Base classes#

Base classes for kinetic backgrounds.

class struphy.kinetic_background.base.KineticBackground[source]#

Bases: object

Base class for kinetic background distributions defined on \([0, 1]^3 \times \mathbb R^n, n \geq 1,\) with logical position coordinates \(\boldsymbol{\eta} \in [0, 1]^3\).

Explicit expressions for the following number density \(n\) and mean velocity \(\mathbf u\) must be implemented:

\[ \begin{align}\begin{aligned}n &= \int f \,\mathrm{d} \mathbf v\\\mathbf u &= \frac 1n \int \mathbf v f \,\mathrm{d} \mathbf v\,.\end{aligned}\end{align} \]
abstract property coords#

Coordinates of the distribution.

abstract property vdim#

Dimension of the velocity space (vdim = n).

abstract property is_polar#

List of booleans of length vdim. True for a velocity coordinate that is a radial polar coordinate (v_perp).

abstract property volume_form: bool#

True if the background is represented as a volume form (thus including the velocity Jacobian).

abstract velocity_jacobian_det(eta1, eta2, eta3, *v)[source]#

Jacobian determinant of the velocity coordinate transformation.

abstract n(*etas)[source]#

Number density (0-form).

Parameters:

etas (numpy.arrays) – Evaluation points. All arrays must be of same shape (can be 1d for flat evaluation).

Return type:

A numpy.array with the density evaluated at evaluation points (same shape as etas).

abstract u(*etas)[source]#

Mean velocities (Cartesian components evaluated at x = F(eta)).

Parameters:

etas (numpy.arrays) – Evaluation points. All arrays must be of same shape (can be 1d for flat evaluation).

Return type:

A list[float] (background values) or a list[numpy.array] of the evaluated velocities.

class struphy.kinetic_background.base.SumKineticBackground(f1, f2)[source]#

Bases: KineticBackground

property coords#

Coordinates of the distribution.

property vdim#

Dimension of the velocity space (vdim = n).

property is_polar#

List of booleans. True if the velocity coordinates are polar coordinates.

property volume_form#

Boolean. True if the background is represented as a volume form (thus including the velocity Jacobian).

property equil: FluidEquilibriumWithB#

Fluid background with B-field.

velocity_jacobian_det(eta1, eta2, eta3, *v)[source]#

Jacobian determinant of the velocity coordinate transformation.

n(*etas)[source]#

Number density (0-form).

Parameters:

etas (numpy.arrays) – Evaluation points. All arrays must be of same shape (can be 1d for flat evaluation).

Return type:

A numpy.array with the density evaluated at evaluation points (same shape as etas).

u(*etas)[source]#

Mean velocities (Cartesian components evaluated at x = F(eta)).

Parameters:

etas (numpy.arrays) – Evaluation points. All arrays must be of same shape (can be 1d for flat evaluation).

Return type:

A list[float] (background values) or a list[numpy.array] of the evaluated velocities.

class struphy.kinetic_background.base.ScalarMultiplyKineticBackground(f0, a)[source]#

Bases: KineticBackground

property coords#

Coordinates of the distribution.

property vdim#

Dimension of the velocity space (vdim = n).

property is_polar#

List of booleans. True if the velocity coordinates are polar coordinates.

property volume_form#

Boolean. True if the background is represented as a volume form (thus including the velocity Jacobian).

velocity_jacobian_det(eta1, eta2, eta3, *v)[source]#

Jacobian determinant of the velocity coordinate transformation.

n(*etas)[source]#

Number density (0-form).

Parameters:

etas (numpy.arrays) – Evaluation points. All arrays must be of same shape (can be 1d for flat evaluation).

Return type:

A numpy.array with the density evaluated at evaluation points (same shape as etas).

u(*etas)[source]#

Mean velocities (Cartesian components evaluated at x = F(eta)).

Parameters:

etas (numpy.arrays) – Evaluation points. All arrays must be of same shape (can be 1d for flat evaluation).

Return type:

A list[float] (background values) or a list[numpy.array] of the evaluated velocities.

class struphy.kinetic_background.base.Maxwellian[source]#

Bases: KineticBackground

Base class for a Maxwellian distribution function. It is defined on \([0, 1]^3 \times \mathbb R^n, n \geq 1,\) with logical position coordinates \(\boldsymbol{\eta} \in [0, 1]^3\):

\[f(\boldsymbol{\eta}, v_1,\ldots,v_n) = n(\boldsymbol{\eta}) \prod_{i=1}^n \frac{1}{\sqrt{2\pi}\,v_{\mathrm{th},i}(\boldsymbol{\eta})} \exp\left[-\frac{(v_i-u_i(\boldsymbol{\eta}))^2}{2\,v_{\mathrm{th},i}(\boldsymbol{\eta})^2}\right],\]

defined by its velocity moments: the density \(n(\boldsymbol{\eta})\), the mean-velocities \(u_i(\boldsymbol{\eta})\), and the thermal velocities \(v_{\mathrm{th},i}(\boldsymbol{\eta})\).

abstract vth(*etas)[source]#

Thermal velocities (0-forms).

Parameters:

etas (numpy.arrays) – Evaluation points. All arrays must be of same shape (can be 1d for flat evaluation).

Return type:

A list[float] (background values) or a list[numpy.array] of the evaluated thermal velocities.

abstract property maxw_params: dict#

Parameters dictionary defining moments of the Maxwellian.

check_maxw_params()[source]#
classmethod gaussian(v, u=0.0, vth=1.0, polar=False, volume_form=False)[source]#

1-dim. normal distribution, to which array-valued mean- and thermal velocities can be passed.

Parameters:

  • v (float | array-like) – Velocity coordinate(s).

  • u (float | array-like) – Mean velocity evaluated at position array.

  • vth (float | array-like) – Thermal velocity evaluated at position array, same shape as u.

  • polar (bool) – True if the velocity coordinate is the radial one of polar coordinates (v >= 0).

  • volume_form (bool) – If True, the polar Gaussian is multiplied by the polar velocity Jacobian |v|.

Return type:

An array of size(v).

property add_perturbation: bool#