Magnetic Field Flux in 1D
Consider the induction equation for a MHD fluid:
For the x axis,
. Hence, only the y component of the above equation is important.This gives us 10 terms to plot on the RHS, but before doing that we take integral wrt x on both sides from x = -R to x (the asteroid surface is taken to be at 0). The resulting plot is shown below for the 3 cases. The plots are labelled in the order they appear in the above equation.
Updates 2/15/21
Early Asteroid Magnetization
Adding lineouts of the day side to illustrate the issues of theoretical estimates of amplification.
Moon Impact Magnetization
Settled on a spherical field distribution of the form:
Will add another blog post about the equations and plot for current, and magnetic potential.
Hot Neptunes
I have forgotten how to compile code it seems. Should be an easy fix.
Initial Conditions for Lunar Impact Magnetization
Based on the impactor conditions from Oran et al. (2020) https://advances.sciencemag.org/content/6/40/eabb1475 and its supplementary material https://advances.sciencemag.org/content/suppl/2020/09/28/6.40.eabb1475.DC1/abb1475_SM.pdf we have most impact plasma conditions apart from the magnetic field (which they do not seem to inject by any mechanism).
Impact Plasma conditions from iSALE-2D :
- Initial Vapour temperature: 2000 K (varies down to 500 K for some models)
- Wind Speed: 400 km/s to 1000 km/s
- Wind Density: Plots in S4, but no analytical form. Looks proportional to y.
- Magnetic field: Probably several equations work.
Assuming the field distribution is similar to that of a very thick (radius
), finite length ( ), current carrying wire, the field and vector potential in cylindrical coordinates are:- Resistivity Profile: Same as used for the NSF proposal.
We can start
Update 9/28
Link to pdf (might ask to be logged into UR email in the same browser): https://bit.ly/3jfJmda
Update 09/21
Theoretical Predictions are Off
Got some initial results from Mach and beta parameter sweep. The theoretical equation doesn't fit the simulations very well. We will probably include this in subsequent papers.
http://www.pas.rochester.edu/~aanand/movies/fall20/
Fixed the plot from last time.
EMAC
Need to fix some links on AstroBEAR website or make the code publicly available before upload.
Update 20 and 27 July'20
Making Sense of Convergence Study
The plot of the convergence series was confusing
So, I made a couple of other plots focusing only on 1 case. Hopefully, this makes more sense.
Earth Magnetosphere
Imported SmoothDipole
from PlanetaryOutflow module. Found SphericalRotation
and InvSphericalRotation
in CommonDefinitions to rotate the dipole and re-rotate the magnetic vector potential.
Still need to decide a few parameters. BlueHive stopped being cooperative during testing.
(Aside: Absolutely do no leave the tracer variable on for the physics module you just turned off..)
Box size? (Bow shock can extend upto 20 R_E for extreme solar wind values)
AMR Levels?
Moon Proposal Video
Need a video to go along with the proposal we submitted (not urgent). A couple of options:
- xy density with field lines (too "jumpy")
- 3D rotation of final frame (need higher resolution run?)
Quals (Progress Paragraph)
Comments on the email thread. Will send it to Laura today.
Update on Early Asteroid Magnetization - 06/29
Created maps of the magnetic field on the front and back side.
(Couldn't quite get them in the same image yet.)
Realized this can be used to visually confirm convergence of simulations to steady state.
Still re-running all simulations and extending some of them to reach convergence. Results all match with what we expect.
Also working on a paper for the results. Might need to run a couple of high resolution cases for proper figures.
Bug in Sweep Scheme
A line of code which was supposed to zero out EMF flux in the y direction inside the boundary of any object was set to ey instead of e2y causing magnetic field to diffuse inside the asteroid.
It disproportional affects high magnetic Reynolds number cases and lowers the max amplification by a little bit (< 0.5).
The results can be contrasted in these movies (Different R_M):
Currently restarting all simulations. Could take upto 2 weeks.
Updates 8th June
Summary of Asteroid Magnetization Cases
Compiled the results of all the cases for the Journal Club. Probably should shift to using L8 or L16 norms for the magnetic field instead of using the global maxima.
Summary of Moon Magnetization Simulations (probably not Steady State)
Focused on cases Resistive limit of the moon resistivity profile (from the Shimizu2013 paper, which in turn references a 1982 model) due to long standard queue.
Link to results:
http://www.pas.rochester.edu/~aanand/movies/moon2.0/
The proposal we submitted just had the plot of the resistive case at 3.8 Ga with atmosphere.
