Plots showing the maximum values of ﹩| {v}_{\theta }| ﹩, B_θ, and the Alfvén speed as functions of time. The sharp, thin dips seen in ﹩| {v}_{\theta }| ﹩ correspond to a change in direction for the pulse, i.e., the velocity is changing from positive to negative or negative to positive—the velocity value decreases, passes through zero, and increases to the correct size. A comparison where the decay period, T, of Equation (19) is changed to 10 T is provided (red lines).