ground-based instruments, had identified different sources triggered by energetic solar electrons. Radio emission, excited at the local plasma frequency, depends upon the square root of the local electron density, which decreases with distance from the Sun. Wild et al. (1963) described radio type III bursts where frequencies decreased rapidly, excited by 10–100 keV electrons that streamed out from a source near the Sun. There are also type II bursts where the source moved at the slower speed of a ∼1,000 km s⁻¹ shock wave. Wild et al. (1963) suggested two types of SEP sources, namely, point sources of mostly electrons near the Sun and fast shock waves that could accelerate energetic protons, like those that produce GLEs. Even though shock acceleration was well-known in other contexts, like the supernova sources of GCRs, Wild et al. (1963) were far ahead of their time in solar physics. After 20 years, the clear 96% association of large SEP events with shocks driven by fast, wide coronal mass ejections (CMEs) was established by Kahler et al. (1984). Yet, 10 years later, Gosling 1993) and Gosling (1994) still needed to point out the error of the “solar flare myth”.

Parker (1965) explained particle transport in terms of pitch-angle scattering as SEPs followed magnetic field lines out from the Sun. Diffusion theory is an important tool when there is actually a physical mechanism, like pitch-angle scattering, to produce the random walk. There is also a random walk of the magnetic field footpoints (Jokipii and Parker, 1969; Li and Bian, 2023) prior to events, which can produce an effective random walk perpendicular to the mean magnetic field, but it is independent of SEP-event parameters and is completely inadequate to explain a huge spread of SEPs far from a presumed source longitude near a flare. Other schemes such as the “birdcage” model (Newkirk and Wenzel, 1978) were also invented to spread SEPs from a flare source (see review, Sec 2.3 in Reames, 2021a). Reinhard and Wibberenz (1974) envisioned a mysterious “fast propagation region” extending 60⁰ from the flare to spread the SEPs prior to their slower interplanetary journey. Could this region actually match the surface of a shock? After decades of resistance, a flare source has mainly been abandoned for the largest SEP events that are now generally attributed to spatially extensive CME-driven shock waves (Mason et al., 1984; Gosling, 1993; Reames, 1995b; 1999; 2013; 2021b; Zank et al., 2000; 2007; Lee et al., 2012; Desai and Giacalone, 2016), especially for GLEs (Tylka and Dietrich, 2009; Gopalswamy et al., 2012; 2013; Mewaldt et al., 2012; Raukunen et al., 2018). Observations (e.g., Kahler et al., 1984) did replace the “fast propagation region” with the surface of a CME-driven shock wave that actually accelerates the particles, beginning at 2–3 solar radii (Tylka et al., 2003; Cliver et al., 2004; Reames, 2009a; Reames, 2009b) and continuing far out into the heliosphere. We will soon study from STEREO observations (e.g., Figure 5) that shocks easily wrap around the Sun, expanding widely across magnetic field lines where SEPs alone cannot pass.

As the element and isotope abundances in SEPs began to be measured, they would present new evidence for two different physical sources of SEPs. The earliest measurements, during large SEP events with nuclear emulsions on sounding rockets, extended element abundances up to S (Fichtel and Guss, 1961) and then to Fe (Bertsch et al., 1969). Later studies showed that average SEP element abundances in large events were a measure of coronal abundances that differed from photospheric abundances as a simple function of the elements’ first ionization potential (FIP; Meyer, 1985; Reames, 1995; Reames, 2014; Reames, 2021a; Reames, 2021b). The FIP dependence of SEPs differs fundamentally from that of the solar wind (Reames, 2018a; Laming et al., 2019), probing the physics of the formation of the corona itself.

