Plasma Parameters and Fields

It is common in Tokamaks to input the plasma parameters and fields as flux functions. However, this approach makes several assumptions that may not be true in non-tokamak devices. In FIDASIM the plasma parameters and fields are mapped onto a 2D R-Z grid. This only assumes axisymmetric profiles within the region of interest. In addition to plasma parameters a boolean mask is used to indicate where the plasma and fields are well defined.

FIDASIM reads the plasma parameters and fields from an HDF5 file structured as follows...

[runid]_equilibrium.h5
├── plasma          
└── fields

where the plasma group has the following datasets

Variable	Type	Rank	Dimensions	Units	Description
`nr`	Int16	0	NA	NA	Number of radii
`nz`	Int16	0	NA	NA	Number of z values
`r`	Float64	1	[`nr`]	cm	Array of radii
`z`	Float64	1	[`nz`]	cm	Array of z values
`r2d`	Float64	2	[`nr`,`nz`]	cm	2D array of radii `r = r2d(r,z)`
`z2d`	Float64	2	[`nr`,`nz`]	cm	2D array of z values `z = z2d(r,z)`
`time`	Float64	0	NA	s	Time when the plasma parameter data was collected
`data_source`	String	0	NA	NA	Source of the plasma parameter data
`mask`	Int16	2	[`nr`,`nz`]	NA	Boolean mask that indicates where the plasma is well defined
`te`	Float64	2	[`nr`,`nz`]	keV	Electron temperature
`ti`	Float64	2	[`nr`,`nz`]	keV	Ion temperature
`dene`	Float64	2	[`nr`,`nz`]	cm^-3	Electron density
`zeff`	Float64	2	[`nr`,`nz`]	NA	Z-effective
`vr`	Float64	2	[`nr`,`nz`]	cm/s	Radial component of the bulk plasma rotation/flow
`vt`	Float64	2	[`nr`,`nz`]	cm/s	Torodial/Phi component of the bulk plasma rotation/flow
`vz`	Float64	2	[`nr`,`nz`]	cm/s	Z component of the bulk plasma rotation/flow

and where the fields group has the following datasets

Variable	Type	Rank	Dimensions	Units	Description
`nr`	Int16	0	NA	NA	Number of radii
`nz`	Int16	0	NA	NA	Number of z values
`r`	Float64	1	[`nr`]	cm	Array of radii
`z`	Float64	1	[`nz`]	cm	Array of z values
`r2d`	Float64	2	[`nr`,`nz`]	cm	2D array of radii `r = r2d(r,z)`
`z2d`	Float64	2	[`nr`,`nz`]	cm	2D array of z values `z = z2d(r,z)`
`time`	Float64	0	NA	s	Time when the fields data were collected/reconstructed
`data_source`	String	0	NA	NA	Source of the fields data
`mask`	Int16	2	[`nr`,`nz`]	NA	Boolean mask that indicates where the fields are well defined
`br`	Float64	2	[`nr`,`nz`]	T	Radial component of the magnetic field
`bt`	Float64	2	[`nr`,`nz`]	T	Torodial/Phi component of the magnetic field
`bz`	Float64	2	[`nr`,`nz`]	T	Z component of the magnetic field
`er`	Float64	2	[`nr`,`nz`]	V/m	Radial component of the electric field
`et`	Float64	2	[`nr`,`nz`]	V/m	Torodial/Phi component of the electric field
`ez`	Float64	2	[`nr`,`nz`]	V/m	Z component of the electric field

Distributions

The fast-ion distribution function typically does not have a functional form. This means that we need to input the fast-ion distribution function into FIDASIM. FIDASIM accepts three different types of fast-ion distributions.

Guiding Center Distribution Function: F(E,p,R,Z)
Guiding Center Monte Carlo distribution
Full-orbit Monte Carlo distribution

Supporting different types of distributions greatly facilitates the study of fast-ion transport.

FIDASIM reads the fast-ion distribution from an HDF5 file that has the following variables depending on the distribution type.

Guiding Center Distribution Function: F(E,p,R,Z)

Variable	Type	Rank	Dimensions	Units	Description
`type`	Int16	0	NA	NA	Distribution type (1)
`nr`	Int16	0	NA	NA	Number of radii
`nz`	Int16	0	NA	NA	Number of z values
`r`	Float64	1	[`nr`]	cm	Array of radii
`z`	Float64	1	[`nz`]	cm	Array of z values
`r2d`	Float64	2	[`nr`,`nz`]	cm	2D array of radii `r = r2d(r,z)`
`z2d`	Float64	2	[`nr`,`nz`]	cm	2D array of z values `z = z2d(r,z)`
`time`	Float64	0	NA	s	Time of the distribution
`data_source`	String	0	NA	NA	Source of the distribution data
`nenergy`	Int16	0	NA	NA	Number of energy values
`npitch`	Int16	0	NA	NA	Number of pitch values
`energy`	Float64	1	[`nenergy`]	keV	Energy array
`pitch`	Float64	1	[`npitch`]	NA	Pitch array w.r.t magnetic field
`denf`	Float64	2	[`nr`,`nz`]	cm^-3	Fast-ion density
`f`	Float64	4	[`nenergy`,`npitch`,`nr`,`nz`]	fast-ions/(dE dP cm^3)	Fast-ion distribution F(E,p,R,Z)

The Guiding Center Distribution Function is a function of Energy, pitch, R, and Z. The distribution is mapped on the same R-Z grid as the plasma parameters and fields.

Guiding Center Monte Carlo Distribution

Variable	Type	Rank	Dimensions	Units	Description
`type`	Int16	0	NA	NA	Distribution type (2)
`time`	Float64	0	NA	s	Time of the distribution
`data_source`	String	0	NA	NA	Source of the distribution data
`nparticle`	Int32	0	NA	NA	Number of MC particles
`nclass`	Int16	0	NA	NA	Number of orbit classes
`class`	Int16	1	[`nparticle`]	NA	Orbit class of the MC particle
`weight`	Float64	1	[`nparticle`]	fast-ions	Weight of the MC particle
`r`	Float64	1	[`nparticle`]	cm	R positions of the MC particle
`z`	Float64	1	[`nparticle`]	cm	Z positions of the MC particle
`energy`	Float64	1	[`nparticle`]	keV	Energy of the MC particle
`pitch`	Float64	1	[`nparticle`]	NA	Pitch w.r.t the magnetic field of the MC particle

The sum(weight) = # of Fast-ions in phase space sampled by the MC particles.

The class variable can take values in the range of 1:nclass. If there are multiple classes of particles the FIDA signal for each class will be calculated.

Full-orbit Monte Carlo Distribution

Variable	Type	Rank	Dimensions	Units	Description
`type`	Int16	0	NA	NA	Distribution type (3)
`time`	Float64	0	NA	s	Time of the distribution
`data_source`	String	0	NA	NA	Source of the distribution data
`nparticle`	Int32	0	NA	NA	Number of MC particles
`nclass`	Int16	0	NA	NA	Number of orbit classes
`class`	Int16	1	[`nparticle`]	NA	Orbit class of the MC particle
`weight`	Float64	1	[`nparticle`]	fast-ions	Weight of the MC particle
`r`	Float64	1	[`nparticle`]	cm	R positions of the MC particle
`z`	Float64	1	[`nparticle`]	cm	Z positions of the MC particle
`vr`	Float64	1	[`nparticle`]	cm/s	Radial component of the MC particle velocity
`vt`	Float64	1	[`nparticle`]	cm/s	Torodial/Phi component of the MC particle velocity
`vz`	Float64	1	[`nparticle`]	cm/s	Z component of the MC particle velocity