<html xmlns:o="urn:schemas-microsoft-com:office:office" xmlns:w="urn:schemas-microsoft-com:office:word" xmlns:m="http://schemas.microsoft.com/office/2004/12/omml" xmlns="http://www.w3.org/TR/REC-html40">
<head>
<meta http-equiv="Content-Type" content="text/html; charset=Windows-1252">
<meta name="Generator" content="Microsoft Word 15 (filtered medium)">
<style><!--
/* Font Definitions */
@font-face
{font-family:"Cambria Math";
panose-1:2 4 5 3 5 4 6 3 2 4;}
@font-face
{font-family:Calibri;
panose-1:2 15 5 2 2 2 4 3 2 4;}
/* Style Definitions */
p.MsoNormal, li.MsoNormal, div.MsoNormal
{margin:0in;
font-size:10.0pt;
font-family:"Calibri",sans-serif;}
span.EmailStyle20
{mso-style-type:personal-reply;
font-family:"Calibri",sans-serif;
color:windowtext;}
.MsoChpDefault
{mso-style-type:export-only;
font-size:10.0pt;}
@page WordSection1
{size:8.5in 11.0in;
margin:1.0in 1.0in 1.0in 1.0in;}
div.WordSection1
{page:WordSection1;}
--></style>
</head>
<body lang="EN-US" link="#0563C1" vlink="#954F72" style="word-wrap:break-word">
<div class="WordSection1">
<p class="MsoNormal"><span style="font-size:11.0pt">The B-field drops at the liner/vacuum interface (not to zero, but low) because the liner has a much lower resistivity than the vacuum. The field doesn’t diffuse much through the liner, so when it gets to the
liner/fill interface, there’s not much left to diffuse into the fill. Due to cylindrical geometry the field must go to zero at r=0.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">There is not necessarily net current in the fill, or at least not a significant current. The current is determined by curl(B), which should be largest at the liner/vacuum interface for most, if not all, of
the implosion. Some pinches will have a ‘secondary’ peak current at the liner/fill interface as well, but the specifics are problem-dependent.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt">In general, Z-pinches in FLASH are not literally simulating an applied current traveling through the domain. What we do is use a circuit model or given current value to set the B-field at the upper-r boundary
with Ampere’s Law, and we let magnetic diffusion, with appropriate values for resistivity, determine the B-field profile throughout the domain. Then curl(B) x B will determine the pinch forces on the plasma. Real life doesn’t have a B-field diffusing inwards
from some radius, but as long as the resulting B-field profile is correct, the approach will give correct results.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt;color:black">--</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:#181A1B">Eddie Hansen</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:#181A1B">Research Scientist</span><span style="color:black"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:12.0pt;font-family:"Arial",sans-serif;color:#181A1B">Flash Center for Computational Science</span><span style="color:black"><o:p></o:p></span></p>
</div>
</div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
<div style="border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in">
<p class="MsoNormal" style="margin-bottom:12.0pt"><b><span style="font-size:12.0pt;color:black">From:
</span></b><span style="font-size:12.0pt;color:black">flash-users <flash-users-bounces@flash.rochester.edu> on behalf of Gines Garcia <gines.garcia@greentownsbyfusion.com><br>
<b>Date: </b>Tuesday, May 16, 2023 at 10:22 AM<br>
<b>To: </b>flash-users@flash.rochester.edu <flash-users@flash.rochester.edu><br>
<b>Subject: </b>[FLASH-USERS] Question about magnetic field behavior in Flash's ZPinch simulation<o:p></o:p></span></p>
</div>
<p class="MsoNormal"><span style="font-size:11.0pt">Greetings everyone, <o:p></o:p></span></p>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt">I have a question regarding the default ZPinch simulation in Flash. I'm curious about two aspects:<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt">The magnetic field abruptly drops to zero when it encounters the fill material. How can this happens if it is supposed to also have a net current inside the fill?<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt">I appreciate any insights or explanations you can provide on these matters.<o:p></o:p></span></p>
</div>
<div>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
</div>
<p class="MsoNormal"><span style="font-size:11.0pt">Thank you in advance for your help.
<o:p></o:p></span></p>
<div>
<p class="MsoNormal"><span style="font-size:12.0pt;color:black"><o:p> </o:p></span></p>
</div>
</div>
</body>
</html>