Base classes#

Base classes for MHD equilibria.

class struphy.fields_background.base.FluidEquilibrium[source]#

Bases: object

Base class for callable fluid equilibria consisting of at least u (velocity), p (pressure) and n (density).

Any child class must provide the following callables:

either u_xyz or override uv
either p_xyz or override p0
either n_xyz or override n0

property params: dict#: Parameters passed to __init__() of the class in equils.py, as dictionary.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

u1(*etas, squeeze_out=False)[source]#: 1-form components of velocity on logical cube [0, 1]^3.

u2(*etas, squeeze_out=False)[source]#: 2-form components of velocity on logical cube [0, 1]^3.

uv(*etas, squeeze_out=False)[source]#: Contra-variant components of velocity on logical cube [0, 1]^3.

u_cart(*etas, squeeze_out=False)[source]#: Cartesian components of velocity evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

p0(*etas, squeeze_out=False)[source]#: 0-form pressure on logical cube [0, 1]^3.

p3(*etas, squeeze_out=False)[source]#: 3-form pressure on logical cube [0, 1]^3.

n0(*etas, squeeze_out=False)[source]#: 0-form number density on logical cube [0, 1]^3.

n3(*etas, squeeze_out=False)[source]#: 3-form number density on logical cube [0, 1]^3.

t0(*etas, squeeze_out=False)[source]#: 0-form temperature on logical cube [0, 1]^3.

t3(*etas, squeeze_out=False)[source]#: 3-form temperature on logical cube [0, 1]^3.

vth0(*etas, squeeze_out=False)[source]#: 0-form thermal velocity on logical cube [0, 1]^3.

vth3(*etas, squeeze_out=False)[source]#: 3-form thermal velocity on logical cube [0, 1]^3.

q0(*etas, squeeze_out=False)[source]#: 0-form square root of the pressure on logical cube [0, 1]^3.

q3(*etas, squeeze_out=False)[source]#: 3-form square root of the pressure on logical cube [0, 1]^3.

s0_monoatomic(*etas, squeeze_out=False)[source]#: 0-form entropy density on logical cube [0, 1]^3. Hard coded assumption : gamma = 5/3 (monoatomic perfect gaz)

s3_monoatomic(*etas, squeeze_out=False)[source]#: 3-form entropy density on logical cube [0, 1]^3. Hard coded assumption : gamma = 5/3 (monoatomic perfect gaz)

s0_diatomic(*etas, squeeze_out=False)[source]#: 0-form entropy density on logical cube [0, 1]^3. Hard coded assumption : gamma = 7/5 (diatomic perfect gaz)

s3_diatomic(*etas, squeeze_out=False)[source]#: 3-form entropy density on logical cube [0, 1]^3. Hard coded assumption : gamma = 5/3 (monoatomic perfect gaz)

u1_1(*etas, squeeze_out=False)[source]#

u1_2(*etas, squeeze_out=False)[source]#

u1_3(*etas, squeeze_out=False)[source]#

u2_1(*etas, squeeze_out=False)[source]#

u2_2(*etas, squeeze_out=False)[source]#

u2_3(*etas, squeeze_out=False)[source]#

uv_1(*etas, squeeze_out=False)[source]#

uv_2(*etas, squeeze_out=False)[source]#

uv_3(*etas, squeeze_out=False)[source]#

u_cart_1(*etas, squeeze_out=False)[source]#

u_cart_2(*etas, squeeze_out=False)[source]#

u_cart_3(*etas, squeeze_out=False)[source]#

class struphy.fields_background.base.CartesianFluidEquilibrium[source]#

Bases: FluidEquilibrium

The callables u_xyz, p_xyz and n_xyz must be provided in Cartesian coordinates.

abstract u_xyz(x, y, z)[source]#: Cartesian velocity in physical space. Must return the components as a tuple.

abstract p_xyz(x, y, z)[source]#: Equilibrium pressure in physical space.

abstract n_xyz(x, y, z)[source]#: Equilibrium number density in physical space.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.LogicalFluidEquilibrium[source]#

Bases: FluidEquilibrium

The callables uv, p0 and n0 must be provided on the logical cube [0, 1]^3.

abstract uv(*etas, squeeze_out=False)[source]#: Contra-variant (vector field) velocity on logical cube [0, 1]^3. Must return the components as a tuple.

abstract p0(*etas, squeeze_out=False)[source]#: 0-form pressure on logical cube [0, 1]^3.

abstract n0(*etas, squeeze_out=False)[source]#: 0-form density on logical cube [0, 1]^3.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.NumericalFluidEquilibrium[source]#

Bases: LogicalFluidEquilibrium

Must provide a (numerical) mapping from the logical cube [0, 1]^3 to the physical domain. Overrides base class domain.

abstract property numerical_domain#: Numerically computed mapping from the logical cube [0, 1]^3 to the physical domain in the form of a Domain object.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.FluidEquilibriumWithB[source]#

Bases: FluidEquilibrium

FluidEquilibrium with B (magnetic field) in addition.

