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 curvat ure. We describe our model of a curved shock wave with zero thickness in two and three dimensions (cylindrical and spherical) and compare th e results of acceleration by plane and curved shock waves. We present a method for the calculation of electron acceleration by a curved shoc k wave of a general shape. We show that the acceleration by the spheri cal 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 t angent plane with variable magnetic field normal component. Even thoug h the zero shock thickness is not very realistic for electron accelera tion, it enables us to elaborate methods and test ideas that will be a pplied in future work on the problem of nonzero shock thickness.