,\]</div>
<p>where <span class="math notranslate nohighlight">\(k_ {xt} = k_x + k_ {xsc}\)</span> is the total stiffness, <span class="math notranslate nohighlight">\(k_x\)</span> is the stiffness of the lens, and <span class="math notranslate nohighlight">\(\displaystyle k_ {xsc} =\frac {4I} {I_a (\beta\gamma) ^ 3}\frac {1} {a (a + b)}.\)</span> As a result, we obtain a system of equations connected through a space charge:</p>
<div class="math notranslate nohighlight">
\[\begin{split}\begin{equation*}
 \b