What type of spiral is it?

Question

I want to write this spiral in cartesian coordinates and parametric or polar coordinates.

and how can I write the distance between two points of this spiral?

$$D= \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$$

I also want a spiral with big curvature to the beginning, then more small, so, $r_1<r_2<r_3<r_4<r_5\ldots $