Boozer chartmap format¶

An extended Boozer chartmap is a NetCDF file with geometry and field data in Boozer coordinates; SIMPLE traces it without a VMEC file. This page specifies the file for writers of converters. All grids are uniform, because the SIMPLE/libneo splines assume constant spacing along each abscissa. Usage and the shipped converters are in Field sources and coordinates.

Radial grids¶

The schema uses two radial coordinates:

rho is uniform and increasing. It is the chartmap coordinate rho = sqrt(s). Geometry, Bmod, B_theta, and B_phi use this grid.
s is uniform and increasing. It spans rho(1)**2 to rho(n_rho)**2. A_phi uses this grid.

A_phi must be a one-dimensional variable over s and must carry radial_abscissa = "s". Files that store A_phi over rho are invalid.

Runtime input keeps the usual SIMPLE meaning: sbeg is normalized toroidal flux s in both VMEC and chartmap runs. A chartmap run evaluates the start surface at rho = sqrt(sbeg).

Angles and signs¶

SIMPLE chartmaps use the same left-handed Boozer orientation as the VMEC path. The scalar global attribute torflux is the edge value of A_theta, the poloidal covariant component of the vector potential:

A = A_theta grad(theta_B) + A_phi grad(zeta_B)
A_theta = torflux*s
A_phi   = -chi

GVEC Boozer coordinates are right-handed for the W7-X/GVEC comparisons, with zeta_GVEC = -phi_VMEC. A GVEC chartmap therefore needs exactly one angle reversal before SIMPLE reads it:

Reversal	Resampling	Components that change sign	Components that keep sign
`zeta -> -zeta` (default exporter path)	geometry and `Bmod` at `-zeta`	`A_phi`, `B_phi`	`torflux`/`A_theta`, `B_theta`
`theta -> -theta`	geometry and `Bmod` at `-theta`	`torflux`/`A_theta`, `B_theta`	`A_phi`, `B_phi`

Raw right-handed GVEC chartmaps and double-flipped chartmaps do not match the SIMPLE/VMEC convention.

Runtime scaling¶

Chartmap files store base-scale CGS quantities. SIMPLE applies the usual vmec_B_scale and vmec_RZ_scale settings when it loads a chartmap, so a chartmap run scales like a VMEC run:

Quantity	Runtime scale
`Bmod`	`vmec_B_scale`
`B_theta`, `B_phi`	`vmec_B_scale * vmec_RZ_scale`
`A_phi`, `torflux`	`vmec_B_scale * vmec_RZ_scale**2`
`x`, `y`, `z`, derived `rmajor`	`vmec_RZ_scale`

test_chartmap_scaling checks the field object, canonical Boozer splines, reference-coordinate wrapper, vector potential, covariant field components, and Bmod.

Dimensions¶

The logical SIMPLE order is shown below. Fortran writers use this order directly. Python netCDF4 writers in this repository use reversed dimension tuples for multidimensional variables and transpose the data before writing.

Dimension	Meaning
`rho`	Uniform `sqrt(s)` grid for geometry, `Bmod`, `B_theta`, `B_phi`.
`s`	Uniform `s` grid for `A_phi`.
`theta`	Endpoint-excluded Boozer poloidal grid.
`zeta`	Endpoint-excluded Boozer toroidal grid.

The file stores no duplicate periodic endpoint planes. Readers append those planes internally when the spline backend requires a full-period grid.

Variables¶

Variable	Logical shape	Units
`rho`	`(rho)`	dimensionless
`s`	`(s)`	dimensionless
`theta`	`(theta)`	radians
`zeta`	`(zeta)`	radians
`x`, `y`, `z`	`(rho, theta, zeta)`	cm
`A_phi`	`(s)`	G cm^2
`B_theta`, `B_phi`	`(rho)`	G cm
`Bmod`	`(rho, theta, zeta)`	G
`num_field_periods`	scalar	dimensionless

Required attributes¶

Global attributes:

rho_convention = "rho_tor"
zeta_convention = "boozer"
rho_lcfs
boozer_field = 1
torflux in G cm^2

Variable attributes:

A_phi:radial_abscissa = "s"
x:units = "cm", y:units = "cm", z:units = "cm"

rmajor is not a schema attribute. The reader derives it from the innermost geometry surface.