A new code, SEMAL, has been developed which solves the linearized Vlasov-Maxwell wave equations to all orders in Larmor radii. Arbitrary density and temperature profiles as well as non-uniform magnetic fields are considered in slab geometry. The vacuum regions adjacent to the plasma slab are limited by perfectly conducting walls and contain an antenna as an excitation source. The linear response is obtained by solving the system of one first-order and two second-order integro-differential equations using a non-polluting finite element discretization. The general equations in the Fourier space, derived in a new comprehensive way, and their inverse transform, using k(y) = 0, are described as well as the convergence and non-polluting properties of the method. We present the results concerning the influence of alpha particles on ICRF heating schemes for ITER, where we show that small alphas concentration can alter the steady-state operation envisaged with ICRF fast wave current-drive.