How to change the gradient progression?

[Novarender]

I don't really know how to word this, but is it possible to change the rate of the progression of the gradient? For example, I have this:

 

 

As you can see, it gradually changes from transparent in the center to blue on the outside, but I need it to be more like a ring, where it's transparent for most of it and on the outer edge it quickly changes to blue. Sort of looking like a pulse. Any help?

[Red ochre]

Alpha Threshold worth a try! - Sorry the images have been sabotaged by the terrible image hosts.

[Reptillian]

I have made a tool just for this - 

Hope this helps.

[MJW]

One method I've used is to create the linear gradient, then modify it with pyrochild's Curves+ plugin. For a transparency gradient, select the Alpha channel.