ACCELERATION OF ELECTRONS BY A NEARLY PERPENDICULAR CURVED SHOCK-WAVE .1. ZERO SHOCK THICKNESS

From the Earth's bow shock observations and theoretical modeling it is known that electrons are accelerated by a nearly perpendicular shock wave. The theory of acceleration is well established for the case of a plane shock wave. In this paper we revisit the role of a shock curvature. We describe our model of a curved shock wave with zero thickness in two and three dimensions (cylindrical and spherical) and compare the results of acceleration by plane and curved shock waves. We present a method for the calculation of electron acceleration by a curved shock wave of a general shape. We show that the acceleration by the spherical shock can be reduced to the acceleration by the cylindrical shock, but this is not true for a general shock (like the Earth's bow shock). We verified the approximation of a nearly perpendicular shock by a tangent plane with variable magnetic field normal component. Even though the zero shock thickness is not very realistic for electron acceleration, it enables us to elaborate methods and test ideas that will be applied in future work on the problem of nonzero shock thickness.