_units

Physical constants and normalization factors for PSI MAS model output.

The MAS (Magnetohydrodynamic Algorithm outside a Sphere) code solves the resistive MHD equations in dimensionless form. Every quantity stored in an HDF output file is a dimensionless ratio

\[q_\text{code} = \frac{q_\text{phys}}{q_0}\]

where \(q_0\) is the characteristic scale for that quantity. This module collects all reference scales so that code-unit values can be converted to physical (CGS or SI) units via astropy.units.

Normalization Scheme

MAS adopts a normalization anchored to two observable solar parameters and one reference number density:

Symbol	Quantity	Value
FNORML = RSUN	Characteristic length	\(6.96 \times 10^{10}\) cm
G0PHYS	Solar surface gravity	\(2.74 \times 10^4\) cm s⁻²
FN0PHYS	Reference number density	\(10^8\) cm⁻³

From these three anchors, the characteristic time is fixed by requiring the dimensionless surface gravity \(G_0^\text{norm} = 0.823\):

\[T_0 = \sqrt{\frac{G_0^\text{norm}\, R_\odot}{g_0}} \approx 1446 \;\text{s}\]

All other normalization factors follow from dimensional analysis:

Symbol	Quantity	Formula
FN_V	Velocity	\(V_0 = L_0 / T_0 \approx 481\) km s⁻¹
FN_RHO	Mass density	\(\rho_0 = m_p n_0\)
FN_T	Temperature	\(T_0^\text{temp} = m_p V_0^2 / k_B \approx 28\) MK
FN_P	Pressure	\(P_0 = \rho_0 V_0^2\)
FN_B	Magnetic field	\(B_0 = V_0 \sqrt{\mu_0 \rho_0} \approx 2.2\) G
FN_J	Current density (SI)	\(J_0 = B_0 / (\mu_0 L_0)\) A m⁻²
FN_HEAT	Volumetric heating rate	\(Q_0 = P_0 / T_0\) erg cm⁻³ s⁻¹

Electromagnetic Units

MAS is formulated in Gaussian CGS, where Ampère’s law reads \(\mathbf{J} = (c/4\pi)\,\nabla \times \mathbf{B}\). Because current density in Gaussian CGS (statampere cm⁻²) is unfamiliar to most users, this module provides both SI (FN_J, FN_E) and Gaussian CGS (FN_J_CGS, FN_E_CGS) normalizations for these quantities.

Magnetic field is expressed in Gauss throughout, since that system is unambiguous and Gauss is the conventional unit for coronal magnetic field strengths.

Custom Astropy Units

Each PSI quantity has a dedicated UnitBase registered at module import time. These units carry the conversion factor from code units to physical units so that astropy can chain conversions automatically — for example, a quantity returned by psi_io.mhd_io in MAS_b units can be converted with a single .to(u.Gauss) call.

Units are registered both under a family name (e.g. MAS_b) and under every individual quantity name in that family (e.g. MAS_br, MAS_bt, MAS_bp), so that the unit embedded in an Quantity always reflects the specific field component.

Registered PSI Custom Units

Unit object	Physical equivalent	Module constant	Registered string names
MAS_b	\(\approx 2.2\) G	FN_B	MAS_b, MAS_br, MAS_bt, MAS_bp
MAS_v	\(\approx 481\) km s⁻¹	FN_V	MAS_v, MAS_vr, MAS_vt, MAS_vp, MAS_zp, MAS_zm
MAS_j	\(J_0\) A m⁻²	FN_J	MAS_j, MAS_jr, MAS_jt, MAS_jp
MAS_t	\(\approx 28\) MK	FN_T	MAS_t, MAS_te, MAS_tp
MAS_n	\(10^8\) cm⁻³	FN_N	MAS_n, MAS_rho
MAS_p	\(P_0\) erg cm⁻³	FN_P	MAS_p, MAS_ep, MAS_em
MAS_heat	\(Q_0\) erg cm⁻³ s⁻¹	FN_HEAT	MAS_heat
POT3D_b	1 (dimensionless)	—	POT3D_b, POT3D_br, POT3D_bt, POT3D_bp
PSI_rsun	\(6.96 \times 10^{10}\) cm	RSUN	PSI_rsun, PSI_radius, PSI_r
PSI_angle	1 rad	—	PSI_angle, PSI_t, PSI_p, PSI_theta, PSI_phi

See Also

astropy.units :

The underlying unit system used for normalization and conversion.

psi_io._models :

Maps each MAS quantity name to its FN_* normalization.

psi_io.mhd_io :

Lazy readers that apply these normalizations on property access.