However, early measurements in space soon identified a completely new type of event, distinguished by extremely high abundances of ³He in some events, such as ³He/⁴He = 1.52 ± 0.1 (e.g., Serlemitsos and Balasubrahmanyan, 1975), vs. a solar value of ∼5 × 10⁻⁴. Production of ³He from ³He by nuclear fragmentation was ruled out by the lack of ²H and Li, Be, and B fragments from C and O, e.g., Be/O and B/O < 2 × 10⁻⁴ (McGuire et al., 1979; Cook et al., 1984). The huge enhancements of ³He were produced by new physics, involving a wave–particle resonance (e.g., Fisk, 1978; Temerin and Roth, 1993) with complex spectra (Liu et al., 2004; Liu et al., 2006; Mason, 2007). The ³He-rich events were associated with the beamed non-relativistic electrons (Reames et al., 1985) and their type III radio bursts (Reames and Stone, 1986) studied by Wild et al. (1965). Element abundances of these “impulsive” ³He-rich events were also different from those of the large “gradual” shock-associated events (Mason et al., 1986; Reames, 1988); here, the enhancements increased as a power of the ion mass-to-charge ratio A/Q (Reames et al., 1994), which was especially clear when it became possible to measure elements above Fe with element groups resolved as high as Au and Pb (Reames, 2000; Mason et al., 2004; Reames and Ng, 2004). Average enhancements varied as (A/Q) ^3.6 with the Q value determined at a temperature of ∼3 MK (Reames et al., 2014a; Reames et al., 2014b). This power law can be used in a best-fit method to determine source plasma temperatures (Reames, 2016; Reames, 2018b). Impulsive SEP events have been associated with magnetic reconnection (Drake et al., 2009) on open field lines in solar jets (Bučík, 2020), which also eject CMEs that sometimes drive shocks (Kahler et al., 2001; Nitta et al., 2006; Nitta et al., 2015; Wang et al., 2006; Bučík et al., 2018a; Bučík et al., 2018b; Bučík et al., 2021) fast enough to reaccelerate the enhanced ³He and heavy ions along with ambient protons and ions (Reames, 2019; Reames, 2022b). Derived abundances from γ-ray lines suggest that flares involve similar physics (Murphy et al., 1991; Mandzhavidze et al., 1999; Murphy et al., 2016), but those accelerated particles are trapped on loops, losing their energy to γ-rays, electron bremstrahlung, and hot, bright plasma. The opening magnetic reconnections that drive jets also must close neighboring fields to form flares (see, e.g., Figure 4 in Reames, 2021b).

Shock waves can also accelerate residual suprathermal impulsive ions that can pool to provide a seed population (Mason et al., 1999; Tylka et al., 2001; Desai et al., 2003; Tylka et al., 2005; Tylka and Lee, 2006). The combination of two fundamental physical acceleration mechanisms, magnetic reconnection, and shock acceleration, as well as two distinctive element abundance patterns, led Reames (2020) and Reames (2022b) to suggest four distinguishable SEP event abundance pathways:

SEP1: “Pure” impulsive magnetic reconnection in solar jets with no fast shock.

SEP2: Jets with fast, narrow CMEs driving shocks that reaccelerate SEP1 ions plus ambient coronal plasma. Pre-enhanced SEP1 ions dominate high Z, and ambient protons dominate low Z.

SEP3: Fast, wide CME-driven shocks accelerate SEP1 residues from active-region pools from many jets, plus ambient plasma. Again, the SEP1 seed ions dominate high Z.

SEP4: Fast, wide CME-driven shocks accelerate ions where ambient plasma completely dominates.

Persistent pools of SEP1-residual seed ions available for reacceleration in SEP3 events have now been widely observed and reported (Richardson et al., 1990; Desai et al., 2003; Bučík et al., 2014; Bučík et al., 2015; Chen et al., 2015; Reames, 2022a), and may be fed by numerous impulsive events too small to be distinguished individually.

Large gradual SEP events are frequently accompanied initially by type III bursts. In principle, these impulsive jets could inject a SEP1 seed population. However, any such injection of SEP1 ions seems to be swamped by coronal seed ions in the many large SEP4 events. The extremely abundant type III electrons can be distinguished from shock-accelerated electrons by their proximity to the event source; the latter emerge only in poorly connected events (Cliver and Ling, 2007).

