An iterative method is developed by which one cancalculate approximately the boundary of a magnetic fieldconfined by a plasma. This method consists essentially ofvarying an assumed surface until the magnetic multipolemoments of the currents, which would flow on that surfaceto balance the plasma pressure, cancel the correspondingmoments of the magnetic sources within the surface. Themethod is applied to two problems.
For a dipole source of moment M emu in a plasma ofuniform pressure p dynes/cm^2 that does not penetrate themagnetic field, the approximate equation of the surfaceis r = 0.82615 M^(1/3) p^(-1/6)(1-0.120039α^2 - .004180α^4 - .001085α^6 + .000200α^8 - .000597α^(10) + .000326α^(12) - .000094α^(14)) cm, where α is the latitude in radians from the plane normal to M.
The surface formed by a cold plasma of density N_0 and pair mass velocity M_t moving past a dipole of moment Me_y with a velocity –U_oe_z extends to infinity downwind.In a coordinate system (x, y, z) centered at the dipole, neutral points, where the surface is parallel to the wind direction, occur at the points (0, ±R_n, .27R_n), and other points on the surface are (0, 0, 1.02R_n), (0, ±2R_n, -∞) and (±1.97R_n, 0, -∞).R_n = 1.0035 (M/(M_tN_oU^2_o)^(-1/2)^(1/3) is about 9 earth radii for the solar wind case.