Any child class must provide the following callables:

either b_xyz or override bv
either gradB_xyz or override gradB1

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

b1(*etas, squeeze_out=False)[source]#: 1-form components of magnetic field on logical cube [0, 1]^3.

b2(*etas, squeeze_out=False)[source]#: 2-form components of magnetic field on logical cube [0, 1]^3.

bv(*etas, squeeze_out=False)[source]#: Contra-variant components of magnetic field on logical cube [0, 1]^3.

b_cart(*etas, squeeze_out=False)[source]#: Cartesian components of magnetic field evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

unit_b1(*etas, squeeze_out=False)[source]#: Unit vector components of magnetic field (1-form) on logical cube [0, 1]^3.

unit_b2(*etas, squeeze_out=False)[source]#: Unit vector components of magnetic field (2-form) on logical cube [0, 1]^3.

unit_bv(*etas, squeeze_out=False)[source]#: Unit vector components of magnetic field (contra-variant) on logical cube [0, 1]^3.

unit_b_cart(*etas, squeeze_out=False)[source]#: Unit vector Cartesian components of magnetic field evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

gradB1(*etas, squeeze_out=False)[source]#: 1-form components of gradient of magnetic field strength evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

gradB2(*etas, squeeze_out=False)[source]#: 2-form components of gradient of magnetic field strength evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

gradBv(*etas, squeeze_out=False)[source]#: Contra-variant components of gradient of magnetic field strength evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

gradB_cart(*etas, squeeze_out=False)[source]#: Cartesian components of gradient of magnetic field strength evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

a1(*etas, squeeze_out=False)[source]#: 1-form components of vector potential on logical cube [0, 1]^3.

a2(*etas, squeeze_out=False)[source]#: 2-form components of vector potential on logical cube [0, 1]^3.

av(*etas, squeeze_out=False)[source]#: Contra-variant components of vector potneital on logical cube [0, 1]^3.

absB0(*etas, squeeze_out=False)[source]#: 0-form absolute value of magnetic field on logical cube [0, 1]^3.

absB3(*etas, squeeze_out=False)[source]#: 3-form absolute value of magnetic field on logical cube [0, 1]^3.

u_para0(*etas, squeeze_out=False)[source]#: 0-form parallel velocity on logical cube [0, 1]^3.

u_para3(*etas, squeeze_out=False)[source]#: 3-form parallel velocity on logical cube [0, 1]^3.

b1_1(*etas, squeeze_out=False)[source]#

b1_2(*etas, squeeze_out=False)[source]#

b1_3(*etas, squeeze_out=False)[source]#

b2_1(*etas, squeeze_out=False)[source]#

b2_2(*etas, squeeze_out=False)[source]#

b2_3(*etas, squeeze_out=False)[source]#

bv_1(*etas, squeeze_out=False)[source]#

bv_2(*etas, squeeze_out=False)[source]#

bv_3(*etas, squeeze_out=False)[source]#

unit_b1_1(*etas, squeeze_out=False)[source]#

unit_b1_2(*etas, squeeze_out=False)[source]#

unit_b1_3(*etas, squeeze_out=False)[source]#

unit_b2_1(*etas, squeeze_out=False)[source]#

unit_b2_2(*etas, squeeze_out=False)[source]#

unit_b2_3(*etas, squeeze_out=False)[source]#

unit_bv_1(*etas, squeeze_out=False)[source]#

unit_bv_2(*etas, squeeze_out=False)[source]#

unit_bv_3(*etas, squeeze_out=False)[source]#

gradB1_1(*etas, squeeze_out=False)[source]#

gradB1_2(*etas, squeeze_out=False)[source]#

gradB1_3(*etas, squeeze_out=False)[source]#

gradB2_1(*etas, squeeze_out=False)[source]#

gradB2_2(*etas, squeeze_out=False)[source]#

gradB2_3(*etas, squeeze_out=False)[source]#

gradBv_1(*etas, squeeze_out=False)[source]#

gradBv_2(*etas, squeeze_out=False)[source]#

gradBv_3(*etas, squeeze_out=False)[source]#

a1_1(*etas, squeeze_out=False)[source]#

a1_2(*etas, squeeze_out=False)[source]#

a1_3(*etas, squeeze_out=False)[source]#

a2_1(*etas, squeeze_out=False)[source]#

a2_2(*etas, squeeze_out=False)[source]#

a2_3(*etas, squeeze_out=False)[source]#

av_1(*etas, squeeze_out=False)[source]#

av_2(*etas, squeeze_out=False)[source]#

av_3(*etas, squeeze_out=False)[source]#

class struphy.fields_background.base.CartesianFluidEquilibriumWithB[source]#

Bases: CartesianFluidEquilibrium

The callables b_xyz and gradB_xyz must be provided in Cartesian coordinates.