The spatial extent of these features and the underlying physics are of considerable interest. Can we find spatial differences in the seed populations sampled by shocks? Unfortunately, each point on a shock moving radially across Parker spiral fields will have spread particles over 50⁰—60⁰ by the time it reaches 1 AU (Reames, 2022a). This tends to blur any initial spatial variations in abundances.

Some of the early Pioneer spacecraft were launched into Earth-like solar orbits, although coverage was only hours per day. When there was no spacecraft near Earth, this led to the awkward comparison of 15-MeV proton data from Pioneer 6 and 7 with GeV ground-level neutron monitor measurements at Earth (Bukata et al., 1969). Fortunately, McKibben (1972) was able to include data from IMP 4 near Earth. Although most of these spatial distributions were analyzed in terms of adjustable coefficients in the fashionable perpendicular diffusion, rather than shock acceleration, McKibben also noted that late in SEP events, proton intensities could be identical over large spans of longitude. Later named “reservoirs” by Roelof et al. (1992), these regions involved particles quasi-trapped magnetically behind the shock; as the volume of this magnetic bottle expands, adiabatic deceleration (e.g., Kecskeméty et al., 2009) decreases all intensities, preserving spectral shapes (Reames et al., 1997; Reames, 2013). Extreme SEP scattering, once used to explain this slow decay, is actually found to be negligible in reservoirs since particles from new ³He-rich events travel scatter-free across them (Mason et al., 1989; Reames, 2021a).

Whenever there was a dependable spacecraft stationed near Earth, like IMP 8, any traveling spacecraft, such as the solar-polar-orbiting Ulysses, allowed two-spacecraft comparisons. The reservoir comparisons by Roelof et al. (1992) found uniform intensities behind the shock, extending radially over 2.5 AU from IMP 8 to Ulysses. Ulysses observed reservoirs at heliolatitudes up to >70⁰, N and S (Lario, 2010), and in other electron observations (Daibog et al., 2003).

The two Helios spacecraft followed neighboring solar orbits from 0.3 to 1.0 AU, beginning in 1974. Beeck et al. (1987) used data from these spacecraft to study the radial and energy dependence of diffusive scattering of protons, while, in a larger study, Lario et al. (2006) fit the peak intensities and the fluence of events to the form R ^-n exp[- k(ϕ - ϕ ₀)²], where n and k are constants, R is the observer’s radius in AU, ϕ is the solar longitude of the observer, and ϕ ₀ is the solar longitude of the event centroid. For a Gaussian distribution, k = (2σ ²)⁻¹. Lario et al. (2006, 2007) also considered the time variation of the point where the observer’s field line intercepts the expanding shock source, an important feature of shock acceleration defined by Heras et al. (1995).

Helios provided an excellent opportunity to study spatial distributions of shock-accelerated particles and their reservoirs, especially during 1978 when the Voyager spacecraft were nearby (Reames et al., 1996; Reames et al., 1997; Reames et al., 2013; Reames, 2023). An especially interesting event is shown in Figure 2 where the intensities of SEPs at Voyager 2 (Figures 2A or 2E) do not begin to increase until after the shock passes S1 (Figure 2B), presumably because this is where it first intercepts the field line to Voyager. Proton intensities then slowly rise as Voyager becomes connected to stronger and stronger regions of the approaching shock until the ESP structure finally arrives at S4 on 6 January. It should be noticed in Figure 2A that the peak intensities near the shock are similar at all four spacecraft. The ESP structure forms as protons streaming away from the shock generate resonate waves of wave number k ≈ B/μP, where B is the field strength, P is the proton rigidity, and μ is the cosine of its pitch angle (Lee, 1983; Lee, 2005; Ng and Reames, 2008; Reames, 2023). These waves trap particles in ESP structures. As the structure moves out to lower B, the resonance shifts so that high energies preferentially leak away early, as also seen in Figure 1E. Voyager sees the pure “naked” ESP event with few of the streaming protons that created it. The shock that eventually arrives at Voyager generated the intense early streaming protons seen early by Helios 1 and an intermediate structure as it passed Helios 2 and IMP 8.

