thanks to those who helped me.
\begin{tikzpicture}[>=latex,scale=1] \begin{polaraxis}[ domain = 0:360, samples = 100, hide axis, ] \foreach \w in {140,160,...,340} { \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+\w))} [arrow inside={end=stealth,opt={black, scale=1.05}}{0.5}];} \addplot[ultra thick, white, domain={97.5:200}] {(1*(1-0.8^2)/(1.2+0.8*cos(x+140)}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+360))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+340))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+320))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+300))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+280))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+260))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+240))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+220))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+200))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+180))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+160))}; \addplot[ultra thick, white, domain={10:300}] {(1*(1-0.8^2)/(1.2+0.8*cos(x+360))}; \addplot[thick, black, domain={295:360}] {(1*(1-0.8^2)/(1.2+0.8*cos(x+360))} [arrow inside={end=stealth,opt={black, scale=1.05}}{0.2}]; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+340))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+320))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+300))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+280))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+260))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+240))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+220))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+200))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+180))}; \addplot[thick, black] {(1*(1-0.8^2)/(1.2+0.8*cos(x+160))}; \addplot[thick, black, domain={285:300}] {(1*(1-0.8^2)/(1.2+0.8*cos(x+140))}; \addplot [->] [thin] coordinates {(0,0) (120,0.9)}; \addplot [->] [thin] coordinates {(0,0) (0,0.18)}; \addplot [thin] coordinates {(220,0.92) (220,0.89)}; \addplot [thin] coordinates {(200,0.92) (200,0.89)}; \addplot [thin, black,dashed] {0.9}; \addplot [thin, black,dashed] {0.18}; \addplot [thin, black, fill=white] {0.02}; \end{polaraxis} \draw[decorate,decoration=brace,rotate around={-230:(1.66,2.3)}] (1.5,3) -- (2.8,2.8); \coordinate [label={[font=\small] center:$\mathit{\Delta}\varphi$}] (D) at (0.45,2.2); \coordinate [label={[font=\small] center:$r_{\text{max}}$}] (rmax) at (2.45,6.5); \coordinate [label={[font=\small] center:$r_{\text{min}}$}] (rmin) at (4.5,3.9); \end{tikzpicture}