abstract b_xyz(x, y, z)[source]#: Cartesian magnetic field in physical space. Must return the components as a tuple.

abstract gradB_xyz(x, y, z)[source]#: Cartesian gradient of magnetic field strength in physical space. Must return the components as a tuple.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.LogicalFluidEquilibriumWithB[source]#

Bases: LogicalFluidEquilibrium

The callable bv must be provided on the logical cube [0, 1]^3.

abstract bv(*etas, squeeze_out=False)[source]#: Contra-variant (vector field) magnetic field on logical cube [0, 1]^3. Must return the components as a tuple.

abstract gradB1(*etas, squeeze_out=False)[source]#: Co-variant (1-from) gradient of magnetic field strength on logical cube [0, 1]^3. Must return the components as a tuple.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.NumericalFluidEquilibriumWithB[source]#

Bases: LogicalFluidEquilibriumWithB

Must provide a (numerical) mapping from the logical cube [0, 1]^3 to the physical domain. Overrides base class domain.

abstract property numerical_domain#: Numerically computed mapping from the logical cube [0, 1]^3 to the physical domain in the form of a Domain object.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.MHDequilibrium[source]#

Bases: FluidEquilibriumWithB

FluidEquilibriumWithB with j (current density) in addition. The mean velocity is returned as j/n (overriding the base class).

Any child class must provide the following callables:

either j_xyz or override jv

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

j1(*etas, squeeze_out=False)[source]#: 1-form components of current on logical cube [0, 1]^3.

j2(*etas, squeeze_out=False)[source]#: 2-form components of current on logical cube [0, 1]^3.

jv(*etas, squeeze_out=False)[source]#: Contra-variant components of current on logical cube [0, 1]^3.

j_cart(*etas, squeeze_out=False)[source]#: Cartesian components of current evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

u1(*etas, squeeze_out=False)[source]#: 1-form components of mean velocity evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

u2(*etas, squeeze_out=False)[source]#: 2-form components of mean velocity evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

uv(*etas, squeeze_out=False)[source]#: Contra-variant components of mean velocity evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

u_cart(*etas, squeeze_out=False)[source]#: Cartesian components of mean velocity evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

curl_unit_b1(*etas, squeeze_out=False)[source]#: 1-form components of curl of unit magnetic field evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

curl_unit_b2(*etas, squeeze_out=False)[source]#: 2-form components of curl of unit magnetic field evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

curl_unit_bv(*etas, squeeze_out=False)[source]#: Contra-variant components of curl of unit magnetic field evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

curl_unit_b_cart(*etas, squeeze_out=False)[source]#: Cartesian components of curl of unit magnetic field evaluated on logical cube [0, 1]^3. Returns also (x,y,z).

curl_unit_b_dot_b0(*etas, squeeze_out=False)[source]#: 0-form of \((\nabla \times \mathbf b_0) \times \mathbf b_0\) evaluated on logical cube [0, 1]^3.

j1_1(*etas, squeeze_out=False)[source]#

j1_2(*etas, squeeze_out=False)[source]#

j1_3(*etas, squeeze_out=False)[source]#

j2_1(*etas, squeeze_out=False)[source]#

j2_2(*etas, squeeze_out=False)[source]#

j2_3(*etas, squeeze_out=False)[source]#

jv_1(*etas, squeeze_out=False)[source]#

jv_2(*etas, squeeze_out=False)[source]#

jv_3(*etas, squeeze_out=False)[source]#

curl_unit_b1_1(*etas, squeeze_out=False)[source]#

curl_unit_b1_2(*etas, squeeze_out=False)[source]#

curl_unit_b1_3(*etas, squeeze_out=False)[source]#

curl_unit_b2_1(*etas, squeeze_out=False)[source]#

curl_unit_b2_2(*etas, squeeze_out=False)[source]#

curl_unit_b2_3(*etas, squeeze_out=False)[source]#

curl_unit_bv_1(*etas, squeeze_out=False)[source]#

curl_unit_bv_2(*etas, squeeze_out=False)[source]#

curl_unit_bv_3(*etas, squeeze_out=False)[source]#

show(n1=16, n2=33, n3=21, n_planes=5)[source]#

Generate vtk files of equilibirum and do some 2d plots with matplotlib.

