The flat time profile seen in many large proton events as in
Figure 1a is a signature of continuous acceleration. Suppose a
shock wave accelerates some fraction of the local solar wind
plasma to the energy of interest and the particles then expand
like R
as they come out to the observer. If the source
solar wind density also varies like R
, the intensity seen by
an observer at distance R from the Sun will not vary with time.
In the diffusive shock acceleration picture [ Lee 1983],
particles near the shock are scattered back and forth across the
shock by self-generated waves, gaining energy on each transit.
The intensity of particles and waves decreases with distance from
the shock to a point where there are not enough particles to
produce sufficient waves; thence the particles stream freely
away. This determines the maximum intensity that particles can
have early in the event, a few x 100 protons/(cm
sr s MeV) on
the saturation plateau at a few MeV [ Reames 1990b, 1993,
1994; Ng and Reames 1994] as seen in Figure 1a
and the lower panel in Figure 3. The intensity peak near the
shock has historically been called the ``energetic storm
particle'' (ESP) event. Note, however, that all the particles
actually can come from the shock, those that arrive early as well
as those in the ESP event.
At higher energies, where the particles are less numerous,
fewer resonant waves are produced and the trapping structure (ESP
event) weakens as the shock front expands like R
. The
decreased trapping results in less efficient acceleration and the
intensity of the higher energy particles decreases with time. At
sufficiently high energies the ESP structure does not survive all
the way out to 1 AU and is not seen. Thus the highest energy
particles are accelerated closest to the Sun. Generally the
highest energy particles (
100 MeV to >20 GeV) reach peak
intensity when the CME is at 5-15 solar radii [ Kahler
1994]. The 1989 September 29 event at 105
W has a CME speed of
1828 km/s and the 21 GeV particle intensity peaks at 5 solar
radii [ Kahler 1994]. This is an event where Adams
et al. [1993] find Q
=12.5 above 200 MeV/amu. Clearly
this suggests that this ``ground-level event'' is caused by a
CME-driven shock propagating across the high corona to accelerate
ambient, unheated plasma on the field line connected the Earth.
However, the story of the profiles of intensity vs. time is somewhat more complex, because of the variation of the profiles with the CME longitude. This variation, described by Cane et al. [1988], is shown for protons of different energy in Figure 3. Events near central meridian produce the intense flat profiles. Behind the shock is a second plateau region that is characterized by bi-directional streaming events [ Marsden et al. 1987; Richardson and Reames 1993] and magnetic clouds where the spacecraft is probably passing through the CME itself. For western events, the peak intensity occurs early when the nose of the shock is best connected to the observer. By the time the shock reaches 1 AU, the observer is connected far around on the eastern flank of the event where the shock is weak, if it is seen at all. For eastern events, the intensity may begin to rise when the coronal shock reaches the base of the observerūs field line, but the peak intensity may occur late, after the weak local shock has passed and the observer reaches field lines that connect to the strong acceleration region near the nose of the shock which is now far out beyond him. Reames [1994] shows large events that are viewed from 3 widely separated spacecraft.