Figure 7.1a shows a normalised contour plot of the omni-directional differential particle inten- sity for 100keV electrons in the standard Parker HMF geometry. The injection is located at φ0 = 90◦and the initial injection broadness isσ0 = 15◦. The level of perpendicular diffusion is a= 0.13(as defined in Chapter4) and the radial mean free pathλris0.08AU. This instance of the transport model includes focusing effects. A white magnetic field line, with its origin at the injection location, is shown in sector III. Figure 7.1b shows the maximum particle intensities at 1AU as a function of azimuthal angle and represents a Gaussian-like distribution. The vertical dashed red line atφ0 = 90◦ indicates the azimuthal angle of the injection at the Sun and the four sectors are shown that correlate with the sectors shown in figure 7.1a. The peak intensity is located atφ= 30◦in sector III which is also seen in the contour plot. The blue region in sector I of figure 7.1a represents the region where no particle onset has taken place during the8hour simulation.
109
110 7.2. SEP INTENSITIES IN A STRUCTURED SOLAR WIND
(a)
(b)
Figure 7.1: (a) Normalised contour plot showing the omni-directional differential particle in- tensity for100keV electrons in the Parker HMF with the injection atφ0= 90◦at8hours. (b) The maximum particle intensities at1AU shown as a function of azimuthal angle for the modelled HMF. Labels used in both plots are explained in the text.
Figure 7.2: Normalised contour plot of the solar wind speed for CR1895as reported byLi et al.
[2016]. This plot has been rotated by 180◦ in order to have the same orientation as the SEP transport model results. The labels in this plot are explained in the text.
Figure 7.2, showing the solar wind speed, is based on figure 6.6a, but rotated by180◦in order to have the same longitudinal orientation as the results from the SEP transport model. Four sectors, namely I, II, III, and IV, are indicated and the long lasting fast solar wind stream is now located in sector II and the smaller fast solar wind stream in sector III. The Earth’s orbit is represented by a solid black circle at1AU.
Figures 7.3a and 7.3b show the normalised contour plot of the omni-directional differential par- ticle intensity for100keV electrons in the modelled magnetic field and the maximum particle intensity at1AU at all azimuthal angles, respectively. Note that the background intensity is a free parameter in the SEP transport model and is equal to10−4 (in the normalized units used here). The modelled HMF and the pitch-angle diffusion coefficient are dependent on the az- imuthal angle (see equations 6.5 and 4.22, respectively). This instance of the transport model ignores focusing effects by specifying L−1 = 0, i.e. L→ ∞. The particle injection takes place in sector III where both slow and fast solar wind streams are present. The red vertical dashed line in figure 7.3b indicates the azimuthal angle of the injection atφ0 = 90◦. Figure 7.3a is sig- nificantly different from figure 7.1a since the former does not conform to a single Gaussian-like intensity distribution, but rather has a rippled peak intensity distribution representing multi- ple, smaller Gaussian-like injections.
112 7.2. SEP INTENSITIES IN A STRUCTURED SOLAR WIND
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Figure 7.3: (a) Normalised contour plot showing the omni-directional differential particle in- tensity for100keV electrons in the modelled HMF with the injection atφ0 = 90◦ at8hours, while ignoring particle focusing/mirroring effects. (b) The maximum particle intensities at 1 AU shown as a function of azimuthal angle for the modelled HMF while ignoring focus- ing/mirroring effects. Labels used in both plots are explained in the text.
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Figure 7.4: (a) The same as shown in figure 7.3a, but now incorporating focusing/mirroring effects. (b) The same as in figure 7.3b, but now incorporating focusing/mirroring effects.
114 7.2. SEP INTENSITIES IN A STRUCTURED SOLAR WIND
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Figure 7.5: (a) Normalised contour plot showing the omni-directional differential particle in- tensity for100keV electrons in the modelled HMF with an injection atφ0 = 0◦ at8hours. (b) The maximum particle intensity shown as a function of azimuthal angle for the modelled HMF.
Labels used in both plots are explained in the text.
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Figure 7.6: (a) The same as shown in figure 7.4a, but now the injection is located atφ0 =−90◦ (b) The same as in figure 7.4b, but now the injection is located atφ0 =−90◦.
116 7.2. SEP INTENSITIES IN A STRUCTURED SOLAR WIND An increase in particle scattering perpendicular to the magnetic field is observed, although the level of perpendicular diffusion in the transport model remains unchanged. This is likely due to the large-scale wandering field lines when the geometry of figure 6.1 is introduced. This also leads to particle onset occurring at all azimuthal angles, in contrast to the standard Parker HMF geometry.
Figures 7.4a and 7.4b are the same as figures 7.3a and 7.3b, but now focusing effects are taken into consideration. The focusing of particles illustrates the increase in differential intensity around the magnetic field line best connected to the SEP source. Including focusing leads to slightly less perpendicular diffusion effects as SEPs propagate faster from the Sun to the Earth.
Once again the rippled intensity distribution is observed.
Next, a SEP injection into the fast solar wind of CR1895is simulated in sector II. Figures 7.5a and 7.5b show the omni-directional differential particle intensity for100keV electrons in the modelled magnetic field and the maximum particle intensity at1AU at all azimuthal angles, respectively, for the instance where the initial injection is located atφ0 = 0◦ (indicated by the vertical dashed line in figure 7.5b). A white magnetic field in sector II is also shown inside the long-lasting, fast solar wind stream. This Parker field line assumes an average solar wind speed ofVsw= 800kms−1inside this sector. Significantly less particle scattering perpendicular to the field line is observed. Two reasons that could be responsible for this result are discussed here. Firstly, it could be that the particles had less time to scatter since the magnetic field line is shorter for a faster solar wind, and hence the SEPs move faster from the Sun to the observer. Secondly, significant mirroring effects are observed inside this sector (see figure 6.9 in the previous chapter) which retards the particles and inhibits particle propagation between the Sun and the Earth. Accordingly, the maximum particle intensity at1AU, shown in figure 7.5b, is a few orders of magnitude less than in figure 7.4b for the same8hour simulation. Once again the rippled intensity distribution is observed caused by the filled and empty flux tubes that correlate well with the focusing and mirroring regions observed in figure 6.9.
Now, a SEP injection into the slow solar wind stream is simulated in sector I. Figures 7.6a and 7.6b show the omni-directional differential particle intensity for100keV electrons in the modelled magnetic field and the maximum particle intensity at1AU at all azimuthal angles, respectively, for the instance where the initial injection is located atφ0 = −90◦ (indicated by the vertical dashed line in figure 7.6b). The white magnetic field line assumes an average solar wind speed ofVsw= 350kms−1. Note that particle onset has almost taken place at all azimuthal angles, with only a small section aroundδφ=−20◦ that has not increased above background intensity. Once again, the rippled intensity distribution is observed.
Figure 7.7 shows the maximum particle intensities of figures 7.1b, 7.3b, 7.4b, 7.5b, and 7.6b su- perimposed and shifted to correspond to injections atφ0 = 90◦, indicated by the vertical red dashed line. A shifted injection atφ0 = 180◦ is also included in figure 7.7. The simulations as- suming a Parker HMF geometry and constant solar wind speed show a Gaussian-like intensity distribution while the modelled HMF illustrates rippled “finger-like” intensity distributions with the maximum particle intensity often not located at the best magnetic connectivity (see e.g. the−180◦injection scenario).
Figure 7.7: The maximum particle intensities at1 AU for different injection locations. All the injections have been shifted to correspond to an injection atφ0 = 90◦(indicated by the vertical red dashed line).