pyoculus.problems.two_waves.TwoWaves Class Reference

A very simple (but still hard) problem for testing the tools and methods. More...

Inheritance diagram for pyoculus.problems.two_waves.TwoWaves:

Public Member Functions
	__init__ (self, k=0.002)
	Set up the problem.
	set_k (self, k)
	Set the value of k.
	B (self, coords, *args)
	Returns magnetic fields.
	dBdX (self, coords, *args)
	Returns magnetic fields.
	convert_coords (self, incoords)
	Convert coordinates for Poincare plots.
	B_many (self, x1arr, x2arr, x3arr, input1D=True, *args)
	Returns magnetic fields, with multipy coordinate inputs.
	dBdX_many (self, x1arr, x2arr, x3arr, input1D=True, *args)
	Returns magnetic fields.
Public Member Functions inherited from pyoculus.problems.toroidal_bfield.ToroidalBfield
	f (self, zeta, st, *args)
	Returns ODE RHS.
	f_tangent (self, zeta, st, *args)
	Returns ODE RHS, with tangent.
Public Member Functions inherited from pyoculus.problems.toroidal_problem.ToroidalProblem
Public Member Functions inherited from pyoculus.problems.base_problem.BaseProblem
Public Member Functions inherited from pyoculus.problems.bfield_problem.BfieldProblem

Public Attributes
	k = k
int	Nfp = 1
bool	has_jacobian = True
int	problem_size = 2
	the problem size, 2 for 1.5D/2D Hamiltonian system
str	poincare_plot_type = "yx"
	by default plotting the yx plane
str	poincare_plot_xlabel = "q"
	by default x axis has label q
str	poincare_plot_ylabel = "p"
	by default y axis has label p
Public Attributes inherited from pyoculus.problems.toroidal_problem.ToroidalProblem
int	problem_size = 2
str	poincare_plot_type = "yx"
str	poincare_plot_xlabel = "x"
str	poincare_plot_ylabel = "y"
Public Attributes inherited from pyoculus.problems.base_problem.BaseProblem
int	problem_size = 2
str	poincare_plot_type = "yx"
str	poincare_plot_xlabel = "y"
str	poincare_plot_ylabel = "x"
Public Attributes inherited from pyoculus.problems.bfield_problem.BfieldProblem
bool	has_jacobian = False
	if the output magnetic field contains the jacobian factor or not

Detailed Description

A very simple (but still hard) problem for testing the tools and methods.

Details in S.R. Hudson, Phys. Plasmas 11, 677 (2004).

The magnetic field is given by

\[ \mathbf{B} = \nabla s \times \nabla \theta - \nabla \chi(s, \theta, \zeta) \times \nabla \zeta \]

The Hamiltonian of the magnetic field is given by

\[ \chi(s, \theta,\zeta) = \frac{s^2}{2} - k \left[ \frac{1}{2} \cos (2\theta - \zeta) + \frac{1}{3} \cos(3\theta - 2\zeta) \right] \]

The magnetic fields are given by

\[ B^s = - k \left[ \sin (2\theta - \zeta) + \sin(3\theta - 2\zeta)\right], \quad B^\theta = s , \quad B^\zeta = 1 \]

To use the class:

ps = TwoWaves(k=0.002)

Constructor & Destructor Documentation

__init__()

pyoculus.problems.two_waves.TwoWaves.__init__	(		self,
			k = 0.002 )

Set up the problem.

Parameters

k	the value used in the Hamiltonian

Reimplemented from pyoculus.problems.toroidal_bfield.ToroidalBfield.

Member Function Documentation

B()

pyoculus.problems.two_waves.TwoWaves.B	(		self,
			coords,
		*	args )

Returns magnetic fields.

Parameters

coordinates
*args	extra parameters

Returns

the contravariant magnetic fields

Reimplemented from pyoculus.problems.bfield_problem.BfieldProblem.

B_many()

pyoculus.problems.two_waves.TwoWaves.B_many	(		self,
			x1arr,
			x2arr,
			x3arr,
			input1D = True,
		*	args )

Returns magnetic fields, with multipy coordinate inputs.

Parameters

x1arr	the first coordinates. Should have the same length as the other two if input1D=True.
x2arr	the second coordinates. Should have the same length as the other two if input1D=True.
x3arr	the third coordinates. Should have the same length as the other two if input1D=True.
input1D	if False, create a meshgrid with sarr, tarr and zarr, if True, treat them as a list of points
*args	extra parameters

Returns

the contravariant magnetic fields

Reimplemented from pyoculus.problems.bfield_problem.BfieldProblem.

convert_coords()

pyoculus.problems.two_waves.TwoWaves.convert_coords	(		self,
			incoords )

Convert coordinates for Poincare plots.

Parameters

incoords

\((p,q,t)\)

Returns

\((p,q \ \mbox{mod} \ 2\pi,t \ \mbox{mod} \ 2\pi)\)

Reimplemented from pyoculus.problems.toroidal_problem.ToroidalProblem.

dBdX()

pyoculus.problems.two_waves.TwoWaves.dBdX	(		self,
			coords,
		*	args )

Returns magnetic fields.

Parameters

coordinates
*args	extra parameters

Returns

B, dBdX, the contravariant magnetic fields, the derivatives of them

Reimplemented from pyoculus.problems.bfield_problem.BfieldProblem.

dBdX_many()

pyoculus.problems.two_waves.TwoWaves.dBdX_many	(		self,
			x1arr,
			x2arr,
			x3arr,
			input1D = True,
		*	args )

Returns magnetic fields.

Parameters

x1arr	the first coordinates. Should have the same length as the other two if input1D=True.
x2arr	the second coordinates. Should have the same length as the other two if input1D=True.
x3arr	the third coordinates. Should have the same length as the other two if input1D=True.
input1D	if False, create a meshgrid with sarr, tarr and zarr, if True, treat them as a list of points
*args	extra parameters

Returns

B, dBdX, the contravariant magnetic fields, the derivatives of them

Reimplemented from pyoculus.problems.bfield_problem.BfieldProblem.

set_k()

pyoculus.problems.two_waves.TwoWaves.set_k	(		self,
			k )

Set the value of k.

Parameters

k	the value used in the Hamiltonian

Member Data Documentation

has_jacobian

bool pyoculus.problems.two_waves.TwoWaves.has_jacobian = True

k

pyoculus.problems.two_waves.TwoWaves.k = k

Nfp

int pyoculus.problems.two_waves.TwoWaves.Nfp = 1

poincare_plot_type

str pyoculus.problems.two_waves.TwoWaves.poincare_plot_type = "yx"

by default plotting the yx plane

poincare_plot_xlabel

str pyoculus.problems.two_waves.TwoWaves.poincare_plot_xlabel = "q"

by default x axis has label q

poincare_plot_ylabel

str pyoculus.problems.two_waves.TwoWaves.poincare_plot_ylabel = "p"

by default y axis has label p

problem_size

int pyoculus.problems.two_waves.TwoWaves.problem_size = 2

the problem size, 2 for 1.5D/2D Hamiltonian system

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The documentation for this class was generated from the following file:

• pyoculus/problems/two_waves.py