The spacecraft distribution for the event shown in Figure 2 is unique; in this spacecraft sample, the SEPs are produced as the source shock moves radially. The width of this CME is limited, but the spacecraft are positioned to follow the evolution of the event: 1) well-connected Helios 1 samples its central production near the Sun, 2) Helios 2 and IMP 8 sample its production near 1 AU, and 3) Voyager 2 scans its western flank and then samples its central strength as it passes 2 AU. A fortuitous occurrence occurred: NASA did not design Voyager as a complement to Helios.

Another fortuitous observation with these spacecraft occurred in September 1978 and is shown in Figure 3. In Figure 3A, well-connected IMP 8 shows a fast increase in intensities and a peak near the time of shock passage, while Helios 1 and 2, far around the west flank, increase more slowly and then join IMP 8 in a reservoir behind the shock on 25 September. Distant Voyagers show a slow SEP increase to a plateau near the time S2, where IMP 8 joins the same intensity once it is no longer constrained by the east flank of the shock. Then, at S3, the western flank of the shock strikes field lines that send particles sunward to IMP 8 and outward to Voyager 2, and then to Voyager 1. This second SEP peak is clearly seen at energies above 40 MeV in Figure 3C and probably even in Figure 3D. A “left” and then a “right” from the same shock are observed; at Voyager, the two peaks are comparable in size.

It should be noted that the second peak in the IMP 8 data in Figure 3C shows significant velocity dispersion corresponding to the ∼6-AU path inward from the new source (actually a larger delay than in the first peak), while none is seen at Voyager 2 (Figure 3D) near this source. Furthermore, the intensities at IMP 8 and Voyager are quite similar in the second peak; any new injection from the Sun would have produced a huge difference in intensities like that seen in the first peak because of the great difference in radial distances since IMP 8 and the Voyagers seem to be on similar field lines. At the second peak, the shock has filled these field lines, forming a reservoir with similar intensities at IMP and Voyager.

Another parameter that can depend upon solar longitude is the solar particle release (SPR) time derived from velocity dispersion (Tylka et al., 2003; Reames, 2009a; Reames, 2009b). If the first particles of each energy to arrive at the spacecraft have been released at nearly a single time, the SPR time, and have scattered little, their travel time will be dt = L/v, where L is the field line length from the source to observer and v is the particle velocity. Plotting the onset times vs. v ⁻¹ will yield a linear fit with slope L and intercept at the SPR time. Figure 4B shows such a plot from Reames and Lal (2010) for the spacecraft distributed, as shown in Figure 4A, during the GLE of 22 November 1977. The parabolic fit for the height shown in Figure 4D, not from this event, is a fit of 26 GLEs observed from Earth (Reames, 2009b); presumably, it is a first-order correction for weaker, more slowly evolving, shock flanks. Gopalswamy et al. (2013) fit the SPR height for GLEs at Earth directly to the source longitude (uncorrected for foot-point motion). Type II bursts begin near ≈1.3 R_S, but they certainly need not correspond to the same field line longitude or shock physics as the measured SEPs. Non-relativistic electrons that produce type II bursts do not resonate with Alfvén waves like ions and hence are more likely to be accelerated by quasi-perpendicular regions of the shocks.

Thus, Helios allowed spatial comparisons of the beginnings of events, their evolution and ESP events at the middle, and their reservoirs at the end (Reames et al., 1997), noted previously.

The launch of Wind in November 1994 began a new era in SEP coverage from Earth, and it was later joined by SOHO and ACE, adding different capabilities. This coverage still exists in 2023. STEREO ahead (A) and behind (B) were launched together in late 2006 at the beginning of solar minimum. By September 2012, they had reached the ±120⁰ longitude, providing three equally spaced observing points around the Sun and optimal coverage for finding the most extensive SEP events.

With STEREO, it has become even clearer that SEP events can be quite extensive. For >25-MeV proton events, Richardson et al. (2014) found that 17% spanned three spacecraft; 34%, two spacecraft; and 36%, one spacecraft, with 13% unclear. Studying the abundances of H, He, O, and Fe at 0.3, 1, and 10 MeV amu⁻¹, Cohen et al. (2017) found only 10 three-spacecraft events, out of 41.

