Compute the JxB - Grad(p) covariant force components. The plasma is in equilibrium when the force of the magnetic pressure balances the plasma pressure. More...

Functions/Subroutines
subroutine	update_force
	Update MHD forces on full radial mesh. More...

subroutine	incfields (jbsupsmnh, jbsupumnh, jbsupvmnh, jpmnh,
	Compute nonlinear or linearized contravariant magnetic field components and pressure in real space. More...

subroutine	lorentz (bsupsijf, bsupuijf, bsupvijf,
	Compute covariant (sub) real-space components of the Lorentz K X B force. More...

subroutine	getmhdforce (fsubsmnf, fsubumnf, fsubvmnf, pijh,
	Compute covariant (sub) components of the MHD force J X B - grad(p). More...

subroutine	initpardamping (parscale, pardamp)
	Compute scaling factors for parallel flow damping. More...

subroutine	get_force_harmonics (pardamp, f_smnf, f_umnf, f_vmnf, pa
	Final computation of the MHD covariant Fourier force components. More...

subroutine	addpardamping (pardamp, f_smnf, f_umnf, f_vmnf,
	Add parallel flow damping terms to forces (for Hessian calculation) to suppress null space at resonances. More...

Detailed Description

Compute the JxB - Grad(p) covariant force components. The plasma is in equilibrium when the force of the magnetic pressure balances the plasma pressure.

F = J X B - Grad(p) = 0                                               (1)

where J is the current density. Updates for B (dB) and p (dp) were computed in siesta_bfield and siesta_pressure, respectively.

B_i+1 = B_i + dB (2a)

p_i+1 = p_i + dp (2b)

Note that the magnetic field and pressure terms contain a Jacobian factor. Updated current density can be found from the updated magnetic field.

J = Curl(B)/mu0 (3)

Actual computation of the contravariant current components is implimented in cv_currents. The curvilinear coordinates, the J X B term becomes

(J X B)_s = (K^u*B^v - K^v*B^u) (4a)

(J X B)_u = (K^v*B^s - K^s*B^v) (4b)

(J X B)_v = (K^s*B^u - K^u*B^s) (4c)

where K^i = sqrt(g) J^i.

Function/Subroutine Documentation

◆ addpardamping()

subroutine siesta_force::addpardamping	(	real (dp), dimension(:,:), intent(in)	pardamp,
		real (dp), dimension(:,:,:), intent(inout)	f_smnf,
		real (dp), dimension(:,:,:), intent(inout)	f_umnf,
		real (dp), dimension(:,:,:), intent(inout)	f_vmnf
	)

Add parallel flow damping terms to forces (for Hessian calculation) to suppress null space at resonances.

Compute parallel (to B) damping force and add it to (linearized) forces to suppress null space in preconditioner.

Parameters

[in,out]	f_smnf	Covariant component of the mhd force in the s direction.
[in,out]	f_umnf	Covariant component of the mhd force in the u direction.
[in,out]	f_vmnf	Covariant component of the mhd force in the v direction.
[in]	jvsupsmnf	Contravariant displacement in the s direction.
[in]	jvsupsmnf	Contravariant displacement in the u direction.
[in]	jvsupsmnf	Contravariant displacement in the v direction.

Definition at line 784 of file siesta_force.f90.

◆ get_force_harmonics()

subroutine siesta_force::get_force_harmonics	(	real (dp), dimension(:,:), intent(inout), allocatable	pardamp,
		real (dp), dimension(:,:,:), intent(inout)	f_smnf,
		real (dp), dimension(:,:,:), intent(inout)	f_umnf,
		real (dp), dimension(:,:,:), intent(inout)	f_vmnf,
			pa
	)

Final computation of the MHD covariant Fourier force components.

Add pressure gradients and parallel damping (to Hessian), and scale and print boundary values.

Parameters

[in,out]	pardamp	Parallel damping.
[in,out]	f_smnf	Covariant component of the mhd force in the s direction.
[in,out]	f_umnf	Covariant component of the mhd force in the u direction.
[in,out]	f_vmnf	Covariant component of the mhd force in the v direction.
[in]	parity	Parity of the fourier components.

Definition at line 595 of file siesta_force.f90.

◆ getmhdforce()

subroutine siesta_force::getmhdforce	(	real (dp), dimension(:,:,:), intent(inout)	fsubsmnf,
		real (dp), dimension(:,:,:), intent(inout)	fsubumnf,
		real (dp), dimension(:,:,:), intent(inout)	fsubvmnf,
		real (dp), dimension(:,:,:), intent(in), allocatable	pijh
	)

Compute covariant (sub) components of the MHD force J X B - grad(p).

