In a recent article Hultquist [1959] has indicated that lines of geomagnetic force projected from a suitable circle in the equatorial plane intersect the earth's surface nearly along a north polar auroral isochasm derived some years ago by Vestine [1944]. The agreement was found very good except in the region of Hudson Bay in northern Canada. Hultquist notes that new auroral data indicated by Gartlein [1959] are more compatible with the theory in this region.The suggestion of Hultquist is based on the theoretical concept of Alfv•n and others that auroral particles might drain into the polar regions from a ringlike electric current configuration in the equatorial plane. It is the purpose here to note that if auroral particles drain from the Van Allen radiation belt, proposed as a possibility by Van Allen, McIlwain, and Ludwig [1959], the proposed modification in the Hudson Bay region seems also to be supported. According to the early theory of StSrmer [1907] charged particles spiraling down the lines of force of the geomagnetic field -•ll be reflected at a certain magnetic field value F and return upward, proceeding to the southern hemisphere where reflection can again take place. According to A1/v•n [1950] the approximate motion accords with the equationwhere a is the pitch angle of the particle, F• is the total geomagnetic intensity at the mirror point, and F is the value of field elsewhere. It has also been shown that the particle will drift in response to the field gradient. The magnetic space gradient causes the particle to drift in a direction roughly parallel to F X grad F, at auroral levels. On this view the use of adiabatic invariants [Al•v•n, 1950; Post, 1956] may be helpful, as Van Allen [1959], following a suggestion of Northrup, has noted for the Van Allen radiation studies. If the equivalent magnetic moment of the spiraling particle, v•2/F, is conserved [A1/v•n, 1953; Van Allen, 1959], v• is the particle velocity perpendicular to the field. Then since v v• ' + v•, where v is the total velocity, and v2/F,• = v•/F, the velocity parallel to the field w is given by (1 --F/F,•)V•v. Consequently an invariant of a particle with a drift velocity small compared with v is I = %/1 --F/Fro dl (2) where integration is along a line of force 1 of the geomagnetic field between the mirror points mr, m•, in the northern and southern hemispheres, and it is convenient to express F in cgs and 1 in terms of the earth's radius as unity. Thus a particle arriving at the auroral zone near northern Norway, say, will on an average drift to the west (or east if negative in sign) to lines of force such that equation 2 is approximately satisfied. If the average direction of drift defines auroral arcs, it may also define an isochasm of auroral frequency. The systematic results will to a considerable extent be mainly geometrical, and determined by the earth's main field as a whole rather than only by the dipole component. Figure i shows curves of equal I for north polar regions, taking F• as 0.45, and integrating equation 2, usin...