Most of the studies of particle distributions with STEREO have involved Gaussian fits of the intensity peaks or fluences at three longitudes. Three points determine a parabola, and a Gaussian is a parabola in logarithmic space, so Gaussians tend to fit the data very well. Xie et al. (2019) studied 19–30-MeV protons in 28 events finding σ = 39⁰ ± 6.8⁰. Paassilta et al. (2018) compiled a list of 46 wide-longitude events above 55 MeV, of which seven were suitable, averaging σ = 43.6 ± 8.3⁰, and for 14 events with E > 80 MeV, de Nolfo et al. (2019) found an average σ ≈ 41⁰. Lario et al. (2013) studied the 15–40 and 25–53-MeV proton peak intensities and found σ ≈ 45 ± 2⁰ for both proton energy ranges. Cohen et al. (2017) found average three-spacecraft events centered at ϕ _θ ≈22 ± 4° west of the flare site and ≈43° ± 1° wide; they found no dependence of the width on the charge-to-mass ratio Q/A of the elements. This lack of dependence on A/Q seems to argue against lateral diffusive transport. Kahler et al. (2023) fit the data on 20-MeV protons to hourly Gaussians, showing substantial broadening of the distribution with time, especially on the western flank where the shock expanded across new spiral field lines. However, all of these similar widths and parameters only apply to the largest ≈20% of events that span three spacecraft. We have no widths from the one-spacecraft third of the events. For electron events, Klassen et al. (2016) examined events for closely spaced (<72⁰) STEREO spacecraft and found they were not well-fit by Gaussians, while Dresing et al. (2018) pointed out that peak intensities used for the Gaussian fits may not represent the real spatio-temporal intensity distribution as the intensity peaks may have been measured at different times.

Some of the space–time coupling in SEP distributions is illustrated by the event shown in Figure 5. Here, the shock itself is seen at each spacecraft, yet the slight onset delay at Wind suggests it misses the base of that field line. Both STEREO spacecraft show fast intensity increases, followed by early declines, but the intensity at Wind peaks well after the shock passage. How do we distinguish variations in space and time? When does a Gaussian spatial distribution apply? Is the Gaussian formed by the peaks, or by the fluences; is it spatial or also temporal? Even hourly Gaussians miss the true behavior late in an event.

The two pink field lines labeled 1 and 2 in the map shown in Figure 5 will be carried, from their initial positions shown, to the red location of Wind by the time the shock reaches 1 or 2 solar radii, respectively, because of solar rotation. Hence, the time profile we see at Wind is greatly enhanced behind the shock by SEPs swept in on field lines that were much more centrally located initially. Meanwhile, STEREO A is rapidly acquiring field lines with decreased intensities of SEPs that have rotated from behind the Sun, and STEREO B eventually joins it in a suppressed reservoir region late on 2 March. Can SEP models follow this mixture of space–time variations? Time variations longer than about a day need to accommodate the 13⁰ day⁻¹ solar rotation. This event evolves over a week.

It should also be noted in Figure 5 that the accelerating shock wave is seen at all three spacecraft, as is often the case. These shock waves are able to wrap around the Sun, crossing field lines that the particles alone cannot cross. Thus, STEREO shows us the way the physics of shock acceleration can easily replace the early confusion of the “birdcage model,” “coronal diffusion,” and the “fast propagation region”—diffusion from a point source—that once held sway.

Spatial distributions of fluences of element abundances were studied extensively by Cohen et al. (2017) using STEREO and ACE data. The Gaussian distributions of H, He, O, and Fe were found to be similar in 10 three-spacecraft events, suggesting that the widths are independent of rigidity or transport. They found the average three-spacecraft Gaussian distributions to be 43° ± 1° wide, although with significant variations. None of these large three-spacecraft SEP events showed any of the enhancements of heavy elements, e.g., Fe/O, typically found in shock-reaccelerated impulsive suprathermal ions of SEP3 events. An analysis of the A/Q-dependence of the element abundances in a typical large SEP4 event is shown in Figure 6, where power-law fits of flat or suppressed heavy elements extend to include protons (Reames, 2020; Reames, 2022b).

