A Neutral-Point Expansion of the Ideal Magnetosphere

The idealized model of the geomagnetic field-solar wind interaction yields a singular (neutral) point on the magnetopause at which the magnetic field vanishes. If we expand the fields in a power series around this point, including quadratic terms, we can derive an approximate equation of the magnetopause in a small neighborhood of the neutral point which is consistent with the idealized boundary conditions to fourth order. We then consider the additional pressure due to multiple reflections of particles in this neighborhood and show that less than a 4 per cent correction to the single-reflection pressure condition is necessary.