Prof. Blackman believes adding crests and valleys to the lunar surface to simulate pockets of magentic field is more important than the resistivity profiles we select. Need to add a custom shape function for that.
Update on Early Asteroid Magnetization
Convergence Plot of Uniform Resistivity Simulation
Plotted the rate of change of Amplification as a function of Max field in each frame for all cases with uniform resisitivity structure and 2 winds (1000 #/cc and 300 #/cc).
We can see that those with high resisitivity start off with Amplification lower than the theoretical predicted max amplification limit and then increase towards their final steady state, while the ones with high conductivity start at high amplification and then decrease to steady state. (Kinks are due to restart with change in boundary conditions and buffer zones.)
New Lunar Proposal
We are trying to submit a proposal for study of lunar samples. Need to simulate the amplification for the present day moon, moon at 3.8 Ga and moon with thin atmosphere at 3.8 Ga.
Most recent experimental data of moon resistivity profile (from Apollo 12):
Approximation of above data into models from recent data (Shimizu et al. 2013):
Current Profiles running on BlueHive (very slow convergence):
Miscellaenous
Will soon be on my 3rd laptop in as many months. In general interest: https://xkcd.com/2083/
HEDSA Talk
HEDSA is organizing a series of talk about the future of Frontier Plasma Science. There will be a talk given by Carolyn Kuranz next week, Monday June 1 at 4pm EDT and I (Prof. Pierre Gourdain) was hoping that you could join the discussion. It is also very important to get students involved because we will be discussing something directly impact you. So, I would encourage you to reach out to all graduate students you know (get that Rolodex smoking), so they can ask questions using the Google form link https://forms.gle/4DupvDRRJKBn8p537
(Email me for link to the Zoom meeting.)
Update 05/05/20
Effect of Resolution, Interpolation and Resistivity Smoothing
The resistivity of the asteroid was being raised to high values from near-zero ambient value. Adding a exponential buffer made the transition of maximum field (in the zone just outside the surface) less step.
The default interpolation scheme (constant) was being used which was causing steep changes in the field across AMR levels. Changing it to 1 (minmod) makes the slope gentler.
(Yet to run Lv 4 simulations for comparison.)
Finalized Movie and Figure for Paper
External Image editing had to be involved for scale bars and labels. Draft was submitted today.
Updates on Magneitic field amplification
Resolution Study and Updated Figure
I noticed the field amplification changes noticeably with grid size, so conducted a resolution study for the max field. It seems to indeed change. All field is on the surface of the asteroid for uniformity.
(Maybe the scale height at the surface is not being resolved yet?)
Another Memory Allocation Bug in Regrid
Updated the code and figure.
Updates on Regrid and Using Cartesian Grid for a Spherical Problem
Desity and Field Plot of Final Frame
Tried to reproduce this figure from the 2018 paper:
Now, however, the Cartesian grid is too grainy and leads to ring like structures (Nodal plot is slightly better).
Trimmed down the boundary and increased resolution (2x) to get this:
But max field has reduced by ~22%, possibly due to new boudary conditions.
Regrid
Regrid was successful to Lv. 4 for the simulation we were using.
The int data type was going into overflow by a bit.
Here are the resulting field lines:
However, when I try to do the same with the higher resolution simulation, it runs out of time. So it probably needs >5x the time from the lower resolution case or there could be another bug.
Bug Hunts
Regrid to Highest Resolution
Get the follwoing error for Lv 4. Callback to exact issue with gdb debug has not been successful so far.
level -2 level -1 HDF5 error: function h5dwrite_f failed with error code -1 . HDF5-DIAG: Error detected in HDF5 (1.8.17) MPI-process 0: #000: H5Dio.c line 254 in H5Dwrite(): not a dataspace major: Invalid arguments to routine minor: Inappropriate type forrtl: severe (174): SIGSEGV, segmentation fault occurred
High Resistivity Bug
We added some checks for the new diffusion, but I do not see any difference in .out or the output.
High Resistivity Issue, Equivalent Resistivity, 3D Plot of Field
Equivalent Resistivity
Computed the table for the cases I had so far. The comet case seems to cause more amplification for a given equivalent (or even just) resistivity, followed by the shell case, and then the uniform case.
Also, can cases with different winds parameters be directly compared?
Here is the table for cases with 300 #/cc, 500km/s, 1e6 K.
(Image and table in Excel)
High resistivity
The present day moon case at least ran completely with some noise. The case with Magnetic Reynolds' number of 0.5 (needed for the above table) runs into major issues:
3D Plot of Field Lines
This is to be added to the Supplementary information of a paper:
Need suggestions on how to add more field lines in the front. Will also need to patch the data into fixed grid to stop the field lines from breaking.
