### Physical Variables used in MHD Simulations

The basic plasma and electrodynamic field variables (written by each MHD model) are:
• Mass density Rho or particle number density N.
• Plasma pressure P.
• Plasma velocity V with its three components V_x, V_y and V_z.
• Magnetic field B with its three components B_x, B_y and B_z.
• B1
• SWMF/BATSRUS model: this is the difference between B and the Earth's dipole field (components B1_x, B1_y, B1_z).
B1 is used to see small variations of B near the Earth.
• UCLA-GGCM/OpenGGCM: B1 is the magnetic field as stored on the original model grid on grid cell faces.
Each B1 component exists on a grid that is offset from the "plasma" grid (where N, T, V are defined) by half a grid position in the direction of the respective field component (i.e., the grid for B1x is offset in X, the grid for By is offset in Y, and the grid for B1z is offset in Z).
When using componentds of B1 for field line tracing, the original grid positions are used for improved accuracy instead of using B field values interpolated onto the plasma grid before performing interpolations during field line tracing (when using components of B).
• BA is the "B-field anomaly", the difference between the total field strength B and the strength of the Earth's dipole field Bdipole.
• Electric current density J with its three components J_x, J_y and J_z.
Primary variables witten occasionally or by some models only:
• Internal Energy En. (P/(γ-1) with γ="ratio of specific heats", usually 5/3).
• Resistivity Eta (some runs).
Derived quantities
Note: everything listed here and below is calculated by CCMC.
Please report errors to us.
• New: Vector components in spherical coordinates for models with cartesian grids.
For example V_r, V_t, V_p: plasma velocity in the radial, theta and phi direction, respectively.
Note: The theta component flips sign around the polar axis of the spherical coordinate system (at X=0 and Y=0).
Spherical components are available for vectors (B, B1, V, J, and E) that exist in primary model outputs.
• B-parallel electric current density J_par with its three components J_par_x, J_par_y and J_par_z.
Note: flow line tracings do not make much sense with this vector!
• Electric field E with its three components E_x, E_y and E_z.
• Plasma-β: "beta"=P/(B2/2μ0).
• Plasma Frequency:
• ωpi = 1.32*103*(N [cm-3])1/2 - ion plasma frequency
• ωpe = 5.64*104*(N [cm-3])1/2 - electron plasma frequency
We assume N=Ne=Ni (electron-proton plasma).
The underscore ("_") indicates subscript level in variable name used in plots.
Gradients and divergences (magnetosphere models SWMF/BATSRUS and OpenGGCM only at this time):
• Vorticity "omega" (curl of V) with components "omega"x, "omega"y, "omega"z,
• Gradients of selected scalar variables (e.g., gradN, gradT, gradP) and divergences of selected vectors (e.g., div.V, div.ExB) and curls of vectors can be requested for visualization and ASCII data output.
A certain discrepancy from expected values can be expected since divergences and gradients are computed based on a finite differencing of data that may have been interpolated before computing the gradient or divergence.
Vector values in some models may be defined on staggered meshes. For visualization and the computation of derived quantities (such as ExB) all vector variables are interpolated to cell center positions (where plasma parameters such as N, P, T already reside).

### Quantities scaled with radial distance in solar coronal and heliospheric models:

Coordinates: r,lon,lat for MAS, ENLIL and x,y,z for SWMF
• Scaled with r2:
N, P, B_r, JxB, E.J (if currents J are available)
• Scaled with r1:
B (B_lon,B_lat or B_x,B_y,B_z),
E (E_r,E_lon,E_lat or E_x,E_y,E_z),
J (J_r,J_lon,J_lat or J_x,J_y,J_z),
J_par(J_par_r,J_par_lon,J_par_lat or J_par_x,J_par_y,J_par_z)
• Not scaled:
T, beta, S (entropy), V (V_r,V_lon,V_lat or V_x,V_y,V_z)

Last updated: Feb. 11, 2015 - Lutz Rastätter

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