Parametric Curve(s)

$$$ \forall\alpha\in\{0,2\pi\}\quad\; \quad0\leqslant\;k_{a}\;\leqslant0.5\quad\;$$$
$$$ \left \{ \begin{array}{r c l} \theta(\alpha) & = &\alpha\\ r(\alpha)& = &k_{a}\times\left(\cos^{0.64}{(\frac{\alpha}{2})}-\frac{4}{3,86}\right) \end{array}\right .$$$