Functions

compose_mas_units(quantity)	Express a quantity in the preferred MAS CGS units basis.
decompose_mas_units(quantity)	Decompose a quantity into the preferred MAS CGS base unit.
get_helium_fractions(he_frac)	Compute fractional abundance multipliers for a hydrogen–helium plasma.

Attributes

BOLTZ	Boltzmann constant in CGS.
C_CGS	Speed of light in CGS: \(c = 2.998 \times 10^{10}\) cm s⁻¹.
FAVORED_UNITS	Tuple of CGS units preferred when composing or decomposing MAS quantities.
FKSPITZ	Spitzer parallel thermal conductivity prefactor in CGS.
FLUX_UNIT	Astropy unit for surface energy flux: erg cm⁻² s⁻¹.
FMP	Proton mass in CGS.
FN0PHYS	Reference number density of the coronal base in CGS.
FN_B	Magnetic field normalization for MAS, in Gauss.
FN_E	Electric field normalization for MAS, in SI (V m⁻¹).
FN_E_CGS	Electric field normalization for MAS, in Gaussian CGS (statV cm⁻¹).
FN_FLUX	Surface energy flux normalization for MAS.
FN_HEAT	Volumetric heating rate normalization for MAS.
FN_J	Current density normalization for MAS, in SI (A m⁻²).
FN_J_CGS	Current density normalization for MAS, in Gaussian CGS (statA cm⁻²).
FN_JB	Lorentz force density (and pressure gradient) normalization for MAS.
FN_KAPPA	Thermal conductivity normalization for MAS.
FN_LENGTH	Alias for FNORML: the characteristic length scale \(L_0 = R_\odot\).
FN_N	Number density normalization: \(n_0 = 10^8\) cm⁻³.
FN_P	Pressure normalization for MAS.
FN_QRAD	Radiative loss function normalization for MAS.
FN_RHO	Mass density normalization for MAS.
FN_T	Temperature normalization for MAS.
FN_TIME	Alias for FNORMT: the characteristic time scale \(T_0 \approx 1446\) s.
FN_V	Velocity normalization for MAS.
FNORML	Characteristic length scale for MAS: the solar radius.
FNORMM	Characteristic mass scale for MAS.
FNORMT	Characteristic time scale for MAS.
G0NORM	Dimensionless surface gravity in MAS code unit.
G0PHYS	Solar surface gravitational acceleration in CGS.
K	Kinetic energy normalization for MAS.
MAS_b	Custom astropy unit for MAS magnetic field quantities.
MAS_heat	Custom astropy unit for MAS volumetric heating rate.
MAS_j	Custom astropy unit for MAS current density quantities.
MAS_n	Custom astropy unit for MAS number density and mass density.
MAS_p	Custom astropy unit for MAS pressure and wave-energy quantities.
MAS_t	Custom astropy unit for MAS temperature quantities.
MAS_v	Custom astropy unit for MAS velocity quantities.
MU0	Permeability of free space (SI).
OMEGA_COROTATE	Default angular velocity of the MAS corotating frame, in physical unit.
PI	High-precision value of π.
POT3D_b	Custom astropy unit for POT3D magnetic field quantities.
PSI_angle	Custom astropy unit for PSI angular coordinate grids.
PSI_rsun	Custom astropy unit for PSI radial coordinate grids.
RSUN	Solar radius in centimeters.
STATAMP_TO_AMPERE	Conversion factor from statampere to ampere.
STATVOLT_TO_VOLT	Conversion factor from statvolt to volt.
VOLUMETRIC_RATE_UNIT	Astropy unit for volumetric energy deposition rate: erg cm⁻³ s⁻¹.
W	Total (integrated) energy normalization for MAS.