Updates on High Resistivity case and Equivalent Resistivity
High Resistivity (Moon-like)
The prior runs of this case (back in October'19) did not have the proper absorbing boundary conditions and the density of the planet was not being used. That was case was running quite fast.
Now, the density of the moon is kept low as it is supposed to be an excellent absorber of plasma. The fields go through quickly and try to pull material out (which there is not much of) leading to smaller timesteps.
Here is the simulation with a higher density wind and moon:
Another one with present day solar wind (and moon with half the density):
We also found an unintended line in the Boundary condition function, so that could have helped.
Calculating Effective Resistivity
To compare effective resistivity of different models we are doing a weighted average of the conductivity with the current (suggested by Prof. Pierre Gourdain). That is (image to be added later. Latex makes blog crash.)
Issue With Conductive Shell Around Asteroid
The problem with enveloping the asteroid with a low resisitivity shell to simulate a mock atmosphere persists.
Things we have tried so far:
- Ramp up Solar Wind; ramp down asteroid density and temperature (for absorbing boundary condition); ramp down resistivity.
- Introduce is a stronger Diffusion factor using fluxes which should have smoothed things out (it didn't).
- Make a function for applying boundary conditions instead of copy-pasting it 12 places. Solved an asymmetry error in the code (still unsure how), but doesn't help otherwise.
- Trying different resisitivites. All with conductive shells have reached Min Timestep (I was too ambitious with the values perhaps).
Notes:
- Simulations stop either by density protections at the night side or zones of high B in the day side.
- The Oran wind mode (700 km/s, 35 particles/cc) seems to run a little longer than our wind (500 km/s, 300 particles/cc).
Update on Magnetization of Asteroids by Solar Winds
Ran the Oran resistivity structure using our solar wind parameter. Both start with uniform B = 100 nT in y direction, constant density and field velocity ramping up.
Magnetic field pile up appears to nearly double for our solar wind conditions.
Our condition (300 particles/cc, 500 km/s, 1e6 K) has 5.7x Final B, 2 different planes are shown:
http://www.pas.rochester.edu/~aanand/movies/xy_a3cl.gif
http://www.pas.rochester.edu/~aanand/movies/xz_a3cl.gif
Oran condition (35 particles/cc, 700 km/s, 50,000 K) has 3.4x Final B:
http://www.pas.rochester.edu/~aanand/movies/or_1_1.7_a3cl_r_151.gif
http://www.pas.rochester.edu/~aanand/movies/oran_xz_a3cl.gif
Common parameters are listed here: http://www.pas.rochester.edu/~aanand/movies/problem.data
Currently need ~6 days of computation time to reach this state.
Moon Case
Ran Moon case using new boundary condition, and uniform field and particle density. Core does not diffuse out field till the last frame; need to start with 0 field inside the moon (work in progress, condition similar to Alex's case).
http://www.pas.rochester.edu/~aanand/movies/moon_0.2_1.7_150r.png
3D Viscosity
Extrapolated Code for 3D Viscosity. Yet to be tested, but should be able to add soon.
Parameters to Change
- Box height and width to be made double (y and z directions).
- Resolution studies.
- Artificially add relative magnetic permeability.
- Add Lineout plots through the center
- Run 6 initial cases, with both wind conditions (except for moon case), making 10 cases:
- Moon with core
- Moon without core
- Oran resistivity
- Conducting layer on top of case ©. Additional parameter needed.
- Uniform resistivity of value close to max resistivity of ©
- Case (e) with an outer conducting shell
- Case (f) with Front side conducting, back side resistive (like a comet).
Base parameter values
Critical Resistivity (Comp. Units): 6.12e6
Resistivity (fraction of critical):
- Moon with core: 1
- Moon without core:
- Oran resistivity:
a3cl: 1.63e-4 to 1.62e-2
a1ht: 2.45e-4 to 1.96e-3
- Conducting layer on top of case ©: Shell of 1.96e-4
- Uniform resistivity of value close to max resistivity of ©: 2e-3
- Case (e) with an outer conducting shell: Body - 2e-3 and Shell - 2e-4
- Case (f) with Front side conducting, back side resistive (like a comet).
Plots Needed
- Peak Magnification vs Effective Resistivity (with M*√γβ)
Found Bug in Resistivity module when AMR is enabled
Accumulation of magnetic field could have been observed at the grids when the AMR level changed. After 3 weeks, we discovered 2 indexing errors.
Images: http://www.pas.rochester.edu/~aanand/plots/?C=M;O=D