Parameters:

n1 (int) – Evaluation points of mapping in each direcion.
n2 (int) – Evaluation points of mapping in each direcion.
n3 (int) – Evaluation points of mapping in each direcion.
n_planes (int) – Number of planes to show perpendicular to eta3.

class struphy.fields_background.base.CartesianMHDequilibrium[source]#

Bases: MHDequilibrium

The callables b_xyz, j_xyz, p_xyz, n_xyz and gradB_xyz must be provided in Cartesian coordinates.

abstract b_xyz(x, y, z)[source]#: Cartesian magnetic field in physical space. Must return the components as a tuple.

abstract j_xyz(x, y, z)[source]#: Cartesian current (curl of magnetic field) in physical space. Must return the components as a tuple.

abstract p_xyz(x, y, z)[source]#: Equilibrium pressure in physical space.

abstract n_xyz(x, y, z)[source]#: Equilibrium number density in physical space.

abstract gradB_xyz(x, y, z)[source]#: Cartesian gradient of magnetic field strength in physical space. Must return the components as a tuple.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.AxisymmMHDequilibrium[source]#

Bases: CartesianMHDequilibrium

Base class for ideal axisymmetric MHD equilibria based on a poloidal flux function \(\psi(R, Z)\) and a toroidal field function \(g_{tor}(R, Z)\) in a cylindrical coordinate system \((R, \phi, Z)\).

The magnetic field and current density are then given by

\[\mathbf B = \nabla \psi \times \nabla \phi + g_{tor} \nabla \phi\,,\qquad \mathbf j = \nabla \times \mathbf B\,.\]

The pressure and density profiles need to be implemented by child classes.

abstract psi(R, Z, dR=0, dZ=0)[source]#: Poloidal flux function per radian. First AND second derivatives dR=0,1,2 and dZ=0,1,2 must be implemented.

abstract g_tor(R, Z, dR=0, dZ=0)[source]#: Toroidal field function. First derivatives dR=0,1 and dZ=0,1 must be implemented.

abstract property psi_range#: Psi on-axis and at plasma boundary returned as list [psi_axis, psi_boundary].

abstract property psi_axis_RZ#: Location of magnetic axis in R-Z-coordinates returned as list [psi_axis_R, psi_axis_Z].

abstract p_xyz(x, y, z)[source]#: Equilibrium pressure in physical space.

abstract n_xyz(x, y, z)[source]#: Equilibrium number density in physical space.

b_xyz(x, y, z)[source]#: Cartesian B-field components calculated as BR = -(dpsi/dZ)/R, BPhi = g_tor/R, BZ = (dpsi/dR)/R.

j_xyz(x, y, z)[source]#: Cartesian current density components calculated as curl(B).

gradB_xyz(x, y, z)[source]#: Cartesian gradient |B| components calculated as grad(sqrt(BR**2 + BPhi**2 + BZ**2)).

static inverse_map(x, y, z)[source]#: Inverse cylindrical mapping.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.LogicalMHDequilibrium[source]#

Bases: MHDequilibrium

The callables bv, jv, p0, n0 and gradB1 must be provided on the logical cube [0, 1]^3.

abstract bv(*etas, squeeze_out=False)[source]#: Contra-variant (vector field) magnetic field on logical cube [0, 1]^3. Must return the components as a tuple.

abstract jv(*etas, squeeze_out=False)[source]#: Contra-variant (vector field) current density (=curl B) on logical cube [0, 1]^3. Must return the components as a tuple.

abstract p0(*etas, squeeze_out=False)[source]#: 0-form pressure on logical cube [0, 1]^3. Must return the components as a tuple.

abstract n0(*etas, squeeze_out=False)[source]#: 0-form density on logical cube [0, 1]^3.

abstract gradB1(*etas, squeeze_out=False)[source]#: 1-form gradient of magnetic field strength strength on logical cube [0, 1]^3. Must return the components as a tuple.

property domain#: Domain object that characterizes the mapping from the logical to the physical domain.

class struphy.fields_background.base.NumericalMHDequilibrium[source]#

Bases: LogicalMHDequilibrium

Must provide a (numerical) mapping from the logical cube [0, 1]^3 to the physical domain. Overrides base class domain.

abstract property numerical_domain#: Numerically computed mapping from the logical cube [0, 1]^3 to the physical domain in the form of a Domain object.

property domain: Domain#: Domain object that characterizes the mapping from the logical to the physical domain.

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