Question: Plot a vector field

Good day to all of you nice people.
I'm currently attempting to plot a vector field where each component of the vector is defined by the equations S_x, S_y, and S_z, which are functions of the radial coordinate. Here is a depiction of how the vectors change with respect to r:

The next step, which I'm unsure how to do, is to plot the vectors around the z-direction, or I should say, in phi direction, to achieve something similar to this example:

Thank you a lot for your kind help. 

Here is my code:

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