The passage of energetic charged particles through interplanetary space

Abstract

The passage of cosmic ray particles and energetic solar particles through interplanetary space is illustrated with a number of idealized examples. The formal examples are worked out from the condition that energetic particles in interplanetary space random walk in the irregularities in the large-scale interplanetary magnetic field. The irregularities move with approximately the velocity of the solar wind. The classical probability distribution is describable by a Fokker-Planck equation. A general expression for the particle diffusion coefficient k ij is worked out, including both scattering in magnetic irregularities and systematic pressure drifts. Magnetometer data from Explorer XVIII is presented to show the close average adherence of the quiet-day interplanetary magnetic field to the theoretical spiral angle, and to show the tendency for particles to move more freely along the field than across, k ∥ > k ⊥. The observed fields show that the diffusion coefficient is of the order of 10 21–10 22 cm 2/sec, as had been estimated from earlier cosmic ray studies. A middle value of 3 × 10 21 cm 2/sec suggests a cosmic ray density gradient of about 10 per cent per a.u. across the orbit of Earth. Direct observations of the interplanetary magnetic field afford the possibility for quantitative estimate of K ij as a function of particle energy. The first example to be considered is isotropic diffusion in a spherical region r < R with uniform radial wind velocity v for the purpose of illustrating the general nature and duration of the passage of a cosmic ray particle through the solar system. It is shown that the cosmic ray density reduction is of the order of exp (− vR/ k), and, hence, that during the years of solar activity vR/ k is not less than about 1 for protons of one BeV or so. It follows from this that the galactic cosmic ray particles will generally have spent several days in the solar system by the time they are observed. During this time they are in the expanding magnetic fields carried in the solar wind and are adiabatically decelerated, losing 15 per cent or more of their energy by the time they are observed. The energy distribution is shown for particles starting all with the same energy T 0 from interstellar space. The incoming probability wave of a single particle is computed as a function of time, showing how the particle is swept back by the wind. The converse problem of energetic solar particles is illustrated. The solar particles may typically lose half their initial energy before escaping into interstellar space. The outward motion of the wind displaces their probability distribution outward so that ultimately the maximum solar particle intensity may lie beyond the orbit of Earth. The outward motion of the wind steepens the decline of the solar particle intensity. The steady-state cosmic ray intensity is calculated throughout the spherical region r < R supposing a uniform cosmic ray density N 0 to obtain in interstellar space. The calculation is carried out for isotropic K ij , which would obtain if the magnetic irregularities were of large amplitude and of a scale not exceeding the radius of gyration of the cosmic ray particles, and for anisotropic k ij with k ∥ ⪢ k ⊥, which obtains when the field is relatively smooth. (The observations at sunspot minimum suggest k ∥ ⪢ k ⊥ at the orbit of Earth.) The particles diffuse only along the spiral lines of force when k ∥ ⪢ k ⊥, so their path in and out of the solar system is much longer than when K ij is isotropic. The result is a much greater reduction of the cosmic ray intensity for a given vR/| K ij |. There is no direct observational information on K ij beyond the orbit of Earth, where the intensity reduction takes place. Indirect information is available, however. There is the fact that the intensity of energetic solar particles at Earth often decays as t − g with g = 1·5–2·0. It is shown that in order for this to follow, it is necessary that | K ij | ∞ r s with s = 0·0–0·5 if k ij is isotropic, and s = 2·0–2·5 if k ∥ ⪢ k ⊥. That is to say, if K ij should continue to be as anisotropic beyond Earth as it is observed to be near Earth, then the diffusion must increase rapidly with distance from the Sun. These qualitative features should be easily detectable with particle, field, and plasma observations beyond the orbit of Earth.