pyrokinetics.local_geometry.metric.MetricTerms

pyrokinetics.local_geometry.metric.MetricTerms#

class pyrokinetics.local_geometry.metric.MetricTerms(local_geometry, ntheta=None, theta=None)[source]#

Bases: object

General geometry Object representing local LocalGeometry fit parameters

Data stored in a ordered dictionary

The following methods are used to access the metric tensor terms via the following

toroidal_covariant_metric
toroidal_contravariant_metric
field_aligned_covariant_metric
field_aligned_contravariant_metric

Examples

>>> g_r_r = MetricTerms.toroidal_covariant_metric("r", "r")

Parameters:: local_geometry (LocalGeometry)

regulartheta#

Evenly spaced theta grid

Type:: Array

R#

Flux surface R (normalised to a_minor)

Type:: Array

Z#

Flux surface Z (normalised to a_minor)

Type:: Array

dRdtheta#

Derivative of \(R\) w.r.t \(\theta\)

Type:: Array

dRdr#

Derivative of \(R\) w.r.t \(r\)

Type:: Array

dZdtheta#

Derivative of \(Z\) w.r.t \(\theta\)

Type:: Array

dZdr#

Derivative of \(Z\) w.r.t \(r\)

Type:: Array

d2Rdtheta2Array: Second derivative of \(R\) w.r.t \(\theta\)
d2RdrdthetaArray: Second derivative of \(R\) w.r.t \(r\) and \(\theta\)
d2Zdtheta2Array: Second derivative of \(Z\) w.r.t \(\theta\)
d2ZdrdthetaArray: Second derivative of \(Z\) w.r.t \(r\) and \(theta\)
JacobianArray: Jacobian of flux surface
qFloat: Safety factor
dqdrFloat: Derivative of \(q\) w.r.t \(r\)
dpsidrFloat: \(\partial \psi / \partial r\)
d2psidr2Float: Second derivative of \(psi\) w.r.t \(r\) - arbitrary to set to 0
mu0dPdrFloat: \(mu_0 \partial p \partial r\)
sigma_alphaInteger: Sign to select if (r, alpha, theta) or (r, theta, alpha) is a RHS system
field_coordsList: List of field-aligned co-ordinates
toroidal_coordsList: List of toroidal co-ordinates
dg_r_theta_dthetaArray: Derivative of toroidal covariant metric term g_r_theta w.r.t \(theta\)
dg_theta_theta_drArray: Derivative of toroidal covariant metric term g_theta_theta w.r.t \(r\)
dg_zeta_zeta_drArray: Derivative of toroidal covariant metric term g_zeta_zeta w.r.t \(r\)
dg_zeta_zeta_dthetaArray: Derivative of toroidal covariant metric term g_zeta_zeta w.r.t \(theta\)

__init__(local_geometry, ntheta=None, theta=None)[source]#

Parameters:: local_geometry (LocalGeometry)

Methods

`__init__`(local_geometry[, ntheta, theta])
`convert_physical_units`(norms)	Convert physical-unit attributes to generic simulation units of `norms`.
`field_aligned_contravariant_metric`(coord1, ...)	Field aligned contravariant metric tensor at requested co-ordinate
`field_aligned_covariant_metric`(coord1, coord2)	Field aligned covariant metric tensor at requested co-ordinate
`k_perp`(ky, theta0, nperiod)	Equation 155
`set_field_aligned_contravariant_metric`()	Sets up field-aligned contravariant metric tensor
`set_field_aligned_covariant_metric`()	Sets up field-aligned covariant metric tensor
`set_toroidal_contravariant_metric`()	Sets contravariant metric components of toroidal system using covariant components
`set_toroidal_covariant_metric`()	Sets up toroidal covariant metric tensor
`set_toroidal_covariant_metric_derivatives`()	Sets up required terms of derivative of toroidal covariant metric tensor
`to`(norms[, context])	Thin wrapper for normalise
`toroidal_contravariant_metric`(coord1, coord2)	Toroidal contravariant metric tensor at requested co-ordinate
`toroidal_covariant_metric`(coord1, coord2)	Toroidal contravariant metric tensor at requested co-ordinate

