  We develop an Explicitly Solvable Energy-Conserving (ESEC) algorithm for the
Stochastic Differential Equation (SDE) describing the pitch-angle scattering
process in magnetized plasmas. The Cayley transform is used to calculate both
the deterministic gyromotion and stochastic scattering, affording the algorithm
to be explicitly solvable and exactly energy conserving. An unusual property of
the SDE for pitch-angle scattering is that its coefficients diverge at the zero
velocity and do not satisfy the global Lipschitz condition. Consequently, when
standard numerical methods, such as the Euler-Maruyama (EM), are applied,
numerical convergence is difficult to establish. For the proposed ESEC
algorithm, its energy-preserving property enables us to overcome this obstacle.
We rigorously prove that the ESEC algorithm is order 1/2 strongly convergent.
This result is confirmed by detailed numerical studies. For the case of
pitch-angle scattering in a magnetized plasma with a constant magnetic field,
the numerical solution is benchmarked against the analytical solution, and
excellent agreements are found.
