How to draw hashed lines on a bended line

diagramstikz-pgf

I'm trying to draw the following figure in TikZ :
enter image description here

But I've been facing problems on how I can draw the hashed lines on my bended line, and how to eliminate a part of some circle :

enter image description here

\documentclass[tikz,border=5mm]{standalone}   %<<< added
\begin{document}    %<<< added

\begin{tikzpicture}[ rotate=5, >=stealth]
\draw[fill=lightgray, opacity=0.3] (2.37,-4.1)circle(0.3);
\draw[fill=lightgray, opacity=0.3] (2.07,-1.71)circle(0.3);
\draw[fill=lightgray, opacity=0.3] (2,0)circle(0.5);
\draw[fill=lightgray, opacity=0.3] (2.18,2.8)circle(0.3);
\draw (0,0) ellipse [x radius=2, y radius=1];
\draw (0,0) ellipse [x radius=4, y radius=2];
\draw (0,0) ellipse [x radius=6.5, y radius=4];
\filldraw[black] (0,0) circle(0.02) node[left] {$x_1$};
\draw[smooth] (2.455,4.6)to[bend right=10](2.455,-4.6);
\draw[smooth, gray,thick, ->] (2,0)--(3,0);
\draw[smooth,thick, ->] (2,0)--(1,0);
\filldraw[black] (2,0)circle(0.03) node[right=0.17, above] {$x_3$};
\draw[smooth, gray,thick, ->] (4,0)--(5,0);
\filldraw[black] (2.07,-1.71)circle(0.03)node[right=0.17, above] {$x_2$};
\draw[thick, ->, black] (2.07,-1.71)--(1, -1.99);
\draw[smooth, gray,thick, ->]  (-2.07,-1.71)--(-2.3, -2.4);
\draw[smooth,thick, ->]  (2.18,2.8)--(1.1,3);
\draw[smooth,thick, ->] (2.37,-4.1)--(1.5,-4.3);
\end{tikzpicture}
\end{document}         %<<< added

I've tried the fill option while drawing the bended line but it didn't work, is there any solution for this, here's what I'm intending to draw :

enter image description here

Best Answer

You can fill a shape with a pattern (using patterns.meta library):

dashed bent zone

\documentclass[tikz,border=3.14mm]{standalone}
\usetikzlibrary{patterns.meta}

\begin{document}
    \begin{tikzpicture}[ rotate=5, >=stealth]
    \begin{scope}
            \clip (2.455,4.6)to[bend right=10](2.455,-4.6) -- ([xshift=20pt]2.455,-4.6) to[bend left=10] ([xshift=20pt]2.455,4.6);
            
            \draw[fill=lightgray, opacity=0.3] (2.37,-4.1)circle(0.3);
            \draw[fill=lightgray, opacity=0.3] (2.07,-1.71)circle(0.3);
            \draw[fill=lightgray, opacity=0.3] (2,0)circle(0.5);
            \draw[fill=lightgray, opacity=0.3] (2.18,2.8)circle(0.3);
        
        \end{scope}
        
        
        \draw (0,0) ellipse [x radius=2, y radius=1];
        \draw (0,0) ellipse [x radius=4, y radius=2];
        \draw (0,0) ellipse [x radius=6.5, y radius=4];
        
        
        
        \path[fill= white,pattern={Lines[
            angle=30, 
            distance=3pt, 
            line width=0.3pt] },
            pattern color=orange] (2.455,4.6)to[bend right=10](2.455,-4.6) -- ([xshift=-20pt]2.455,-4.6) to[bend left=10] ([xshift=-20pt]2.455,4.6);
            
        \draw[smooth] (2.455,4.6)to[bend right=10](2.455,-4.6);

        
        
        
        \draw[smooth, gray,thick, ->] (2,0)--(3,0);
        \draw[smooth,thick, ->] (2,0)--(1,0);
        \filldraw[black] (2,0)circle(0.03) node[right=0.17, above right] {$x_3$};
        \draw[smooth, gray,thick, ->] (4,0)--(5,0);
        \filldraw[black] (2.07,-1.71)circle(0.03)node[right=0.17, below right] {$x_2$};
        \draw[thick, ->, black] (2.07,-1.71)--(1, -1.99);
        \draw[smooth, gray,thick, ->]  (-2.07,-1.71)--(-2.3, -2.4);
        \draw[smooth,thick, ->]  (2.18,2.8)--(1.1,3);
        \draw[smooth,thick, ->] (2.37,-4.1)--(1.5,-4.3);
    \end{tikzpicture}
\end{document}
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