Append to each element by class name

We are looking for a vanilla js solution that will append a common html block after each instance of a dd class name = "alpha".

Example of current state:

<div class="image><dl><dd class="alpha">text string 1</dd></dl></div>
<div class="image><dl><dd class="alpha">text string 2</dd></dl></div>
...
<div class="image><dl><dd class="alpha">text string n</dd></dl></div>

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Example of desired state:

<div class="image><dl><dd class="alpha">text string 1</dd><dd class="beta">New html string </dd></dl></div>
<div class="image><dl><dd class="alpha">text string 2</dd><dd class="beta">New html string</dd></dl></div>
...
<div class="image><dl><dd class="alpha">text string n</dd><dd class="beta">New html string </dd></dl></div>

Select all Open in new window

We've been trying insertBefore to no avail.  Many thanks in advance.