# Hall MHD

Added some documentation on MHD in AstroBEAR (including Hall terms)

# HEDLA Jet meeting 12/15/2020 -- Baowei

## 1. setup and parameters

Box: 60x60 mm radius_wire = 0.25 mm distance_between_centers = 7.5 mm MagField_direction = 0, 1, 0 WindMaterial = 27 rhoWind = 1e18 1/cc velWind = 6e1 km/s BWind = 1T !varies see table TempWind = 12 ev or 1.39e5 K dx= 15.625e-4 cm ratio_sizeWire_dx= 32 runTime: 426ns or ~0.4 domain crossing time, or 3.4 wire distance crossing time imomentumProtect=1 Boundary & Clump for wires lBoundary=.true. ! Use a boundary (instead of a high density barrier) DiffusionFactor = 1 !Factor to multiply velocity and finest level dx by for determining the diff_alpha2 parameter... Shouldn't be larger than 1.... MagneticDiffusionLength = 0.3 !cm MagneticDiffusionLengthWire = 0.0 !cm lBoundary=.false. ! Use a boundary (instead of a high density barrier) DiffusionFactor = 1 !Factor to multiply velocity and finest level dx by for determining the diff_alpha2 parameter... Shouldn't be larger than 1.... MagneticDiffusionLength = 0.3 !cm MagneticDiffusionLengthWire = 0.0 !cm

## 2. Results: Click for movies

runs | 298 ns | 426 ns |

setup 2, bounary | ; | ; |

setup 2, clump | ; | ; |

Note

and Each picture shows lineouts at three locations shown hereEach plot shows

- ram + thermal pressure
- magnetic pressure
- total pressure
- density
- magnetic field
- velocity (in x)
- Temperature

And the values are scaled as follows

Density | 1e17 cm^{-3
} |

Pressure | Mbar |

B | Tesla |

T | eV |

v | 10 km/s |

### The middle panel time range varies !!

runs | 298 ns | 426 ns |

setup 2, line-outs, boundary | ; | ; |

setup 2, line-outs clump | ; | ; |

### More movies

boundary run | rhoScaled;Zoomed rhoScaled;Temp; mach;magPressure; |

clump | rhoScaled;Zoomed rhoScaled;Temp; mach;magPressure; |

# Dust in AstroBEAR - Update 2020/12/14 & 2020/12/21

Link to the code flow chart with suggestions re sub-cycling. (EDIT 1: pdf was locked, should work now)

EDIT 2: I have added a schematic outline of the code for the gas drag routine to showcase the dependence on the time step and the move between different FORs. It can be found here. Some more notes of the equations can be found in this blog post from May.

# Changes in climate sensitivity as a function of Temperature

So apparently radiative forcing going like log CO2 has a name … https://en.wikipedia.org/wiki/Svante_Arrhenius#Greenhouse_effect though the explanation is somewhat complicated… See

https://escholarship.mcgill.ca/downloads/db78th05j?locale=en

Also, from Wikipedia, we have

where the climate sensitivity

and we can approximate the logarithmic response of radiative forcing to changes in CO2

Combining these we get

or

or

and

So the climate sensitivity is not constant - but falls off by a factor of

every 4.3K change in temperature.# Wind-Clump interactions

Here are lineouts from 4 of the runs with Bz field only. Note

and Also - the time reported should be scaled by 12.3 - so the final time is 426 nsEach picture shows lineouts at three locations shown here

Each plot shows

- ram + thermal pressure
- magnetic pressure
- total pressure
- density
- magnetic field
- velocity (in x)
- Temperature

And the values are scaled as follows

Density | 1e17 cm^{-3
} |

Pressure | Mbar |

B | Tesla |

T | eV |

v | 10 km/s |

Click for movies

No Cooling | Cooling | |

No Diffusion | ||

Diffusion |

# Integer Values of Beta

The following runs were conducted using values of Beta ranging from -1.0 (far left) to +3.0 (far right). For each type of plot, the integer values are in the top row while the half-integer values are in the second row.