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<div>Thank you for your response.</div>
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<div class="elementToProof">I have one more question regarding this. In my case, I have a modified ZPinch simulation where the Line specie has been removed, leaving only Fill and Vacuum. In this simulation, we tried to initialize a Bennet pseudo-equilibrium
(as close as possible, since it is challenging to initialize in equilibrium since in the first timestep magz=0 meanwhile thermal pressure already makes the fill move to the right). Still, we got close to the parameter's radial profiles (mainly density, temp,
and magnetic field) of the equilibrium according to the literature. Theoretically, the magnetic field should go smoothly down to zero at the axis from the peak at the fill column radius (Image 1). In our case, however, the magnetic field abruptly goes to zero
at the left side of the fill column radius (Image 2). I believe this is because the magnetic field barely diffuses through the Fill. Outside the Fill, everything behaves as it should. We did not change diffusion runtime parameters from those of the default
Z-pinch (DaviesWen, parallel, implicit, vacuum res...)</div>
<div class="ContentPasted0">Do you have any suggestions to fix this problem with the magnetic diffusion? By the way, we read a previous conversation on a similar subject where a bug in the HYPRE solver was found and fixed with a patch we also used.</div>
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<div class="ContentPasted0">Thank you very much for your help and attention.</div>
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Best regards
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<div id="divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>De:</b> Hansen, Eddie <ehansen@pas.rochester.edu><br>
<b>Enviado:</b> martes, 16 de mayo de 2023 17:35<br>
<b>Para:</b> Gines Garcia <gines.garcia@greentownsbyfusion.com>; flash-users@flash.rochester.edu <flash-users@flash.rochester.edu><br>
<b>Asunto:</b> Re: Question about magnetic field behavior in Flash's ZPinch simulation</font>
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<p class="x_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.</span></p>
<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
<p class="x_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.</span></p>
<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
<p class="x_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.</span></p>
<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt; color:black">--</span><span style="color:black"></span></p>
<p class="x_MsoNormal"><span style="font-size:12.0pt; font-family:"Arial",sans-serif; color:#181A1B">Eddie Hansen</span><span style="color:black"></span></p>
<p class="x_MsoNormal"><span style="font-size:12.0pt; font-family:"Arial",sans-serif; color:#181A1B">Research Scientist</span><span style="color:black"></span></p>
<p class="x_MsoNormal"><span style="font-size:12.0pt; font-family:"Arial",sans-serif; color:#181A1B">Flash Center for Computational Science</span><span style="color:black"></span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_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</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Greetings everyone, </span>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">I have a question regarding the default ZPinch simulation in Flash. I'm curious about two aspects:</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_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?</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">I appreciate any insights or explanations you can provide on these matters.</span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt"> </span></p>
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<p class="x_MsoNormal"><span style="font-size:11.0pt">Thank you in advance for your help.
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