Effects of interplanetary shock waves on energetic charged particles

Abstract

The influence of interplanetary shock waves on energetic charged particles is studied in this work. Emphasis is given to the acceleration of protons in almost perpendicular shock waves (the angle ψ between the shock normal and the upstream magnetic field being greater than about 80°). The special case of protons accelerated in ideal perpendicular shock waves is treated analytically. The protons gain energy by repeated crossings of the shock front until they are finally permanently transmitted downstream. The resulting energy gain complies with the conservation of the first adiabatic invariant. It is found that the times required by protons to reach a given relative energy gain at the shock front are longer for higher proton energies. In about 3 min a 0.3-MeV proton has almost tripled its energy at a shock front of strength 3, whereas a 10-MeV proton has barely started gaining some energy in the same time interval. The acceleration of protons by reflection at oblique shock waves as well as the required times is also examined: significant energy gains are found for ψ greater than about 80°, increasing with ψ. Intensive acceleration of protons thus occurs when the upstream interplanetary magnetic field is almost parallel to the shock front. However, because of the directional magnetic fluctuations that characterize the interplanetary medium the magnetic field vector ahead of the shock stays almost parallel to the front for only a short time (a few minutes, in general). This time is enough for the low-energy protons (Ep ≲1 MeV) to be accelerated to about 2–3 times their original energy but not enough for the high-energy protons (Ep > 10 MeV) to be noticeably affected by the shock wave. This result explains the absence of ‘spike’ events from the high-energy proton observations. The intensity and energy spectrum variations of a given proton population interacting with a perpendicular shock wave are also obtained theoretically as functions of time. It is found that a softer spectrum results after the intense acceleration in perpendicular shock fronts; also, large intensity enhancements created within a few minutes are predicted that can account for the observed impulsive low-energy storm proton events (spikes or LESP's). Simultaneous low-energy proton (Ep > 0.3 MeV) and magnetic field observations from July 1967 to December 1970 by the Iowa particle experiments and the Ames magnetometers on board the satellites Explorer 33 and 35 are analyzed, and the experimental results are found to be in excellent agreement with the theoretical predictions. Large spike events are observed only in association with almost perpendicular shock waves. On the other hand, oblique shock waves are associated only with weak spike events, which can be accounted for by sweeping and albedo acceleration.