The MHD forces are sum of Lorentz and pressure gradient forces

F = J X B - Grad(p) (1)

where J is the plasma current density. In curvilinear coodinates, the forces components becomes

F_s = (K^u*B^v - K^v*B^u) - dp/ds (2a)

F_u = (K^v*B^s - K^s*B^v) - dp/du (2b)

F_v = (K^s*B^u - K^u*B^s) - dp/dv (2c)

where K^i = sqrt(g)*J^i . Note this routine works on one parity at a time. When l_linearize is true, calculate the perturbed Force only (Ignores F(xc=0) part). When l_linearize is false, calculate full non-linear force(F(xc=0) part only)

Parameters

[in,out]	fsubsmnf	Covariant force in the s direction.
[in,out]	fsubumnf	Covariant force in the s direction.
[in,out]	fsubvmnf	Covariant force in the s direction.
[in]	pijh	Real space pressure.
[in,out]	KxBsij	Covariant component of the lorentz force in the s direction.
[in,out]	KxBuij	Covariant component of the lorentz force in the u direction.
[in,out]	KxBvij	Covariant component of the lorentz force in the v direction.
[in,out]	pardamp	Parallel damping.
[in]	parity	Parity of the fourier components.

Definition at line 429 of file siesta_force.f90.

◆ incfields()

subroutine siesta_force::incfields	(	real (dp), dimension(:,:,:), intent(in), allocatable	jbsupsmnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	jbsupumnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	jbsupvmnh,
		real (dp), dimension(:,:,:), intent(in), allocatable	jpmnh
	)

Compute nonlinear or linearized contravariant magnetic field components and pressure in real space.

Parameters

[in]	jbsupsmnh	Contravariant B field in the s direction.
[in]	jbsupumnh	Contravariant B field in the u direction.
[in]	jbsupvmnh	Contravariant B field in the v direction.
[in]	jpmnh	Pressure on the half grid.
[in]	djbsupsmnh	Contravariant B field perturbation in the s direction.
[in]	djbsupumnh	Contravariant B field perturbation in the u direction.
[in]	djbsupvmnh	Contravariant B field perturbation in the v direction.
[in]	djpmnh	Pressure perturbation.
[out]	jbsupsijh	Real space contravariant B field in the s direction.
[out]	jbsupuijh	Real space contravariant B field in the u !direction.
[out]	jbsupvijh	Real space contravariant B field in the v direction.
[in]	iparity	Fourier parity.

Definition at line 231 of file siesta_force.f90.

◆ initpardamping()

subroutine siesta_force::initpardamping	(		parscale,
		real (dp), dimension(:,:), intent(inout), allocatable	pardamp
	)

Compute scaling factors for parallel flow damping.

Parameters

[in,out]	parscale	Scratch array.
[in,out]	pardamp	Parallel damping.

Definition at line 536 of file siesta_force.f90.

◆ lorentz()

subroutine siesta_force::lorentz	(	bsupsijf,
		bsupuijf,
		bsupvijf
	)

Compute covariant (sub) real-space components of the Lorentz K X B force.

Parameters

[in]	bsupsijf	Contravariant component of the B field in the s direction.
[in]	bsupuijf	Contravariant component of the B field in the u direction.
[in]	bsupvijf	Contravariant component of the B field in the v direction.
[in]	ksupsijf	Contravariant component of the current in the s direction.
[in]	ksupuijf	Contravariant component of the current in the u direction.
[in]	ksupvijf	Contravariant component of the current in the v direction.
[in,out]	KxBsij	Covariant component of the lorentz force in the s direction.
[in,out]	KxBuij	Covariant component of the lorentz force in the u direction.
[in,out]	KxBvij	Covariant component of the lorentz force in the v direction.
[in]	fcomb	Control flag to sum the components with previous values.

Definition at line 348 of file siesta_force.f90.

◆ update_force()

subroutine siesta_force::update_force

Update MHD forces on full radial mesh.

Updates force using the advanced values of B and p obtained from calls to siesta_pressure::update_pres and siesta_bfield::update_bfield Update values of fsub*mn*f stored in quantities. Linearized force is

Flin ~ delta_v

has only the linear part. Not DC part and not non-linear.

Definition at line 70 of file siesta_force.f90.

Functions/Subroutines

Detailed Description

Function/Subroutine Documentation

◆ addpardamping()

◆ get_force_harmonics()

◆ getmhdforce()

◆ incfields()

◆ initpardamping()

◆ lorentz()

◆ update_force()