[[spi:math]] (21) we can transform (15) into the Schrodinger equation (22) in which [[spi:math]] is the potential function. This recognition, provides us with the adoptation of quantum mechanical methods in solving (15) and (16) which is more suitable for numerical procedures than the highly non-linear transformation (21). Further, implementation of the boundary conditions (18) and (20) is much simpler in (z,t) coordinates than in (u,t) coordinates. Under the assumption of constancy of [[spi:math]] and B0, both (15) and (16) reduce to the same wave-equation form. As in Scholer (1970), we can write the general causal solution in terms of the Laplace transform for each segment j=1, ..., 15. [[spi:math]] In (25) B0(j) and [[spi:math]] are constant magnetic field and ambient plasma density 23 [[spi:math]] where (23) [[spi:math]] (24) [[spi:math]] (25)
RkJQdWJsaXNoZXIy MTU5NjU0Mg==