t \mathrm {volt}} \right).\]</div>
</div>
</div>
<div class="section" id="Longitudinal-beam-dynamics">
<h2>Longitudinal beam dynamics<a class="headerlink" href="#Longitudinal-beam-dynamics" title="Permalink to this headline">¶</a></h2>
<p>The equation for the longitudinal dynamics of the beam can be solved independently of the equation for the envelope, so that the ready-made function of the beam energy of $ z $ is already used in the equation for the envelope. Assuming that the electron velocity is close 