Attributes

`B_magnitude`
`B_theta`
`B_zeta`
`alpha`	inherits correct \(\sigma_\alpha\) from `dalpha_dtheta` integrate over theta
`d2alpha_drdtheta`
`dB_magnitude_dr`
`dB_magnitude_dtheta`
`dB_theta_drho`
`dB_theta_dtheta`
`dB_zeta_dr`
`dJacobian_dr`
`dJacobian_dtheta`	Differentiate eq 9 w.r.t theta
`dalpha_dr`	Equation 39 inherits correct \(\sigma_\alpha\) from `d2alpha_drdtheta` integrate over theta
`dalpha_dtheta`

property B_magnitude#

Returns:: B_magnitude – Magntiude of total field
Return type:: Array

property B_theta#

Returns:: B_theta – Poloidal field in toroidal coordinates
Return type:: Array

property B_zeta#

Returns:: B_zeta – B_zeta which is the current function (I or f) (equation 16)
Return type:: Array

property alpha#

inherits correct \(\sigma_\alpha\) from dalpha_dtheta integrate over theta

Returns:: alpha – Field following coordinate in field alligned system
Return type:: Array

convert_physical_units(norms)[source]#: Convert physical-unit attributes to generic simulation units of norms.

property d2alpha_drdtheta#

Returns:: d2alpha_drdtheta – Second derivative of alpha w.r.t \(\theta\) and \(r\) (equation 38)
Return type:: Array

property dB_magnitude_dr#

Returns:: dB_magnitude_dr – Derivative of magntiude of total field w.r.t r
Return type:: Array

property dB_magnitude_dtheta#

Returns:: dB_magnitude_dr – Derivative of magntiude of total field w.r.t theta
Return type:: Array

property dB_theta_drho#

Returns:: dB_theta_drho – Derivative of B_theta w.r.t \(r\)
Return type:: Array

property dB_theta_dtheta#

Returns:: dB_theta_drho – Derivative of B_theta w.r.t \(r\)
Return type:: Array

property dB_zeta_dr#

Returns:: dB_zeta_dr – Radial derivative of \(B_\zeta\) w.r.t \(r\) (equation 19)
Return type:: Array

property dJacobian_dr#

Returns:: dJacobian_dr – Derivative of Jacobian w.r.t \(r\) (equation 21)
Return type:: Array

property dJacobian_dtheta#

Differentiate eq 9 w.r.t theta

Returns:: dJacobian_dtheta – Derivative of Jacobian w.r.t :math:` heta`
Return type:: Array

property dalpha_dr#

Equation 39 inherits correct \(\sigma_\alpha\) from d2alpha_drdtheta integrate over theta

Returns:: dalpha_dr – Derivative of alpha w.r.t \(r\)
Return type:: Array

property dalpha_dtheta#

Returns:: dalpha_dtheta – Derivative of alpha w.r.t \(\theta\) (equation 37)
Return type:: Array

field_aligned_contravariant_metric(coord1, coord2)[source]#

Field aligned contravariant metric tensor at requested co-ordinate

Parameters:

coord1 (str) – Co-ordinate of first index in metric tensor. Can be r, alpha, theta
coord2 (str) – Co-ordinate of second index in metric tensor. Can be r, alpha, theta

field_aligned_covariant_metric(coord1, coord2)[source]#

Field aligned covariant metric tensor at requested co-ordinate

Parameters:

coord1 (str) – Co-ordinate of first index in metric tensor. Can be r, alpha, theta
coord2 (str) – Co-ordinate of second index in metric tensor. Can be r, alpha, theta

k_perp(ky, theta0, nperiod)[source]#

Equation 155

Returns:

k_perp – Perpendicular wavevector along the field line

Return type:

Array

Parameters:

ky (float)
theta0 (float)
nperiod (int)

set_field_aligned_contravariant_metric()[source]#: Sets up field-aligned contravariant metric tensor

set_field_aligned_covariant_metric()[source]#: Sets up field-aligned covariant metric tensor

set_toroidal_contravariant_metric()[source]#: Sets contravariant metric components of toroidal system using covariant components

set_toroidal_covariant_metric()[source]#: Sets up toroidal covariant metric tensor

set_toroidal_covariant_metric_derivatives()[source]#: Sets up required terms of derivative of toroidal covariant metric tensor

to(norms, context=None)[source]#: Thin wrapper for normalise

toroidal_contravariant_metric(coord1, coord2)[source]#

Toroidal contravariant metric tensor at requested co-ordinate

Parameters:

coord1 (str) – Co-ordinate of first index in metric tensor. Can be r, theta, zeta
coord2 (str) – Co-ordinate of second index in metric tensor. Can be r, theta, zeta

toroidal_covariant_metric(coord1, coord2)[source]#

Toroidal contravariant metric tensor at requested co-ordinate

Todo

Make type hints literals

Parameters:

coord1 (str) – Co-ordinate of first index in metric tensor. Can be r, theta, zeta
coord2 (str) – Co-ordinate of second index in metric tensor. Can be r, theta, zeta

pyrokinetics.local_geometry.metric.MetricTerms

Contents

pyrokinetics.local_geometry.metric.MetricTerms#