For each time period, the observed abundances of Z ≥ 6 ions are divided by the corresponding coronal abundances and fit to power-laws. Most SEP4 events show flat fits, i.e., abundances the same as coronal, or declining power laws, as shown in Figure 6. The declining power laws may result from reduced scattering of heavier ions that allows them to leak more easily from the acceleration region SEP3 events have both enhanced protons and power-law heavy-element enhancements that increase with A/Q, reflecting shock acceleration of seed populations of normal ambient coronal ions and impulsive suprathermal ions with their characteristic high-Z enhancement. SEP3 events can be very large. In solar cycle 23, about half of the GLEs were SEP3 events (Reames, 2022a) and half SEP4 events. In weaker cycle 24, when STEREO was available, we found only one of the two-spacecraft events listed by Cohen et al. (2017) that was an SEP3 event (4 August 2011); this is an SEP3 event at Wind (figure 10 in Reames, 2020) and shows similar enhancements at STEREO A, although with poorer statistics. Why are there so few wide SEP3 events? Is it the weak solar cycle or are SEP3 events inherently narrow, perhaps because the primary pools of seed particles are confined?

A distinction of impulsive SEP events is that their longitude spread is much more limited than that of gradual events (Reames, 1999), but the width of that distribution depends upon the sensitivity of the instruments observing them and has increased somewhat with time (e.g., Reames et al., 2014a). A significant factor in this width is that variations in the solar wind speed vary with the longitude of the footpoint of the observer’s field line, but there is also variation due to the random walk of the footpoints of the field lines (Jokipii and Parker, 1969; Li and Bian, 2023) prior to the event.

A search for ³He-rich events between ISEE 3 and Helios (Reames et al., 1991) found several corresponding events. The well-studied event of 17 May 1979 (e.g., Reames et al., 1985) with ³He/⁴He ≥ 10 was seen with similar ³He enhancement by Helios 1 near 0.3 AU, as shown in Figure 7 as a sharp spike of very short (∼1 h) duration, presumably resulting from reduced scattering. Associated electron trajectories were tracked spatially, using the direction and frequency of the radio type III burst as measured from ISEE 3 (Reames et al., 1991).

The time history for the Kiel Instrument on Helios 1 in Figure 7 shows composite He; isotope ratios were tabulated separately using pulse-height data. Despite differences in He energies at the two spacecraft, both show the event at 0550 UT with ³He/⁴He ≈ 10 and that at 1700 UT with ³He/⁴He ≈ 1.

In the early STEREO era, before the spacecraft were widely separated, Wiedenbeck et al. (2013) found electrons and ions ±20⁰ ahead and behind Earth, during an event that occurred during a solar quiet time. The ions showed strong intensity gradients. The event was associated with a weak CME. Moreover, Klassen et al. (2015) studied an electron beam event early in the STEREO mission.

The discovery of fast CMEs associated with impulsive SEP events (Kahler et al., 2001) suggested that impulsive SEPs could be spread laterally when nearly radial shocks in these SEP2 events distributed particles across spiral field lines. Particles from SEP1 jets without fast shocks would be expected to follow any open field lines from the jet, presumably less widely distributed. Suggestions of greater spreads for SEP2 impulsive events with shocks, based upon current understanding, have not been explored, particularly because the available spacecraft are too widely separated.

Opportunities for multiple measurements of impulsive SEP events are rare. Perhaps the best opportunity is for measurements of the radial variation in SEP scattering between Parker Solar Probe (PSP) or Solar Orbiter and spacecraft near Earth. Are the time profiles of SEPs at PSP near the Sun similar to those of X-ray profiles of the event? To what extent are the jets that release SEPs part of more-extensive flaring systems? Magnetic reconnection that opens some field lines must also close others (e.g., see Figure 4 in Reames, 2021b), but reconnecting closed field lines with other closed lines would allow no escape.