is headline">¶</a></h3>
<p>Kapchinsky-Vladimirsky distribution:</p>
<div class="math notranslate nohighlight">
\[f = A\delta (1 -\displaystyle\frac {\beta_x x '^ 2 + 2\alpha_x xx' +\gamma_x x ^ 2} {\epsilon_x} -\displaystyle\frac {\beta_y y '^ 2 + 2\alpha_y yy '+\gamma_y y ^ 2} {\epsilon_y}),\]</div>
<p>where <span class="math notranslate nohighlight">\(A\)</span> is the Courant-Snyder invariant. Axes of the ellipse:</p>
<div class="math notranslate nohighlight">
\[a =\sqrt {\epsilon_x\beta_x}, b =\sqrt {\